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Fragmentation of Quark and Gluon Jets in Proton-Antiproton Collisions at Center-of-Mass Energy of 1.8 TeV


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Y !#$,N)H = == = == === == ====== == === == = == === == r &Fn$ N)H = == === == ====== == === == = == === == r nr K$+$ B$ = == === == ====== == === == = == === == Y 0 2 $DAnr$ = = == === == ====== == === == = == === == Y 2@= 0 4$ 5 = == === == ====== == === == = == === == Y 2@= V #5 $@5 5 ) == == ====== == === == = == === == Y 2@= !X5 = == ====== == === == = == === == Y 2@= QE5 & n == ====== == === == = == === == Y 2@= Y (9 5 5 5 = ====== == === == = == === == Y 2D= Y = 0 ) = === == ====== == === == = == === == W 2D= Y = V 8 r5 "== == === == = == === == V 2D= Y = 5 9 = ====== == === == = == === == 2@= 5 X5&n = == ====== == === == = == === == Y 2@= ) 5 E5 ===== == === == = == === == #2 $ZK$@EA )Nn)HBr%nr%A$ n)H $?$ ')HFrA)H $ == === == W @= 0 #5 $@5 5 == === == ====== == === == = == === == W @= V !X5 rE5 ?5 X9 ) 5 === == = == === == @= & 5 5 5 X5&n == ====== == === == = == === == n @= & 5 5 === == ====== == === == = == === == 2 V @= Y 5 5 (9 5 5 5 === == = == === == 2 V 0 W $D)H$?$@nA$D+$ = == ====== == === == = == === == 2#2 0 W = 0 (9 Q)n #5 & 5 ,!X5 == == 2#2 0 W = V 5 r )n #5 & 5 ,!X5 = ====== == === == = == === == 0#0 $@ Kn)n)H$+ n=OQrErr<&r$D&:)LJ6A$ === == Qrn)HA$N= === == = == === == ====== == === == = == === == 0 WZV 8L &Fr)LP$D )HFM== === == ====== == === == = == === == 0 W

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$@NRB8HA$ r 5 #5 0 O0 & 5 5 5 =U= === == ====== == === == = == === == 0 V & 5 5 7= == === == ====== == === == = == === == 0 #5 r 5 n?5 $ D5 === == = == === == V O0 n 5 ?5 n?5 5 r nX5 5 n?5 (9 5 r r n?5 5 r/nn7=A= 0 O0 n?5 9 ?5 ?5 O5 D5 5 5 5 n?5 5 5 5 r 5 L575 5 5 r n D5 = = === == V 2 V n?5 9 ?5 ?5 O5 D5 5 5 5 n?5 5 5 5 r 5 L575 5 5 n?5 r 5 5 = = == === == ====== == === == = == === == W n?5 9 D5 ?5 O5 ?5 5 5 5 5 n?5 5 5 5 r 5 :5 5 5 n r r 5 = D0 O0 $@5 5 5 5 5 n?5 )H )L5 )n r 5 7=Q= === == ?0 V n?5 )H) 5 5 E$ 9 5 #5 #5 ?5 5 5 5 = == 2O0 5 5 5#5 G0 WXW 5 5 45#5 r ?5 Fr5 &9 n n 5 r 7=O=== == ====== == === == = == === == Y 2 V 5 5 n?5 5 5 5 n n?5 #5 X5 5 ?5 X9 !#"%$'& / ?0 576 = = = == === == ====== == === == = == === == n 2 5 5 n?5 5 5 5 n n?5 #5 X5 5 ?5 X9 !#"%$'& / Y#V = Y 5 6 = = == === == ====== == === == = == === == Y 2 n?5 (' 5 ?5 5 5 5 n 5 r 5 :5 5 5 5 5 5 5 n == == === == = == === == 2 Y E5 n?5 5 5 5 n n?5 ?5 5 = == === == #2 2 5 *),+ /. ?5 9 n?5 n#5 5 n (9 n ?5 nD5 5 5021/ W = @=B==== == === == = == === ==

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2 )n #5 5 n 5 ?5 5 5 nD5 r r /nn 5 5 #5 9#=>== O0 n?5 9 9 5 5 5 n?5 5 5 5 r r / r D5 n?5 O5 5021Q/ W 1 @= == == 2 Y V n?5 9 9 5 5 5 n?5 5 5 5 r r / r D5 n?5 O5 5021Q/ W 1D= == == 2 n?5 9 9 5 5 5 n?5 5 5 5 r r / r D5 n?5 O5 5021Q/ W 1 V 2D= == == 2r 5 n nD5 n 5 5 5 9 5 5 5 =S= == ====== == === == = == === == 2r 0 W >0 5 ) 5 n X5 5 n 5 ?5 5 5 n?5 D= = == === == V 0 W V 5 5 D5 n?5 5 n r r n r r n#5 5 5 = = === == ====== == === == = == === == 0 W 5 5 D5 n?5 5 n r r n r r n#5 5 5 7=M= === == ====== == === == = == === == r 0 W 5 5 ?5 n?5 5 r r2 r n #5 5 5 7= ==== == === == = == === == #2

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$@ A$ 5 #5 V O0 5 n?5 n r n #5 5 #5 5 5 n 5 5 n?5 5 5 = ==== == === == = == === == 0 W V V nD5 5 5 n?5 n 5 5 r /n 7== == === == ====== == === == = == === == 0 Y O0 F 9 5 5 5 n?5 n #5 5n 5 5 =C= == ====== == === == = == === == V O0 X5 5 nD5 5 r 5 5 5 = === == = == === == V nD5 )H ?5 5 7=R= ====== == === == = == === == #2 nD5 )L) 5 5 5 = == == ====== == === == = == === == W 2O0 O5 5 n 5 5 #5 n n 5X5 5 5 7= === == ====== == === == = == === == Y 2 V X5 5 5 ?5 X9 O5 5 n 5 n 5 5X5 5 5#5 5 5 = == === == = == === == Y 2 5 5 5 5 7= = == = == === == Y 2 2 5 n?5 n r #5 n ?5 021/ W = nD5 5 5 =B=== == = == === == W 2 Y 5 r 5 :5 5 X5 5 5 5 r r 5 5 r r 5 5 5 #5 =r= = == === == ====== == === == = == === == D0 2 5 n?5n r 5X5 n 9 D5 #5 5 9 5 =?= ====== == === == = == === == V 2 n?5 ?5 r 5 5 9 ?5 = = = == === == 2@2 nD5 5 r 5 :5 5 n (9 5 5 9 ?5 O5 5X5 5 n (9 5 E5#5 = ==== == === == = == === == n 2 nD5 n?5 5 5 5 ?5 X9 X5 n D5 5 5 #5 nD5 5 5 ?5 X9 5 5 ) 5 #5 =R== = == === == r

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2O0 W nD5 nD5 5 5 5 5X5 ?5 5 5X5 n?5 5 ) 5X5 = === == r O0 nD5 r 5 ?5 W = n 5 5 = @0 V ?5 X9 r 5 n r n r =M= == = == === == n ?5 X9 r 5 ,F5 5 ) n r n r = == n 5 5 5 n#5 5 n 5 r 5 L575 5 5 5 n 5 5 5 ?5 5 =<=== == === == = == === == n Y 5 5 5 n#5 5 n 5 r 5 L575 5 5 5 n 5 5 5 ?5 5 =<=== == === == = == === == 5 r 5 :5 5 nD5 5 n?5 5 5 5 5 = == == ====== == === == = == === == O5 Q 5 ) 5 5 5 ="== X2 @2 5 ?5 X9 n r n 5 5) 5 5X5 7= = = == === == ====== == === == = == === == 2D0 nD5 5 5 5 n 5 nD5 5 D5 9 ?5 n 5 5 r 5 n?5 n 5 n?5 n 5 D5 9 r 5 ) 5 r r 5 n 5 (9 r 5 n?5 X5 5 n = == == === == = == === == 2D0 0 W O0 nD5 n #5 5 n 5 5 5 nD5 = = ====== == === == = == === == 2 0 W V #5 #5 n #5 5n 5 5 5 n ?5 4=== ====== == === == = == === == W 0 W ) )H 5 n #5 5 n (9 5 n 5 5 ?5 ?5 O5 D5 5 5 & = = W 0 W ) Q 5 ') 5 X5 #5 n #5 5 n 5 5 = = === == = == === == V 0 W Y ) H 5 ') 5 n?5 n X5 5 5 5 =R== == = == === == 0 W nD5 5 n r r n?5 5 / %0 R/ '! $'& r n #5 5 5 7=M= === == n 0 W nX5 5 r r n r r n #5 5 5 =C= === == = == === == ====== == === == = == === ==

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0 W @2 nX5 5 n r r n r r n X5 5 5 =C= === == = == === == ====== == === == = == === == r 0 W nD5 5 n r r r n #5 5 5 7=:=== == ====== == === == = == === == #2

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r 5 ,& 5 5 5 n?5 5 $ n nD5 nX5 (9 Q & r 5 n?5 E5 5 5 n?55 5 5 Q&n nZ9 nrnrn n"!#$ %n"& n'(nr%&n*)$+ n$,"./"0#1324576 8:9 5 5 &=>& 9 V W#WZY )n 579 9 E5 5 5 5 & nZ9 5 5 n?5r ?5 D5 O5 ?5 5 5 5 n #5 5 n 5 5 r r 5 n?55 n 5 5 %' 5 ?5 X9 0X= 2 576 5 ?5 r 9 n?5 ) ?5 L5 5 5 r =4 n?5 5 5 5 5 ?5 5 n #5 X5 5 ?5 5 D0 Y 576 r 9 n #5 5 ?5 n O5 5 021/ W = V 2 r W = r W = n?5 5 7=Q n?5 5 5 n ?5 "/!#"%$'& 021 5 n?5 #5 0 V 5 6 V#Y 576 =Z / 0D= V 5 6 r n?5 n 5 / n n r 5 0#=n W = 0 r n?5 5 9 5 5 5 5 ?5 5 = n?5 5 5 5 5 5 n 5 5 O5 r n#5 )H @' 5 5 n 5 5 5 5 5 7=

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)HFr&EAM0 %nE)Ln n?5 ?5 D5 n?5 r r n#5 5 n nD5 n 9 n?5 n 5 5 %= n 5 r 5 #5 5 n 5 #5 n?5 nr O5 5 n?5 "! #!$%&!'( n) n+, n n n?5 O5 n?5 9 ?5 r n?5 5 ?5 5 n?5 5 = n?5 $ ?5 r 5 9 ?5 5 D5 n?5 5 5 r n n?5 VXW n 5 9#= ./+. 0213547683596;:=<>6?@A
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V ?5 #5 n?5 ?5 5 =r nD5 5 5 5 r 5 5 r 50 O0 r 0 V 0 D= n?5$ ?5 r 5 n?5 9 n n n r 5 nD5 #5 9 5 9n V nn0 r 0 =Q nn #5 ?5 n?5 9 5 9 n?5 5 rn n?5 9 5 9 n?5r?5 5 5 L5 5 r V %0 = n?5 $ ?5 ?5 r D5 n?5 D9 r n n?5 5 5 n?5 5 n #5 X5 r 7=: n?5 5 5 5 D5 9 5 5 5 5 = nD5 5 %' 5 5 5 5 n?5 W 9X5 n X5 9 n n 5#5 5 9 r 5 :5 5 P$ P ?5 5 7= n?5 r 5 nn 5 5 5 r 5 :5 5 n?5 9 5 O5 n 5 n?5 n X5 5 n?5 f r V r gr r Y r r 9 n?5rr 0 r V r )Hn n?5 r 9 n?5)H W r n?5 B5 r = n?5 5 5 5 r 9 nD54$ @' D5 9#5 r 5 n X5 5 n?5 nZ9 n?5 75 F r n n n 5 n?5 9 n#5 5 n?5 5 = n?5 5 n n?5F r n D5 n?5 5O5 5 r 5 r 5 5 5 V n?5 B5 n?5 5F) 5 5 5 = ./ 34"1 7F !#"9O<"FG< 6 J8483F NPQR )n D9 )H nD5 n?5 9 5 r 5 :5 5 n #5 r 5 n n 5 =: n?5 nn 9 )H n n?5 ?5 n?5 ?5 nD5 5 0 W$ 7= n ?5 5 ?5 5 (9 5 n?5 r 5 #5 n?5 $@)S5 5 5 D5 5 ?5 5 5 5 n r = nD5 5 n n?5 5 5 %' 5 5 D5 9 n?5 D5 (9 n?5 5 5 5 = 5 r n 5 8 X5 %r 2 r 5 n n n#5 5 5 n 5 5 X5 5 D5 nD5 #5 5 7= n X5 n 5 n?5 S T ?5 &r 2 r n n n?5 ?5 n L5 5 ?5 r?5 n =M n n?5 5

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r 5 0 O0 &O5 5 5 = nD5 r n X5 5 5 5 n 5X= & 5 $ )n X5 0 & #5 ?5 0OX V 0 W = Y 0 W n#2 V W = W#W#W#WXW#W#W 576EX ] $ 0OX V W 45 6X V #5 ?5 Z 0OX V 0 0 W#Y = Y 2 W = W#W#WXW#W 5 6X ]O_ 0OX V W
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r 50 #5 r 5 n?5r$ ?5 = n?5 5 5E5 n 5 5 5 5 5 n 5 n X5X= 8 5 $ )n #5r #r3576EX X5r 5 5 D5 0 W P0 W f :5 0 40 2 W 1 V#Y W 1 W X2 0 W g :5 0 W D0#1 0 2rn W 1 W#W#V 0 0 W i 0 W W 0 n?5& 5 5 r 5 5 n #5 ?5 O5 (9 r 5 r r 5 5 n?5 5 =L nn O5 (9 5 r 9 575 r 5 r 0#0 = n?5 r 5 n n 5 n n 5 )H n?5 #5 9 r 9 & 75 r 75 n?5 9 9 5 5 r?5 n?5 9 n?5 @'J r 5 #5 n?5 5 #r 0 V =L r 5 5 5 n n?5 X5 9 5 9 n ?5 n?5 9 n?5 n?5 9 5 9 n n n #5 ?5 5 r 9 n?5 5 n n?5 @'( r 5 5 n = n?5 5 5 r n 575 r 5 n #5 5 5 r 5 n?5 5 5 5 5 n?5 n?5 #5 r 5 n?5 5 5 5 n 9 r 5 n#5 = nn ?5 r 5 5 )n D9 = n?5 O5 5 n?5, )n D9 5 r D5 5 n?5 9 5 5 = n?5 5 ?5 5 r ?5 5 n n n?5 5 5 575 n #5 5 r 5 #5 5X= n:5 575 n n n 5 5 r = n?5 5 5 5 r D5 5 #5 n nD5 5 r 5 :5 5 r 5 5 #5 9 #5 5 n n?579 5 r #5 n?5 7= nD5 n?5 5 O5 (9 )H n?5 9 @' 5 5 n n 5 n ?5 n X5 9 n n 5 n r 5 nX5 575 5 = n?5 9 5 5 n 5 r 5

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Y n?5 8 X5 n n n?5 r n 5 r 5 #5 $D )S5 O5 5 ?5 5 ?5 5 r =:8 n 9 5 5 r ?5 5 5 n?5 5 ?5 5 5 5 5 5 :5 5 r 5 n n?5 )H (?=I n?5 ?5 O5 D5 5 n?5 ( n?5,5 ?5 X9 5 ( nX5 r 9 nD5 n?5 5 5 r 0 ( / c %0#= 0 n?5 5Dc/ n V n r n n?5 r 5 #5 n n r n nD55 ?5 X9 5 5 5 5 5 n n 5 5 ?5 X9 n n n?5 nX5 X5 H5 5 4=, n?5 ?5 ?5 O5 nD5 5 n?5 5 r r 5 #5 n r 5 ?5 r D5 5 ?5 ' 5 ?5 = 5 5 5 5 5 n?5 r 5 r n?5 5r 0 r #5 nX5 :9 5 ?5 VXW#W 5 6 r 0 = n?5 =0#= 0 #5 nn?5 ( r 5 5 X5 5 r n?5 9 r 5 r 5 r 5 n n?5 5 n?5 n n r7 0 5 6 => nn n n n?5 r D5 5 ?5 n 9 5 D5 5 nD5 n nD5 5 r n n 5 n?5?5 5 5 n n 5 n 5 n?5 9 5 5 = n r 5 n n?5 )H n?5 5 n?5 +'( r 5 5 n?5 5 n n n 5 75 r 9 nD5 5 5 5 5 5 #5 r r nD5 n?5 9 n 5 5 ' #5 r X5 5 = n n?5 5 5 n X5 )H n n?5 5 D= ./ n2?Q1ORY
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O5 5 n 5 7= nX5:9X5 5 r nD5H5 O5 n 5 Q&EE r 0 #5 nD55 5 5 5 5 = #5 ?5 n 5 nO5 r L5 ?575 ?5 5 r 5 n =R n?5 5 5 5 n 5 n nX5 r 9 n?5 :5 %r 0 / ( r V 0 n 0 r r r %0#= V ( r/ V c r / G0 V n / n %0#= n?5 5# / n n?5 r 5 n?5 5 =8:9 5 n n r L5 5 5 n 5 #5 r 9 nD5 ?5 X ,5 r 0 Hd &d bndd r ( 0 %0#= n?5 5 n 5 r X5 5r5 n X5 5 5 5 5 r nL5 #5 r n r r (9 r 0 d &d d"! #!$!i% r ( & 0 %0#= Y n?5 #5 ?5 D5#5 5 n?5 L5 r 9 n?5 n #5 n?5 n?5 nL5 n ?5 n?5 5 r 5 5 r 5 r 5 n 7= n?5 5 5 r 5 n 5 5 :5 #5 5 O5 5 9 5 5 (' 7=

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)HFr&EA V nrnrn n"!#$ nn n 5 nX5 #5 5 n?5 n?5 5 5 5 5 = 5 ?5 5 9 r 5 5 r nX5 )H > )H n r 5 r 5 r 5 n n (9 n #5 5 7= 5 5 5 ?5 n 5 5 n 5 5 5 5 ) 5 #5 #5 ?5 = >/. 483@J>1ONP 3@KM? 91 8973U1N"?9O<"35P"n KrE1< n2?Q1 93HF%? 4"13U1ON\<"4 n?5 9 r nX5 ?5 5 O5 5 r L5 n #5 5 5 r 5 n nD5 5 n 5 r n 9 5 5 r ?5 5 5 5 n?5 5 =B&B5 r nX5 )H r 5 9 nD5 r ( r n 5 #5 9 r n?5 5 5 nn 5 5 n?5 n?5 5 5 5 =r n X5 n?5 n?5 ?5 D5#5 r n r n?5 5 5 =F :5#5 r n :5 5 5 D5 5 5 r n n n 5 5 nD5 r ?5 5 X5 5 = nn 5 n 5 r nD5 r 5 5 #5 r 5 ?5 5 r n?5 9 ?5 5 n#5 =" 5 9 r = 0#= 0 #5 r n 5 5 nX5 9 5 5 r 5 n n?5 5 n n 0 5 6 =A n r :5 9 nO5 n n n n?5 5 5 ?5X5 5 nD5 r n n nn?5 5 5 n 5 5 5 r 9 n = n?5 ?5 5 r 5 n rn?5 5 9 r n r n X5 9n 7=H nnn 5 n?5 n 9 nD5 n n (9 &AFr r 0 2 =N n?5 &F n ?5 r 5 L575 n?5 O5 r #5 )H 5 5 n?5:5 5 5 r 5 r 5 n =B n?5

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2 5 >) &F n?5 5 9 O5 r n#5 n & )H 5 nZ9 =Q nD5 n n n ?5 r 5 n?5 5 n?5 n n r 5 n n?5 n 5 5 5 5 n?5 n @9 7=r8A9 n?5& 5 n 5 O5 n 5 r :5 r n?5 5 r (9 n?5 n n O5 r #5 n = n?5 5 n?5 ?5 ?575 ?5 5 $ 5 ?5 5 5 )H ?5 =AF n 9 r 5 n 9 n@' D5 n?5 ?58 X5 r 5 n n 5 n?5 ?5 #5 5 n?5 5 ,5 n r 0 = n?5 r nD5 r 5 nD5 ?5 ( 5 5 5 ?5 n 5 n?5 5 n X5 5 ?5 5 5 = n?5 nn ( r 5 #' 5 n?5 n nD5 $ #5 5 5 ?5 n n 5 5 r 5 =E n r 5 5 X5 %' X5 5 5 r n r r (9 ( r r 5 5 = 0X= =R n?5 5 5 5 n?5 ?5 r n#5 5 nD5 n =B n?5 5 5 ?5 nD5 n 5 n?5 5 r 5 5 r W 1 0 0#1 W = 5 5 5 $ r nD5 5 n r 9 D5 @' 5 5 n n r 5 D9 n = 0X= Y )n 5 0 r n 5 r 9 nD5 5 = n?5 D9 5 5 r 5 5 5 r 5 r 9 n?5 5 I r 5, r VXW = n?5, 9 ?5X5 5 5 9 5 ?5 ?5 9 5 r 5 n r r ( 0 r n 5 ?5 5 r n?5 ?5 ( 0 ( 0#=: n n n n?5 5 9 5 5 5 n?5 )H ?5X=Q n?5E r ?5 5 ?5 5 ( n r 5 n 5 ?5 5 45 n Oi r i i i 5 5 r r 5 n?5

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5 ?5 X9 5 5 = n?5 ?5 nX5 5 n 9 X5 9 nn45 ?5 5 7=F L5 #5 r 5 9 5 #5 D5 Z9 5 5 5 5 = 5 n?5 5 n nD5 5 5 5 5 9 n?5 ?5 X5 5 ?5 7= ) n?5 5 5 5 5 5 9 #5 n?5 9#=Q 5 5 rn?579 n 5 nD5 5 #5 5 #5 9 5 5 n 5 n 5 5 5r5 ?5 5 '! + + "%$'& = )nD5 5 5 5 5 5 r #5 #5 r h#! r V 0 5 nX5 5 n 7= n?5 5 5 5 H n n n?5 ?5 nL5 5 9 ?5 D5 5 r 9 5 5 5 ?5 5 =: n?5 5 5 )H n?5 5 5 n?5 5 n?5 D5 5 5 9 r r 5 B n D5 O5 ?5 E5 5 5 9 5 #5 = n r r n?5 5 r 9 r 5 #5 5 ?5 (?= >/./+. : < 67N7? 6n ? 36N+4 < 9O= n?5 9 5 5 r$ r n?5 n?5 n :5 5 n 5 O5 n?5 5 =r 5 n?5 :5 n?5 (9 r n r 9 n?5 5 nD5 5 5 #5 7= nD5 $ n r 5 ?5 5 n?5 5 r 5 n n @' 5 r nX5 n 5 5

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0 W 0 r 2 r 4 r 6 r 8 r 1 0 r 1 2 r 1 4 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r1 / Nj e t d N / d kTk T G e V / c c o n e q c = 0 4 7 E j e t = 4 1 G e V 5 V O0 5 n?5 r n X5 5 X5 5 5 n 5 O5 n?5 5 5 =r n?5 n r n r D5 5 n ?5 021/ W = 5 5 E5 #5 = 5 n?5 5 =4 n?5 ?5 $ ?5 r ?5 n?5 nD5 9 r r n?5 n r 5 ?5 5 D5 5 5 n 5 9#= ?= V O0 n 5 5 n?5 r n #5 5 #5 5 5 n 5O5 n?5 5 5 r r= n r?5 5 5n 5 n #5 r 0 576 r n?5 5 5 r r 5 n?5 5 n?5 5 9 5 X5 9 n 5 ?=A$ O5 #5 5 5 r r r #5 n r ?5 n?5 r 5 5 ?5 5 5 r $ n r 5 n?5 ?5 5 n 5 576 $ VXW#W 5 6 = >/./ <>P 3@ KM3591<"4 369O<"4%83@+N1nJ J '<1 "8?RINR K r n?5 > )H n 5 r 5 n r n?5 n #5 5 5 n n n X5 D5 r 9 %' r ?5 5 = 5 ?5 r 5 5 r n r 5 :5 5 n ?5 r 9 nD5 nZ9 n?5n n (9 rZ&F r 0 2 =

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0#0 n?5:&F 5 n n?5 n 9 n?55 n?5 nL5 ?5X5 5 = nD5 r nD5 X5 n n 5 (9 5 n?5 ?5 n 5 $ 5 n 5 576 r +5 ?5 5 nD5 5 n?5 9 n 5 r nX5 9 5 5 7= n?5 5 5 r 5 r D5 n r $ n 9 n L5 = nD5 nn (9 n nD5 5 r?5 5 O5 5 r V n?5 )H ?5 nD5 n X5 n 9 O5 5 n?5 ?5 5 5 5 5 5 n?5 ?5 = n?5 #5 5 5 n?5r&F n 5#5 9 n@' ?5 nD5 5 r 5 5 n n n 5 5 r 5 nD5 5 5 n?5 =Q n?5 5 5 r D5 5 n 5 9 nX5 r 5 r 5 n?5 5 n n 1 1 1 2/ )n 1 1 1 $ & V = 0 nD5 r n?5 nX5 5 n r n 5 5 n?5 5 r 5 = n?5 5 n r 5 ?5 n?5 X5 #5 n 5 5 r / )n & 21 V = V n 5 n ?5 n 5 O5 D5 ' ?5 n r 5 :5 5 n 5 #5 r 9Z'(5 #5 r r r 9 n?5 X5 #5 r 5 n L5 n?5 #5 #5 = 9 r n?5 &F 5 5 5 r 5 9 9 5 r 5 5 nD5 5 n(9 n?5 ?5 5 5 n n?5 5 45 D5 9#=

PAGE 25

0 V >/ K K(9O? 6NP 1ON<"4R n 5 r L5 n?5H& 5 nD5 5 n #5 5 n 5 5 7=Q n?5 5 n 5 #5 9 5 n 5 n 5 r n?5 9 5n#5 ?5 r 5 5 5O5 5 5 5 5 = n?5 5 5 n 5 5 5 r 5 @' 5 n?5 5 B r 0 L5 5 r V r VXY r V r V r 5 5 5 n n?5 &F nZ9 n?5 r 0 2 =L 9 r n?5 > )H 5 5 r ?5 n?5 n (9 5 r & r n?5 r / & n & r n 5 5 = n?5 5 9 r n?5 n (9 5 5 D5 9 $ & 5 ?5 ?5 r D5 r 9 5 5 r 021 r n?5 5 n?5 5 5 i i 5 5 r 0 =B nD5 (9 & D5 O5 9 ?5 r 5 ,/ $ / !#"%$'& 021% $ r n?5 5 / !#"%$'& 021 n n?5 5 nD5 $ n n?5 ?5 r $ r 5 X5 = 5 nD5 n (9 5 5 5 5 5 D5 n #5 5 n?5 5 rn?5 n?5 5 5 5 5 5 5 D5 ?5 X5 n 5 nD5 n?5 5 r 021Q/ V =$ 9 5 r n@5 r 579 n?5 5 n n?5 > )H n?5 5 ?5 5 n5 =F L5 #5 r 5 5 5 "/ V $'& d '021 V n n n?5 5 n 5 5 5 5 #5 5 n 5O5 r n?5 5 5 = n?5 n?5 5 r n?55 ?5 X9 5 r 5 5 "/ V !#"%$'&J= nD5 D5 r 5 n?5 5 n 5 5 5 L5X5 n 5 #5 5 n 5 5 5 n n?5 5X5 5 r L5 ?5 nn n ?5 n 5 n?5 5 L5 5 5 5 r ?5 D5 7=

PAGE 26

0 r 5 V O0 n 5 ?5 n?5 5 r nX5 5 n?5 (9 5 r r nD5 n 5 r/ = W = V 2 W W =r W = VXW W = 0 2 Y W = V W = 0 2 W = V W =n W = 0 V W = 0D0 W =rX2 W = W 2 W Y W =D0 W = W 0 W = 0#0 V W = 0#2 W = Y 0 W W = W D0 >/>/+. : ?354 : @\1N 7@+NPQN1J%
PAGE 27

0 $ 9 O5 r nD5 ?5 '" 5 n?5 ?5 ?5 n?5 r n?5 D5 n?5 r n 5 5 7= F L5 #5 r n?5 5 5 5 5 5 5 5 r 5 5 nD579 ?5 5 D5 9 5 X5 5 #5 9#= >/>/ N ? 9O?47P ?'? 1??4 8359 3476 @ 8<"4&?Q1OR T )H r n #5 5 5 r r 5 n?5 r / Xn n / # / 5O5 nX5 9 r 5 ?5 9 5 5 5 n #5 5 r n?5 5 5 5 O5 5 n 5 5 r 9 5 n r 5 5 5 n?5 5 5 5 7= nn 5 5 5 n r 5 n 5 5 r 9 n?5 n n 5 5 r / nn = n?5 9 !#"%$'&r ?5 # n n 9 r/ n / r r 5 5 5%= r V 2 =A 5 5 5 ?5 5 r nL5 #5 r n?5 9 ?5 r 5 n 5#5 nD5 n?5 5 O5 r V = n?5 ( 5 r V ?5 P5 D5 9 5 r V#Y 5 #5 5 5 nD5 r 5 O5 #5 9 r *V 1 0 r 0#1 r5 O5 5 9 5 r 5 5 ?5 5 7= #5 n n?5 ?5 5 n n nD5 n n nD5 5 5 r /nnr 5 r D5 n?5 ?5 ' ?5 ' ?5 ' 5 ?5 r V / n 0 + + + V = n?5 5 +5 5 $(/ 07' 5 #5 r 5 V O0 r + n ?5 r D5 r 5 + / V n( ( / V + 0 V + 1 n?5 nD5 5 5 n 5 r #5 n?5 5 5 5 5 ?= V V =B5 5 n?5 n 575 nD5 r 5D5 r nD579 5 L5 ?5 5 ?5 5 n?5,5 ?5 X9 5X=I n?5 5 n n?5 5 nX5 5 n?5 n n?5 ?5 ( 5 ,5 D5 9 5 = n?5

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0 Y Q G e V 1 0 1 0 0 r = Ng/ Nq 0 1 2 3 C a p e l l a e t a l 2 0 0 0 L u p i a & O c h s 1 9 9 8 C a t a n i e t a l 1 9 9 2 G a f f n e y & M u e l l e r 1 9 8 5 L L A & N L L A r = C A / C F = 2 2 5 5 V V nD5 5 5 n?5 5 5 r/ = B5 ?5 X9 5 5 n?5 r 5 n 5 5 r 5 ?5 5 #5 5 5 9 r 9 n?55 5 5 9#= nn n 5 5 5 5 %= r V =Q n?5E5 5 5 5 n?5 r / n r r 9 n?5 0 W 5 n nD5 5 7= 5 D9 5 ?5 r #5 rn?5 )H 5 5 9 nX5 n?5 (9 5 r r nD5 n 5 5 r / 2 = nD5 5 5 r n?5 5 n?5 (9 5 r r 9 #5 r 9 :/ + r V & / n n 1 5 V b b V b + V V b V b + V 0 n 1 V = Y 5 n n #5 5 n n?5 n?5 5 n 5 r #5 5 O5 %' 5 nD5 n 5 r = 5X= r 5 n 'r X' 4.7' 9X= 9 r nD5 5 5 O5 n n 5 5 ?5 r 9

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0 = V = V r / )n & = n?54&F 5 n n?5 )n n n?5 5 n = / n2?Q189O3 "FG?4H1I3U1ON\


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0 5 B5 5 0 1 r n?5 5 n ?5 r?5 r 9 E/ 1 1/ 1 ! 1 V = n?5 5 r 1 r !1 5 n?5 5 5 ?5 5 c b = n?5 ( R = V = n 5 5 5 n?5 #5 5 5 5 nD5 r n D= n?5 1 n n 5 #5 ?5 5 n?55 D5 9 n 0 n n 5 =E n?5 )H n?5 5 5 5 5 5 ?5 r n F5 &Q9 n rn:5X5 r n 5 5 5 5 = n r F5 n 5 n 5 5 n?5 ?5 r 5 5 5 5 5 5 = V = =T nD5 5 &Q9 n r n?5 ?5 5 5 5 ?5 $ (9 #5 @' ?5 5 5 = nn 9 5 5 D5 9 r n n?5 5 5 R5 5 5 n ?5 RF5 I&Q9 n D= n?5 5 5 n 5 n Fr5 n #5 r 9 n n?5r r n n?5 n 575 5 5 5 5 9 nn = r n #5 ?5 r n?5 n:5 n 5 5 n?5 nD5 5 r 5 1 & #= n?5 5 5 5 5 r 5 :5 5 F5 &Q9n nD5 5 5 n?5 n =Fr5 5 5 5 ?5 n r n n n 5 r 9 n?5 5 r?5 5 r V O5 (9 n?5 r n ?= n?5 n4' 5 5 n?5 5 ?5 n n?5 ?=Q n?55 n?5 nL5 r 5 5 @' O5 r #5 9 7= n5 n r n?5 ?5 5 n n ?5 9 n 9 n?5 5 5 9 n = $ 5 5 5 n #5 X5 9 n 5 r n n 5 :5 ?5 9' 5 n r #5 9 n?5 9 5 n n ?5 9 5 r 5 5 ?5 9 n 7= 8 9 5 5 5 ?5 9 r 9@' r 9 r = 5X= 5 nD5 5 #5 9 n #5 5 r 9 r 5 7= 5 nD5O5 r #5 n :5

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0 2 rn?5 n 5 nn 5 5 r 5 n?5 $ 5 nX5 r 9 r r (9 r '0 =B n?5 #5 n?5 5 ?5 (9 n n?5 r 5 #5 n 5 n?5 n 5 O5 5 #5 9 ?5 5 ?5 r 9 n?5 5 5 r. 1 & r Z' 5 n?5 nL5 r 5 5 5 5 r 9 n?5 n 5 n 5 n n = n?5 n n 9 #5 r 9 n?5 r 5 n 5 5 5 ?5 9 r n?5 r r 9 n?5 5 O5 n n n 9 9 ?5 5 ?5 #5 = n?5 #5 n I&Q9 n nn?5 r 9 n?5 $R ?5 r n = n 5 5 ?5 n?5 5 5 5 5 n?5 n =Anr5 5 n?5 5 n?5 r n?5 5 #5 5 5 r 5 ?5 X9 n?5 r 5 r n n 5 X5 r r 5 :5 5 n?5 = n?5 n n 5 D5 9 O5 5 n r 5 ?5 r 5 =r n?5 nD5 r 5 n nn D5 5 5 r 5 = n?5 5 n?5 rD5 n 9 9 5 5 ?5 X9 5 5 n 5 = r 5 5 5 r nD5 5 5 #5 5 5 5#5 ?5 5 r n = n 5 5 ?5 5 ?5 r 9 5 n?5 5 5 n?5 9 5 n r r r n?5 &5 5 r Y b c 7=48 9 ?5 r 9 #' r 5 5 5 =A 5 n?5 r 5 L575 r 9 r 9 :5 = n?5 ?5 n 5 5 5 ?5 r 5 n?5 5 ?5 X9Z' 5 5 5 n Z9 5 5 ?5 r 5 n?5 =I n?5 ?5 5 5 5 5 #5 9 nL5

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0 5 5 5 5 5 5 n n?5 D=LF L5 #5 r n 5 5 n?5 5 5 5 #5 r 5 n?5 5 5 5 5 n n n?5 O5 r #5 =

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)HFr&EA $@E%A$ nr* n"!#$ nn)n 5 5 5 n?5 n 5 5 5 5 5 5 5 )H ?5 #5 5 5 9<5O5 5 5 = n?5 5 r (9 5 X9 n?5 9 r)H 5 5 = >/. Kn"HJ8RINPQRr: <1NU3U1ON\

)H 5 9 =H n?5 9 n 5 #5 n?5 r 5 L575 nD5> )H @' > )H = ?5 O5 5 5 n n?5 5 5 5 n?5 5 n #5 5 n 5 5 = n 5 )n 5 V r > )H n X5 9 D5 r 5 5 r n?5 n?5 5 n 5 r / n =I n?5 5 5 5 r 5 :5 5 5 n?5 n?5 )H = nD5 5 5 r n 9 r n X5 n n B5 5 5 5 5 =A 5 5 5 n?5 n (9 5 5 5 r 5 :5 5 5 n X5 nn 9#= n?5 5 5 5 5 5 ?5 = n?5 > )H 9 0X= 0#= nD5 X5 A5 5 n 5 @' 9 5 r 5 5 r5 ?5 5 7=H n?55 5 5 5 5 nD5 / L5 5 n 5 n 0 5 5 r r r n?5 ?5 5 = X5 n?5 0 W 'J9X5 &G5 r n?5 5 5 D5 5 40X= 0 40#= Y r n n n 5 5 :5 5 r 9 r 5 n?5 nD5 5 5 r 0#= 0#= 5 5 D= O0 =: n n r 5 5 n n?5 5 n 5 #5 9 5 nD5 5 5 5 5 5 5 n?5 5 r 5 r 5 n?5 ?5 5 (9 D5 9 5 n 575 5 5#5 n?5 9 5 5 r& n 5 n?5 ?5 5 =H n?5 5 5 r n?5 #5 V W

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V 0 5 n 5 ?5 5 ?5 5 5 5 5 5 5 5 n 7= n?5 5 5 5 n #5 5 #5 9 ?5 5 5 n?5 5 5 7=Q n?5 5 5 5 5 X5 ?5 #5 5 5 ?5 5 Y 5 6 0 WZY 576 = n?5 n?5 n r n?5 5 5 9 ?5 ?5 O5 D5 5 5 5 5 O5 5 L5 ?5 r ?5 5 575 ?5 5 = n ?5 r 5 9 5 5 5 5 7= 9 r 5 5 n?5 5 5 5 5 5 5 R5O5 5 r ?5 5 nD5 nX5 (9 5 = n?5 5 n n 5 5 = ?5 5 5 n?5 5 nn@' nZ9 n?5 B5 5 F) 5O5 5 7=M n?5 5 5 5 5 5 r 5 5 5 nX5 5 )H r 5 5 5 n rc 5 X 5 f g ?5 9 =< D5 nD5 9 5 n n 5 9 r 5 ?5 r n n?5 D9 5 5 rd d c c n?5 r n?5 5 n?5 n 5 n?5 r Z9 5 = 9 9 5 5 9 n 5 r 9 5 ) 5 #5 #5 ?5 5X= ?= r 5 Q5 D5 9 5 r 5 5 r 5 =5 5 nD5 n r nFr5 &Q9 n :5 5 D5 5 5 5 5 n r n 5 n n?5 9 O5 U5 9 :5 nD5n n 5 5 n#5 5 5 5 7= n X5 X5 9 5 5 5 5 ) ?= / C '? 9N+FG?4H1I3@ N+R1<9OJ E5 9 5O5 5 5 n?5 5 5 5 r 5 L575 5 5 n ?5 =L$ D9 5 n n

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V#V ?5 n Oi 5X5 ?5 n 9 n n nD5 n 575 5 n n?5 5 = r 5 5 5 n?5 5 5 5 5 #5 r 5 = ?5 nD5 r 5 5 r / nr r ?5 r 9 n?5 Fr$ r = n?5 9 r 5 5 5 n 5 5 9 5 Oi 5 #5 n?5 5 n?5 5 :5 5 5 r n?5 5,5 ?5 5 0 W 576 r X2 = n?5 r r (9 5 n X5nn?5 n (9 5 5 r 9 n?5 & n n (9 n r ?5 5 ?5 5 n n?5 n 5 5 5 #5 9 #5 = ?5 /"0#1 V + n + r ?5 = n?5 r 5 "& r ?5 r 9 nD5& r r =B n?5 K n O5 5X5 g + L5 5 5 5 5 n?5 9 n = n?5 r 5 n 5 n (9 r / 0#1 WZV W 1 W = r 5 n 5 ?5 5 r V 576 = n?5 9 n r 5 n n?5 (9 5 5 n?5 nnD5 5 n 5 5 n?5 ?5 n n 5 O5 n?5 n 5 5 5 L5 #5 ?5 ?5 n?5 n nD5 5 D5 9 5 = n?5 +' #5 5 5 :5 5 5 n?5 9 7= n?5 5 L5 5 5 5 5 n?5 r = n?5 5 r n n #5 5 n?55 5 n 5 5 n D5X= n?5 K n O5 5X5 g + 5 L5 5 5 n?5 D5 & r W = n?5 nn?5 5 ?5 X9 5 5 r 5 5 = n?5 :5 5 ?5 X9 5 :5 5 5 5 5 n 5 7= nD5 5 r 5 L575 P5 n n?5 :5 5 ?5 X9 5 n?5 5 5 :0 YXW 0 W = n?5 5 n r ?0 5 5 5 5 nD5 =: n?5 n #5 5 n 5 5 :5 5 ?5 #5 @' X5 5 @5 5 7=L 5 ) 5 r n?5 n?5 5X= n?5 5 :5 5 5 5 5 nD5 5 ?5 X9 5 / $ &/ V 576 =O nD5 #5 #5 n X5 5 5 5 :5 5 E/ @1 0 W W 1 0 W / D132 W 1 W 5O5 nX5 9

PAGE 36

V n?5 5 n?5 rBnr 5 = n?5 r ?5 / n / 0#1 V W 1 WZY W 1 W nD= n?5 5 :5 5 5 5 ?5 5 5 5 5 = n?5 $@ r 5 I5 5 9 n?5 5 5 n ?5 n?5 5 5 K (9 5 5 #5 r V = n?5 9 5 5 5 n 5 :5 5 5 5 n 7= n?5 5 :5 5 5 5 nD5 5 ?5 X9 5 / $'& / V R576 = n?5 5 5 / n /C0#1 V n W 1 W n + + + + = n?5 & 5 5 5 r 5 5 9 5 O5 5 n?5 5 r W D9 n 9 n X5 5 7=r n 5 r ?5 5 ) 5 ?5 nX5 5 5 (9#=r n?5 5 ?5 L5 5 / @1 0 W W 1 W W 1 W r / @1 V W 1 W W 1 W 2 /nn /0#1 V#Y 0 W 1 WZV W 1 W nD= n?5 ?5& 5 r r n?5 5 n 5 D9 5 5 5 r 5 :5 5 n 5 5 7= n?5 5 5 L5 5/ D1 0 W 1 W W 1 0 V r / D1 0 2 W 1 W W 1 0 / n / 0#1 W W 1 W #2 W 1 W V = n?5 5 :5 5 5 5 n?55 D5 9 5 "/ $ & / V ?1 5 6 =? X5 n n 5 5 5 :5 5 5 O5 5 n nD5 ?5 5 r D5 n (9 5 5 n?5 5 ?5 / W = n?5 5 5 L5 5 E/ @1 0 2 W 1 W W 1 0 r / Y 1 W 1 WZY W 1 W // n /0#1 0 Y W 1 W D0 W 1 WZV @= n?5 5 5 n ?5 5 "/ !#"%$'& / V ?1 5 6 = n?5E&F r n 5 5 K n O5 5 #5 n?5 g + O5 r Y :5 9 n?5 5 5 n & I$D = n r 5 L5 5 n 5 Lb c 5 = n?5 5 ?5 X9 5 / !#"%$'&/ V 5 6 r A&F n 5 5 n?5 5 / & r 0 r n?5 ,* .-b -c 5 5 g + 5 0 ?= Y r V D= r V D=n r 0D=n V 0#= V r 5 5 #5 9#=

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V D1 W W 1 0 W W 1 V r / @1 W W 1n W 1 V r4/ n /U0#1 V r W 1 W 2n W 1 W#V#V /nn /0X1 0 W 1 W#V W 1 W 0D= 6 5 n D5 L5 5 5 9#5 9 n?5 g + O5 r 9 n?5 &Fr r r r = 5 L5 5 5 9 5 K ' (9O5 5 5 ?5 ' (9O5 5 #5 =: r n 5 #5 (9 5 r 5 #5 @5 5 :5 5 5 r n 5 5 = K 5#5 r n?5 nn?5 5 ?5 X9 5 5 r 5 >=Q n?5 5 ?5 r 5 r 9 D5 n?5 :5 r5 ?5 X9 5 c O= n?5 5 n?5 D5 5 n n?5 +9r ?= 5 5 ?5 5 #5 r n?5 5 r 5 L575 5 0 V W N0 Y 7= n?5 5 ?5 r 5 r 9 n?5 5 c = n?5?' r ?5 5 5 5 7= ?5 5 ) 5 ?5 #5 5 5 n (9X= n?5 n?5 9 n K ' (9O5 5 #5 5 5 r 5 /nn /"0#1 V n W 1 WZV 0 W 1 WZVXW =Q n?5 5 5 n?5 9 5 5 ?5' (9 5r5#5 / n /"0#1 V W 1 WZY W 1 WZVXW n?5E5 ?5 X9 5 N/ $ & / W 1 576 =Z n?5 5 n?5 9 n 9 5 i 5 #5 :5 5 5 nD5 5 O5 r = n?5 5 n n n?5 9 K ' (9 O55#5 = n?5 5 ?5 r?5 r 9 ?5 n?5 :5 5 D5 9 5 hc >= n?5 n (9 5 5 5 5 ?5 X9 r ?5 5 #5 =Q nD5 r n :5 5 5 5 5 5 = n?5 5 5 5 D5 9 5 M/ !#"%$'&/ V D1 5 6 =O n?5 5 5 ?5 n 0#0 r n n n 9 5 5 nD5rnr 5 = n?5 5 r D5 n n :5 5 / n 1 B/0#1 V V W 1 WZV#V W 1 W 0 2 / n 1 B/C0X1n W 1 W 0 W 1 W Y r 5 O5 #5 9#= n?5 9 5 5 L5 5 r 5 nD5 5 n 5 5 9 5 5 5 #5 = n?5 5 5 5 5 5 5 ?5 r 5 nD5 r 5 5 5 n 5 5 5 ,5#5 n n

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V#Y n?5 9 ?5 O5 D5 n?5 ?5 n n?5 5 r n n 5 5 5 c @. = 5 D5 5 r n?5 5 r ?5 n 5 5 n L5 5 X5 9 n 5 =I n?5 nD5 r r 5 5 5 O5 n 5 n?5 5 ?5 X9 5 n?5 nD5 9#= n r n?5 5 L5 5 5 5 nD5 5 5 ?5 X9 n?5 5 5 =rF L5 #5 r 5 n 5 %= r Z2 n n?5 5 :5 ?5 X9 n n ?5 r 5 n?5 5 5 n 575 5 5 #5 = n?5 5 5 r nD5 5 5 5 r 5 r 5 5 n?5 9 5 )H D= n?5 r 5 D5 r 5 r #5 L5 5 5 5 ?5 n?5 5 5 5 5 r 9 )HA ,& =?)HA n r ?5 n?5 r 9 (9 i i 5X5 r r = n?5 n (9 nn 5 5 5 ?5 r ?5 nX5 9 r 5 n #5 5 D5 nD5 n?5 5X= n?5 5 5 5 5 5 n?5 5 n?5 b L5 5 5 9 n?5 5 = n?5 5 L5 5 5 5 n?5 5 n?5 #5 576 r" 5 6 =# nD5 5 5 /C0#1 W W 1 WZV W 1 WZY = n?5E5 ?5 X9 5 n 5 5 5 5 9 5 5n?5 5 5 5 r 5 :5 5 5 7= nD55 5 r YXW r n?5)H: r n 5 5 nD5 5 n?5 n X5 5 n (9 5 n?5 5 r" "H/C0 W 1 576 V H/ D1 W 1 W W W 1 W Y = n?5 &O r 5 ?5 5 K n 5 5 #5 n nD5 r 9 r?5 5 n r Y 0 = ?5 9 n r 5 5 5 5 5X5 n?5 5 5 5 n ?5 5 =, n n 5 #5 n D5 n?5 nnD5 5 r 9 n?5 ?5 5 O5 n?5 n 7= #5 hc 5 L5 5 5 5 r 5 nD5 5 n?5 n?5 5 7= n?5 n (9 5 n?5 ?5 r?5 #5 9 n #5 5 n?5 nn?5 5 =A nD5 #5 X5 5 5 ?5 X9 $ & / D1 V 576 = 5 n n?5 5 5 n 5 ?5 r ?5 n?5 5

PAGE 39

V 5 = ?5 5 5%= r Y#V n n?5 5 5 5 5 5 5 ?5 r 5 r X5 5 X5 9 5 9 n?5 O5 5 5 5 5 5X=A n?5 n (9 5 ?5 r ?5 #5 9 n n?5 n (9 hg + .5 #5 =A nD55X5 n n?5 n 5 5 5 5 @= nD5 #5 X5 5 D5 9 5 $ & / Y 1576 = nD5 n (9 5 5 5 n?5 5 %' 5 5 5 ?5 X9 5 5 =& 5 r n 5 2 W r 2 n 5 r L5 5 r D5 r 5 !X5 5 : 5) n = nD5 5 5 :5 5E/C0?1 W 1X2 W 1 W r / D1 YXW W 1 W W 1 V / 2 / 0#1 YXY#V W 1 W ?0 W 1 W W = n?5 5 5 5 ?5 X9 5 "/ V $ & / X2D1 576 = n?5 ?5 &O 5 5 5 r Y r Y r 9 5 O5 5 n r 5 5 n?5 5 9 r Y 0 = n?5r Y 5 L5 5 4/ 0?1 V W 1 V W 1 W r / 0 W 1 0 W W 1 W 0 W 1 0 2 r / n /0#1 @0 W 1 WZV W 1 W r r n nD5 5 5 D5 9 5 "/ V !#"%$'& / 2@1r 5 6 = n?5 5 r ?5 r Y L5 5 E/"0?1 V 2 W 1 0 2 W 1D0 /nn /"0#1 Y 0 W 1 W 0 W 1 W nD= n?5 5 N/ V !#"%$'& /S2 W 1 V 576 = n?5 5 r #5 )HA r r r YXW I& r Y 0 r Y r Y 5 5 5 5 n?5 9 D5 D5 O5 ?5 5 5 5 r 5 n 5 @' n n?5 5 9 :5 ?5 r D5 5 ?5 X9 5 7= 5 5 9 5 O5 5 5 n?5 5 5 5 r 5 :5 5 5 5 75 r 5 >0 rr V 5 5 5 4 ?= O0#=B n?5 5 5 5 ?5 ?5 5 ?5 5 5 n?5 n (9 5 n?5 / n O5 5 r 9 & )HL=? nD5 5 5 5 5 5 n 5 r 5 = n?5 &O r n 5 5 9 5 5 5 5 nD5 5 5 5 7= n?5 r ?5 ?5 5 ?5 D9%r Y#Y r nD5 n ?5 ?5 9 5 9 n 5 5 5 5X5 9 5X5 r 9 K' n O5 5 #5 :5 5 5 D5 n?5 9 7= n?5 n (9 5 E5 5 n?5 n (9

PAGE 40

V H i s t o r y o f m e a s u r e m e n t s o f t h e r a t i o o f c h a r g e d p a r t i c l e m u l t i p l i c i t i e s i n G l u o n a n d Q u a r k J e t s Q G e V 1 0 1 0 0 r = Ng/ Nq 0 1 2 3 L L A r = C A / C F = 2 2 5 C a p e l l a e t a l 2 0 0 0 L u p i a & O c h s 1 9 9 8 C a t a n i e t a l 1 9 9 1 M u e l l e r 1 9 8 4 C L E O H R S O P A L D E L P H I A L E P H S L D 5 O0 F n 9 5 5 5 nD5 n X5 5 n 5 5 = 5 5 #5 r 9n n?5 5 r #2 n n n 9X= n?5 n (9 r 5 5 r ?5 n?5 r r n?5 #5 n (9 / .5X5 n 5 X5 r b -c = n?5 5 5 5 ?5 X9 5 / = n 5%= r Z2 n r 5 5 5 ?5 X9 5 r 5 5 5 L5#5 =: n?5 5 n (9 5 n?5 r / n r :5 5 5 5 n?55 D5 9 5 nD5 #5 / 0#0#= 0 5 6 / W = Y 576 =@ / W 5 6 r n?5 5 5 /0#1 V#V W 1 W#W W 1 WZY 0X= nD5 ?5 5 5 5 r Y r 5 5 5X5 :5 5 5 r 9 @' 9 n?5 5 5 r n r Y n n 5 r 9 n?5 5 / r n?5 5 n n?5 5 = n?5 ?5 n 5 V =

PAGE 41

V 2 r 5 O0 n?5 9 ?5 ?5 O5 D5 5 5 5 n?5 5 5 5 r 5 :5 5 5 5 n ?5 = n?5 5 5 r D5 r 5 5 7= n?5 5 5 r n?5 9 r 5 5 9 5 n?5 9 )H 5 7= nr nn n "!$# &%' )(+*-, -)n. /1032 45)6 798n:<;-=?>@rABC D D >E FGH3IJ K$L M IJ N-O PBQ3RS 2 4G"6 7 8n:<; =TF)UVABC D D >W @XFYB@W @ZU[\]nZW_^ PBQ3RS 2 UX@"6 798n:<;-=TF)UVABC GW>`@XYB@Wa>@ ?bdcfehg )ijbdcfekg l W 5 l YB@W @G >W 4XF l YB@W @Xm)UYB@W @Xn)4 0 Spo 2 UXF)6 q\7 8n:<;$r =TFZUrABC D D ij )s+t g >W FGZUuYB@W @ l U H3IJ InN-v M IJ InO$N PBQ3RS 2 UX4"6 ?bdcfehg )ijbdcfekg wx D`@XYB@W @XnYB@W @G nW FXnYB@W @unYB@W @5 >W Fm>"YB@W @XF)UYB@W @FZG z .jD"YB@W @XmYB@W @m >W @G l YB@W @XFZ4uYB@W @FZ4 PBQ3RS 2 UU)6 ? )s+tjg )ij )s+tjg wx D l YB@W @XnYB@Wa>`F l W mGXYB@W @ l YB@Wa>@ >W 4G@XYB@W @45uYB@W @4F z .jD`5XYB@W @ l YB@Wa>4 mW UUuYB@W @XmYB@W @ZU >W>`4mYB@W @4>)YB@W @FZG RS Q 2 UXm`6 ? )s+tjg )ij )s+tjg 7 8n:<; gTF)UVABC GW G@XYB@Wa>@uYB@W_Fn nW G@XYB@W UUuYB@W_F l >W FZUGXYB@W @5ZUYB@W @FF bdcfe g ij bdcfe g 5W F5 l YB@W @GXYB@W FF >W>`GZUuYB@W @XFnYB@W @>G o SfQ |{j2 U l 6 ? )s+t'}~ng )ij )s+t'}~-g wx D@W @?ABC mW_nZ5XYB@W @ l mW UX4XYB@W G@ >W @ l YB@Wa>5 wx D`mW @?ABC l W l UuYB@W @G mW mZUuYB@W UX4 >W F@XYB@W @G wx D`5XYB@Wa>"n nW mFYB@W 4 l >W @GXYB@W @ l wx D`4XYB@Wa>U nW 45XYB@W 44 >W FZUuYB@W @ l w x€DW FmYB@W @Xn w x€D`@W l nYB@W 44 5W FZUuYB@W>)n >W FGXYB@W @m w x€D>W 5 l YB@W l 5 5W l >"YB@W F@ >W 45XYB@W @G w x€DW F4FYB@W @XFFXYB@W @>5 XD‚y]` 7 8n:<; g?>@W @?ABC nW @UuYB@Wa>@ mW UUuYB@W 5Xm >W FGXYB@W_FZ@ XD‚y]` 7 8n:<; g?>`mW @?ABC nW GXmYB@Wa>U l W_nZ4XYB@W 5> >W>`5XYB@Wa>U XD‚y]` 798n:<;-gTFZ@W @?ABC GW 4XmYB@Wa>G nW U l YB@W m4 >W FmYB@W @G XD‚y]` 798n:<;-gTFmW @?ABC >`@Wa> l YB@W UX4 nW m@XYB@W 44 >W 4XmYB@W @ l XD‚y]` 798n:<;-gB4@W @?ABC >>Wa>5XYB@W Un 5W>`GXYB@W>`G >W 4unYB@W @Xn XD‚y]` 798n:<;-gB4mW @?ABC >>W_FnYB@W_n)U 5W F@XYB@W F4 >W 4unYB@Wa>@ XD‚y]` 798n:<;-g1U@W @?ABC >"FW l >"Y?>W 4XF 5W Uƒ>"YB@W> l >W m@XYB@Wa> l XD‚y]` q\7d8n:<; r gTF l W l ABC D D >W 4 l GXYB@W @>GuYB@W @4m )ij )s+tjg wx DW FXn)GXYB@W @XF>)YB@W @FZ@ w x€DW 4XFZ4XYB@W @XmZ4uYB@W @FZ@ w x€DW FmZ4XYB@W @XFZ5uYB@W @ZUU

PAGE 42

V D5 )H r Y 2 = nn 5 n ?5 r n?5 n X5 n?5 Oi45X5 r 5?5 5 ?5r5 5 n?5 n #5 n?5 n?5 n?5 H5 5 n?5 n #5 n?5 O= n?5 5 5 r Oi 5#5 D5 O5 ?5 5 = 9 5 5 5X5 r 5 n 5 r 5 D5 O5 ?5 9 r 5 r #' r 5 n?5 5 n?5 5 r 5 r ?5 9 5 45#5 n n?5 5 Yi i 5 #5 5 = n 5 5 5 r n?5 9 5 K' n 5 5X5 :5 5 5 5 5 r 9 nD5 5 nD5 n ?5 n 9 5 9 n 5 5 5 5#5 95#5 = nD5 5 n (9 r 5 :5 5 r ?5 n?55 ?5 X9 5 r / V "%$'& / V $'&. V n nD5 5 r 5 L575 L5 5 ?5 X9 5 r n?5 X5 0 W = Y 5 6 Y = 576 =@ r n?5 5 ,/ n r n?5 n (9 5 5 n?5 (9 r 5 5 5 5 n?5 5 5 n 5 =R n?5 5 5 0#1 V 0#1 Y 0 W = Y Y = 5 6 = 5 5 n?5 n O5 5 5 nn 9 L5 5 5 9 ?5 5 D5 r 9 Z9 n?5 5 rn?5 5 5 5 r 5 ?5 5 5 r 5 5 5 H5X5 5 5 r n?5 5 Ei iI5 #5 5 r 5 ?5 X9 5 L5 5 5 n?5 n :5 ?5 r ?5 5 7= 5 X5 r n?5 r ?5 r 9 5 5 5 5 #5 5 5 E5X5 V 5 E5X5 7= n?5 )H r n n r ?5 5 n?5 / 2 ?5 ?5 5 ?5 9 5 5 5 45 #5 = 8 n 5 5 5 L5 5 O5 5 5X5 ?5 #5 5 5 r V 5 6 r"'" W 576 =: n?5 9 5 :5 5 ?5 nD5 5 5 5 ' 5 r n #5 5 :5 5 5 ?5 n?5 5 5 '021 UW = = n?5 r 5 5 5 #r Y r nD5 E5 5 n?5 r n?5 5 n (9 5 n n?5 5 D5 9 5 = nD5 r 5 #/ 0#= W =@= n?5 n?5 9 r W r n?5 r D5 r 9 ?5 n?55 n?5

PAGE 43

W r 5 V n?5 9 ?5 ?5 O5 D5 5 5 5 n?5 5 5 5 r 5 :5 5 5 5 n?5 r 5 5 7= n?5 5 5 r 5 5 9 5 n?5 9 )H D= nrX 1Z-`$ )!$# ?%] )(+*n, nZ$a. z9S P 2 UXG`6 U ABC 88 1n&ABC D D i+ )s+t'} g FZ)g >W @ZUuYB@W @XFYB@W @Xm 88"g1UW_m?ABC UW 55uYB@Wa>@[ '-)`W ^ D D 88"gTmW_m?ABC mW_FZ5uYB@Wa>@[ '-)`W ^ D D 88"g l W_m?ABC mW l mXYB@Wa>`F[ '-)`W ^ D D z9S P 2 m@`6 88 g?>@W 4rABC FZ g D D GW 44GXYB@W @G@XYB@W @UXm D D PBQ3RS 2 m>-6 )s+tjg Zi+ )s+tjg F798n:<;$g nZ5W UrABC >UƒW l 4XYB@W 45uYB@W l @ GW_mZ@uYB@W @ZUYB@W_F)U >W_mmFXYB@W @ZUƒ>"YB@W @ l @ PBQ3RS 2 m4`6 F7 8n:<; gB54W l ABC >UƒW 4XFYB@W_FZ4uYB@W U@ >@W>`@XYB@W @>"YB@Wa>5 >W Uunu>)YB@W @FZUuYB@W @ZUX4 PBQ3RS 2 mZU"6 F798n:<;$gB5@W_F?ABC >UƒW F5XYB@Wa>5uYB@W 4> D >W_m>UYB@W @>`GXYB@W @4U n #5 5 5 5 n n?5r5 ?5 X9 5 =Q n?5 5 5 nn 9 n X/ 0#= W = Y = n?5 5 n?5 5 5 5 5 r #5 5 75 n?5 r 5 D= >/ ?35RIN 7N@+N1nJL=R n?5 9 5 r 5 n

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D0 r 5 n?5 9 ?5 D5 O5 ?5 5 5 5 5 n?5 5 5 5 r 5 L575 5 n r* r 5 = nrX 1Z-`$ƒ F g Zi+&% PBQ3RS 2 mm`6 g x gB4@VABC >W UXFFYB@W @@ l YB@W @Xm> >>Wa> ABC >`@W l YB@W FXY?>W 5 >W 4>)YB@W @4uYB@W_FF >"FW l ABC >>W @XYB@W 4uY?>W n >W_FZGuYB@W @4uYB@W_FZ@ >UWa> ABC >>W_FYB@W 4uY?>W n >W_FmXYB@W @4uYB@Wa>G >"mW_mrABC >`4W @XYB@W 4uY?>W G >W 4GuYB@W @ZUYB@W_FZ@ >)nuW @VABC >`4W_FYB@W UY?>W 5 >W 4mXYB@W @ZUYB@Wa>G >`5W U ABC >`4W 4XYB@W UY?>W n >W 4>)YB@W @ZUYB@Wa>"n >`GW GVABC >UW UuYB@W mXY?>W_F >W 45uYB@W @mXYB@Wa>`F F>W U ABC >UW_mYB@W mXY?>Wa> >W 4ZUUuYB@W @U l YB@W @G5 FFW GVABC >"mW @@uYB@W_mFYB@W 5un >W 4m4XYB@W @UunYB@W @un)G FZUW @VABC >"mW_mZ4uYB@W_mnYB@W GU >W 4Xn>"YB@W @XmZ@XYB@W @54 FmW U ABC >"mW 5XYB@W l Y?>W_m >W 4 l YB@W @mXYB@Wa>4 F l W n&ABC >"mW GXYB@W l Y?>W G >W 4ZUYB@W @mXYB@Wa> l FXnuW GVABC > l W_mYB@W_nYTFW_m >W 4XnYB@W @ l YB@W_F> F5W n&ABC >)nuW GXYB@W_nYTFW @ >W U l YB@W @ l YB@Wa> l FGW l ABC >)nuW l YB@W_nYTFW 4 >W UXFXYB@W @ l YB@Wa>5 4@W_FrABC >`GWa>"YB@W_nY?>W l >W_mZ4uYB@W @ l YB@Wa>4 4@W_mrABC >`5W_FYB@W_nY?>W G >W UXmXYB@W @ l YB@Wa>`m PBQ3RS 2 m l 6 g FZ7 8n:; g FZ798n:;nr [fiZF^g >`@W_m4mW UU&ABC D >W 4>W m >`@W_mZ@rABC GW l @ l YB@W @ l @uYB@W @GU D >>W G l ABC >`@W 45@XYB@W @ l @XYB@W>"F)U D >`4W G l ABC >>W 4mZUuYB@W @ l @XYB@W>U5 D > l W 5 l ABC >"FW_mZ5XFYB@W @ l @XYB@W>`5@ D F>W 5ZUVABC >UW nZm l YB@Wa>`FZUuYB@W>"m)U D F5W U5rABC >)nuW_F)UYB@W_F l YB@W F@ D 4XmW UUVABC >`GW @ZUYB@W l @XYB@W ll D z9o 2 mZGZ6 nFrABC 88 1n"UX@&ABC D >W nYB@W 4 z9o 2 l @Z6 nFrABC 88 1n"UX@&ABC D >W GXYB@W m

PAGE 45

V 5 n #5 r 5 5 ?5 r021 r n?5 5 5 > )H 5 021"S0 = n r r n?5 r (9 5 5 D5 n?5 r 5 B5 9 5 5 5 = 5 5 n?5 #5 D9 5 n ?5 n n?5EB5 r n?5 5 5 n n?5 9 7=Q X5 n r nD5 n 5 n 9 5 r 9 5 ' 5 n?5 ?5 9 5#5 n 5 r n r 5 5 9 r 5 = n?5 5 n 5 $D +' ?5 r 5 :5 5 r 5 = 5 5 n?5 ?5 5 nD5 5 5 5 5 5 5 r 5 #5 5 n 5O5 r 5 5 5 n #5 r 5 5 5 5 n?5 9 7= n?5 5 5 5 n 5 5 n?5 5 r n 5 9 5 #5 5 5 5 5 5 5 'n n r 5 5 =Q 9 r 5 5 ?5 X9 5 5 5 n 5 5 r 5 5 n?5 O5 ?5 X9 5 n n?5 ?5 9 5 #5 n 9 5 5 n?5?5 5 n r nD5 D5 ?5 X9 n r 5 ?5 5 n?5 5 5 = >/ 43@J8RINR0H19O3U1? J 3U1 n?5 )H 9 n 5 5 n #5 9 ?5 O5 D5 n?5 5 ?5 5 = nn ?5 O5 D5 5 n n 5X5 r 9 5 n?5 5 5 5 5 5 5 45 #5 5 5 #5 n =B 5 H5X5 n #5 #5 5 r 5 5 n?5 ?5 n?5 5 #5 9 / V .#= 5 5#5 r nD5 5 n 9 >=: n 5 5 5 5 5 nn 5 n?5 O5 5 5 r = n r L5 n #5 n 5 r 5 :5 5 5 n?5 5 5 45#5 =

PAGE 46

n?5 #5 #5 n X5 5 5 O5 5 r "'"r 5 5 5 r 5O5 nX5 9 r r 5r5 5 5 n?5 n 5 5 r "L/ " 0 "'" % D= 0 "/ 0 n D= V n?5 5 " 5 5 5 5 r5X5 7=E 5 r 5 5 B5X5 r 9 5 n n 5 )n 5 2 r = D= V n r 5 r 5 "/ %0 % 0 D= n?5 5 n?5 5 n n?5 n 5 r n n?5 n (9 n?5 5 5 nD5 5 n = = D= 0 r D= 5 n?5 #5 #5 n #5 5 n 5 5 r / r :5 n?5 r / / /0 (, '(,<0 " n %0 "'" ( D= / "'" "'" G0 0 D= Y :/ "'" "'" G0 0 D= n?5 5 :5 5 (I/ n "r r 5 5 5 5 r 5 :5 5 5 5 5 E5X5 5 5 X5 n = 9 r L5 5 5 nD5 #5 #5 n X5 5 n 5 5 r r :5 n?5 r/ nr r 9 5 9 5

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n 5 nD5 ?5 O5 D5 5 5 n (9 5 5 5 5 5#5 r " 5 5 5 5#5 r " (9 n?5 5 5 r n 5 5 5 5 5 #5 5 5 5 n r(:=A n?5 5 5 5 5 r 5 ?5 r 5 )n 5 2D=

PAGE 48

)HFr&EA ))HAECnCE:)L n?5 >5 n 5 5 r 9 Qn rA 5 r n nD5 5 (9 n?5L5 5 n 5 5 n 9 7= 5 r n?5 n 5 n ?5 5 n?545 = n?5 B5 n n?5 L5 5 5 7= n?5 5 n?5 r n?5 #5 5 =: n?5 5 n n 5 L5 5 #5 ?5 n X5 9 nD5 nZ9 n?5 75 IF r n?5 V n?5 5 = n?5) D5 5 5 >5 r )H ?5 n?5 n?5 n?5 D5 n W n 5 ?5 5 r n n?5 B5 = n?5 9 n 5 5 5 n 5 n r 5 nD5 5 5 5 r 9 )H n?540>0 Y 5 n?5 5 = 8/+. ? 53U1I9<"4 6 89 N4 G1 "8? ^. 744N+4 GKM? 9N\< 6 n?5>5 r 5 5 5 n nD5 D= O0X= n?5 n n?5 5 5 ' 5 ?5 X9 0#=32B5 6 L5 5 5 r 9 5 ?5 5 r #5 n 5 5 =L r ) 5 5 r 5 ?5 n#5 nZ9 #5 YXW 5 6G5 ?5 X9X=Q n?5 r n?5 :5 5 5 5 n?5 5 #5 n?5 5 ?5 r 9 n?5: = n?5H 0 Y r #5 ?5 5 5 n n?5 5 5 n?5 5 D5 9 W 0#= Y 576 = 5 n?5 r 5 5 nD5 ?5 #5 rn?5 :5 5 5 nD5 5 5 r 9 nn r =& 5 n?5 5 5 5 nD5 8 5 = nD548 5 n 9 n 5 5 r 0 YXW 5 5 7= 5 5 5 5 2 5 6 =nr5 r L5 5 5 5 n?5 5 5 5 n?54 ?=E n?54 n 0 n D5 n n n 5 V W 5 5 ?5 5 5 5 Y

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Main Ring Protons Antiprotons Tevatron Booster Antiproton Storage Ring Cockroft-Walton Linac CDF 5 O0 X5 5 nD5 5 r 5 5 5 =* nD5 n?5 5 5 ' 5 ?5 X9 0#= 2,576 5 5 r 9 5 ?5 5 r X5 5 5 n?5 ) r r 8 5 rO r 5 = r 5 r = n?5 5 X5 7=: ?5 5 0 VXW 576 n n L5 5 5 5 r 5 ,0 Y W 576 r 5 5 5 nD5 n?5 5 = D5 5 r r0 VXW 5 6U5 ?5 X9:5 5 5 n?5r 4 5 #5 =B n?5 5 9 5 9 5 ?5 7=< n 5 L5 5 5 5 5 5 n?55 r n?5 n?5 5 n?5 9 :5 5 n 9 5 5 5n?5 5 5 = n?55 nn 5 rn?5 :5 5 5 4 r n?5 9 :5 5 ?5 5 ?5 nD5B5 = n?55 5 Y r 5 nD5 n?5 5 ?5 = n 9 n 5 5 n 5 5 V 0 5 O5 ?5 5 ?= r 9 n?5 = 9 r+0 YXW 576 L5 5 5 5 n?55 n?5 5 n?579 L5 5 n ?5 9 5 5 5 W#W 576 = nD5 5 5 r nD5 5 5 %' 5 @' 5 X9 r 5 0#=32 B5 6 =Q n?5 5 5 5 r n?5 n n :5 5 D5 5X5 9 D= Y Z 7= n?5 r n?5

PAGE 50

r ?5 5 9 V E0 W r n?5 r n?5 n V &E0 W + =Q n?5 0 8 r nD5 n 5 n 5 9 n?5 r D5 n X5 #5 VXY Z n n r n W n 5 = n?5 ?5 (9 n?5 B5 n nX5 r 9 & / ?= 0 n?5 5/ 5 nD5 r 5 O5 r n r n?5 5 ?5 9 r n n nD5 5 5 nX5 5 n?5 r 5 = n?5 0 8 r n?5 #5 #5 (9 & 0#=&E0 W = n?5 +' ?5 (9 5 ?5 9 D5 5 5 n n 5 ?5 #5 5 5 n?5 r 5 5 n =A n?5 5 5 n?5 n?5 5 r n?5 ?5 ?5 5 5 = n?5 (9 5 nD5 0 8 r L2O0 2 n 7= n?5 (9 ?5 5 5 r 9 5 9 D5 ?5 n?5 5 n 5 5X= 8/ ?RINH4 3476 "? 9 8N\? n?5 )H 5 ?5 ?5 5 5 ?5 n?5 r 5 5 = ?5 D5 D9 ?5 X5 5 5 7= nD5)H r 5 #5 5 5 n?5 5 5 5 r n r 5 5 r n #5 n 7= n?5 n?5 )H ?5 5 r 5 ?= V =L n?5 )H n 5 9 9 9 9 5 r n?5 r 5 5 = r 0 W nn r+5 5 r V U5 5 r L5 n #5 YXW#W#W = nD5 )H 5 n n ?5 ) 5 5 9 5 n n?5 5 5 5 n?5 D5 5 = n?5 nX5 n n n?5 r 5 5 r #5 Z' n #5 9 r nD5 n#5 ?' n?5 5 5 nD5 B5 ?= nD5 nnn 5 5 5 n?5 r 5

PAGE 51

#2 CENTRAL MUON UPGRADESOLENOID RETURN YOKE CENTRAL MUON CHAMBERSCENTRAL HADRONIC CALORIMETERCENTRAL ELECTROMAGNETICCALORIMETERSUPERCONDUCTING SOLENOID CENTRAL DRIFT TUBES CENTRAL TRACKING CHAMBER VERTEX TPC SILICON VERTEX DETECTOR PLUG ELECTROMAGNETIC CALORIMETER WALL HADRONICCALORIMETER PLUG HADRONICCALORIMETER CENTRAL MUONEXTENSION BEAM-BEAM COUNTERS FORWARDELECTROMAGNETICCALORIMETER FORWARDHADRONICCALORIMETER FORWARDMUONTOROIDS BEAMLINE CDF q f z y x(OUT OF THE PAGE) (EAST) 5 V n?5 )H ?5 5 7=L ?5 5 5 = n n?5 #5 ?' 7=Q n?5 5 0 ?5 r D5 n?5 5 5 5 n?5 #5 n n =, n 5 5 n n?5 5 (9 rD/ '0 V r n 5 5 n?5 5X= n?5 5 (9 r 5 ?5 r ?5 n 5 5 n?5 n?5 5 #5 5 5 #5 n 5 5 n?5 5 5 nD5 D5 5 ?5 5 n?5 ?5 n?5 )H ?5 5 5 5 r 5 $ 65 5 45 5 $+6r; =# n?5r$+6; ?5?5 5 5 5 5 5 n?5 nD5 5 X5 5 n?5 ?5 = 65 5 G n 5 & 5 )n r 5 6H; =H 5 5 n?5 n n?5 5 X5 5 = )L5 + )n r 5 )L) = n?5H)L) ?5 5 5 5 5 +' 5 5 5 $ 5 5 nD5 ?5 r?5 8/ 0#=4 = ) 5 9 5 r 5 5 = (9 5 5 5 rD5 5 ?5 : n Fr r 5 5 5 5 nD55 D5 9 n r 5 5 n 5 5 =

PAGE 52

)L5 & 5 ?5 5 )H& )L5 5 D5 $ )n r 5 )H:$ = n?5 )H& )HA$ 5 n ?5 n?5 n 5 5 ?5 r = $+9 5 D5 9#5 n n r 5 = nD5 $ 9 5 ?5 9 r 5 n O5 5 nX5 575 r n n r r 5 n 9 5 O5 n?5 5 5 L5 5 n = 8:5 '%8L5 ) 5 8H8) = nD5 8H8H) D5 5 5 5 n?5 +' ?5 (9#= n?5 )H ?5 5 ?5 r 5 5 %= r D0 5 5 5 5 nD5 5 = n?5 5 n n 5 :5 n 5 ?5 n n?5 r ?5 5 5 9 5 5 nn 9 n = 8/>/+. (?91? ?Q1?P 1<9 R 3476 0 r n?5$ 5 5 $+6r; n?5 r 5 9 r 5 5 =Q n?5 $+6r; r W X5 nD5 5 D= W += = 9X5 5 n?5 r 5 ?5X=B n?5$+6r; #5 0#1 W 5 n 5 5 W n #5X= 5 n 5 n?5 #5 5 ?5 0 W Z = n?5,$+6r; n n?5 9 5 n 6H; )L)=> ?5 X5 9 5 5 5 5 5 n?5 #5 5 nD5 5 #5 X5 5 = 5 9 ?5 n?5 $+6r; n?5 65 5 G 5 & 5 )n r 5 6H; ?5 5 = nD5 6H; n V = 2 n 5 5 5 ?5 2 VXV n?5 r 5 5 = n D5 2 5 ?5 2 5 5 :5 X5 =A n?5 n r 5 5r 5 n 5 YXW YXW 5 n D5 5 7=r n?5 6H; ?5 n n n n 5 ?5 5 ?5 n?5 n?5 5 #5 5 n 5 n n?5 5 0 =

PAGE 53

W 5 n?5 )L) 5 5 5 = 8 nR$ 6; 6H; 5 nD5 ?5 n?5 )H ?5 5 5 Z9 9 5 =4 n?579 5 n 5 9 ?5 5 ?5 n?5 n 9 5 :5 D5 9 5X5 nn 5 5 = 8/>/ !? 4"19O3@ 9O3P N4 !#"3F '? 9 ! r n?5 )L5 ,)n r 5 )L)r5 5 D0 0 V n?5 r 5 O5X= ?5 #5 #5 0#1 Y r n:5X5 r 5 5 n?5 5 0#1 W =B nD5)L) n r 5 9 n 5 = n 5 9#5 5 7= n?5 5 9#5 5 ?5 Y 5 5 5 9#5 = X5 9 9X5 n 0 V 5 5 5 #5 n?5 r 5 D5X= n?5 5 O5 %' 9X5 n ?5 = n 5 5 9X5 n 5 5 5 n n 5 5 n 5 5 n?5 r 5 7= n?5 5 5 9X5 D5 n r 5 $ 5 9X= nD5 5 r n 5 5 9#5 5 X5 ?5 n n X5 Y 5 n 5 O5 5 5 5 n?5 5 r 9 n?50X=

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?0 r 5 O0 $@5 5 5 5 5 n?5 )H )L5 )n r 5 = n r 5 5 5 5 W r Y W n r 5 9#5 2 n r 5 O5 %' 9X5 Y 5 5 n r?5 0 Y W 6EX E5 rVXWXW Z O5 5 5 9 #2 O5 n r 5 5 rY 0 W#W n 5 W n n 5 5 n 5 5 5 W 1 W#WZV r @0 0 V ?5 r 5 r 0X=4 ?5 r 5 =< ?= n n?5 5 5 5 n?5 )L) r 5 n?5 5 5 5 5 n?5 )L) 5 75 r 5 O0#= n?5)L) 5 5 5 n?5 5 5 5 5 $ 5 9 r 9 n 5 r 9 ?5 5 5 5 5 n 5 9X5 n?5 5 9#= n?5 n n?5 r n?5 r ?5 n n?5 5 $ 5 9 n?5 ?5 r 5 =Q n?5 5 5 n?5 )L) ?5 n r 5 5 n W 1 W#WZV =R n?5 5 n #5 n?5 6H; rO$+6; )L) n r ?5 = 8/>/ K9O?R "8< ?9346 0&"8< ? 9h:=3r8N+F F ?Q1?P 1<9R !3@<9NFG?Q19J n?5 )L5 & 5 45 5 )H& ?5 r 5 :5 5 n?5 5 @' 5 n?5 5 n 5 5 = n?5 5 5 X5 n #5 W nD5 n 5 5 @' n:5 n 5 ?5 5 5 n?5 )H& = nD5)H& n 9 V n 5 n r 5 ?5 5 n n :5 X5 n?5 5 n 5 5 = n n r 5 5 5 @= ?5 %0 Y V = 2n n n n V 5 5 5 = n?5 5 5 5 5 5 r n 5 5 nX5 5 0#= 0#0 5

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V W = W#W Y = n?5 5 5 )H&A 9 ?5 E0 V n n X5 n?5 5 r 5 :5 5 nZ/r' V #2 nZ/ V Z2 0#1 W 5 = n?5)L5 5 ?5 $ n r 5 )HA$ 5 n?5 5 5 5 ?5 n 5 5 ?5 n r Y = 5 n n n 5 n?5 n?5 5 nn 5 5 ?5 n:5 ?5X5 5 7= n?5 )HA$ ?5 5 ?5 n?5 nL5 #5 5 nL5 ?5 #5 5 r 9 5 n?5 n #5 ?5 5 n 5 7=H) n?5 5 #5 n?5 n n 5 n 5 r n 5 ?5 5 5 #5 n?5 n 5 n?5 5 = n?5,)HA$ 5 T0 2n n?5 r 5 ?5X=B n?5 5 5 V n r 5 5 5 nL5 #5 n?5 5 5 = n?5 5 5 5 5 5 L5 #5X=: n?5 ?5 r 5 :5 5 5 5 n / 0 V 0#= V = n?5 r 5 rn?5 5 5 0#=r ?5 n n r n?5 5 r 5 :5 5 D= V 0 V 0#= V = nD5 5 5 r n?5 5 5 Y V = W 0 ?5 n nr n?5 5 r 5 :5 5 0 V 0#= V V D= =B n?5 5 5 n V 5 5 n 5 n nn 5 = n?5 5 5 n?5r)HA$ ?5 5 D5 n :5 5 V 5 n 5 YXW 5 6C5 5 7= n?5 )H& T)HA$ D5 5 5 n?5 5 5 5 n?5 n ?5 r = n?5 n?5 5 ?5 5 5 5 n?5 ?5 5 r :5 ?5 5 D5 n?5 (9 n?5 n 5X=I n?5 5 5 5 n?5 5 n n?5 n 5 r 5 R5 n?5/>' X5 r r (9 n?5 )H&=Q 5 n?5 #5 5 r 5 n?5 5 5 D5 n :5 5 5 r 9 nD5 )HA$ ?5 5 = n?5 )H n 5 9 5X5 n 5 5 9 5 )HA )L5 5 ?5 r&A & 5 ?5 r : 5 ?5 r )HF )L5 HF r F F rQ&AF & F RQFr %' F = n?5 )H n 5 5 9 5 ?5 V nn #5 X5 r H5 5 ?= V 5 (9X=Q n?5 5 5 (9 #5 #5

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r ?5 n n?5 n 5 5 ?5 5n#5 r 5 V = 5 n?5 D5 5?5 n?5E)HA r+)HF Fr 5 5 r 5 5 nD579 5 5 9 5 n 9 = n?5 )H 5 5 9 5 n 5 #5 X5 5 9 r = 5X= :5 n?5 5 5 n?5D5 5 = n L5 n?5 5 5 5 5 n 5 5 9X5 r r 5 5 )HA )HF F nX5n 9 (9 5 ?5 )H: 9 )HF Fr 5 D= n?5 5 5 n n n?5 D5 5 r r 5 5 5 n 5 5 5 ?5 X9 nL5 5 9 5 7= nD5 r 5 9 5 5 n nD5 #5 5 5 n n n n 5 5 X5 5 n?5 5 ?5 X9 5 5 5 = nD5 5 5 ?5 n:5 ?5 #5 9 5 n n nL5 r n?5 5 5 n?5 5 5 ?5 5 5 ?5 5 n?5 5 = n?5 )HA 5 5 n?5 :0n VXW 2 n?5 r 5 ?5X=B n ?5 n?5)HA 5 nL5 5 r 0 2 5 n = n?5 )HF n 5 n 5 n?5 )H: =8 n )HF Fr n X5 5 D5 n r ?= Y 5 5 n = n?545 ?5 X9 5 nD5 )HA 5 5 n r 5 L575 P0 W 0 WXW 576 n '! / 0D1 Y 0#1 ?= V n?5 5 n?5 #5 5A5 ?5 X9 n?55 5 n r n?5 9 r 5 n ?5 5 ?5 5 5 ?5 5 = n?545 ?5 X9 5 n?5 )HF F n #5 r 5 L575 P0 W 0 YXW 5 6 !n / YXW ?= '!n / Y f 5 O5 #5 9#= n?5 r n?5r5 5 D5 n 5 5 5 5 n YXW 576"5 5 n X5 n?5 5 r 5 =

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r 5 V n?5 )H ) 5 5 $ 9 5 #5 #5 ?5 5 5 5 = 5 5 & 5 (9 r 5 5 )HA W = W 0X= 0 W 1 0#0 P0 Y )L5 ) 5 5 )HFr W = W W = W 1 0 0 Y Fr W = 0X= W 1 0#0 P0 Y &A 0#= 07' V = W 1 W Y ) 5 5 &F 0#= V = W 1 W Y QA V = V D= V W 1 0 Y QA V = D= V W 1 0 Y nn 9 n?5 5 5 5 ?5 5 D5 n?5 5 5 n 5 = 8/ 9 N ?9 0HJ8R 1?F n?5 ?5 5 .P/ 0X1 2 B5 6 r YXW r YXW E0 W = (9 ?5 (9 2&4/ 0X1 0 W X :5 n #5 r 2 W#W r W#W#W D5 n 5 5 )HL= n?5 )H 5 5 5 5 #5 #5 9 5 5 nZ9 9 r 5 545X5 n nn 5 )HR 0 #5 5 5 5 5X5 5 5 =: 5 #5 r n?5 5 5#5 5 5 r 5 5 n?5 )H n 9 = nD5 5 nD5 n 9 5 n 5 n?5 ?5 @' 5 n n?5 L5X5 n r 5 5 n?5 ?5 5 5 5 5 5 =: 5 5 n?5 5 5 5 5 nX5 9 5 9 5X5 5 5 5 nZ9 r nD54)H ?5X5 5 n 5 @' ?5 n 5 5 5#5 5 #5 0 r 5X5 V G 5X5 X5 9 5 r V =N n ?5 #5 5X5 5 ?5 5:5 5 #5 r 5 5 ?5 = n?55 #5 A0 5 #5 V #5 5 5 n 5 n 5 5 5 n r n 5 n?5 5X5 #5 n 5 5 5 5 n?5 5 5 7= n?5 #5 n r 5 5 5 n n 5 9 5 #5 9 n?5 #5 5 5 5 5 5 =r n ?5 5 5 n?5 #5 5 #5 r 5 nX5 5 ?5 5 (9 5 5 7=

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Y n?5)H" 5#5 0 #5 5 ?5 5 #5 9 r n 5 #5 ?5 n n D= Y Z r 5 L575 r n r n n ?5 +' n 5 =Q n?5 5X5 0 5 nD5 r 5 ?5 X9 5 5 L5 n n?5 9 5 = 5 5 n?5 5 V 2 W @F ,0 +FX= n?55 #5 V #5 5 5 r V#Y Y Z 5 5 #5 n#5 n?5 5X5 0 X5 ?5 @' 5 5 O5 5 = n?55 #5 V 5 n 5 r W Y F X= n?54 5X5 V n 5 n?5 r nn 5 5 5 n 5 5 Q5 ?5 X9X= nD5 TS" ?5 ?5 r 9 n?5 #5 r n?5 n?5 r 9 5 5 5 5X5 D= n?5E 5 #5 #5 n @' D5 5 r 5 r 5 r 5 #5 n?5 ?5 5 ?5X=B+5 #5 n n nD5L 5X5 X5 5 5 n O5 n (9 5 2 F X=

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)HFr&EA Y !#$ N)H !X5 )H 5 D5 r ?5 n ?5 5 n r 5 n?5L$ #5 r =A!X5 5 5 5 n 5 5 A5 ?5 5 n?5 n?5 9 #5 5 = n?5 5 n n n 5 5 5 n?5 )H ?5 !#)H =O n?5 5 ?5 n 575 5 5 5 r 5 r 5 ?= 5 5 n 5 5 E5 ?5 5 n?5 D5 5 5 ?5 5 n 9 5 5 7= !X5 5 r 5 r 9 5 n n 5 5 L5 n 0 5 6 n n 5 5 5 5 L5 7=S n?5 5 5 5 5 ?5 ?5 5 = & 5 5 5 5 r 9 r 5 5 :5 n ?5 / 5 =: 5 5 :5 ?5 n?5 5 5 n n 5 5 L5 n n 5 D9 ?5 n?5 5 5 = !X5 5 (9 9 5 5 n 575 ?5 5 / W = r W = r 0#= W = n 9 n r 5 5 ?5 r?5 n?5 / W = 9,)H 9 5 r)H = n?5 5 5 O5 5 n?5 L5 n 5 5 5 5 1 1 1/ ! Y = 0 1/ !

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n?5 5 n?5 5 5 #5 5 5 :5 n?5 5 5 =< n?5 :5 5 n r ?5 r 9 / ! n n Y = V / ! n n n?5 5 ! n 5 #5 5 5 ?5 5 ?5 5 nD5 5 5 ?5 : n F n?5 & n 5 5 :5 r n n 5 nD5 5 n?5 5 5 ?5 n ?5 n?5 L5 5 n 5 5 n?55#5 #5 5 n?5 5 n?5 #5 5 5 5 n?5 )H ?5 5 = ?5 5 n?5 5 5 5 7= :5 n C0 W#W 576 5 5 #5 5 n n?5 5 5 n n?5 D5X= ?5 5 5 n 5 5 n?5 L5 n nD5 ?5 r ?5 ?5 n 5 = n?5 5 ?5 n?5 ?5 5 r 5 5 r 5X= nn 5 5 5 O5 5 5 5 7= 5 n?5 5 #5 r n?5 5 r 5 5 :5 n n 5 n 5 r 9 5 5 = D5 5 n 5 5 9 n nD5 n?5 D5 r n?5 n?5 5 5 n O5 =: 5 9 #5 r X5 5 r 9 nD5r! n 5 :5 n?5 r 9 nD5 5 5 7= n?5 5 5 5 #5 n nn n r #5 W = Y =r n?5 n 5 n W = Y r n?5 5 5 5 n X5 n?5 L5 5 ?5 n?5 ?5 5 5 5X= 5 n?5 :5 5 ?5 9 ?5 5 r n?5 5 5 5 5 5 5 O5 5 5 5 r 5 = 5 5 5 5 5 r 5 5 r n 5 nD5 5 5 ?5 X9 n?5 ?5 O5 5 n?5 @' ?5 (9 @' n (9 n?5 5 ?5 X9 5 5 n?5 5 5 r n?5 5 ?5 X9 ?5 5 n?5 5 ?5 r 9 5 n?5 n n?5 ?5 9 5#5 r n 5 5 5 =

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Z2 n?5 5 ?5 X9 5 r 9 n?5 n?5 5 ?5 ' D5 5 =

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)HFr&EA &AF n$ )H &n ?5 r )H r 5 n 5 5 r O5 5 n n 5 ?= n?5 n 545 O5 5 r 5 r 5 X5 5 5 ?5 5 5 ?5 5 ?5 X9 n?5 n 5 5 n n n 5 n #5 5 n n?5 =Q n?5 5 5 n n 9 ?5 r nL5 #5 =E n #5 5 5 @' 5 5 n?5 n r 5 r ?5 9 #5 n n?5 ?5 9 5X5 =n D5 nD5 5 r nn n ?5 n?5 r 5 n n n n n 5 5 = n?5 n D5 r 5 n r 5 n?5 5 5 r nL5 ?5 5 )H:$ r n r 5 n ) = n?5 5 D5 9 5 n?5 n 5 5 n 5O5 n?5 5X5 X5 5 = n?5 ?5 n 5 r 5 r 9 5 5 n?5 5 ?5 n 5 5 :5 5 5 5 D5 nL5 5 9 ?5 D5 :5 n 5 #5 ?5 n r :5 = n?5 5 5 5 5 5 9 5 Y 5 6 5 ?5 X9 nX5 5 n 0 V = Y n5 D5 9 r 5 #5 n?5 n 5 5 5 ?5 #5 5 5 D5 r 5 5 n?5 5 ?5 X9 n?5 n n?5 5 5 D5 5 D5#5 5 n?5 n:5 = n?5 5 5 5 5 5 ?5 5 5 5 5 r 5 n 5 = n n r?5 #5 5 5 ?5 X9 nD5 n 55 ?5 X9 5 5 :5 n ?5 / W = n?5 5 n r 5 r 5 5 n 5 n 9 0 576 n?5 )H 9 5 n = nn 5 5 5 nD5 5 n ?5 r 5 n r 5 = n?5 5

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YXW n 5 r 5 ?5 n n?5 r n?5 5 5 n?5 5 r 9 5 r 9 nD5 D5 r 5 5 = nn 5 5 5 n?5 5 5 ?5 r n 5 ?5 #5 + $ $ 5 5 5 = n?5 n 5 5 5 5 nX5 n n 5 n?5 5 5 ?5 5 =C nn 5 5 5 9 5 n r 5 :5 5 n ,5 5 = n?5 = 5X= 5 n?5 n 5 n D5 5 ?5 r 5 n?5 n?5 nL5 nn n 5 5 r 9 n?5,)HA$ n r 5 7= n?5 5 5 5 n?5 n 5 n?5 5 5 ?5 nL5 5 5 5 n?5 )HA$ 5 r 5 5 nD5 5 5 n?5 n 5 r = n?5)HA$ n :5 r 5 r r 9 5 5 r 5 5 n n 5 n = n?5 (9 ?5 r ?5 r 9 n?5 5 r Y / V D= 0 n?5 5 n?5 n r n?5 5 5 #5 r 9 / D= V / r W 1 WZV W 1 W 0 W n + 1 n?5 5 5 5 5 n 5 n?5 n 75 5 nn (9 5 n?5 5 5 5 5 n?5 n = n?5 n?5 L5 5 ?5 5 ?5 5 9 5 r 5 D=

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)HFr&EA nr K $@$, $ 5 ) 5X5 #5 ?5 n #5 r 5 5 r 5 n n5 D5 9 nZ9 7=A nD579 5 5 X5 5 (9 n n ?5 r r 5 n 5 r#5 5 5 5 5 n rE5#5 5 5 n 5 5 9 5 n r r 5 r 5 ?5 5 5 5 rO5 = n?5 5) 5 #5 #5 D5 5 5 n?5 5 ?5 n nn 5 ?5 #5 nZ9 5 5 =A n#5 5 O5 r 5 r n?5 9 5 n r 5 nD5 5 D=B 5 r n?5 r ?5 5 5 5 5 n 9 5 ?5 5 ?5 5 5 5 5 5 7=A 5 r 5 r 5 #5 n?5 n 5 n 5 5 n n 5 ?5 5 5 r 5 5 5 n n 5 5 5 = 5 5 nD5 5 ?5 5 5 5 r nD5 n?55 #5 #5 ?5 5 nn D5 5 nn n n #5 n?5 #5 ?5 5 5 5 r 5 r 5 n?5 ?5 5 5 = ?5 n 5 O5 r n 5 5 c b 5 = D=nr i n r n?5 5) #5 ?5 n 5 n?5 r D5 5 c ?5 =E n n ?5 n?5 B& n r & $ = n n 5 n?5 n 5 5 n 9 5 nD5 5 D=B nD5 5 n?5 5 5 ' A5 ?5 X9 n?5 n 5 5 r rn 5 5 n?5 5 n?5E5 ?5 X9 nD5 5 5 ' r r r 9 ./ .#=B 9 r n?5 5 n 5 5 c b D5 O5 5 n?5 5 n r n?5 5 5 r 9 n?5 r 5 nn 5 r = Y 0

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Y#V n 9 rXF5 Y = r W &9 n D= 0X0 Y r D0? 5) #5 ?5 5 5 =Q )H n 5 r r n #5 D5 5E5 D5 )H r 5 5 5 5 r = 5 5 r F5 &9 n 5 n?5 5 5 5 5 5 5 5 5 7=F F5 D5 r 9 5 n?5 5 ?5 n 5 &Q9 n 5 n?5 ?5 = n?5 5 n ?5 r n #5 ?5 n #5 r 575 5 D9 5 D5 $@5 V =@= Fr5 r r 9 n?5 5 #5 ?5 5 n n?5 n?5 5 5 5 5 7=C n n n?5 n 9 5 n RFr5 r 5 ?5 5 ) #5 ?5 n 9 n = )H r n?5 D5 5 nn ?5 r 9 5 X5 5 Q r = Q 5 5 9 5 5 n?5 5 5 5 ) 5X5 #5 ?5 5 n?5 nn n?5 D5 5 =E nn 5 ?5 n?5 5 5 5 n n 5 5 r ?5 9 n #5 5 r n #5 n?5 5 5 n?5 5 =* nn 5 n?5 5 5 ?5 5 ?5 5 L5 n?5 #5 5 5 D5 5 5 7=

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)HFr&EA"2 $DrrAnr$ nn n 5 5 5 D5 5 n n?5 5 5 5 = n n?5 ?5 5 5X5 5 5 :5 r 9 n?5 5 n n?5 ?5 5 ?5 5 5 5 $@5 @= 5 5 5 = n?5 5 5 5 n 5 = >/+. 3 13 0>3F `@\?R nn 9 n r 5 R5#5 5 n 5 5 %' 5 ?5 X9 / 0#=32 B5 6 5 D5 r 9I)H n?5 0n 0 Y O5 0 8 =? n?5 5 5 (9 n Y r = n?5 5 5 n 5 r 9 n?5 nX5 5 #5 n n 5 n@' VXW 5 6 !X5 VXW X5 = n?5 #5 n 5 5 r 9 0 W#W#W = ?5 5 ?5 r 5 5%= r r = n?5 5 5 4!X5 YXW r?!X5 W !X5 0 W#W #5 r r 5X5 n?5 5 5 5 5 5 n?5 9 7= n?5 5 5 n 5 5 n?5 #5 n X5 n n 5n V Y W 576 B=P 5 5 nD5 5 n n?5 :5 5 ?5 X9r 5 5 r n?5 V 5 6 #5 5 5 n r =35 = 5 #5 5 5 D5 9 n?5 n 5 5 ?5 X9 ?5 n r 5 5 L5 n?5 5 n r 5 5 n 576 =Q 5 ?5 5 r n #5 r 5 5 %= r #2 = >/ C "?4H1 0>?@\?P 1ON<"4 1OR n 5 5 5 r n?5 5 5 ?5 r ?5 r 9 ?5 n n ?5 S/ / W 1 nD5 5 E5 ?5 X9 n 5 5 n?5 5#5 n?5 !X) ; = )H ?5 5 5 )n 5 Y = n?5 5 5 n?5 ?5 5 5 n?5 5 E5 #5 Y

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Y 0X= 5 5 n 5 n n?5 r D5 5 ?5 n?5 )H ?5 5 L5 5 O5 9 n?5 5 5 = V =rn r 5 5 5 V r 5 r L5 :5 n n 5 5 n n?5 "5 D5 5 :5 5 r 5 576 r 5 5 5 n 5 5 9 r 5 ?5 r 5 5 = @=r8 n 5 5 5 5 5 r 5 n?5 5 5 r 2"%$'& GW 1D= n?5 5 5 n 575 5 nn nn 5 ,! n n?5 ?5 nD5 5 9 n 5 rA5 5 5 <)L) r 5 5 9 D5 r 5 ?5 r D5 9 5 n?5 5 5 575 $@5 I2D= Y = r 5 = D= nD5 5 nX5 r 5 L5 r 5 n r '! n r W 1 0 Y r n n 5 r V 5 #5 5 #5 n #5 n = Y =rn r 5 9 X5 5 5n V 5 5 9 5 #5 5 5 #5 nX5 ?5 5 9 5 5 n?5 = @= nD5 n?5 9 X5 5 n r 5 n n W 5 n X5 5 ?5 5 5 9 5 5 = +=r 5 #5 n 9 5 r 5 5 n X5 5 r 9 n?5 n (9#= n?5 5 r 5 L575 #5 5 n 5 5 r 5 n n 0 V 5 0 V r 5 = n?5 X5 5 n n n?5 X5 D5 n / W = n?5 5 5 n X5 r 5 n?5D5 5 n n?5 n n = n?5 5 A5X5 n A5 9 n?5 5 5 n?5 n ?5 5 n 9 5 r n D5 r 5 5 5 7= D5 9 n r :5 5 &AF n?= )H ?5 n n?5

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Y#Y 0X=) n?5 5 5 ?5 X9 r 5 #5 n?5 n 5 5 & & W 1 0 V#Y n 5 n?5 ?5 5 r 5 5 n r = V =r 9 ?5 n 5 n VXW 576 = @= 5 #5 5 #5 n?5 5 n n ?5 n?5 5 #5 n?5 n 5 5 :5 #5 r n?5 5 5 r 5 ?5 X9 9 5 5 r 5 5 5 r n?5 r n J' 5 n?545 5 ?5 n:5 r 5 5 5 5 5 0@1 Y 0 g NV 0 = D=r&n 0576 nD55 #5 55 ?5 X9 ?5 S/ W 1 n?5 n 5 5 #5 5 n 5 ?5 5 5 = Y =rn # )L) 5 5 n?5 : 5 5 n n 5 5 #5 5 5 n?5 5 5 5 r = @=r?5 X9 n?5 5 )H:$ 5 n?5 5 L5 #5 n?5 n n 5 5 0 576 5 5 n?5 5 n 5 5 r = += nD5 5 5 ?5 #5 5 nL5 r 5 5 5 r 9 n?5 )H:$ n r 5 5 n n 5 n VXW = n?5 5 5 5 G5 #5 5 n?5 r ?5 r r n n n D5 r ?5 / '! b b r n?5 5 5 n?5 5 nI5 ?5 X9 5 5 5 5 5 5 r 5 = n?5 r n #5 n / W = r n n n n 5 r 5 5 5 n nD5 5 5 D5 5 5 5 r 0 W = n?5 L5 r V n 576X b r 5 WZV 5 V#Y#V 5 5 #5 n #5 #5 E2 V 5 6X b = nD5 nD5 r n 0 VXW 576EX b n 0nX2 5 D0 W 5 5 #5 n #5 #5 E0 WZY 576EX b = n?5 n 5 #5 r V 576 0 VXW 576 r n 5 7=4 5 5 #5 n V

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Y 0 r 0 0 1 r 0 0 2 r 0 0 3 r 0 0 4 r 0 0 5 r 0 0 6 r 0 0 7 r 0 0 8 r 7 5 r 8 0 r 8 5 r 9 0 r 9 5 r 1 0 0 r 1 0 5 r 1 1 0 r 1 1 5 r 1 2 0 r 0 r 0 0 1 r 0 0 2 r 0 0 3 r 0 0 4 r 0 0 5 r 0 0 6 r 0 0 7 r 0 0 8 r 7 5 r 8 0 r 8 5 r 9 0 r 9 5 r 1 0 0 r 1 0 5 r 1 1 0 r 1 1 5 r 1 2 0 r P h o t o n j e t s a m p l e D i j e t s a m p l e G e V / c 2 G e V / c 2 M j j M g j1 / N e v d N / d M j j 1 / N e v d N / d M g jB i n 1 M j j = 8 1 9 G e V / c 2 B i n 1 M g j = 8 0 8 G e V / c 2 B i n 2 M j j = 1 0 5 1 G e V / c 2 B i n 2 M g j = 1 0 4 6 G e V / c 2 52O0 5 5 n 5 5 #5 n n 5 #5 5 5 = 576 r 5 5 n?5 9 r 5 5 5 5 5 n?5 5 5X5 5 r 5 r 9 #5 5 5 5 #5 9 5 5 5 n 5 ?5 5 5 n?5 #5 n 5n = nn 5 ?5 5 0 VXW 576 r nD5 5 5 n 5 n 7=: nD5 r! O5 r n 5 r 5 D=2O0 r32 V = / 89O3P 1N<"4
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Y M e a n r 3 8 6 1 r M e a n r 4 8 9 2 r M e a n r 3 8 0 7 r M e a n r 4 8 7 6 r M e a n r 3 6 6 2 r M e a n r 4 7 2 4 r 0 r 0 0 2 5 r 0 0 5 r 0 0 7 5 r 0 1 r 2 0 r 3 0 r 4 0 r 5 0 r 6 0 r 0 0 0 2 5 0 0 5 r 0 0 7 5 r 0 1 r 3 0 r 4 0 r 5 0 r 6 0 r 7 0 r 0 r 0 0 2 5 r 0 0 5 r 0 0 7 5 r 0 1 r 2 0 r 3 0 r 4 0 r 5 0 r 6 0 r 0 r 0 0 2 5 r 0 0 5 r 0 0 7 5 r 0 1 r 3 0 r 4 0 r 5 0 r 6 0 r 7 0 r 0 r 0 0 2 5 r 0 0 5 r 0 0 7 5 r 0 1 r 2 0 r 3 0 r 4 0 r 5 0 r 6 0 r 0 r 0 0 2 5 r 0 0 5 r 0 0 7 5 r 0 1 r 3 0 r 4 0 r 5 0 r 6 0 r 7 0 r D i j e t D i j e t P h o t o n j e t P h o t o n j e t P h o t o n j e t P h o t o n j e t r G e V G e V G e V1 / N e v d N / d E TM a s s b i n 8 2 G e V M a s s b i n 1 0 5 G e V G e V G e V G e V j e t E T j e t E T j e t E T j e t E T p h o t o n E T p h o t o n E T 52 V #5 5 5 ?5 X9 5 5 n 5 n 5 E5 #5 5 5X5 5 5 7= n?5 5 5 n#5 9 P/ V 5 5 5 ?5 5 5 nD5 9 = >/ 9O3P 1ON\


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Y 2 G l u o n f r a c t i o n i n D i j e t a n d g + j e t s a m p l e s M j j ( d e t e c t o r l e v e l ) G e V r 7 0 8 0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 G l u o n f r a c t i o n 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 D i j e t C T E Q 4 M D i j e t C T E Q 4 A 4 g + j e t C T E Q 4 M g + j e t C T E Q 4 A 4 r 5 2 5 5 5 5 = )H&A =X n?5 r 5 5 n 5 n?5 5 5 5 n?5 #5 5 r 5 n?55 5 ?5 n:5 n?5r)L5 > 5 ?5 $ n r 5 )HA$ 5 r 9 5 n r = n?5 #5 5 n n X5 n n 5 9 5 5 5 n n $ 5 X5 r n 5 n?5 r 5 5 n r 5 5 5 5 r n?5 5 r 5 5 ?5 5 W 576 =# 9 n r :5 ?5 n n W 576 r n?5 5 5 r 5n?5 X5 5 n 5 5 5 n?5 ?5 )H&A Fr= )HL= n?5 #5 5 n r 5 5 n?5 r r (9 #5 n?5)H& n n?5 L5 n 5 5 ?5 5 =AE5 n n #5 #5 r r (9 Z 4/ 0 n n?5 5 5 n n?5 )H& r n 5 X5 r r 5 9 +r =35 = n r n #5 nn?5 #5 r r (9 Z 0 %0 Z / V Z Z 575 5 %= r #2 5 ?5 = nD5(9 ?5 2Z hZ 5 W = W =32 r 5 5 n#5 9X= n?5 5 5 r

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Y r 5 2O0 5 5 5#5 N0 WXW 5, 5 5X5 r ?5 Fr5 &Q9 n n 5 n r 7= n n rnn r"!#n$ %&(')%*!#n$ r+!#n$ %&(')%,!#n$ -.n0/21436587:98;#<>=?#n@?A B2DC E')FErG%IHJE'KIF E')%LLIHE'KIL E')&ErGFIHE'KIM E')&%FIHE'KrG% -.n0/21436587:98;#IN& E')F&OIHJE'KIF E')%M%IHE'KIL E')&ErGLIHE'KIM E')&%OIHE'KrG% -.n0/21436587:98;#IN E')FErGOIHJE'KIF E')%IPQFIHE'KIL E')&ErGLIHE'KIM E')&F&IHE'KrG% SR(0T UA36587.9V;#< E')F&OIHJE'KIF E')%MLIHE'KIL E'UrGMIPHE'KIM E')&%QHE'KrG% D5 n n 5 r n n%Z n X5 r n?5 r 5 5 n r r 55 5 n?5 5 / Z / Z Z = n?5 5 n r r r 5 Y 2 V 576EX b W %0 WZY 576X b = n?5 :5 D5#5 O5 n?5 5 5 n O5 n?5 X5 n 5 7= n ?5 r 5 I)n 5 @= n?5 5 n X5 5 5 n n?5 )H&A :5 n7= / : @1ON 7@N+PQN1nJ : ? 3R 89O? F%? 4"1OR n?5 9 n 5 n?5 5 n 5 5 5 ' 5 r n !#"%$'& / b V = 5 n #5 5 5 n 5 5 n 5 5X5 " 5 5 5 5 5 5 D5 021/ W = V 2 r W = r W =r r n?5 5021 n?5 5 r 5 L575 nD5 5 n n?5 ?5 ?5 5 5 = n?5 n 5 5 75 O5 5 '?= n?5 5 5 n 5 5 5 5 5 :5 nX5 ?5 n n?5 5 n?5 n (9 n #5 5 5 r n 5 0X= #5 r),+ ?5 9 r 5 5 n 5 5 V = 5 9 5 r ?5 9 5#5 5 5 5 r r 5 5 n 5 5 @=)L) 5 ?5 5 9X=

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W 2 1 0 1 2 3 4 8 6 4 2 0 2 4 L o g ( P T ) v s L o g ( | d | )L o g ( P T ) P T i n G e V / cL o g ( | d | ) d i n c m r 5E2 5 n?5 n r #5 n ?5 #021/ W = n?5 5 5 = Fr5 5 r n nD5 X5 5 5 n n?5 5 5 7= n?5 ?5 n?5 5 5 n n r 9 n?5 ?5 r n 5 nD5 n r 9 n?5 n?5 D5 5 5 5 n?5 9 5 5 (9#= >/ >/+. 9O3P !# 1OR 5 9 X5 5 5 ?5 5 9 5 r2 X5 r ),+ ?5 9 r n?5 r 7= n?5 r n n?5 n 5 5 r r?5 r ?5 n?5 n 5 5 ?5 r 5 :5 5 nD5 5 5 5 r 9 n?5 $ 6; ?5 5 n?5 5 5 9 r ?5 r 9 n?5 )L) n r = ?=G2 n n?5 r X5 n?5 5 5X5 n?5 r r r"'"7/2 V 5 6 r n?5 5 nD5 #5 5 5 5 5 n?5 5 r n?5 n ?5 5 5 n?5 n n?5 5 5 X5 n 5 nD5 r 5

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D0 5 2 Y 5 r 5 L575 X5 5 5 5 r r n 5 5 r r 5 5 5 #5 7= r 5 :5 5 n?5 6H; n?5 )L) n r 5 = r 5 n 575 ?=2 Y n 5 5 5 #5 n?5 r 5 D5 r r n #5 n?5 5 W 1 0 Y 2D= 0 n?5 5 5 5 5 5 5 rn?5 ?5 r 5 B5 r n b = n?5 ?5 n?5 5 5 5 5 9 n n r n?5 r J' ?5 r 5 nD5 5 n?5 ?5 5 5 ?5 r ?5 r 9 n?5 5 / 0 / W ?5 D=2 = n?5 5 #5 5 5 n r ?5 r ?5 n?5 5 5 5 r 5 :5 5 n?5 n n?5 n?5 5 n nD5 r 5 ?5 n?5 n?5 9 #5 5 5 5 r 9 n?5 #5 5 ?5 5 575, ?= 2 =

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V 5 6 6 8 / 3 7 r C o n s t a n t r 1 2 4 6 r 9 4 1 9 r M e a n r 0 8 1 0 1 E 0 1 r 0 7 1 4 3 E 0 2 r S i g m a r 1 0 7 4 r 0 7 4 6 5 E 0 2 r 0 r 2 0 0 r 4 0 0 r 6 0 0 r 8 0 0 r 1 0 0 0 r 1 2 0 0 r 1 4 0 0 r 1 6 0 0 r 1 0 r 7 5 r 5 r 2 5 r 0 r 2 5 r 5 r 7 5 r 1 0 r D z = | z z v t x | c m rN u m b e r o f t r a c k sd e f a u l t c u t d e f a u l t c u t 5,2 5 n?5 n n r 5 #5 n 9 ?5 X5 5 n 9 5 =B 5 5 n D5 021/ W = n?5 5 5 = nn n?5 5 #5 n?5 5 9 5 = n?5 D5 ?5 n n n D1 W = 5 9 #5 5 r n?5 5 r 5 5 5 r 5 r 9 D5 X5 =U n?5 5 5 5 n 5 r 9 X #5 n?5 D5 5 nn #5X= nn n r 5 D= Y = >/ >/ 3P 9< 476 935P R ?FG< 53@ n?5?5 9 E5 #5 r n 5 5 n?5 5 r n n 5 #5 n #5 5 r Z9 n?5 5 5 r r 5 5 9 r 5 #5 X5 5 5 9 D5 = 5 5 9 ?5 ?5 r D5 n n nD5 n?5 D5 n?5 5 5 n?5 5 5 n?5 5 n ?= 2 n n?5 5 n?5 5 5 9 ?5 =n 5 n n ?5 9 r 5 D5 r ?5 5 n?5 5 Y 021 0 Y 5 n" $'& MW 1 = n?5 5 ?5 5 5 O5 5

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J e t 1 J e t 2p l a n e p e r p e n d i c u l a r t o j e t s b e a m l i n eq q 5 2 n?5 D5 r 5 5 9 ?5 7= nD5 r 5 5 5 n?5 @5 ?5 5 5 9 5 0 V = 5 n 9 n?5 5 5 5 r n?5 ?5 n?5 5 =SF :5#5 r n?5 5 r 5 5 n 5 n n n?5 9 nD5 5 5 9 ?5 = n?5 5 5 5#5 n = n 5 5 #5 r nD5n (9 nD5 n ?5 n?5n?5 n?5 5 5 9 ?5 n r 5 n n n?5 5 ?5 =r 9 r n?5 5 n 5 r 5 :5 5 n?5 (9 n?5 5 5 9 ?5 n?5 n (9 ?5 5 575 ?= 2@2 = 5 n 5 nD5 ?5 r n?5 5 5 r r L5 ?5 D5 r n?5 ?5 5 ?5 5 5 5 5 9 ?5 n (9 5 n (9 5 5X5 5 n 5 5 = nD5 5 nn 5 5 5 n 5 nD5 5 5 r r n?5 5 ?5 W = Y#Y W = r 5 ?5 021/ W = 5 n 5 5X5 r 5 5 #5 9 = >/ >/ 9O3P N+4 GCLPQN\? 4P J 5 5 5 n?5 5 5 5 n?5 )L) 5 ?5 5 9#= 5 5 n?5 5 n?5 5 n ?5X5 5 5%= r W = n 5 n n r 5 5 r 5 n?5 )L) n 5X5 5 5X5 5 n?5 )L) 5 = n 5 r 5 5 5 ?5 n?5 5 5 :5X5 n 5 0 2 W nD5 5 5 %' 5 r 5 r 5 D5 n?5

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n 6 5 6 2 / 4 2 r A 0 r 1 0 9 2 r 0 1 6 0 1 E 0 1 r A 1 r 0 7 4 9 8 E 0 2 r 0 8 1 7 5 E 0 3 r 1 8 3 7 / 2 4 r A 0 r 1 1 5 5 r 0 6 1 8 0 E 0 1 r A 1 r 0 7 4 8 2 E 0 2 r 0 4 2 3 0 E 0 2 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 3 5 r 4 r 4 5 r 5 r 0 r 5 r 1 0 r 1 5 r 2 0 r 2 5 r 3 0 r 3 5 r 4 0 r 4 5 r 5 0 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 3 5 r 4 r 4 5 r 5 r 0 r 5 r 1 0 r 1 5 r 2 0 r 2 5 r 3 0 r 3 5 r 4 0 r 4 5 r 5 0 r d i j e t m u l t i p l i c i t y d i j e t m u l t i p l i c i t yc o m p l i m e n t a r y c o n e m u l t i p l i c i t y rd i j e t m a s s r a n g e : 7 2 ~ 1 2 0 G e V / c 2 d i j e t m a s s r a n g e : 7 2 ~ 7 4 0 G e V / c 2 5E2@2 n?5 5 r 5 :5 5 n (9 5 5 9 D5 O5 5X5 5 n (9 5 5#5 = n?5 5 ?5 r r 1 1 $/ + $'& 5 n = 5 r n?5 ?5 O5 ?5 5 n?5 5 $'& Y r r 5 5 n?5 r 5 5 r 5 n?5 5 (9 n 5 =Q n?55 O5 5 n (9 5 5 r ?5 nD5 5 5 E5 n 5 n =L n?5 5 nD5r 5 n?5 5 n n D5 5 #5 n X5 9 5 5 5 n n 5 #5 9 ?5 5 ?5 5 n?5 5 5 9 ?5 n (9 nD5 5 5 ?5 X9X= r 5 2 V 5 5 n?5 5 5 5 n n?5 #5 #5,5 D5 9 $ & / ?0 576 = $ #5 n (9 5 5 5 n (9 ?5 r` TS n r TS 5 5 r r r TS :)L)M5 5 9 5 r TS 5 5 X5 rTS 5 5 9 ?5 r r2TSn = .r } g @E_FZ5 } g @E 4 l .r } g @E Uun o 'j D' o ƒD'j o 'j D' mW>>&[]>@@&^ UW nu>V['>`@@&^ l Wa>5 ['>`@@?^ mW l m []>@@&^ nW UX4 []>@@&^ l W n"Uh['>`@@&^ UƒW GXF [ G l E U&^ UƒW m@ [ GmE m?^ mW G@ [\GmE m&^ mW 44k[\GUE_m!&^ l W GG [ GZUEa>"&^ l W FG [ G4E 4?^ $# UƒW m4 [ 55E n%&^ UƒW @4 [ 5mE m?^ mW UXF [\5XnE_n!&^ UW n l [\5UE 4&^ l W Uƒ>&[ 5 l E 4&^ mW l >&[ 54E 4?^ '& UƒW 5@ [ GZUEa>"&^ UƒW F5 [ G@E 5?^ mW nn [\G4E U'&^ mW @Xn [\5GE 5&^ l W 5@ [ G>E l &^ mW GXm [ 55E U'?^ ( UƒW l n [ G>E U&^ UƒW> l [ 55E 4?^ mW_mZG [\G@E U'&^ UW G>V[\5unuE @&^ l W mm [ 55E_F!&^ mW_n)U [ 5mE F?^ ) UƒW UX5 [ 5XnuE n%&^ UƒW @>&[ 5mE>*?^ mW_FZG [\5mE l &^ UW l Uh[\5XFE_F!&^ l W @Xm [ 5>E_m!&^ mW 4>&[
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Y r 5 2 5 5 n?5 5 5 5 n n?5 #5 #5,5 D5 9 $ & / Y#V = Y 576 = $ #5 n (9 5 5 5 (9 ?5 r TS n r TS 5 5 r r r TS :)L)M5 5 9 5 r TS 5 5 X5 rTS 5 5 9 ?5 r r2TSn = g @E_FZ5 .r?g @E 4 l g @E Uun o 'j D' o ƒD'j o 'j D' mW 5XF []>@@&^ mW_FZGk['>`@@&^ l W G5 ['>`@@?^ l W FG []>@@&^ 5W 44 []>@@&^ nuW UGk['>`@@&^ mW l >&[ G l E 4&^ mW @ l [ GmE m?^ l W ll [\GmE U'&^ mW Gm [\GUE_m!&^ nW 5Xm [ GZUEa>"&^ l W GG [ G4E 4?^ $# mW> l [ 55E n%&^ UƒW UX5 [ 5ZUƒE_n!?^ l Wa>>r[\5XnE m&^ mW_FZGk[\5UE @&^ nW>`G [ 5 l E 4&^ l W F@ [ 5FE_n!?^ '& mW mZU [ GmE_F!&^ UƒW 5XF [ G>E>*?^ l W_m l [\GZUƒE @&^ mW l Gk[\G@E U&^ nW_nF [ GFE n%&^ l W l n [ 5GE @?^ ( mW 45 [ GFE_m!&^ UƒW l 5 [ 55E U'?^ l W 4m [\G>E @&^ mW_mZ@k[\5unuE U&^ nW UU [ 5GE_F!&^ l W UuF [ 5mE_n!?^ ) mW>`G [ 5GE_F!&^ UƒW m4 [ 5mE l ?^ l W @m [\5 l E_n!&^ mW_FZ4k[\54E_F!&^ l W GU [ 54E 4&^ mW GG [ 5@E @?^ n?5 5 = n?5 r n?5 5 5 n?5 5 5 5 5 n n?5 ?5 r 5 5 5 r 5 ?= ) 5 r ?5 nn 9 X5 n?5 5 5 9 ?5 O5 ?5 5 5 E5 ?5 X9 r 5 5 r 5 5 n 5 O5 n?5 5 n =Q nD5 5 n?5 5 5 #5 #5 n 5 '(2 r ?5 5 n 5 5 ?5 X9 ?5 5021 = n?5 5 n (9 5 5 5 n ?5 5 5 r 5 r 5 2 V r 2 D= >/ C ?P 1
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r 5 2 n?5 (' 5 D5 5 5 5 n 5 r 5 :5 5 5 5 5 5 X5 n = n?5 O5 5 50 / W 1 V 2 W 1 W 1 @= $'& !n$ 5 n1 n $'& r !#n$ -9r! 7.-N T 2@ AQ0A E')&L rrQ')% rQ'KQ&IHE'KrGL rQ'KILIPHJE'KrGM rQ'KI& 4HE'Krr r E')OF r P rQ'KI&%IHE'KrGF rQ'KPQ%IHJE'Kr P rQ'KI&%IHE'Krn E' 4P rGM(')& rQ'KIO&IHE'KrG% rQ'KIL 4HJE'KrGF rQ'KIOQHE'KIM E')&L r P rQ'KQIHE'KIOEr rQ'KI%FIHJE'KI&M rQ'KI&FIHE'Kr %&(')% E')OF rGL(')M rQ'KI&OIHE'KI&L rQ'KI%FIHJE'KI&M rQ'KIO%IHE'KrGO E' 4P & P rQ'KHE'KI&F rQ'KI%%IHJE'KI&IP rQ'KIOIPHE'KrG& 5 5 #5 r 9 r Y 5 5H ?=B2O0 W = n?5 5 5 r 5 r #5 #5 r n X5nn?5 ?5 n n?5 5 5 ?5 =A) 5 ?5 9 r n?5 5 r 5 9 5 n 5 5 #5 n n?5 ?5 ?5 n n?5 5 r nD5 5 5 5 #5 = n r D5 5 n n?5 nn?5 ?5 5 ?5 X9 9 5 n nD5 n (9 n?5 5 5 n?5 X5 n 9 5 5 5 5 5 5 5#5 = 5 n 5 5 5 X5 r r 5 (9 9 5 O5 5 nn?5 n n 5 5 5 5 5 #5 r " =B r 5E2 5 5 n?5 5 n?5 (/ " r ?5 n?5 5 5 = n 5 5 ?5 5 ?5 9 5 n n?5 5 r ?5 n r ( n?5 5 5 r 9 r 9 n n?55 ?5 X9 ?5 n?5 5 r 9 nD5 5 O0 W = n n?5 nX5 n 5 n :5 n #5 r ?5 5) nn =B D5 H5 n 5 ( r :5 X5 n?5 X5 #5 5 r ?5 Fr r>&KEF( r nn 5 5 D= n?5 5 n ?5 5 5 5 r 5 n n L5 5 n n?5 5 ) 5 5 5#5 = n 9 r F5 5 5 n G&Q9 n 5 5 5 7=N :5n n?5 5 5 r 5 n #5 r #5 X5 r :5 5 n (9 n?5 n?5 5 r n?5 5 5 r 5 n r 5 n n 5 5 5 5 5 nn,5 ?5 X9 =

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r M e a n r R M S r 0 9 0 2 3 r 0 7 5 2 8 E 0 1 r M e a n r R M S r 0 9 2 9 2 r 0 7 4 7 1 E 0 1 r M e a n r R M S r 0 8 7 7 2 r 0 7 3 5 4 E 0 1 r M e a n r R M S r 0 8 9 2 9 r 0 6 7 8 1 E 0 1 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 0 6 r 0 7 r 0 8 r 0 9 r 1 r 1 1 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 0 6 r 0 7 r 0 8 r 0 9 r 1 r 1 1 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 0 6 r 0 7 r 0 8 r 0 9 r 1 r 1 1 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 0 6 r 0 7 r 0 8 r 0 9 r 1 r 1 1 r1 / N e v d N / dD r D = E T ( Q F L ) / E T ( H e r w i g ) r D = E T ( Q F L ) / E T ( P y t h i a ) r 8 2 G e V m a s s b i n 1 0 5 G e V m a s s b i n1 / N e v d N / dD r8 2 G e V m a s s b i n 1 0 5 G e V m a s s b i n r f a k e g j e t e v e n t s f a k e g j e t e v e n t s f a k e g j e t e v e n t s f a k e g j e t e v e n t s 5r2 nD5 n?5 5 5 5 ?5 X9 5n ?5 5 5 #5 n?5 5 5 ?5 X9 5 5 ) 5X5 = 1 8 9 1 / 2 5 r C o n s t a n t r 4 8 4 8 r 0 2 0 1 2 r M e a n r 0 9 4 9 6 r 0 2 7 3 4 E 0 2 r S i g m a r 0 8 0 7 5 E 0 1 r 0 2 0 3 0 E 0 2 r 1 8 9 4 / 2 0 r C o n s t a n t r 4 7 6 4 r 0 3 9 0 6 r M e a n r 0 9 6 8 6 r 0 5 4 2 3 E 0 2 r S i g m a r 0 7 8 7 0 E 0 1 r 0 4 2 5 8 E 0 2 r 2 6 7 9 / 2 8 r C o n s t a n t r 4 4 1 7 r 0 2 3 2 8 r M e a n r 0 9 2 7 5 r 0 3 5 2 8 E 0 2 r S i g m a r 0 8 6 6 6 E 0 1 r 0 2 9 2 5 E 0 2 r 5 6 6 5 / 1 0 r C o n s t a n t r 5 1 0 6 r 0 4 9 2 6 r M e a n r 0 9 5 0 4 r 0 5 8 1 2 E 0 2 r S i g m a r 0 7 5 0 0 E 0 1 r 0 4 4 4 9 E 0 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 0 8 r 1 r 1 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 0 8 r 1 r 1 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 0 8 r 1 r 1 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 0 8 r 1 r 1 2 r1 / N e v d N / dD D = m a s s ( Q F L ) / m a s s ( H e r w i g ) r D = m a s s ( Q F L ) / m a s s ( P y t h i a ) r 8 2 G e V m a s s b i n 1 0 5 G e V m a s s b i n1 / N e v d N / dD8 2 G e V m a s s b i n 1 0 5 G e V m a s s b i n f a k e g j e t f a k e g j e t f a k e g j e t f a k e g j e t 52O0 W nD5 nD5 5 5 # 5 5X5 ?5 5 5#5 n?5 5 ) 5#5 =

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#2 r 52 Y E5 n?5 5 5 5 n n?5 ?5 5 = nD5 5 5 5 #5 r# "r n 5 5 #5 r# r D5 5 5 5 ),+ ?5 9 5 = 798n:<; U> ABC mFW mrABC } @W_FZ5?n @W 4 l @W Uun n @W_FZ5?@W 4 l n @W Uun gB798n:<;Z} >>W_m?ABC >UW n?ABC >`GW_F?ABC >UW n?ABC >5W GVABC F)UW n?ABC T88 UW Uun l YB@W @Fm mW F5XnYB@W @Fn l W @mFYB@W @FG mWa>GXYB@W @U l W @mXYB@W @ZU l W GZUuYB@W @U 8 UƒW @>"YB@W @ZU UW l UuYB@W @U mW 4>"YB@W @m UW_mZ4XYB@W @un mW_FZ4uYB@W @5 l W @@XYB@W @5 88 @W l >"mYB@W @@ l $& nZr @W m55XYB@W @@5 nZr nZr 8 @W_F> l YB@W @@G $& nZr @W Fm l YB@W @>`m nZr nZr @W_nmYB@W @ZU $& nZr @W G@XYB@W @un nZr nZr >W @ZUX@XYB@W @> l >W @4mXYB@W @>U >W @ZUƒ>"YB@W @>"m >W @4FYB@W @>`F >W @4 l YB@W @>> >W @4ZUuYB@W @>> >/ N43@ !<9O9O?P 1ON<"4R346 h? R7@1OR n n :5 5 5 A5 5 "r r "'" r r ( 5 5 r 52 Y r :5 5 r / nr = D= D=D=r ?5 r n?5 r 5 r 5 r 5 5 =P n?5 5 5 5 ?5 nX5 5 ) 5 5 5 5 r 5 5 5 r n n X5 n?5 r 5 5 n?5 ?5 7= n?5 5 ),+ $ ?5 5 5 (9 5 = n?5 n?5 5 5 n 5 n 5 5 b (9 5 5 5 5 = n?5 5 5 r n?5 ?5 9 r nD5 5 5 5 nD5 n #5 5 n 5 7= ?5 n?5 5 nD5 #5 5 n 5 D5 ),+ ?5 9 = F :5X5 r n?5 5 ?5 r 5 n#5 5 nD5 5 ?5 9 n n nD5 7= ?5 45 5 5 #5 nn r n?5 D9 O5 5 = 5 5 I 5 ) 5 ?5 5 n #5 r ) + ?5 9 n?5 Q r n?5 5 n 9 #5 nD5 Q '?=+) n?5 ) 5 #5 n 5 r L5 :5 5 r 5 r n?5 5 ),+ ?5 9 7= n n?5 ?5 5 5X5 ) n 5 r L5 n n?5 5 5 5 n?5 = #5 nD5 5 r 5 r L5 r ?5 n (9 5

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r 5 2 5 ),+ ?5 9 n?5 n #5 5 n (9 n D5 n?5 O5 5 021/ W = += n?5 5 5 5 5 n?5 r 5 5 r 5 IF5 ?= (9 5 5 5 5 9 n?5 5 &Q9 n 5 O5 5 r 021/ W = V 2 r W =D= In: R( A 0 @T 'AQ00nB2G A 0 @DT 'SAQ0nB2G < B202BUn2 R @ + A n nA R( @ nAGRE:/.T rT A00n0 0G'S@?A !JBU LI 4P E')MF ( AQE MI FI E')MF ( AQ rG%I %FI E')M& ( AQ rn 4 E')MF AB B4 AQ( rn MI E')M% r 52 )n #5 5 n 5 ?5 5 5 n?5 r r r / n 5 5 #5 9#= 5 ?5 n #5 5 ),+ D5 9 = $'& 021 /! $ & 021 / W = V 2 0#0#= Y 5 6 ?=#2 W = W W = YXV D= V 2 W = 0#0 W = 0#= Y#V W = W 2 W = 0 ?0 5 6 W =n 0?=4 5 6 D= WZV W = W 2 W = YXY D= W W = 0#0 W = W 0#= W = W W = 0 W =r 0D= V 5 6 D=n W = W 2 W = Y 2 ?= V W = 0 V W =r 0#=n W = W W = 0 W = V 2 0?=4 5 6 Y =n W = 0 V W =n D= W W = 0 W = 0#= W W = 0 V W = 0 Y#V = Y 576 W =n 0 2D= 5 6 @= WZV W = 0 W = V ?= V#V W = 0 2 W = 0#= W = 0 W = V W W =r V ?=4 5 6 2D= W 2 W = 0 W = V ?=32 W = 0 W = Y 0#= W = 0 W = 0 2 W = 5 W = Y 5 7=5 n?5 5 5 r 5 r 5 2 D= 9 r n?5 5 5 5 :5 5 5 5 5 D5 n?5 ?5 r 5 n?5 5 nD5 5 5 9 5 n W#W 576 9 5 = X5 n 5 r :5 5 5 n?5 5 ) n r 5 5 D5 5 n n W#W 576 r 5 nn n 5 n r n #5 5 Qnn n n 9 = n?5 5 V 5 0 5 7= n?5r 5 n?5 ?5 r 5 r X5 5 r / n r 5 5 5 5 r 5 2 @=

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)HFr&EA $ K$+E: ) n)H%n%A$n)H $?$ '%)HFA)H$ n?5 5 9 5 5 5 5 5 n?5 5 5 5 r 5 >0 r V r D= >/. C "?4H1 02? @\?P 1ON\


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@0 2 7 9 2 / 1 9 r A 0 r 2 0 2 1 r 0 9 3 2 2 E 0 2 r 1 0 8 6 / 1 9 r A 0 r 2 2 7 0 r 0 1 4 1 1 E 0 1 r 2 0 8 4 / 1 9 r A 0 r 1 7 7 3 r 0 1 4 3 7 E 0 1 r 2 4 7 6 / 1 9 r A 0 r 1 9 4 0 r 0 2 4 9 4 E 0 1 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 0 r 1 r 2 r 3 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 0 r 1 r 2 r 3 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 0 r 1 r 2 r 3 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 0 r 1 r 2 r 3 rd i j e t e v e n t s r E j e t = 4 1 G e V r q c = 0 4 7 r a d r r d i j e t e v e n t s r E j e t = 5 2 5 G e V r q c = 0 4 7 r a d r r p h o t o n + j e t e v e n t s r E j e t = 4 1 G e V r q c = 0 4 7 r a d r r p h o t o n + j e t e v e n t s r E j e t = 5 2 5 G e V r q c = 0 4 7 r a d r r b r a d b r a d b r a d b r a d1 / Nj e t d n / d b r 1 / Nj e t d n / d b r 5 O0 n?5 r 5 D5 W = 5 5 =Bn 5 n?5 n?5 5 55 5 r 5 #5 r 5 9 = n?5 n?5 5 5 5 5 5 #5 n?5 5 nX5 n?5 5 5 ?5 (9 5 n?5 5 5 5 5 / V 5 5X5 / W 5 E5 #5 = r U/ 5 n 5 r 5 :5 5 5 5 =r ?= O0 n n n?5 n r 9 = n?5 5 5 r n?5 n?5 5 5r5 5 5 ?5 r 5 r 5 5 nD5 n 5 :5 5 5 5 5 5 5 5 5 5 5 575 5%= r V 5 D5 = n?5 ?5 5 :5X5 5 5 n 9 X5 5 5 #5 =A nD5 / V 5X5 5 0 = ?5 n?5 5 :5 5 5 n 5X5 n n n?5H)H& 5 n ?5 #5 5 n n 5 5X5 n 5 #5 5 9 / 0 / V 5 #5 r n r5X5 = n?5 nD5 n r nD5 5 5 5 n?5 5 X5 5 5 5 r 5 #5 5 n n 5 5 5 5 5 n (9 5 D5 X5 5 5X5 7=

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V 5 n 5 n?5 9 5 5 (9 5 n n5 5 r L5 5 O5 n?5 9 n 5 n#5 9 n n 5 n 5 / 0 / V 5X5 5 n?5 5 = 5X= r 5 " 5 " = n?5 5 5 n?5 n 5 n 5 n r 5 07' V =L n?5 5 ?5 5 (9 n?5 V = 5 ?5 X9 r 5 n 5 5 5 5X5 n :5 5 5 5 7= n?5 5 n 5 5 #5 5 5 5 5 9 n?5 5 n ! n RW = 0 Y =B n 5 5 5 5 5 5 n 5 5 #5 n #5 n?5 5 O5 5 =LF :5#5 r 9 n?5 55 ?5 X9 r 5 5 #5 r n 5 5 r = n?5 n 5 ?5 X9 5 n n n r 5 5 n n 5 7= n?5 5 5 r n n#5 5 r '$ &d r 5 n5 5 5 r 5 r 5 5 :5 n &dJ'$ &d D5X= n?5 5 r 5n?5 5 5 n n 5 r ?5 n?5 '$ &d r 5 r :5 575 n &d &dJ'$ &d 5 n?5 5 5 5 ?= V = ?5 n?5 5 n?5 5 5 5 5 n n 5 ?5 5 5 0 W 5 n ,5 ?5 5 5 5 n?5 = n?5 n?5 n 5 #5 5 n ) n?5 5 @' 5 X9 5 r 5 5 5 5 5 r ?5 X5 #5 5 5 5 = n?5 5 5 r 5 5 r 5 i n n r r 5 r D5 #5 ?5 >' &d r 5 =8L5 5 n?5 5 5 5 ?5 r 5 r X5 5 5 n?5 5 n 5 9 5 n?5r L5 n 9 9 5 5 (9 5 n nD55 5 n?5 5 ?5 X9 r 5 =4 5 5 n 5 5 :5 5 n 5 5 r 9 ) 5 5 54 ?= n 5 5 #5 n r n r W = 0 V#Y = n?5 5 5 5 r 5 n?5 0 V n?5 5 5 5 r =

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n 2 3 5 2 / 1 7 C o n s t a n t 5 3 6 6 0 1 3 5 2 M e a n 0 2 3 3 6 E 0 3 0 2 1 9 3 E 0 2 S i g m a 0 7 9 7 9 E 0 1 0 3 3 5 4 E 0 2 2 0 6 5 / 1 6 C o n s t a n t 5 5 6 1 0 2 0 1 6 M e a n 0 4 8 2 9 E 0 2 0 3 1 8 4 E 0 2 S i g m a 0 7 8 7 6 E 0 1 0 5 0 9 7 E 0 2 1 5 4 6 / 1 8 C o n s t a n t 5 1 6 1 0 1 5 1 4 M e a n 0 2 4 3 6 E 0 2 0 2 9 0 3 E 0 2 S i g m a 0 8 8 1 2 E 0 1 0 4 7 4 4 E 0 2 2 0 4 5 / 1 4 C o n s t a n t 6 2 9 1 0 3 0 1 8 M e a n 0 1 8 6 2 E 0 2 0 3 2 1 6 E 0 2 S i g m a 0 6 2 4 9 E 0 1 0 4 2 4 8 E 0 2 0 1 2 3 4 5 6 7 8 9 1 0 0 2 0 0 2 0 1 2 3 4 5 6 7 8 9 1 0 0 2 0 0 2 0 1 2 3 4 5 6 7 8 9 1 0 0 2 0 0 2 0 1 2 3 4 5 6 7 8 9 1 0 0 2 0 0 2 8 2 G e V m a s s b i n 8 2 G e V m a s s b i n 1 0 5 G e V m a s s b i n 1 0 5 G e V m a s s b i n D i j e t s a m p l e P h o t o n + j e t s a m p l e I S O < 1 G e V D = ( E 1 x y + E 2 x y ) / ( E t 1 + E t 2 )1 / N e v d N / d D 5 V ?5 X9 r 5 n r '! n = 2 2 0 5 / 1 7 r C o n s t a n t r 5 1 6 8 r 0 7 0 8 5 E 0 1 r M e a n r 0 1 2 3 8 E 0 2 r 0 1 3 2 7 E 0 2 r S i g m a r 0 8 5 0 3 E 0 1 r 0 2 1 7 5 E 0 2 r 2 5 1 1 / 1 6 r C o n s t a n t r 5 4 9 6 r 0 8 7 5 6 E 0 1 r M e a n r 0 1 4 1 0 E 0 2 r 0 1 3 6 2 E 0 2 r S i g m a r 0 7 6 8 3 E 0 1 r 0 2 0 8 0 E 0 2 r 8 4 0 4 / 1 5 r C o n s t a n t r 5 7 0 6 r 0 1 0 5 5 r M e a n r 0 6 3 0 0 E 0 3 r 0 1 5 0 6 E 0 2 r S i g m a r 0 7 3 4 5 E 0 1 r 0 2 3 5 0 E 0 2 r 6 7 7 2 / 1 3 r C o n s t a n t r 6 3 1 8 r 0 1 1 5 5 r M e a n r 0 1 3 3 2 E 0 2 r 0 1 2 2 8 E 0 2 r S i g m a r 0 6 2 4 8 E 0 1 r 0 1 8 3 8 E 0 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 1 0 r 0 2 r 0 r 0 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 1 0 r 0 2 r 0 r 0 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 1 0 r 0 2 r 0 r 0 2 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 r 1 0 r 0 2 r 0 r 0 2 r 8 2 G e V m a s s b i n 8 2 G e V m a s s b i n 1 0 5 G e V m a s s b i n 1 0 5 G e V m a s s b i n M C d i j e t s a m p l e M C p h o t o n + j e t s a m p l e I S O < 1 G e V D = ( E 1 x y + E 2 x y ) / ( E t 1 + E t 2 )1 / N e v d N / d D 5 ?5 X9 r 5 Fr5 5 ) n r '! n =

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Y r 5 5 n?5 n r 5 = n?5 5 r 5 r 5 r r 5 5 X5 r 9 n?5 5 r?5 ?5 5 5 5 5 5 5 7= n?5 n 5 5 r 5 5 #5 D5 O5 n?5 5 D5 5 n?5 5 ?5 X9 n?579 n 5 =Q 5 r 5 r n?5 5L5 ?5 X9 5 / W = r 5 5 5 `d / W = 5 r 2 W n?5 5 / W = 5 r 2 W W n?5 5 =E8 5 n5 5 r ?5 ?5 n ?5 / W = 5 n #5 n n 5 L5 r 5 n D5 / 0X= W 5 n n n 5 D5 5 5 5 5 = r 5 r 5 5 5 5 5 5 5 ?5 575 ?= = $+5 r n?5 5 5 n?5 n?5 5 5 5 5 +5 ?5 n n?5 5 Z9 n?5 r 5 = n O5 5 5 ?5 9 ?5 / 0X= W 5 n ?5 / W = 5 = n?5 5 5 r O5 5 021 ?5 9 5 n?5 5 r 5 :5 5 r 5 n?5 5 n?5 ?5 (9 5 = nnA5 nD5 (9 r 5 n ?5 n 5 5 + "%$'& + $ & + $'&J=Q n?5 n #5 #5 O5 5 7= n r X5 n n?5 n 5 ?5 / 0#= W 5 n 5 r 5 5 5 n ?5 / W = 5 = n '! '! '! + / ! r n?5 5 !n n n?5 n (9 5 r 5 nI5 ?5 X9 = n?5 5 5 r n 5 X5 9 X5 O5 5 D5 r n 5 r 5 = nn 5 n 9 nD5 n (9 r 5 n #5 O5 5 n 5#5 5 + "%$'& + $ & + $'&J= n?5 9 5 5 (9 ?5 n 5 5 5 #5 n?5 5 5 n5 5 r 9 5 ) 5 = n?5 5 5 5 r 5 L575 n?5 n (9 D5 nD5 5 5 5 5 nD5 n (9 ?5 n?5 ?5 5 5 r 5 5 5 n?5 5 9 5 5 (9X=A nD5 5 5 O5 r 5 ?5 r 5X=

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n 0 2 r 0 3 r 0 4 r 0 5 r 0 6 r 0 7 r 0 8 r 0 9 r 0 9 5 r 1 r 1 0 5 r 1 1 r 1 1 5 r 1 2 r 1 2 5 r o p e n i n g a n g l e r 0 2 r 0 3 r 0 4 r 0 5 r 0 6 r 0 7 r 0 8 r R a t i o o f m u l t i p l i c i t i e s r 0 9 r 0 9 5 r 1 r 1 0 5 r 1 1 r 1 1 5 r 1 2 r 1 2 5 r N J e t 0 4 / N J e t 1 0 r N J e t 0 7 / N J e t 1 0 r 0 2 r 0 3 r 0 4 r 0 5 r 0 6 r 0 7 r 0 8 r 0 9 r 0 9 5 r 1 r 1 0 5 r 1 1 r 1 1 5 r 1 2 r 1 2 5 r 0 2 r 0 3 r 0 4 r 0 5 r 0 6 r 0 7 r 0 8 r 0 9 r 0 9 5 r 1 r 1 0 5 r 1 1 r 1 1 5 r 1 2 r 1 2 5 r r N J e t 0 4 / N J e t 1 0 r N J e t 0 7 / N J e t 1 0 r N J e t 0 4 / N J e t 1 0 r N J e t 0 7 / N J e t 1 0 r N J e t 0 4 / N J e t 1 0 r N J e t 0 7 / N J e t 1 0 r o p e n i n g a n g l e rR a t i o o f m u l t i p l i c i t i e s ro p e n i n g a n g l e rR a t i o o f m u l t i p l i c i t i e s ro p e n i n g a n g l e rR a t i o o f m u l t i p l i c i t i e s rM C j e t d i r e c t i o n G l u o n j e t Q F L j e t d i r e c t i o n G l u o n j e t M C j e t d i r e c t i o n Q u a r k j e t Q F L j e t d i r e c t i o n Q u a r k j e t M a s s b i n 1 M a s s b i n 1 M a s s b i n 1 M a s s b i n 1 5 5 5 5 n #5 5 n 5 r 5 L575 5 5 5 n 5 5 5 ?5 5 7= n?5 n (9 r + $'& n + $ & + "%$'& + $ & r 5 5 5 5 nD5 O5 5 021 =EE5 5 r ?5 r 9 5 nD5 ?5 5 n?5 5 5 5 5 5 =L) r 0 5 5 5 = n?5 X5 5 (9 nD5 5 5 ?5 X9 5 n Y = P5 5 5 5 n?5 5 5 5 r L5 5 n?5 )H ?5!X) ; 9 n?5 5 5 ?5 X9 n?5 5 5 ?5 = ?5 r n 9 5 OS !' nn n?5 r 5 5 ?5 X9 5 n?5 5 n#5 r ?5 5 ?5 r 5X=, 5 5 n n nD5 5 5 ?5 X9 5 r n?5 5 5 5 n 5 5 5 5X5 5 5 5 5 5 n ?5 = n?5 n 5 X5 5 n 5 n?5 5 9 5 5 (9#=, 5 5 5 #5 nD5 5 5 ?5 X9 5 n?5 nD5 5 5 9 5 5 5 nD5 9 7= n?5 75 n 5 (9 V Y n?5 n 5 5 n?5 r / = n?5 5 nD5 5 5 5 9 5 5 n?5 5 45 ?5 X9 5 5 5 = E5X5 r 5 L575 r = nX5 n?5 0 W 5 5 ?5 X9 5 r 5 $ 5 5 5 ?5 X9 5 r 9 L5 nn?5 D5 5

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0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 9 5 1 1 0 5 1 1 1 1 5 1 2 1 2 5 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 9 5 1 1 0 5 1 1 1 1 5 1 2 1 2 5 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 9 5 1 1 0 5 1 1 1 1 5 1 2 1 2 5 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 9 5 1 1 0 5 1 1 1 1 5 1 2 1 2 5 o p e n i n g a n g l eR a t i o o f m u l t i p l i c i t i e s N J e t 0 4 / N J e t 1 0 N J e t 0 7 / N J e t 1 0 N J e t 0 4 / N J e t 1 0 N J e t 0 7 / N J e t 1 0 N J e t 0 4 / N J e t 1 0 N J e t 0 7 / N J e t 1 0 N J e t 0 4 / N J e t 1 0 N J e t 0 7 / N J e t 1 0 o p e n i n g a n g l eR a t i o o f m u l t i p l i c i t i e so p e n i n g a n g l eR a t i o o f m u l t i p l i c i t i e so p e n i n g a n g l eR a t i o o f m u l t i p l i c i t i e sM C j e t d i r e c t i o n G l u o n j e t Q F L j e t d i r e c t i o n G l u o n j e t M C j e t d i r e c t i o n Q u a r k j e t Q F L j e t d i r e c t i o n Q u a r k j e t M a s s b i n 2 M a s s b i n 2 M a s s b i n 2 M a s s b i n 2 5 Y 5 5 5 n #5 5 n 5 r 5 L575 5 5 5 n 5 5 5 ?5 5 7= n?5 n (9 r + $'& n + $ & + "%$'& + $ & r 5 5 5 5 nD5 O5 5 021 =EE5 5 r ?5 r 9 5 nD5 ?5 5 n?5 5 5 5 5 5 =L) r V 5 5 5 = M e a n r R M S r 0 7 1 2 7 E 0 1 r 0 5 4 5 7 E 0 1 r M e a n r R M S r 0 6 1 9 4 E 0 1 r 0 5 0 7 8 E 0 1 r M e a n r R M S r 0 7 2 7 7 E 0 1 r 0 5 9 4 9 E 0 1 r M e a n r R M S r 0 6 3 7 5 E 0 1 r 0 5 4 6 7 E 0 1 r M e a n r R M S r 0 8 6 6 6 E 0 1 r 0 7 5 7 8 E 0 1 r M e a n r R M S r 0 7 3 3 1 E 0 1 r 0 6 7 1 7 E 0 1 r 0 r 5 r 1 0 r 1 5 r 0 r 0 1 r 0 2 r 0 3 r 0 4 r 0 5 r 0 r 5 r 1 0 r 1 5 r 0 r 0 1 r 0 2 r 0 3 r 0 4 r 0 5 r 0 r 5 r 1 0 r 1 5 r 0 r 0 1 r 0 2 r 0 3 r 0 4 r 0 5 r 0 r 5 r 1 0 r 1 5 r 0 r 0 1 r 0 2 r 0 3 r 0 4 r 0 5 r 0 r 5 r 1 0 r 1 5 r 0 r 0 1 r 0 2 r 0 3 r 0 4 r 0 5 r 0 r 5 r 1 0 r 1 5 r 0 r 0 1 r 0 2 r 0 3 r 0 4 r 0 5 r A n g l e q b e t w e e n o u t g o i n g p a r t o n a n d r e c o n s t r u c t e d j e t r i n c e n t e r o f m a s s f r a m e1 / Nj e t d N / dqC o n e 0 4 Q u a r k j e t C o n e 0 4 G l u o n j e t C o n e 0 7 G l u o n j e t C o n e 1 0 G l u o n j e t C o n e 0 7 Q u a r k j e t C o n e 1 0 Q u a r k j e t q r a d r 5 5 r 5 L575 n?5 5 n?5 5 5 5 5 =

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X2 0 r 0 0 1 r 0 0 2 r 0 0 3 r 0 0 4 r 0 0 5 r 0 0 6 r 0 0 7 r 0 0 8 r 4 0 r 6 0 r 8 0 r 1 0 0 r 1 2 0 r 1 4 0 r 0 r 0 0 1 r 0 0 2 r 0 0 3 r 0 0 4 r 0 0 5 r 0 0 6 r 0 0 7 r 0 0 8 r 5 0 r 7 5 r 1 0 0 r 1 2 5 r 1 5 0 r 0 r 0 0 1 r 0 0 2 r 0 0 3 r 0 0 4 r 0 0 5 r 0 0 6 r 0 0 7 r 0 0 8 r 4 0 r 6 0 r 8 0 r 1 0 0 r 1 2 0 r 1 4 0 r 0 r 0 0 1 r 0 0 2 r 0 0 3 r 0 0 4 r 0 0 5 r 0 0 6 r 0 0 7 r 0 0 8 r 5 0 r 7 5 r 1 0 0 r 1 2 5 r 1 5 0 r G e V / c 2 G e V / c 21 / N e v d N / d M j j 1 / N e v d N / d M g jM C D i j e t B i n 1 M C D i j e t B i n 2 M C g j e t B i n 1 M C g j e t B i n 2 r M s m e a r = 8 1 1 G e V / c 2 M u n s m e a r = 7 9 8 G e V / c 2 M s m e a r = 1 0 4 8 G e V / c 2 M u n s m e a r = 1 0 2 2 G e V / c 2 M u n s m e a r = 7 9 1 G e V / c 2 M s m e a r = 8 1 1 G e V / c 2 M s m e a r = 1 0 4 8 G e V / c 2 M u n s m e a r = 1 0 2 1 G e V / c 2 M j j M g j 5 O5 : 5 ) 5 r 5 5 7= n?5 ?5 nn n n?5 D5 5 5#5 5 5 r =G n?5 n?5 D5 nn n?5 5 5 n r = ?545 D5 9#= nn 5 nD5 5 5 5 55X5 n r = n n?5 5 n 5 5 D5 r 5 X5 #5 5 5 #5 nD5 5X5 n?5 n n?5 5 5754 ?= = 5 n r n?5 5 5 r V 5 n nD5 5 5 5 5 ?5 =H nX5 n?5 n n?5 n (9 ?5 5 n?5 n n?5 5 ?5 X9 n n 5 5 5 n 5 n nD5 5 (9 nD5 5 :5 D5 9 5 r L5 ?5 D5 9 Z9 5 5 nD5 @=R8 r 5 5 n#5 r L5 nD5 5 9 5 5 (9 n n n5 5 r 9 n?5 ?5 5 n n?5 5 r ?5 r 9 9 n?5 5 5 5 5 5 5 r 5 n 5 L5#5 =A n?5r5 5 n?5 5 5 r 5 ?5 r 5 r n r =

PAGE 92

n >/ K(9?R&?4P ?W
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2 W 5 5 9 5 ) nn n?5 5 5#5 =C 5 5 n ) ?5 ?5 5 D5 n?5 5 5#5 r L5 nD5 5 n n r 5 nD5 5 5 5 n O5 n?5 5 ?5 X9 r 5 n X5 = n r n?5 H5 ?5 X9 ?5 M/ W = 5 n 9 D5 n?5 ?5 9 5 #5 n r n n 5 945 ?5 n O5 n (9 X5 #5D5 W = Y 5 6 5 ?5 / W = r r = nD5 5 n 5 r n?5 5 ?5 X9 ?5 5 n n 5 r 9 r 5 ?5 r 7= 5) n r n?5 n 5 ?5 X9 ?5 5 n 9 n r 575 ?= @2 = ?= @2 r :5 5 n n?5 r n 5 X5 9 n n X5 :5 n 5 n?55 ?5 n n n n n?5 ?5 9 5 #5 r n n?5 X5 r ?5 X5 = ?5 r n?5 :5 n r 55 5 5 5 5 5 5 n?5n 5 5 = 5 9 5 nn 5 r 5 :5 5 n?5 5 5 n 5 n?5 5 n n?5 5 n 5 n 9 nX5 =A n r L5 O5 #5 9 5 = 5 5 n 5 n?5 5 ?5 n?5 5 X5 n?5 5 / r576 / 576 575 ?= @2 = n n 5 n 5 r 9 X5 r :5 n?5 5 n?5 r 5 5 O5 5 n?5 5 5 n 5 n r 9 n = ?= n n?5 nn 5 5 n n?5 I)H& r 5 5 7= ?5 5 5 n 5X5 n +e WY -S r :5 r 5 #5 9 5 5 5 = nn 5 nX5 r ?5 5 n 5 ) 5 9 5 5 O5 5 5 n = 9 r :55 5n?5 9 5 5 (9 5 n n?5 ( 5 = nn 5 ?5 5 n?5 5 ) n X5 n n n 5 5 5 ?5 =" n?5 5 D5 5 5 5

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2D0 0 0 2 0 4 0 6 0 8 1 1 2 0 5 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 0 0 2 0 4 0 6 0 8 1 1 2 0 5 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 I s o l a t i o n I s o l a t i o n G e V G e V1 / N e v d N / d I S Om a s s b i n 8 2 G e V m a s s b i n 1 0 5 G e V D a t a r H e r w i g ( f a k e g ) r P y t h i a ( f a k e g ) D a t a r H e r w i g ( f a k e g ) r P y t h i a ( f a k e g ) I S O c u t I S O c u t 5 @2 5 ?5 X9 r n 5 5 ) 5 A5X5 7=: nD5 5) n r 5 5 r 5 n?5 5 n?5 5 D= W 576 9 5 r 9 X5 = 0 r 0 1 r 0 2 r 0 3 r 0 4 r 0 5 r 0 6 r 0 7 r 0 8 r 0 9 r 1 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r R e a l p h o t o n f r a c t i o nC D F P R E L I M I N A R Y I s o l a t i o n G e V 5 nD5 5 5 5 n 5 n?5 5 ?5 X9 ?5 n 5 5 r 5 n?5 n 5 n?5 5 ?5 X9 r 5 ) 5 r r 5 n 5 (9 r 5 n?5 X5 5 n =E n?5 5 5 5 5 5 5#5 r n r

PAGE 95

2 V F5 &Q9 n 5 X5 9 5 5 = 5 5 5 n?5 5 5 5 n?5F5 &Q9 n r 5 ?5 n?5( 5 5 =Q nD5 5 5 5 r 5 :5 5 5 n 5 r 5 9 5 5 (9 5 n n?5 ?5 O5 ?5 5 n?54 5 ) 5 ?5 n?545 n?5 ( 5 5 = n?5 5 5 r 5 = / K 4P ? 913N4H1ON\? R 5 ?5 $+5 2D= r nD5 n 5 5 5X5 r " r 5 5 5X5 r r 5 ?5 5 ?5 F5 &Q9 n 5 ) #5 ?5 %' nI& 5 )LEA rA)LEA # V r )LEA # D=P n?5 5 r D5 n Fr5 )LEA 5 X5 ?5 = n?5 X5 5 (9 9 0 r ?5 n 5 5 r 5) X5 ?5 &A 5 5 5 5 n 5 n?5 5 9 5 5 5 = >/ 47P ? 913N4H1ON\?RYN+4 : @\1N 7@+NPQN1JG: ? 3R 89?FG?4H1R n?5 n 5 n?5 5 5 5 r 9 n?5 n r 5 5 n?5 r J' ?5 575 $@5 2D= Y ?=2 = n?5 nD5 n ?5 n?54 ?= 2 5 n 9 n?5 n 5 5 5 = nn nD5 n?5 5 5 X5 5 r r r H5 5 n?5 n nD5 n 5 5 5 = n?5 5 n = n r n?5 nD5 ?5 5 5 5 n 5 ?5 n?5 5 %1 & n?5 ?5 n?5 ?=2 =E 5 5 ?5 r n?5 5 %' 5 5 5 n ?5 n?5 9 5 5 (9 5 n nD5 5 5 5 5 5 7= n?5 5 5 n n 5 5 ?5 ?5 5 9 5 n?5 5 r n ?=Q ?=2 n n n r 5 5X5 n 9 D5 X5 5 = n?5 n D= W 5 n 5 n?5 5 5 5 n n 0 V = W n?5 5 n 9 X5 5 #5 5 5 #5 5 n?5

PAGE 96

2 5 #5 5 5 ?5 r 5 5 5 =E 5 n 5 n?5 9 5 ?5 n 5 n r L5 5 O5 n?5 5 5 5 n n 5 ?5 n ?= W n n n n 575 5 5 n n?5 n 5 r 5 :5 5 #5 5 = n?5 r 5 r 9 5 n 5 5 n nD5 5 5 9 5 5 (9 (9 ?5 n Y '(2 n?5 5 5 5 (9 5 = n?5 5 n 5 r n?5 5 n #5 5 5 (9 9 5 n n?5 5 5 5 n?5 r / n7= nD5/ #5 5 5 n?5 #5 5 r n?5 5 r 5 5H) 5 5 = 5 5 nX5 9 5 5n?5 5 5 (9 r 5 5 n?5 5 5 (9 D5 D= Y = n?5 5 5 n 5 5 n?5 5 5 #5 5 ?5 9 @' ),+ .r= n?5 5 5 5 r 5 5 ) 5 7= n?5 5 9 5 5 (9 5 #5 9 5 r 5L5 nD5 5 5 n (9 ?5 Y = n?5 r 5 5 r n (9 5 D5 ?5 5 D5 n?5 5 5 9 ?5 5 n ?5 = n?5 n (9 W = Y#Y 5 ?5 #021 / W = 5 5X5 W = r n 5 5X5 r n r 5 5 9 ?5 5 n n 5 r #' E5 5 r 5 5 ?5 r 5 $@5 2D= Y =: 5 5 n?5 9 5 5 (9 ?5 5 5 r r r :5 5 O5 n?5 5 5 5 n n?5 X5 #5 5 5 5 5 9 ?5 n (9#= 5 D5 5 5 rn?5 5 (9 n 5 5 )L) ?5 5 9#= nn 5 n?5 5 5 n 5 5 = n?5 ?5 5 n5 D= 5X5 n 5 5 ?5 X9 $ & / ?0 576 @= Y !#"%$'& / Y#V = Y 576 r n 5 5 5 021/ W = =R 5 n 5 n?59 5 5 5 )L) 5 n?5 r :5 5 O5 n?5 5 5 5 n )L) 5 n r n -S"+Y S --Y +, )L) 5 5

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2n 5 5 5%= r W r W = n?5 5 r 5 ?5 r 5X= nD5 5 n #5 5 n 5 5 r n?5 5 5 5 n?5 5 r D5 n -S"Y +, S --Y +, 5 n ?5 r 5 n?5 5 9 5 5 (9 rV = nD5 5 9 5 5 (9 n n?5 5 r 5 5 n?5 ?5 r 5 n?5 5 = 55 5 nD5 F5 ?= n?5 5 r 5 n rV r :5 5 nX5 9 5 n 5 nD5 5 5 (9 r 5 5 5 5 n%=

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2 r 5 V n?5 9 9 5 5 5 n?5 5 5 5 r r /nn r ?5 n?5 O5 5 021/ W 1nD= n?5 5 5 ?5 = o \ n 0'`Wn $nZaX 798n:;ng1U> ABC 798n:;ngTmFW m&ABC .$n $a. )rZ$a. &. & &?% g b b & &?% g b b .$n $a. $ b 88 8 "!# K gTF $D<@W @Xm @W @un D<@W @U D<@W @G @Wa>U D@W @Xn  %& a(' V)3W W)$*% +),.-/0+1-&2 z G l3 .n.1' 4 o6575 Q o6585 o1o9585 o 4 585 o1Q:585 @Wa>U D<@W @un @W @Xn D<@W 4U @Wa>5 D@Wa>U  %& y Z (' @E>"Fm ;< =?> H < =?> ; @ =?> H =?> BA @W>"m [ .Z$.0C'j|.r^ D<@W @un @W>`@ D<@W @ l @W @F D@W @4 @W @XF {W Vn $ƒ W .$n $a.1')D.E R R *a @W @ @W @> @W @ D<@W @> @W @ @W @ |r%.nF' 4 z .r$ $. .(' z .HG gB@W nn'jn G gB@W U@W nu3>W @ 'j@W_Fm @W>> @W @F @W 4> @Wa>@ @W @4 {r dƒZ-ZkWI' J KLJ l(M s J KLJ 4 M s D<@W F5 D<@W F4 @W @F D<@W 4@ D@W_Fn @W @U J ON J l J ON J U D<@W>`@ D<@W @5 @W @> D<@W>> D@Wa>> @W @XF $VZa*% D W .$`WI')4 z D5 @W>`@ @W @ @W_F> @Wa>`F @W @ P I t ZƒRQ S .$`WI')4 z D`5 @W @F @W_FZ5 @W_F> @W @XF .n$$aZ$ y UT %ƒWI' ju$-Z.( )n .r‚W rn .&* W .T $aa .T $aa @W @Xn D<@W @U @W @4 D<@W>> @W @ l D@W @m o \ z 2 z .VBV W .$n $a. D.E R D.E R @W @ D.E R D.E R @W @> BW a .nW X].$ara]$ Y .$`W D<@W @ l D<@W @4 @W @ D<@W @G D@W @m @W @ X]n]ara]$ Y .nW @W @m @W @4 @W @ @W @G @W @m @W @ x |4@@O4hC n T WI' 4 z .n$ n. .$n $a. D<@W @5 D<@W @U D<@W @> D<@W>> D@W @4 D@W @> |n $a.1' 4 z .r$ $.1' $ .'n $`' S 'jWn4 z 'j @W @G @W @Xm @W @ @Wa>> @W @ l @W @ n n. .(%(‚W 'j-' z 2 91U R F&CBZ I% D<@W @4 @W @ D<@W @> D<@W @Xm @W @4 D@W @F z 2 91U[4\CB|Z r% z 2 91U R UCBZ I% @W @> D<@W @XF @W @> @Wa>@ D@W @ l @W @Xm n n. .( z9Q /]nZ$ D<@W @Xm @W @un D<@W @Xm D<@W @Xm @W @Xn D@W @ZU $` .$.' ^d UT D< Z]nn% @W @ l D<@W>`@ @W @ l @W @G D@Wa>4 @W @5 B\( z9Q / _iS` I -)$ @W @> D<@W @XF @W @F @W @> D@W @> @W @> rj.u PbaLES` I -)$ D<@W @XF @W @XF D<@W @XF @W @ @W @> @W @ D .$n $a.1' IV$ yjZ9 Sn(%|.( (I3rj€W |Z r%c Q Xa @W @> D<@W @Xm @W @F D<@W @ l @W @F D@W @F

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2r r 5 n?5 9 9 5 5 5 n?5 5 5 5 r r /nn r ?5 n?5 O5 5 021/ W 1 V 2D= n?5 5 5 ?5 = o \ n 0'`Wn $nZaX 7 8n:; g1U> ABC 7 8n:; gTmFW m&ABC .$n $a. )rZ$a. &. & &?% g b b & &?% g b b .$n $a. $ b 88 8 "!# K gTF $D<@W @4 @W @Xm D<@W @4 D<@W @ l @W @G D@W @m  %& a(' V)3W W)$*% +),.-/0+1-&2 z G l3 .n.1' 4 o6575 Q o6585 o1o9585 o 4 585 o1Q:585 @Wa>U D<@W @un @W @Xn D<@W 4XF @Wa>`m D@Wa>U  %& y Z (' @E>"Fm ;< = > H < = > ; @ = > H = > BA @W>"m [ .Z$.0C'j|.r^ D<@W @un @W>> D<@W @un @W @ D@W @> @W @> {W Vn $ƒ W .$n $a.1')D.E R R *a @W @ @W @> @W @ @W @> @W @> @W @ |r%.nF' 4 z .r$ $. .(' z .HG gB@W nn'jn G gB@W U@W nu3>W @ 'j@W 4F @W>"m @W @4 @W U> @Wa>`m @W @Xm {r dƒZ-ZkWI' J KLJ l(M s J KLJ 4 M s D<@W Fm D<@W>`G @W @> D<@W FXn D@W_FZ4 @W @4 J ON J l J ON J U D<@W @un D<@W @ l @W @> D<@W @5 D@W @5 @W @XF $VZa*% D W .$`WI')4 z D4 @W @G @W @ @Wa> l @Wa>@ @W @ P I t ZƒRQ S .$`WI')4 z D l D<@W @> @W_F)U @Wa>5 D@W @> .n$$aZ$ y UT %ƒWI' ju$-Z.( )n .r‚W rn .&* W .T $aa .T $aa D<@W @> D<@W @XF @W @ D<@W @4 D@W @> @W @ o \ z 2 z .VBV W .$n $a. D.E R D.E R @W @ D.E R D.E R @W @> BW a .nW X].$ara]$ Y .$`W D<@W @U D<@W @4 @W @ D<@W @un D@W @ZU @W @ X]n]ara]$ Y .nW @W @m @W @4 @W @ @W @Xn @W @m @W @ x |4@@O4hC n T WI' 4 z .n$ n. .$n $a. D<@W @Xm D<@W @4 @W @ D<@W @un D@W @F @W @ |n $a.1' 4 z .r$ $.1' $ .'n $`' S 'jWn4 z 'j @Wa>> @W @ l D<@W @> @Wa>4 @W @Xn @W @ n n. .(%(‚W 'j-' z 2 91U R F&CBZ I% D<@W @XF @W @ D<@W @> D<@W @U @W @F D@W @F z 2 91U[4\CB|Z r% z 2 91U R UCBZ I% @W @> D<@W @> @W @> @W @ l D@W @ZU @W @Xm n n. .( z9Q /]nZ$ D<@W @4 @W @Xm D<@W @U D<@W @U @W @ l D@W @4 $` .$.' ^d UT D< Z]nn% @W @m D<@W @un @W @m @W @Xn D@Wa>@ @W @un B\( z9Q / _iS` I -)$ @W @> D<@W @XF @W @> @W @ @W @ @W @ rj.u P a ES` I -)$ D<@W @> @W @> D<@W @> D<@W @> @W @> @W @ D .$n $a.1' IV$ yjZ9 Sn(%|.( (I3rj€W |Z r%c Q Xa @W @F D<@W @Xm @W @4 D<@W @ l @W @4 D@W @F r 5 5 n n?5 n 5 5 5 9 5 5 5 7= 5 5 r 5 C)H& L5 n 5 r 9 )H&A Fr= )H ?5X=  %( [‚ABCT^ o B\( z9Q /]-)$ ^d UT )$$na% _iS` I P a E#` I U> @W_nmYB@W @ZU @W n)5uYB@W @ZU @W_nZ@XYB@W @ZU @W n)4XYB@W @U @W nZmYB@W @U mFW_m @W G@XYB@W @Xn @W GZUYB@W @Xn @W 5XmYB@W @Xn @W G@XYB@W @un @W G@XYB@W @un

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)HFr&EAU0 W $D)H$?$@nCIrA$Dr@$ n)n 5 r n?5 5 5 5 5 n?5 5 5 5 r 5 :5 5 5 n L5 5 r ?5 n D9 5 5 5 5 5 n?5 nD5 9 r n?5 5 5 n 5 5 5 5 5 ) 5 = /+. : 7@1ON`@N+PQN1nJG0 r ?5 n 575 n n?5 5 5 5 nR5 D5 9 5 = n 5 n n 9 r r r 5 5 r n 9 5 5 5 5 9 5 5 = 5 E5 D5 9 $ & / ?0 5 6 O5 5 021 / W = V 2 W = / 0#0#= Y 5 6 0D= V 576 r :5r X/ %0D= V 5 6 0#0X= Y 576 / W = 0 V W = W#V W = W#Y 9 n n n V r 5 5X5 = ?=L0 W V n nD5 5 5 n X5 5 n 5 5 = n I D=P0 W V 5 n?5 r )H r ?5 r 9 5 5 #nrN5 5 nr V n n?5 9 5 5 5 5 n?5 n?5 5 5 $ 5 V W 5 6 r W =H nD5 r 5 2X2

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2 Q G e V 1 0 1 0 0 r = Ng/ Nq 0 1 2 3 C a p e l l a e t a l 2 0 0 0 L u p i a & O c h s 1 9 9 8 C a t a n i e t a l 1 9 9 2 G a f f n e y & M u e l l e r 1 9 8 5 C L E O O P A L C D F E j e t = 5 3 G e V C D F E j e t = 4 1 G e V N L L A l i m i t r = C A / C F = 2 2 5 5 0 W >0 n?5 n X5 5 n 5 5 5 n ?5 r n n / !#"%$'& 021 )H / 1 / V $ & D=A)H 5 5 r ?5 ?5 75 021/ W = V 2 r W = r W = = n?5 nr #5 r V r VXY r V r V 5 5 $ / V W 576 r W = n?5 9 ?5 r n 9 n?5 n?5 n#5 r n / / QXn r 5 O5 #5 9#= 5 ?5 5 ?5 =, n?5 n r 5 nD5 5 (9 n?5 #5 = ?= 0 W V r ?5 5 5 n n?5 n 5 5 n?5 5 5 5 n 5 r5 ?5 X9 O5 5 / !#"%$'& 021 = nD5 D5 D5 O5 ?5 5 r r Y r Y 5 5 )HA Y 576 n n?5r r r n r 5 5 5 5 n )H 5 = n n r n:5X5 r 5 r 5 5 n?5 5 5 5 5 ?5 #5 9 5 5 5 D5 9 5 7= ?= 0 W n nD5 n )H 5 n (9 5 n 5 5 ?5 ?5 5 ?5 5 5 & r YXY r Y =L nD5 #5 5 ?5 X9 5 n n?5 5 r n 5 O5 n 5 r n 5 n = ?5 5 5 n )H & 5 5 5 5 = 5 n?5 5 n 9 n n?5 5 A 54) 5 #5 #5 ?5 r L5 5Fr5 Y = &Q9 n D= 0#0 Y n,Q D5 5 n =

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W 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 1 0 1 0 2 Q G e V rC h a r g e d p a r t i c l e m u l t i p l i c i t y 2 Ng a n d 2 Nq u d sq u a r k j e t s : O P A L D E L P H I L E P 1 & S L D M A R K 2 & T P C C D F q u a r k j e t s 3 N L L A f i t ( C D F r d a t a ) q u a r k s G l u o n j e t s : O P A L C L E O C D F g l u o n j e t s 3 N L L A f i t ( C D F r d a t a ) g l u o n s 5 0 W V #5 X5 n #5 5 n 5 5 5 n ?5 r n n / !#"%$'& 021 )H / 1 / V $ & D= n?5 5 n n?5 5 5 5 rB)H 5 n ?5 n #5 5 ) + ?5 9 5 5 r 9 ?=A n?5 r )H 5 r ?5 r 9 n?5 5 5 n "5 5 E5%= r V n n?5 9 5 5 5 5 n?5 n?5 5 5 $ 5 V W 576 r W = nD5 n n?5 r 5 n?5 5 (9 n?5 #5 = 0 5 1 0 1 5 2 0 2 5 3 0 5 6 7 8 9 1 0 2 0 3 0 4 0 5 0 C D F p r e l i m i n a r y Q G e VC h a r g e d p a r t i c l e m u l t i p l i c i t y i n g l u o n j e t s 2 Ng O P A L E u r P h y s J C 2 3 ( 2 0 0 2 ) 5 9 7 O P A L P h y s R e v D 6 9 ( 2 0 0 4 ) 0 3 2 0 0 2 C D F r 3 N L L A f i t P h y s L e t t B 4 5 9 ( 1 9 9 9 ) 3 4 1 5r0 W ) n )H 5 n #5 5 (9 5 n 5 5 ?5 ?5 O5 D5 5 5 &O=? n?5 n?5 5 #5 n nD5 Xn r r n ?5 ?5 O5 ?5 5 (9 5 nr YXW r Y =

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D0 r :5 #5 5 n n?5 O5 5 5 5 5X5 5 n n 5 n 5 5#5 = 5 5 n?5 D5 5 5 5 #5 5 5 5 r :5 5 n?5 n #5 5n 5 5 nD5 5 5 D5 5 n?5 n 5X5 n?5 X5 ?5 r 5 5 n?5 ?5 5 n = n?5 5 5 5 n (9 5 nD5 5 (9 5 r ,!T(' 5 r 5 n 5 5 (9 9 0#1 Y =B n?5 5 5 r 5 ) @5 5 nD5 nX5 (9 5 = n 5 5 nD5 L5 5 5 r n?5n 5 5 n?5 0 ?5 5 5 5 #5 9 r V D5 5 n 5 H5 #5 9 r n?5 5 r 5 = D= D=D=B ?5 9 =nD= 5E) r L5 r 5 r X5 X/ 0#= n?5 r nD5 ) #5 = D= 5 / /"0 0 n " n %0 W = 0 n?5 5 n 5 5 5 n 5 r 55 5 9 n?5 5 rn?5 r D5 5 5 5 5 5 r 50 W >0#= nn r :5 5 #5 n 7= r&Q9 n 5 n n?5 n (9 5 5 Fr5 0#= @= ,0#= ?= W r?5 O5 nD5 ?5 5 =$@5 r n?5 5) 5 n?5 $ & 021 ?=B n r n?5 5 5 5 r 5 L575 5 ) n 5 5 5 L5 n n?5 5 5 nn 5 5 5 r n?5 n (9 P 5,) 5 n r W NV & nn?5 n n n?5 5 5r ?=D0 W =Q 9 rZ 5) 5 n?5 r / r r 5 n?5 #540#1 V C0X1 5 5 ?= 0 W Y n n n L5 r 9 n?5 5 V & n n?5 5 5 n?5 r 0#1 Y "0#1 +=

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V r 5 0 W O0 5 ) 5 n X5 5 5 D5 5 5 n?5 r r / n 5 5 n#5 9X=A 5 ?5 n #5 5 ) + ?5 9 = 4 z %€W 798n:<; U@W l ABC mFW UVABC .' } @W_FZ5?@W 4 l @W Uun n @W_FZ5&n @W 4 l n @W Un gB7 8n:; } >>W UVABC >UƒW l ABC >GW> ABC >UW n&ABC >5W GrABC FZUW l ABC mW @mXYB@W @4 l W @ZUYB@W @F nuW_FZ@uYB@W @F mW GFYB@W @U nuW @mYB@W @Xm 5W FXnYB@W @4 |Z r% ?% UWa>GuYB@W @F UW n)5uYB@W @F mW UunYB@W @F UW nnYB@W @4 mW U@XYB@W @4 l W>`5XYB@W @U Tg b b >W_F>)YB@W @> >W_FnYB@W @> >W 4FXYB@W @> >W_FmYB@W @> >W 4FYB@W @> >W 4UuYB@W @> mWa>UYB@W @m l W_FnYB@W @4 nuW_m>)YB@W @F l Wa>>"YB@W @5 nuW 44XYB@W @ l 5W l mYB@W @ l Q Xa ?% UW_F l YB@W @ZU UW G4uYB@W @ l mW l FXYB@W @ l UW 5mYB@W @U mW_mZ5XYB@W @4 l W 4XFYB@W @un Tg b b) >W_F>)YB@W @> >W_FZGuYB@W @> >W 4ZUYB@W @> >W_FZ5XYB@W @> >W 4ZUuYB@W @> >W 45XYB@W @> 0 r 5 r 1 0 r 1 5 r 2 0 r 2 5 r 3 0 r 3 5 r 4 0 r 4 5 r 5 0 r 1 0 r 1 0 r 2 r Q G e VC h a r g e d p a r t i c l e m u l t i p l i c i t y 2 Ng a n d 2 Nq C D F P r e l i m i n a r y Q u a r k j e t s : G l u o n j e t s : H e r w i g 5 6 P y t h i a 6 1 1 5 H e r w i g 5 6 P y t h i a 6 1 1 5 C D F d a t a C D F d a t a 3 N L L A f i t s E u r P h y s J C 2 3 ( 2 0 0 2 ) 5 9 7: g l u o n j e t su d sq u a r k j e t s e + e d a t a e + e d a t a (u d sq u a r k s ) 5 0 W ) n : 5 ') 5 #5 X5 n X5 %' 5 n 5 5 = n?5 nD5 9 #5 5 #nr r r V ,5 O5 n 5 = nD5 r 5 5 5 X5 n?5 r D5 5%= r Y =H nn n 5 n?5 9 X5 n n 5 9 r 9 X5 5 5 = n?5 5 ?5 9 D5 D5 O5 ?5 5 5 5 =

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M e a s u r e m e n t s o r f t h e r a r t i o o f r c h a r g e d r p a r t i r c l e r m u l r t i p l i c r i t i e s r i n G r l u r o n a n r d Q r u a r k r J e t s r Q r G e r V r 1 0 r 1 0 0 r r = N rg r/ N rq r 0 r 1 r 2 r 3 r L L A & N L L A r = C A / C F = 2 2 5 C D F P r e l i m i n a r y H e r w i g 5 6 C L E O O P A L C D F E j e t = 5 3 G e V C D F E j e t = 4 1 G e V P y t h i a 6 1 1 5 C a p e l l a e t a l 2 0 0 0 L u p i a & O c h s 1 9 9 8 C a t a n i e t a l 1 9 9 2 G a f f n e y & M u e l l e r 1 9 8 5 5 0 W Y ) n E 5 ') 5 nD5 n #5 5 n 5 5 =Q nD5 9 X5 5 5 5 5 nD5 5 D= 0 W O0#= nD5 5 ?5 9 ?5 ?5 O5 ?5 5 5 5 = .8/ :=<"FG?4H1 7F N+R19N 81N<"4 <"B !#"8359"?6 KM3U9O1N+PQ@\?RYN+4 @<"4 346 8359 nH?Q1OR / #5 X5 n 5 r :5 r D5 n?5 5 n r +' r n r n?5 5 / n n 5 $ 5 r n#5 5 5 r L5 n?5 r/ n r r n r r r $ & / ?0 576 r021/ W = = n?5 5 n ?5 n?5 5 rD5 5 n n?5 5 +' 5 n X5 5 r ?5 r n / W 1 Y n 5 :5 5 5 5 5 n r = nD5 5 5 5 5 r 5 0 W V r 0 W r 0 W 5 5 5 7=H0 W 0 W D= n 5 5 ?5 nD5 5 n r r r n #5 5 5 = n?5 n 5 5 r r n n X/ n / V = V#Y n?5 9 n r 5 5 45 @' 5 5 = F L5 #5 r nn 5 5 r 5 5 n?5 5 #5 5 5 5 ?5 5%r V = n?5 5 5 n 5 5 r n?5 5 5 = n r n?5 9 r 5 5 5 n $ &(= n?5 nX5

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n 0 2 5 0 1 / 4 r A 0 r 1 7 7 5 r 0 1 2 1 6 r 0 1 4 2 4 / 5 r A 0 r 1 7 6 9 r 0 7 2 8 9 E 0 1 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 3 5 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r 0 r 0 5 r 1 r 1 5 r 2 r 2 5 r 3 r 3 5 r 0 r 1 r 2 r 3 r 4 r 5 r 6 r C D F p r e l i m i n a r yr ( x ) = ( 1 / Nj e t d n g / d x ) / ( 1 / Nj e t d n q / d x )x = l n ( 1 / x ) E j e t = 4 1 G e V r q c = 0 4 7 r a d r Q = 1 9 2 G e V E j e t = 4 0 1 G e V r Q = 8 0 2 G e V O P A L 50 W n?5 5 n r r n?5 5 "/ %0 P/ '! $ & r n #5 5 5 =) n )H & D= 5 n?5 5 5 n n #5 #5 5 n 5 #5 n n 5 =: 5 r nD579 9 575 n?5 n X5 n?5 = n rn?5 5 5 5 r & r n ?5 O5 n?5,5 D5 9 5 n n n?5 9 ?5 & n / V = V#Y = D5 575 ?=N0 W rn?5 n r 9 r 5 (9 5 ?5 #5 5 r 9 5 5 #5 5 = n?5 O5 5 & 0#=32 n n r n:5X5 r r 5 n?5 9 ?5 n / V = V#Y =Q n 5 5 5 n nD5 &O r Y 5 O5 5 r 5 X5 n?5 5 r 5 n n n?5 5 & 40#=32D= #5 ?5 5 5 n nD5 n?5 n 5 5 5 5 r 5 :5 5 5 ) r :5 5 #5 5 r n #5

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Y 5 = r 5I0 W V ?= 0 W r ?5 575 n Fr5 Y = 5 n#5 5 5 5 5 5 5 5 5 n n 5r&Q9 n @= 0#0 Y 5 5 n n n?5 r 5 n #5 5 n?5 5 nD5 O5 n r r V = Y D= Y = n?5 5 5 5 5L r 5 0 W R ?= 0 W @2 r r nPF5 P&Q9 n n 5 5 n r 9 r n &Q9 n 5 n 9 nn?5 r 5 5 n 0#= Y D= Y n,Fr5 D= n?5 5 5 5 n?5 5 r 5 n 5 r n r r n?5 5 5 5 5 n?5 =Q n r r n Fr5 &Q9 n #5 9 ?5 r 5 n?5 r r 5 :5 n n?5 5 5 #5 5 5 5 5 r 5 0 W ?= 0 W =P n 5 5 5 n n?5 n O5 HF5 (' r 5 n r 5 5 5 5 r 5 n?5 5 5 #5 n?5 n?5 5 O5 n &Q9 n D=

PAGE 109

0 0 5 1 1 5 2 2 5 3 3 5 0 1 2 3 4 5 6 x = l n ( 1 / x ) 1 / Ng j e t d n / dxG l u o n j e t s :E j e t = 4 1 G e V r q c = 0 4 7 r a d r Q = 1 9 2 G e V C D F p r e l i m i n a r y P y t h i a 6 1 1 5 H e r w i g 5 6 5r0 W #5 5 n r r n r n?5 5 / r n #5 5 5 = n?5 5 5 5 5 5 $ & / ?0 5 6 n?5 O5 5021 / W =r =Q n?5 5 n?5 r #5 n?5 #5 #5 n X5 5 n (9 5 =P nD5 5 r 5 9 5 5 5 ?5 5 = r 5 0 W V 5 5 ?5 n?5 5 r r n r r n #5 %' 5 5 = n?5 5 5 5 5 5 !#"%$'& / ?0576 n?5 O5 5 021/ W = @= / n Fr5 &Q9 n W = VXY W = W#V W = 2 Y W = W 0 W = WXWZVXW W = W#W#WZY W = W#WZY#V W = W#W#W W = Y W = 0 Y W = V W = WZY W = W n W = W#W V W = W 2D0 2 W = W#W Y 0#= VXY W = W = 0 W = WZY W = Y V W = W#W 2 W = rn W = W#W 0#= Y 0#=r W = 0 W W = 0 0#= YXW W = W 0 0#= V W = W 0 V = VXY V = V W = 0 W W = 0 2 V = ?0#0 W = W 0 V =D0 W = W 0 V = Y V = 2X2 W = W W = 0 V =D0 W = W 0 D= 0 W = WZV#V D= VXY V = 2n W = W W = 0 V =32rn W = W 0 D= 0 W = WZV#V D= Y V = 0 W = 0 W W = 0 2 V = 0#0 W = W 0 V =D0 W = W 0 ?= VXY 0#=@0 W = 0#0 W = V#V 0#= 0Z2 W = W 0 V 0#= V n W = W 0 ?= Y W = W = 0 W = 0 W = Y#Y W = W#W 2 W = Y#V#Y W = W#W

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r 0 0 5 1 1 5 2 2 5 3 3 5 0 1 2 3 4 5 6 x = l n ( 1 / x ) 1 / Nq j e t d n / dxQ u a r k j e t s :rE j e t = 4 1 G e Vr qc = 0 4 7 r a d r Q = 1 9 2 G e V C D F p r e l i m i n a r y P y t h i a 6 1 1 5 H e r w i g 5 6 5r0 W @2 #5 5 n r r n r n?5 5 / r n #5 5 5 = nD5 5 5 5 5 5 !#"%$'& / ?04576 n?5 O5 5021 / W =r =Q n?5 5 n?5 r #5 n?5 #5 #5 n X5 5 n (9 5 7= n?5 5 r 5 9 5 5 5 ?5 5 = r 5 0 W 5 5 ?5 n?5 5 r r n r r n #5 %' 5 5 = n?5 5 5 5 5 5 $'& / D0576 n?5 O5 5 021/ W = @= / n Fr5 &Q9 n W = VXY W = W W = 2 Y W = W 0 W = W ?0 2 W = W#WZV W = WZYXW W = W#W Y W = Y W = V 2 W = V W = W W = V W = W#W 2 W = V n W = W#W 0#= VXY W = W W = 0 Y W = W W =32#2 W = W 0 W =32 W W = W 0 0#= Y 0#= W W = 0 V W = 0 Y 0#= Y#Y W = W 0 0#=#2n W = W 0 V = VXY 0#=n W = 0 V W = 0#0 0#=X2 W W = W 0 0#= W 2 W = WZV#V V = Y 0#= Y W = 0 V W = 0 V = WZV W = WZVXW V = 0 Y 2 W = WZV D= VXY 0#=n W = 0 V W = VXW 0#=nr W = WZVXW V = WZV W = WZV#V D= Y 0#= 0 W = 0#0 W = 0 Y 0#= ?0 W = W 0 0#= W = W 0 ?= VXY W = Y W = 0 V W = 0 W =n#2 W = W 0 V W = W W = W 0 ?= Y W = V W = 0 W = W W = V n W = W#W W = W 0 W = W#W

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#2 0 0 5 1 1 5 2 2 5 3 3 5 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 C D F p r e l i m i n a r yr ( x ) = ( 1 / Ng j e t d n / d x ) / ( 1 / Nq j e t d n / d x )x = l n ( 1 / x ) P y t h i a 6 1 1 5 H e r w i g 5 6 E j e t = 4 1 G e Vrq c = 0 4 7 r a drQ = 1 9 2 G e V 50 W n?5 5 n r r r n #5 5 5 = n?5 5 5 5 5 5 $ & / ?0 576 n?5 O5 5 021/ W = = n?5 5 r 5 9 5 5 5 ?5 5X= r 50 W 5 5 ?5 n?5 5 n r r r n #5 5 5 = nD5 5 5 5 5 5 #! $'& / D0576 n?5 O5 5 021 / W = @= / Fr5 &Q9 n W = V#Y W = Y#V W = r W = Y W = W Z2 W = W 0 V W = 0 W W = W 0 W = Y W = Y W = 0 Y W = VXY W = V n W = W 0#0 W = V X2 W = W 0 0#= V#Y 0#= W 2 W = 0 W = 0 W = V W = W 0 W =D0 W = W 0 Y 0#= Y 0#=#2 W = 0 W = V 2 0#= W W W = W 0 W = W = W 0 V = V#Y 0#= W = 0 W = V 0 0#= Y W = W 0 0#= V#Y W = W 0 V = Y 0#= W = 0 W = 0 V 0#= rn W = W 0 0#= r W = W 0 D= V#Y 0#= W = 0 W = 0 0#= X2 W = W 0 2 0#= Y Y W = WZVXW D= Y 0#=32#2 W = V#V W = 0 0#= r W = WZV 0 0#= W = WZV ?= V#Y 0#= Y W = V W = V 0#= Y#Y W = W W 0#=32 W W = W ?= Y 0#=D0 W = r W = V 0#= V W = W 0#= Y W = W

PAGE 112

)HFr&EAU0#0 $@ Kn)n)H$+ n=OQrErr<&r$D&:)LJ6A$ n?5 D9 5 5 nn n 5 n?5 r D5 D5 O5 ?5 5 5 5 5 5 5 n #5 5 n ?5 5 5 =R r 5 n 5 = n?5 5 5 5 5 =: X5 5 r 5 #5 n 5 5 +' n X5 9 n 5 =, 5 5 9 n?5 5 n #5 r 5 5 9 D5 D5 O5 ?5 5 5 5 n 5 5 5 :5 ?5 r ?5 5 ?5 X9 5 r YXW r Y = n 9 #5 D5 5 5 #5 n 5 5 5 r 5 5 9 5 #5 9 D5 D5 O5 ?5 9 n 7= n D5 O5 ?5 5 n 5#5 r 9 5 n?5 5 5 5 5 5 5 :5 #5 5 A5X5 = n?5 9 5 nD5 5 5 5 5 %' 5 r n?5 5 n?5 #5 X5 5 r5 ?5 5 5!#"%$'& / D0 Y 576 = n?5 n#5 5n 5 5 5 5 5 5 5 ?5 n 021/ W = V 2 r W = r W = r n?5 5 021 n?5 5 r 5 :5 5 n?5 5 n n?5 ?5 D5X= 5 5 5 n (9 r :5 5 5 5 nD5 5 @' 5 r 5 = n r :5 5 5 9 n n r #' r 5 n?5 5 5 5 5 5 5 7= nD5 5 r n?5 5 nD5 ?5 r #' r #5 5 9 B5X5 r5 5 r %' 5 5 5 =: n?5 r n?5 D5 9 5X5 n r 5 r 9 5 ?5 5 5 9 ?5 = n?5 5 n?5 9 n 5 5 nD5 nD5 5 5 r 5 5 5 O5 r n#5 )H 5 nD5 5 n?5 n

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0 W#W r 5 5 4 n r VXV H5 5 r V r V#Y r V r V r 5 5 5 n n?5 nZ9 n?5 & @'(F (9 r 0 2 =A n?5 5 5 n?5 5 5 5 n 5 5 ?5 X9 O5 5 / $'& 021 = nD5 #5 5 n ?5 0 V 5 6 V#Y 576 r n?5 5 5 n #5 5 n 5 5 r P/ 2 r 5 r 5 L575 N0#= Y S0X= @= / 0 5 6 r n?5 n r 5 X/ 0#= W = 0+=L nn n 575 5 n 5 5 5 r nX5 )H r 0#= 0#=32 r V r V#Y r V r V = #5 r n?5 5 5 5 5 r :5 n?5 r 5 5 9 ?5 r 5 r 9 5 5 An T5 5 E5%= r V n?5 5 $ / V W 5 6 r W =Q nn r n > )H 9 n?5 5 nD5 5 5 X5 9 5 r 5 ?5 5 5 E)H ?5 ?5 5 ?5 5 #r Y r W = n?5 5 5 n 5 5 5 r 5 5 n nD5 5O5 5 r YXW r Y r Y#Y r Y r Y = nn 5 9 ?5 @' 5 n?5nX5 (9 5 5 5 5 5 5 7= n?5 5 nX5 5 r r r n X5 5 5 n?5 r* r #5 n n?5 n (9 L5 ?5 #5 5 n n nD5 5 n 5 W 0#1 W = n?5 n?5 n r 5 n #5 X5 (9 5 7= n?5 5 5 r 5 :5 X5 n n?5 5 5 n?5 5 O5 & M0X1 2D=: n?5 5 r 5 n 5 5 r 9 & r Y = n?5 n?5 5 nD5 9 5 5 n 5 ) 5 r :5r n F5 Y = &Q9n D= 0#0 Y 5 5 n?5 5 5 9 L5 r r n?579 9 5 9 X5 5 5 n?5 n 5 5 r 9 n n W = n?5 9 n n?5 5 r 5 5 #5 n n?5 575 5 r 5 :5 5 5 ) nD5 5

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0 W 0 5 5 5 5 $ 5 n?5 O5 nD5 r =B 5 D5 5 5 5 D5 5 D5 ?5 5 nD5 n n 5 5 5 = n?5 5 5 5 5 5 nn 5 r n 5 5n r r 5 5 5 5 0#1 Y 0#15 #5 5 n#5 9 5 E5 ?5 5 '! $ & W YXW 5 6 5 5 W 1 021 GW 1 Y = nn 9 5 r (9 5 n?5 5 5 5 r 5 L575 5 5 )H 5 r Z9 5 5 5 n 5 f g ?5 9 5 = D=nr5d d c c f f c c n?5 5 n?5 n 5 n?5 r n Z9 5 = n?5n n (9 > V nD5L5 O5 9 5 5 5 5 5 5 5 5 5 r 5 :5 5 5 = n 5 5 n?5 #5 5 A5 ?5 5 n?5 5 n?5 5 5 r 5 ?5X=Q ?5 n?5 r 5 5 5 5 r r 5 5 5 D9 5D5 #5 5 r 5 = D=nr* r r r* r 5 = 5 5 = nD5 5 5 5 5 5 n n r 5 ?5 n?5 D9 n?5 n n?5 n (9 n r n#5 5 5 7= n?5 5 O5 5 5 5 ?5 nn5 5 5 7=F :5#5 r n?5 5 n G n 5 7= 5 X5 r n?5 5 5 n n?5 ?5 5 n?5 ?5 9 D9 nQ5 O5 5 5 5 %=B nD5 5 5 r nn 5 5 5 ?5 r 5 9 n #5 ?5 5 5 = r 9 r nD5 5 5 5 5 5 ?5 r 5 9 n?5 5 X5 n?5 ?5 5 5 ) 5 #5 #5 ?5 = nn r 5 5 5O5 9 n nX5 n?5 n Z9 5 5 5 n ?5 nD5 9 5 9 5 ) nn D5 r 5 5 ?5 X9 5 r5 5 r r>5 n 5 5 5 rO5 =

PAGE 115

rQn)HA$ r 0 !D=3L= n?5 rX= n r 8= = F 5 r 9 n?5:$ D5 r ) r #5 n & 54&n 9 rn 5 &nZ9 ) X9 r )Hr& r0n 5 5 = r V =? n r r 0 ) r rD&nZ9 =O 5 =>8 r 0 W %0#2 = r &=>8 r r V ) r r+& nZ9 = 5 = 8 r %0#2 = r =? n r r 0 ) r rD&nZ9 =O 5 =>8 r #2 %0#2 = r Y &=>8 r r V ) r r+& nZ9 = 5 = 8 r 0 W %0#2 = r :=+ r 5 r3)H ) r rZ&nZ9 =@5 O=D 5 = r V V %0 Y @$ = r n r W ) r r@&nZ9 7=O5 => 5 = r V V 0 Y r =D8 5 ?5 r n rD&nZ9 = E5O=@5 = r n Y %0 ?!D=3=D 5 F = = 5 rD =>E5O=On = & =O$ 5 5 r VXW %0r V = r 2 !D=3 = 8 X5 rO&n 9 7= E5O= r 0 Y 0 = r =3&B= 579 rL* T Q! +,U r"= = 8:5 r nr5 K %0r V = r 0 W =X5 '% r &nZ9 = 5 = r V 0 2 %0n # = :5 rX)HnE'(2n?0 'JEFE' ?0 V 0nn = r 0#0 = "=O 5 5 r 5 r>&nZ9 7= E5O=> 5 = r Y #2 %0n = r 0 V = !D= := 5 rB&nZ9 7=E5O= 5 = rA0nr 0r F =3 =& 75 r &nZ9 = 5 O=>5 = r 0nr 0n = r 0 =34= n r "= !D=$ 8=3 = 5 rr 5 r7 "!n !* ),r) r #5 n & 5&nZ9 rDn 5 H&nZ9 ) X9 r@)H& r 0D= r 0 & r &nZ9 7= E5O=> r 0 VXW#WZV = r 0 Y =3L=>$ n 5 r>&nZ9 =O5 O=>5 = r 0 VXW 0 Y = 4= F r &nZ9 = 5 => 5 = r 0 W 0r Y = r 0 = 8 D5 r $?$D ) r r>&nZ9 = 5 = 8 r V r%0rn r r 0#2 W =3&B=>8 r 5 r rM) r r+& nZ9 = E5O=> 5 = r>2n W 0n 0 WZV

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0 W )n =>8L5 #5 r &A*) r r+&nZ9 7= 5 =>8 r ?0 2 0rn "=>8 5 r !XG) r r+& nZ9 =O 5 =>8 r 0 V 0X2 W = r 0K = n 75 rQ6 = n75 r = ?5 5 $ =B 9 r ,* n+ e + 7 rX5 5 r 94!D=# nn 6 Q 5 5 r n ' KX5 5 r 0nD0 = r 0 2K @=3 =: n rLK =L n 5 r6 =: n75 $ =: 9 r =:& nZ9 =) r Y %0#2 Y r V 0 %0#2 = r 06 = n= r = n= rX$ = !D= n = & nZ9 = rnr#2 %0r V #=3n = r $ O=+!D=Zn =#&nZ9 = r 0r Y + =X 5 4&=Z& rZn =Z&n 9 7=@8 r V #2 0rn @K = = n 5 rO$ O= &nZ9 = !#E& r n?0 0 = r VXW "=H rr =H&5 & rn =L&n 9 7=E8 r VXY 0n = 8 5 r =) 4= nD5 r n = &nZ9 =8 r r0X2 W K = =O n 75 r 6 = $ =O 6 =3 = n 5 rO&nZ9 = 5 =O8 .". r V V 0X2 V =?& nZ9 = ) r VXY %0#2 V = r V 08r=3 = 9#5 6 = $O=X rX!#E& 5 = r V 2 Y %0#2D0 X = F=# ?5 5 r#&nZ9 = 5 =>8 r 0D0 0X2D0 = r V#V K = =# n 5 $ = =X 9 r+& =D0 & 5 $ n n?5n& rX6 =@0 r = 0n r> 5 5 rn& VXV %0#2n ? = F= ?5 5 r>n = &nZ9 = 8 r 2 Y %0#2 = r V =A 4=65 ?5 rE&nZ9 =E 5 =H8 r2r %0rn =H8 5 rr = ) = n?5 r &nZ9 7= 5 = 8 r VXW %0rn = n?5 r= 5 D5 =D65 D5 r>n = &nZ9 7= 8 . r Y 0X2D0 = r V !D=38=O ?579 = F=> ?5 5 r>n = &nZ9 7=O8 r 0 W 0X2 Y = r V#Y $O=O) r n = &nZ9 7= 8 r Y 0n V = r V =O) O5 r?& nZ9 = E5O=> r W W#W V W#W#W = r V $O=> "=O n r &nZ9 =O 5 =>8 7. r V 0 %0#2 = r V 2 $O= !D=D8 Z9 !D= L=D rD&nZ9 =D5 =D 5 = r WZV %0rn D =+ nn r@ = r =D65 D5 r>n =>&n 9 7= 8 r Y 0r = r V 6 =3 = n75 r $O=? "= n r &nZ9 7=> 5 =?8 r Y 0 %0 @ = &nZ9 = !D=O) r 0X2 = r W = n?5 8r= = 5 rr 5 rDn =Z&n 9 7=D8 r 0 0X2n r rD0 0X2n => n?5 r>) =>&n 9 7= ) n = r r Y 0n V = r D0F= '( =8:5 =E$ r ) =&nZ9 7=r) = r r %0#2r = $ r>) =>&nZ9 = ) n = r V #2 VXW#W 0 =

PAGE 117

0 W r V 6 = n= r = n= r$ O=B!D= n =& nZ9 = r Y 0r V e&! r r Y =3n = r$ O=A!D=An =&nZ9 = r n 0r Y E =Q 5 T4=& n r n =Q&nZ9 =8 r V X2 0rn K =3= n 75 r:$ O=&nZ9 =A!#E& r n?0 %0r = r =3 =? 5 $ = n r+n =D&n 9 7=>8 8. r Y 0#2n D8= = 5 rr 5 r n = &nZ9 = 8 r r V %0#2n = r n ; = 4 =# 5 ?5 5 r n = &n 9 7=Z8 rr%0r Z = =X8 5 r =X&nZ9 = ) .. rA0 %0#2D0 8= D5 r = 8=$ D5 r 5 r =&n 9 7=) @0 0#2n Dn =>&nZ9 7=O8 r V 0X2 = r Y )=>&5 5 r &nZ9 7=O5 => r 0 WZY 0X2 = r = => 5 !D= "=O 9 r &nZ9 = 5 = r W 0 VXW#W 0 = r r6 =# n75 r 8\ > D n, A* ),"!Qe 7 r = V r = 0#0 W 0 r?5 5 r 9, =3 = $ nn $ 5 r r VXW#W 0 = r #2 =>5 r Fr$ ) r r+&nZ9 7=O5 =>8 r r 0#2 Y = r =? 5 ?5 r &O ) r r@& nZ9 =O 5 =>8 r V 0@0 = r W &= = r3& R) r r = &nZ9 = ) r #2r %0 = r ?0 $O=O) r &nZ9 =O 5 =>8 r r V %0D0 = r V K = nD5 $DM) r r $@)A'(&8A' Y r rO 0 rO& 5 5 5 & r> r ?5 D5 r n r> V r 0n ?K => n?5 $DM) r r?$D )A'%H' Y r W r $D ) 5 r $ r 0 Y = r r = 5 r & R) r r = &nZ9 = ) r 0n 0 Y = r =? 5 ?5 r &O ) r r = &n 9 7= ) r Y r 0n = r Y = 8 r &F ) r r &nZ9 7= 5 =#8 rr#2%0 Y Z&nZ9 = 5 =>8 r Y 0n = r r&= r 5 r &FrH) r r = &nZ9 7= ) r 0n 0n = r "=>8 5 r !XG) r r = &n 9 7= ) r V %0#2 = r Z2&=>?5 r => 6 =3 => n 5 r> =O&n 9 7= !D=O) .. r n Y 0n = r r )HA rO = $ => =nr &nZ9 =OE5O=O %0r0@= r YXW )HA rO = $ => =nr &nZ9 =OE5O=O %0 V Z2 V#V = r Y 0 =? 5 ?5 r &O ) r r@& nZ9 =O 5 =>8 r Y 0n = r Y#V !D= "=O 9 r &n 9 7= E5O= r YXW 0n =

PAGE 118

0 WZY r Y = X5 r3&OR) r r@7=O& nZ9 = !D=O) r n 0n#2 = r Y =? rr 5 r & ) r r@ =>&nZ9 = !D=O) .. r V 0 %0 = r Y#Y =? rr 5 r & ) r r@ =>&nZ9 = !D=O) r Y r VXW#WZV = r Y =? rr 5 r & ) r rn?5 +'(5 5X W D0 W#W #2 r Y &=>?5 4= rO!#FrA& r Y r 0#2 = r Y 2 =B rB&nZ9 7=Q 5 =8 r Y %0#2 = =&B5 5 r n =O& nZ9 = 8 r r %0#2#2 O8=>D5 r = =O r r n =>&n 9 7= 8 r 0n W = r Y = ?5 r3)H ) r r+&nZ9 =O5 O= 5 = r V 0X0 2 W VXW#W 0 = r W =D r )HT) r r+& nZ9 =OE5O=O r W 0 VXW#W V W#W = r D0:=? r 5 r>n =? =O 5 n &n 9 7= E5 7= 2. r #2r %0#2#2 = r V =D ?5 r?n = => 5 n r&nZ9 7=O5 => r #2 %0#2#2 = r !D=QFn rL& = n?5,& W 5 D9 F& rA$ rL) r $ 5 r 0 W = r n :=? r 5 r>&nZ9 =O5 O=> r 0Z2 %0 V = r Y :=? r 5 r>&nZ9 =O5 O=> r V #2 %0 r = $ n r = 8 n r !D= 8L5 n r = F r = rO&B= $ n r = 5 n r )H 540 2D0 W = r r = ?5 r &nZ9 = 5 O=> r r W VXW#W 0 VXW#W 0 = r #2 =D r>& nZ9 =OE5O=> r 0#0 VXW#W VXW#WZV = r F= => r>&nZ9 7=O5 => r 0 V 2 W 0r = r W = 9 r =$ r 5 --Un, 2) rA)H 5 Z2#2n r 5 r 9 r 0nD= r @06 =3 => n 5 r"= !D=O$ r = &n 9 7= ) r Y %0r = r V 8r= rr r W ) r r@&nZ9 7=O5 =>8 r 0 Y 0 = r n $O=? nn rn8"!n ) L r?)H 5 0 Y#Y rD r 5 r 0D0#= r =O 5 rD!D=> 9 r ( "! "! \r +U! ) )r> I 2 n rO)H 5 n#2 rD5 5 r 5 r 0nD= r Y ) r = &B= )= r&n 9 7=E5O= 5 = r V#Y 2 W %0#2 Y E&A) ) r = F=O n rO&nZ9 7= 5 =O8 r V 0X2r O)HAM) r = = $ =

PAGE 119

0 W 5 = r &nZ9 = 5 =O r Z2 V#V 0n V $D) r = => r 5 rO&nZ9 = 5 =8 r Y 0n &Fr ) r = &B=B r 5 r7=Q&nZ9 7=!D=) rH0 0 &n 9 7= 5 =8 rH0X0 2 VXW#W#W e&! r #2 VXWXW#W &O ) r = 4= X5 r+7=@&nZ9 =?!D=D) r n 0n#2 @ =Z rr 5 r &nZ9 = 5 =>8 r VXWXWZV = r n = => 5 !D= "=O 9 r &nZ9 = 5 =>8 r n?0 %0 =

PAGE 120

8L &Fr)LI$@)HF 5 5 &B=B& r E0 rL0r r n?5 X5 !Z9 8L5 =, 5 n n n 0 r n?5 ?5 n5 n?5 N 5 &n 9 5 n X9 rO %& $ 5 #5 (9 = C0r nD5 5 5 nX5 n 8 nD5 $ 5 5 ?5 575X= "0 n?5 5 5 n#5 nn 5 $ ?5 575 '\ -(! 2, n?5 5 #5 (9#= n 5 D9 %& r n?5 X5 n?5 5 r n?5 5 O5 5 B&nZ9 n & 5 HK = 5O= 5 5 $ 5 5 n 5 5 n?5 n ?5 @' r nD5 FrE'%8G5 O5 n 5 = n?5 5 r0 5 5 &= & r 5 5 5 D5 n?5 5 5 B&nZ9 r> n#5 (9 D= VXWXW 0 n?5 ?5 n?5)HI) r 5 n & 5 5 9 9 O5 5O5 5 nZ9 r 9 n?5 5 5 = VXWXW 07' V W#WZY 5 5 5 D5#5 5 5 n?5 )nD5 5 (9 ) 5 V r)HL= V W#WZY r 5 5&=D& 5 n?5 nX5 (9 n n?5 ?5 575 Q &n n 9X= 0 W


Permanent Link: http://ufdc.ufl.edu/UFE0010127/00001

Material Information

Title: Fragmentation of Quark and Gluon Jets in Proton-Antiproton Collisions at Center-of-Mass Energy of 1.8 TeV
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
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Title: Fragmentation of Quark and Gluon Jets in Proton-Antiproton Collisions at Center-of-Mass Energy of 1.8 TeV
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FRAGMENTATION OF QUARK AND GLUON JETS
IN PROTON-ANTIPROTON COLLISIONS AT / = 1.8 TeV















By

ALEXANDRE P. PRONKO


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005


































Copyright 2005

by

Alexandre P. Pronko

















I dedicate this work to my wife Anna and my parents, Vera Vladimirovna and

Pavel Antonovich Pronko.















ACKNOWLEDGMENTS

I am very grateful to my advisor Prof. Andrey Korytov for his guidance and

support throughout my research. His knowledge of and dedication to high-energy

physics were a true inspiration for me. The greatest lessons I have learned from Prof.

Korytov are that all things (even small ones) must make sense and that you really

understand something if you can explain it in a few words.

I am very thankful to Dr. Alexei Safonov for his invaluable help and patience

while I was making my first steps in this analysis. He also gave me an example of

how to work hard and still enjoy physics.

I would like to thank Prof. Guenakh Mitselmakher and Prof. Jacobo Konigsberg

for their contribution to the successful completion of this dissertation.

I also thank Prof. Anwar Bhatti, Prof. Luc Demortier, Prof. Sally Seidel, Dr.

Robert Plunkett, Prof. Richard Field, and Prof. Joey Huston for their help and

useful suggestions that were very important at different stages of this work.

I appreciate the opportunity I had to be a part of the University of Florida

group at the Collider Detector at Fermilab (CDF). I enjoyed working with such great

colleagues as Dr. Sergei Klimenko, Dr. Alexander Sukhanov, Dr. Song Ming Wang,

Dr. Roberto Rossin, Valentin Necula, George Lungu, Sergo Jindariani, and Lester

Pinera. I especially want to emphasize the role which Prof. Jacobo Konigsberg, the

UF CDF group leader, played in making us a strong team.

I am thankful to Lester Pinera for carefully reading the manuscript and his

helpful suggestions.

Special thanks are due to Bobby Scurlock, Valentin Necula, and Roberto Rossin

who were my officemates at different periods of time. Without you guys, I would have










completed this thesis much faster, but my whole experience as a graduate student

could have turned into a misery of solitary confinement in front of a computer. I

very much enjoyed talking to you about what men can talk about: politics, society,

science, music, life.

To my friend and colleague Dr. Maxim Titov, thank you for your friendship

which started when I was at summer school at DESY and which continues today.

Finally, but most of all, I would like to thank Anna, my wife and best friend,

and my parents for their unconditional love and continuous support.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ....... iv

LIST OF TABLES ............ .......... .......... viii

LIST OF FIGURES ................................ x

ABSTRACT .................................... xiii

CHAPTER

1 INTRODUCTION .. ............. ........ 1

1.1 Standard Model of Elementary Particles ........... ... 1
1.2 Quantum Chromodynamics .................. ...... 2
1.3 Jets of Hadrons ............................ 5

2 FRAGMENTATION OF QUARK AND GLUON JETS ......... 7

2.1 Analytical Perturbative Approach (APA) to Jet Fragmentation 7
2.1.1 Modified Leading Log Approximation (MLLA) ....... 9
2.1.2 Local Parton Hadron Duality Hypothesis (LPHD) . 10
2.2 APA Predictions . . . ..... ....... 12
2.2.1 Mean Multiplicity of Charged Particles . .... 13
2.2.2 Difference between Quark and Gluon jets . ... 14
2.3 Jet Fragmentation in Monte Carlo Event Generators . ... 16

3 STUDIES OF QUARK AND GLUON JETS . . . ... 20

3.1 Physics Motivation ..... . . ........ 20
3.2 Experimental History . . . ..... ..... 21
3.3 Feasibility of Quark and Gluon Jet Studies at CDF . ... 30
3.4 Analysis Strategy at CDF ....... . .. . 32

4 ACCELERATOR AND DETECTOR . . . .. 35

4.1 Tevatron during the 1993-1995 Running Period . ... 35
4.2 CDF Design and Overview . . . ... .... 37
4.2.1 Vertex Detectors (VTX and SVX) . . .... 39
4.2.2 Central Tracking Chamber (CTC) . . .... 40
4.2.3 Preshower and Shower Maximum Detectors, Calorimetry .41
4.3 CDF Trigger System . . ... . 44










5 JETS AT CDF .................. ............. 46

6 PHOTONS AT CDF ................... ....... 49

7 ANALYSIS TOOLS ............................. 51

8 MEASUREMENTS .................... ..... .. 53

8.1 Data Samples ................... ...... 53
8.2 Event Selection Cuts ................... .... 53
8.3 Fraction of Gluon Jets ................... ... 56
8.4 Fraction of Real Photons ................. .... .. 57
8.5 Multiplicity Measurements .. . . . .. 59
8.5.1 Track Cuts ....... .. .... ......... 60
8.5.2 Background Tracks Removal . . . 62
8.5.3 Tracking Efficiency .... . . . .. 63
8.6 Effect of Fake Photons .... . . . ..... 65
8.7 Final Corrections and Results .... . . . 68

9 SYSTEMATIC UNCERTAINTIES AND CROSS-CHECKS . .. 70

9.1 Event Selection ... . . . . ... 70
9.2 Jet Reconstruction and Energy Corrections . . .... 74
9.3 Presence of Fake Photons . . . ..... ..... 79
9.4 PDF Uncertainties .... . . ....... 82
9.5 Uncertainties in Multiplicity Measurements . . .... 82

10 DISCUSSION OF RESULTS .... . . .... 88

10.1 Multiplicity of Charged Particles in Gluon and Quark Jets .. 88
10.2 Momentum Distribution of Charged Particles
in Gluon and Quark Jets. .... . . . .. 93

11 SUMMARY AND CONCLUSION. FUTURE PERSPECTIVES ..... 99

REFERENCES ........ . ... .................. 102

BIOGRAPHICAL SKETCH ... . . .......... 107















LIST OF TABLES
Table page


1-1 Properties of leptons. ......................... 3

1-2 Properties of quarks. ..... . . . . . 3

1-3 Gauge bosons and forces of the Standard Model. . . ... 4

2-1 Numerical values of the perturbative corrections for the parton multi-
plicity in gluon jets, Ng, and the ratio of multiplicities, r = Ng/Nq. 13

3-1 The summary of model-independent measurements of the difference be-
tween quark and gluon jets conducted on e+e- machines. . 28

3-2 The summary of model-independent measurements of the difference be-
tween quark and gluon jets conducted at e+e- machines using unbi-
ased gluon jets. ..... . . . . 30

3-3 The summary of model-dependent and indirect measurements of the
difference between gluon jets and light flavor, u-, d-, s-, quark jets. 31

4-1 Selected parameters of the CDF Central Tracking Chamber. . 41

4-2 The CDF Calorimeter System coverage and detector segmentation. 44

8-1 Fractions of gluon jets in dijet events and in 100% pure 7-jet events
obtained using Herwig and Pythia along with various sets of parton
distribution functions. . . . ............ 59

8-2 Efficiencies of the track selection cuts for jets with the average energy
Ejtt=41 GeV. ....... .... . .. ...... 64

8-3 Efficiencies of the track selection cuts for jets with the average energy
Ejtt=52.5 GeV. ........ .. . ........... ..65

8-4 The a-correction due to difference in multiplicities between a regular
jet and a jet opposite to a fake photon. . . ..... 66

8-5 Results of the measurements with the default set of cuts. ...... ..68

8-6 Effect of K and A decays on the charged particle multiplicity within a
cone of the opening angle c=0.47. ..... . . ..... 69










8-7 Charged particle multiplicities in small cones around gluon and quark
jet directions and their ratio, Ng, Nq and r = Ng/Nq respectively. 69

9-1 The summary of systematic uncertainties in the measurements of Ng,
Nq, and r = Ng/Nq obtained for the opening angle 0c = 0.47. . 85

9-2 The summary of systematic uncertainties in the measurements of Ng,
Nq, and r = Ng/Nq obtained for the opening angle 0c = 0.36. . 86

9-3 The summary of systematic uncertainties in the measurements of Ng,
Nq, and r = Ng/Nq obtained for the opening angle 0~ = 0.28. . 87

9-4 Fraction of real photons in the photon+jet sample and its associated
systematic uncertainties. .. . . . .... .. 87

10-1 Monte Carlo results for charged particle multiplicities in small cones
around gluon and quark jet directions and their ratio. . ... 92

10-2 Measured values of the momentum distribution, 1 N of charged par-
Njet dQ o
ticles in gluon jets. ..... . . . ......... 96

10-3 Measured values of the momentum distribution, dNof charged par-
Pjet dQ o
ticles in quark jets. ..... . . . ......... 97

10-4 Measured values of the ratio of momentum distributions, r($), of charged
particles in gluon and quark jets. . . . ..... 98















LIST OF FIGURES
Figure page


2-1 Example of the distribution of charged particle transverse moment
with respect to the jet direction. ..... . . ..... 10

2-2 Theoretical predictions for the ratio of multiplicities in gluon and quark
jets, r = Ng/nq ........ . .... ........... 15

3-1 History of measurements of the ratio of charged particle multiplicities
in gluon and quark jets. .. . . . ...... .. 27

4-1 Overview of the Fermilab accelerator complex. . . .... 36

4-2 Drawing of the CDF detector. .. . . . 38

4-3 The CTC end plate view. .. . . . . 40

8-1 Invariant mass spectrum of dijet and photon+jet events which pass
event selection cuts. ..... . . . ...... 56

8-2 Transverse energy spectrum of jets and photons from dijet and pho-
ton+jet events after event selection cuts. . . ..... 57

8-3 Fractions of gluon jets in dijet and 7+jet samples . . .... 58

8-4 Example of the distribution of log pT versus log d for tracks within a
cone of 0c=0.47 rad around the jet direction. . . .... 60

8-5 Illustration of correlation between transverse particle momentum, PT,
and impact parameter, d, for electrons and positrons produced in
7-conversions. ..... . . . . . 61

8-6 Example of the Az distribution for tracks from events with only one
vertex (primary interaction). .. . . . 62

8-7 Illustration of the definition of complementary cones. . ... 63

8-8 The correlation between multiplicity in complementary cones (per event)
and dijet multiplicity (per event). ..... . . ..... 64

8-9 The ratio of the measured energy of a fake photon (detector level) to
the real energy of a parent jet (MC parton level). . ... 67










8-10 The ratio of the measured invariant mass of a fake 7+jet event (de-
tector level) to the real invariant mass (MC parton level). . 67

9-1 The angular distribution of particles in cone 0.47 around jet direction. 71

9-2 Energy balance in data: IET1 + ET2,/(ET1 + ET2) . . .... 73

9-3 Energy balance in Herwig Monte Carlo: I, + ET2 /(ET + ET2). 73

9-4 Difference in charged particle multiplicities between jets reconstructed
with different clustering cone sizes. . . . 76

9-5 Difference in charged particle multiplicities between jets reconstructed
with different clustering cone sizes. . . . 77

9-6 Angle between the direction of an outgoing parton and the direction
of a reconstructed jet. .. . . ... . .. 77

9-7 Invariant mass spectrum of Monte Carlo dijet and 7+jet samples. 78

9-8 Isolation energy distribution in photon+jet data and Monte Carlo fake
7+jet events. ..... . . .. . 81

9-9 The predicted real photon content as a function of the cut on isolation
energy in a cone around photon candidate (dots-prediction based
on the shape of the isolation energy distributions in data and Monte
Carlo fakes, band-real photon fraction and its uncertainty based
on the standard conversion method). . . . 81

10-1 The ratio of charged particle multiplicities in gluon and quark jets as
a function of jet hardness Q. . . . 89

10-2 Average charged particle multiplicities in gluon and quark jets as a
function of jet hardness Q. . . . ...... 90

10-3 Comparison of CDF results on charged particle multiplicity in gluon
jets with recent model-dependent and indirect results from OPAL. 90

10-4 Comparison of Monte-Carlo predictions to data: average charged par-
ticle multiplicities in gluon and quark jets. . . .... 92

10-5 Comparison of Monte-Carlo predictions to data: the ratio of charged
particle multiplicities in gluon and quark jets. . . ... 93

10-6 The ratio of momentum distributions, r(') (where Z = ln(1/x) =
ln(Ejet/p)), of charged particles in gluon and quark jets. . 94

10-7 Inclusive momentum distribution, 1 d, of charged particles in gluon
Njet d 9
jets .................................... ..... 96










10-8 Inclusive momentum distribution, 1 ,d of charged particles in quark
Njet d4
jets ................................... .. 97

10-9 The ratio of momentum distributions, r(), of charged particles in
gluon and quark jets. .. . . ......... 98















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

FRAGMENTATION OF QUARK AND GLUON JETS
IN PROTON-ANTIPROTON COLLISIONS AT s = 1.8 TeV

By

Alexandre P. Pronko

May 2005

Chair: Andrey Korytov
Major Department: Department of Physics

We report the first model independent measurement of charged particle multi-

plicities in quark and gluon jets, Nq and Ng, produced at the Tevatron in pp collisions

with center-of-mass energy 1.8 TeV and recorded by the Collider Detector at Fermi-

lab. The measurements are made for jets with average energies 41 and 53 GeV by

counting charged particle tracks in cones with opening angle of 0O=0.28, 0.36, and

0.47 rad around the jet axis. The corresponding jet hardness Q = EjtOc varies in the

range from 12 GeV to 25 GeV. At Q=19.2 GeV, the ratio of multiplicities r = N,/N,

is found to be 1.640.17, where statistical and systematic uncertainties are added in

quadrature. The results are in agreement with re-summed perturbative QCD calcu-

lations and are consistent with recent e+e- measurements.















CHAPTER 1
INTRODUCTION

The quest to understand the building blocks of our universe is as old as the history

of the human race itself. With time, our knowledge of nature has evolved from the

Doctrine of the Four Elements of Empedocles to the Standard Model of Elementary

Particles which is the most compelling theory describing the fundamental constituents

of matter and their interactions. The Standard Model can be truly considered one of

the great scientific triumphs of the 20th century.

1.1 Standard Model of Elementary Particles

The Standard Model states that all visible matter consists of fundamental parti-

cles of two kinds: leptons and quarks. Both leptons and quarks are spin 1/2 fermions.

There are six leptons and six quarks which are grouped into three generations accord-

ing to their mass. The known leptons are electron (e), muon (/), tau (7) and their

associated neutrinos (vy, v,, v,). The known quarks are up (u), down (d), strange

(s), charm (c), bottom (b) and top (t). Fermions are involved in four known interac-

tions: gravitational, electromagnetic, weak interaction and strong interaction. With

the exception of gravity, all interactions in the Standard Model are mediated by the

exchange of another type of elementary particles with spin 1 known as gauge bosons.

The electromagnetic interaction involves charged particles (all fermions except neu-

trinos), and it is mediated by the exchange of photons (7). All known fermions

participate in the weak interaction which is responsible for such processes as nuclear

beta decay. The weak interaction is mediated by the exchange of three bosons: W+,

W- and Z. Among all the fermions, only quarks participate in the strong interaction

which is mediated by gluons (g). The strong force is responsible for, among other

things, binding quarks together to form nucleons (protons and neutrons) and holding









protons and neutrons together inside atomic nuclei. The properties of fermions and

bosons are summarized in Tables 1-1, 1-2 and 1-3.

The Standard Model is a quantum field theory which is based on the gauge sym-

metry SU(3)c x SU(2)L x U(1)y [1]. This gauge group includes the symmetry group

of the strong interaction, SU(3)c and the symmetry group of the unified electroweak

interaction, SU(2)L x U(1)y. The Standard Model defines the dynamics of both the

interacting fermions and the exchange vector bosons. It allows for the calculation of

cross-sections of various processes and decay rates of different particles. The numer-

ous experimental studies of the past 30 years show a very high level of consistency

between data and Standard Model predictions. The best illustration of this agree-

ment between theory and experiment is the discoveries of the W [2, 3] and Z [4, 5]

bosons by the UA1 and UA2 collaborations at CERN and the top quark by the CDF

and DO collaborations at the Tevatron [6]. The last particle predicted by the Stan-

dard Model and yet to be discovered is the long hypothesized Higgs boson (H) which

is introduced in theory to give particles their masses. The search for the Higgs boson

is one of the most important experimental problems to be addressed during Run 2 at

the Tevatron and the future LHC experiments.

1.2 Quantum Chromodynamics

Quantum Chromodynamics (QCD) is the theory of strong interactions between

color charged objects which are quarks and gluons. The history of QCD starts with

the idea of the parton model in the late 1960's. This idea arose out of necessity to

explain the scaling observed in the SLAC experiment on deep inelastic scattering of

electrons on hadrons [7]. The surprising result was that the measured cross-section

did not fall off exponentially as the inelasticity of the reaction increased. Instead, it

had a so-called Bjorken scaling [8] behavior which suggested existence of a point-like

structure inside the target nucleons. This gave rise to the parton model [8, 9] in which

the constituents of hadrons were identified with partons. This phenomenological










Table 1-1: Properties of leptons. The spin, charge (e) and mass are listed for each
particle.

Particle Spin Charge Mass
1st generation e 1/2 -1 0.510998920.00000004 MeV/c2
Ve 1/2 0 < 3 eV/c2
2nd generation p- 1/2 -1 105.6583690.000009 MeV/c2
v, 1/2 0 < 0.19 MeV/c2
3rd generation 7- 1/2 -1 1776.990_ MeV/c2
ge1-01776.99_26 MeV
VT 1/2 0 < 18.2 MeV/c2

Table 1-2: Properties of quarks. The spin, charge (e) and mass are listed for each
particle. Additionally, each quark can also carry one of three color charges (blue,
green, red) responsible for the strong interaction.

Particle Spin Charge Mass
1st generation u 1/2 +2/3 1.5-4 MeV/c2
d 1/2 -1/3 4-8 MeV/c2
2nd generation c 1/2 +2/3 1.15-1.35 GeV/c2
s 1/2 -1/3 80-130 MeV/c2
3rd generation t 1/2 +2/3 178.04.3 GeV/c2
b 1/2 -1/3 4.1-4.4 GeV/c2


understanding of SLAC scaling was soon extended to other hard scattering processes

such as e+e- annihilation into hadrons and inclusive high p hadron production in

hadron-hadron collisions. However, the idea of what exactly a parton was remained

elusive despite the phenomenological successes of the parton model.

Another important moment in the history of QCD is the idea of quarks. Quarks

were proposed in 1964 [10] by Gell-Mann and Zweig based on the studies of hadron

spectroscopy. As they pointed out, the observed patterns can be understood in terms

of the hypothesis that hadrons are composite structures built from an elementary

triplet of spin-1/2 quarks (u-, d-, s- quarks; the other three quarks, c-, b-, t-, were

discovered much later), corresponding to the fundamental representation of SU(3)

group. The quark model appeared to be quite successful in describing the properties

of existing hadrons and predicting new states. However, this model, in order not







4


Table 1-3: Gauge bosons and forces of the Standard Model. There are eight different
species of gluons each corresponding to a particular color charge.

Boson Force Spin Charge [e] Mass [GeV/c2] Range [fm]
7 electromagnetic 1 0 < 6 x 10-23 oo
W weak 1 +1 80.425 0.038 10-3
Z weak 1 0 91.1876 0.0021 10-3
g strong 1 0 0 <~ 1


to contradict the Pauli exclusion principle, required quarks to have one property,

less obvious but of central importance for the strong interaction. This property was

proposed by Greenberg [11] and is known as color.

The final step in this chain of arguments which led to QCD is the discovery by

Pollitzer, Gross and Wilczek of the asymptotically free field theory among the class

of non-Abelian gauge theories [12]. It became apparent that the gauge symmetry of

this new theory is the local color transformation and the symmetry group which is

generated by these transformations is the non-Abelian Lie group SU(3)c. Therefore,

three possible color charges of a quark are assumed to be the fundamental repre-

sentation of the group and the gauge bosons mediating the strong interaction are

eight gluons carrying double color charge. This model became known as Quantum

Chromodynamics.

The most intriguing properties of the Quantum Chromodynamics are confine-

ment and the asymptotic freedom. The consequence of confinement is that the free

quarks (i.e. free color charges) are not observed in nature. What we see is hadrons

which are colorless combinations of quarks. The existence of confinement suggests

that the interaction between quarks becomes very strong at large distances so that

they remain bound together. The other peculiar property of QCD is the asymp-

totic freedom which predicts that quarks inside hadrons (i.e. at very short distances)

should behave almost as free particles. The asymptotic freedom is responsible for









the Bjorken scaling which was for the first time observed in a famous SLAG experi-

ment on deep inelastic scattering [7]. Both asymptotic freedom and confinement are

the consequences of unusual (different from electroweak interaction) behavior of the

QCD coupling as. The dependence of the coupling as(Q) on the energy scale Q

(also known as running of as) is given by the solution of the renormalization group

equation [13]:

47t
as (Ql) 2T
S nbln (Q2/A2 1)

where b = (33 2nf)/3, nf is the number of active quark flavors (for which mq < Q),

Q is the energy scale or momentum transfer and A is a parameter with dimension of

energy at which the coupling would diverge if extrapolated down to small Q. The

value of A depends on the renormalization scheme, number of active flavors and can

also be defined to leading or next-to-leading order. Experimental measurements of A

(in the modified minimal subtraction scheme [13] and five active flavors) yield values

of around 200 MeV [14]. The form of Eq. 1.1 suggests that the as(Q) becomes large

and perturbation theory breaks down, for scales comparable with the masses of the

light hadrons, i.e. Q 1 GeV. This is an indication that the confinement of quarks

and gluons inside hadrons is actually a consequence of the growth of the coupling at

low scale, which is opposite to the decrease at high scales that leads to the asymptotic

freedom. This behavior of the QCD coupling is the result of the non-Abelian nature

of the strong interaction which is characterized by the presence of self-interaction of

gauge bosons (i.e., the theory contains three- and four-gauge-boson vertices). It is

these additional interactions that makes QCD so rich in various phenomena.
1.3 Jets of Hadrons

One of the most spectacular manifestations of the QCD is the existence of jets

of hadrons which we see in detectors as collimated sprays of particles. It was first

observed by the MARK1 collaboration at SPEAR in 1975 [15] that quarks produced in









ee- collision appeared as hadronic jets. Five years later, the experiments at PETRA

[16] proved the existence of jets from gluon emission in quark pair production. To get
an idea of how jet formation happens, we need to consider a process of bremsstrahlung

gluon radiation off a parton (quark or gluon). The differential spectrum of gluon

radiation off a quark with momentum p is given by the well-known formula [17]:

dw(q*+ = k 2F [ + 1- )] ddk (1.2)
27r
as(k) = / CF =(N 1)/2N = 4/3, (1.3)
b In (kj/A)

where Nc = 3 is the number of colors and k is the gluon momentum. By examining

this formula, we can see that jet formation is driven by the quasi-collinear and/or

soft gluon emissions [17]:

Intrajet activity : k < k < p -* w ~ as In2 p ~ 1 (1.4)

At the same time, large angle emission off a parton with large momentum p can lead

to an extra gluon jet, however, with a small probability [17]:

Multijet topology : k ~ k ~ p -* w ~ as/wT < 1 (1.5)

The stage of parton cascade development is then followed by the hadronization stage

when quarks and gluons from the parton shower pick up color matching partners from

the sea of virtual quarks and gluons and become observable hadrons. Therefore, jets

of hadrons are as close as we can get experimentally to "seeing" quarks and gluons.















CHAPTER 2
FRAGMENTATION OF QUARK AND GLUON JETS

This chapter gives an overview of the theoretical picture of quark and gluon

jet fragmentation. We will consider currently available perturbative QCD (pQCD)

tools for calculating a basic jet observable such as multiplicity of charged particles.

We will also review models of jet fragmentation implemented in Monte Carlo event

generators.

2.1 Analytical Perturbative Approach (APA) to Jet Fragmentation

When trying to obtain a quantitative description of jet properties, we have to

remember that the fragmentation is a manifestation of both asymptotic freedom and

confinement properties of the strong interaction. Perturbative QCD is applicable only

if the strong coupling, as, is relatively small, i.e in the regime of high momentum

transfers when the concept of free partons is valid. It is during this stage when the

cascade of quarks and gluons develops, thus, forming the structure of a jet. However,

what we see in detectors are not quarks and gluons but hadrons which are formed

during the confinement stage of jet formation. In this regime, the strong coupling

becomes too large, rendering perturbation theory ineffective. Fortunately, as Eq.

1.1 suggests, it happens at relatively small momentum transfers compatible with

the masses of light hadrons (<1 GeV). Thus, we may hope that much of the jet

structure developed during the parton branching with higher momentum transfers

should remain unaltered by hadronization. The data from e+e- and ep collisions

indeed confirmed that, phenomenologically, distributions of hadrons and partons look

very similar. This has led to the hypothesis of local parton hadron duality (LPHD)

[18]. The LPHD has provided an important link between the perturbative QCD

calculations performed for partons and the experimental observables for hadrons. The









framework of pCQD and LPHD forms the so-called analytical perturbative approach

(APA) to QCD jet physics. The goal of which is to describe the structure of the multi-

hadronic final states with the minimal reference to the hadronization dynamics. By

confronting the APA predictions with experimental data, we aim to find the areas of

applicability and the limitations of this perturbative approach.

The success of the parton description of deep inelastic scattering (DIS) prompted

detailed studies of QCD parton cascades. Historically, attempts to quantify logarith-

mic deviations from the true Bjorken scaling behavior has led to the development of

the so-called Leading Log Approximation (LLA) [19]. In the LLA, the contributions

to structure functions on the order of a ln "(Q2) are resumed in all orders while

the terms without large logs are neglected. The origin of this as In Q2 scaling break-

down stems from the fact that the parton's transverse momentum inside hadron is

not restricted to be small. Thus, a quark can emit a gluon and acquire large trans-

verse momentum k_ with probability wqq+9 ~ f as dkI/k2 (see Eq. 1.3). The

integral extends up to the kinematic limit k_ ~ Q2 and gives rise to the famous log-

arithmic scaling violation. The LLA was also extended to the e+e- annihilations for

fragmentation functions in the region of finite momentum fractions, 0.1 < x < 1.0.

Despite its success in DIS, the LLA is not enough to obtain a satisfying descrip-

tion of jet fragmentation which, as it was already shown (Eq. 1.5 in Chapter 1),

is dominated by the soft gluon emissions. The dynamics of soft particles in jets is,

to some extent, accounted for by the so-called Double Log Approximation (DLA)

[20]. The DLA was initially developed for pure gluonic systems and was designed

to account for only leading double logarithmic contributions, as In2 Q2 ~ 1, while

neglecting contributions of the order as In Q2 < 1 and as < 1. This approximation

is the simplest analytical representation of the QCD parton cascade. In the DLA, one

re-sums in all orders terms a Iln2n Q2 arising from double logarithmic (DL) infrared

and collinear singularities of gluon emission (q-+qg, g-+gg processes), but ignores the









energy and momentum conservation. The DLA is too crude for making quantitative

predictions and is only valid at very high energies. However, it is conceptually simple

and allows for qualitative description of many effects in jet fragmentation.

It is important to mention the role that color coherence effects play in the de-

velopment of partonic cascades. Color coherence effects are common to any gauge

theory. In jet fragmentation, they manifest themselves in a suppression in production

of very soft particles compared to those with intermediate energies (Ehdd ~ Ee' 0.4)

Coherence effects also result, on average, in a strong angular ordering (AO) [21] of

consecutive gluon emissions. The essence of AO is that the soft gluon in a parton

cascade is emitted only inside a cone formed by its two immediate predecessors. The

effect of strong AO in QCD helps to present the pattern of the parton cascade in terms

of purely probabilistic picture of Markov chains of independent elementary radiation

events. This probabilistic scheme significantly simplifies large log re-summation in

all orders of as.

2.1.1 Modified Leading Log Approximation (MLLA)

In order to make successful a quantitative description of jet evolution, one has to

account for the sub-leading single logarithmic (SL) effects (g--qq and q-+qg, g-+gg

splitting with hard moment) on the order of ag In2n-1 Q2 along with the leading

double logs, a' in2n Q2 (DLA accuracy). This is done within the so-called Modified

Leading Log Approximation (MLLA or also referenced as next-to-Leading Log Ap-

proximation, NLLA) [22], where SL and DL contributions are re-summed in all orders

of as.

The only MLLA parameter, Qeff, is the cut-off on the minimal allowed parton

momentum with respect to the parent parton. It sets the lower limit on the parton

virtuality, thus, playing the role of the effective parton mass. The Qeff cutoff can

also be considered as the scale below which non-perturbative hadronization effects











14
cone 0c=0.47
12 Ejet=41 GeV
12

++
10 +
+

+
z +

+
z +
S-+


+
+
4

2 ++


0 0.5 1 1.5 2 2.5 3
kT, GeV/c


Figure 2-1: Example of the distribution of charged particle transverse moment with
respect to the jet direction. The distribution is obtained for particles within a cone
0c=0.47 around jets from dijet events.


dominate in the jet formation. The value of Qeff is not defined in the theory, but

rather has to be determined experimentally.

Fig. 2-1 shows an example of the distribution of charged particle transverse

moment with respect to the jet direction, k From this plot, one can see that most

of particles have k < 1 GeV and, therefore, belong to the region where analytical

calculations are very challenging. Spectrum of transverse moment, k1, in data also

suggests that, in order for the MLLA to be a successful model of jet fragmentation,

Qeff has to be on the order of a few hundred MeV (Qeff ~200 MeV).

2.1.2 Local Parton Hadron Duality Hypothesis (LPHD)

The application of pQCD to multiparticle production is not possible without

an additional assumption about the hadronization stage of jet evolution which is

governed by color-confinement. As mentioned before, such a link between partons

and hadrons is provided by the hypothesis of local parton hadron duality, LPHD [18].










The LPHD assumes that the hadronization occurs locally at the end of the parton

shower development. In other words, the conversion of partons to hadrons happens

at a low virtuality scale on the order of hadronic masses (Qeff ~ few hundred MeV),

it does not depend on the scale of the primary hard process, and it involves only small

momentum transfers. Therefore, results obtained for partons with k > Qeff should

apply to hadrons as well. The origin of this local duality is in the pre-confinement

properties [23] of the QCD cascade: the color charge is locally compensated and the

color neutral clusters of limited masses are formed in the cascade.

The naive interpretation of the LPHD is that every parton picks up color match-

ing partners from the sea of virtual quarks and gluons and becomes a hadron which

"remembers" the direction and momentum of the original parton. Therefore, one can

assume that for sufficiently inclusive observables the following relation should hold:


O(xi, X2, 2 .) hadrons = KLPHDO(xI, 22, ..., Qeff, A) partons (2.1)


In other words, the inclusive momentum distributions for partons and hadrons in jets

are the same apart from a possible normalization. The same should be also true for

the average multiplicities in jet:


Nhadrons = KLPHDNpartons. (2.2)

It is important to mention that one should not expect a one-to-one match between

partons and hadrons on event-by-event basis, but only in their average behavior

as well as in fluctuations around the average. Finally, the LPHD is expected to

be asymptotically correct because the sensitivity to the cut-off decreases with the

increasing energy.









2.2 APA Predictions

In this section, we will discuss the APA predictions for the mean charged particle

multiplicities in gluon and quark jets. The multiplicities of hadrons are a very funda-

mental characteristic of jets, and they are given considerable attention in experimental

measurements. The predictions for particle multiplicities in jets are based on calcu-

lations carried out in the framework of MLLA [17] and its extensions [24, 25, 26, 27],

supplemented with the LPHD hypothesis [18]. Traditionally, the solutions of pQCD

equations are obtained for the multiplicity of partons in gluon jets, Nparton, and for

the ratio, r = Narto"n /ortto, of parton multiplicities in gluon and quark jets.

Theoretically, the parton multiplicity in a jet of energy Ejet is calculated for

partons in a small cone defined by an opening angle, 0c, around the direction of the

initial quark or gluon emerging from qq or gg color singlet source [17]. The multiplicity

NParton(y) depends only on one scaling variable y = In (Q/Qeff) = In (EjetOc/Qeff),

where Q = EjetOc is the jet hardness and Qeff is the kT cut-off for partonic cascade (in

MLLA, Qeff can be taken as low as A). To accommodate the multiplicity measure-

ments performed at e+e- colliders for all charged particles in the full solid angle, the

theoretical predictions are often extended to cones as large as a whole hemisphere, or

OC = 7/2. Strictly speaking, this goes beyond the precision of the pQCD calculations

and there is no unique prescription for doing such extrapolations. However, it seems

natural to use Q = 2Ejettan(Oc/2) that has the correct limit at small opening angles

and remains Lorentz-invariant for large angles with respect to boosts along the jet

direction. For a full hemisphere, the energy scale becomes Q = 2Ejet. The definition

of a scale in the case of three-jet events in e+e- collisions with all jets at large angles

with respect to each other is even more ambiguous and we postpone this discussion

till next chapter where we will review results obtained at e+e- colliders.










Table 2-1: Numerical values of the perturbative corrections for the parton multiplicity
in gluon jets, Ng, and the ratio of multiplicities, r = Ng/N,.

nf al a2 a3 rV r2 r3
3 0.280 -0.379 0.209 0.185 0.426 0.189
4 0.297 -0.339 0.162 0.191 0.468 0.080
5 0.314 -0.301 0.112 0.198 0.510 -0.041


2.2.1 Mean Multiplicity of Charged Particles

According to the recent so-called next-to-next-to-next-to-Leading Log Approx-

imation (3NLLA extension of MLLA) [26], the mean parton multiplicity in gluon

jets is given by

N arton(y) = y-ac2 exp 2c/ +

2 2C2 (n2y + 2) +
Vf 02
C2I[aa2 a (In 2y + 1)] (2.3)


where coefficients ai (i=1-3) are given in Table 2-1, and other parameters are defined

below:

y= In (Q/Qf) = In (EjetOc/Qeff), c= (4Nc/ o)1/2
S= 11N 2nf 17N, n/(5Nc + 3CF)
-o --1 =
3 3

In Eq. 2.3, the pre-exponential term and the first term in the exponent correspond

to the MLLA expression for multiplicity. The second term in the exponent, pro-

portional to c/vy, is the NNLLA [25] correction. The third term in the exponent,

proportional to c2/y is the 3NLLA result. The role of the 3NLLA correction is not

important compared to the lower order terms because of the smallness of a3. It is

interesting to note that the NNLLA and 3NLLA corrections are almost constant

and somewhat compensate each other at currently accessible energies. Therefore, the

MLLA expression for gluon jets is a good approximation to the higher order result.









Strictly speaking, the next-to-MLLA calculations (NNLLA and 3NLLA) are not

the next order calculations of the contributions into the amplitudes of the branching

processes. However, these terms are of some relevance because they include energy

conservation at improved level of accuracy.

2.2.2 Difference between Quark and Gluon jets

In QCD, quarks and gluons have different probabilities (proportional to their

color factors, CF=4/3 and CA=Nc=3 respectively, also frequently referred to as

"color" charges) to emit gluons, and it is therefore expected that jets produced by

quarks and gluons will exhibit a difference in their fragmentation properties. This

difference is best characterized by the ratio of hadron multiplicities in gluon and

quark jets, r = Ng/Nq. The asymptotic (at Ejet -+ oo) value of r is simply a ratio

of gluon and quark color factors, r = CA/CF = 9/4 (DLA, see ref. [28]). At present

energies, however, the asymptotic value of r can be achieved in the soft limit of

the particle spectrum [29]. The inclusion of two loop as corrections [24] (one loop

in MLLA) and energy conservation [25] up to NNLLA level reduces the ratio to,

respectively, r ~ 2.1 and r ~ 1.7 at experimentally accessible energies. Even higher

order corrections which further diminish the predicted ratio, r = Ng/Nq, are obtained

in the next-to-next-to-next-to-leading order (3NLLA [26]):

CA 2 (2.4)
r = F(1 r7yo r270o2 370), (2.4)


where coefficients ri (i=1-3) are given in Table 2-1, and o7 is defined below:

2 27[ /3 ln(2y)]
o = 2Ncas/T, as = 1 .

The theoretical results discussed above for the ratio are presented in Fig. 2-2. Despite

the fact that various calculations disagree on the absolute value of ratio, they all

predict a weak dependence on the energy scale. These calculations also show the

relative importance of the higher order as corrections and energy conservation. The










3

LLA & NLLA, r=CA/CF=2.25

2
z



Gaffney & Mueller, 1985
Catani et al., 1992
Lupia & Ochs, 1998
-- Capella et al., 2000
0
10 100
Q, GeV

Figure 2-2: Theoretical predictions for the ratio of multiplicities in gluon and quark
jets, r = Ng/n,.


strict energy conservation and a corresponding limitation on the available phase space

can be included even more accurately by solving the evolution equations numerically.

This solution is presented in ref. [27]. The exact numerical solution reduces the ratio,

r = Ng/N,, by another 10% compared with the 3NLLA predictions.

As it was already mentioned above, the pQCD equations are traditionally solved

for the multiplicity in gluon jets, N,, and for the ratio of multiplicities in gluon and

quark jets, r = Ng/Nq. Therefore, the 3NLLA prediction for the multiplicity in

quark jets, Nq, is simply given by Nq = Ng/r + 0(75) [26]:

CF ale 2
Nqarton(y) = A-2 exp {2cy +
A CA

r~ + 2a2C2 + %(ln2y+ 2) +

c 2 C2a2 1 1
-[2 r ac2 a (ln2y + 1) }. (2.5)
+ a3: 0
y 2 Po

We also have to mention that the theoretical calculations discussed above are per-

formed in the limit of massless quarks, i.e. applicable to light u-,d- and s- quarks only.

Finally, the corresponding expectation of hadron multiplicities in jets is provided by









Eq. 2.2, Nhadrons = KLPHDN rtnS. The LPHD assumes that the constant KLPHD

is the same for gluons and light quarks.

2.3 Jet Fragmentation in Monte Carlo Event Generators

In this section, we will consider implementation of jet fragmentation in Monte

Carlo (MC) event generators. Nowadays, Monte Carlo simulation is widely used for

visualization of not only detector performance but also of physics phenomena. There

are a number of specialized and general purpose MC event generators, among which

Herwig [30] and Pythia [31] are, probably, the most popular general purpose ones.

Jet fragmentation in both Herwig and Pythia includes two steps: perturbative

initial- and final-state parton branching, and conversion of final partons to hadrons

via phenomenological hadronization models. This approach gives a good description

of diverse jet evolution phenomena with relatively few adjustable parameters. Both

generators were tuned to reproduce inclusive event characteristics (charged particle

multiplicity and momentum spectra, event shapes, etc.) and inclusive spectra of

identified hadrons in e+e- hadrons reaction at the center-of-mass energy around

the Zo pole.

The parton shower models of Herwig and Pythia are very similar. The cascade

evolution is treated as a branching process based on the LLA. There are three types

of parton splitting in this picture: q -+ qg, g -* gg and g -* qq. The probability

for the decay of parton a with virtual mass ma into partons b and c is given by the

"DGLAP" evolution equation [32] (used to be known as Altarelli-Parisi evolution

equation):

b dzr 2 Pabc(), (2.6)
dt 27

where the evolution parameter t is related to parent's virtuality by t=ln (m /A2) in

case of Pythia. The evolution in Herwig is done in terms of t=ln (( /A2) (essentially
""U V'J "' 'U UV'U'V 11 IUIyl IUUVIU111UUIII V Vlll~(''/A)(essentiall









in terms of emission angle Obc), where (C is defined by


E. F &c, Gc = Eb E, (2.7)
EbEc '

where Pb, Pc, Eb and Ec are the four-momenta and energies of partons b and c.

The strong coupling as(Q2) in Eq. 2.6 is evaluated at Q2 equal to the transverse

momentum squared of the branching. The splitting function Patbc(z) is used to

generate the energy fractions z and 1 z of daughter partons. The QCD coherence

effects are included in both Herwig and Pythia, however, with some difference. Thus,

Herwig has an exact implementation of the angular ordering in initial- and final-state

radiation via its evolution parameter (a (see Eq. 2.7). In the case of Pythia, the

angular ordering is implemented via ordering parton's virtuality and vetoing non-

ordered angles. Azimuthal asymmetries for gluon decays both from coherence and

spin effects are also included in Herwig and Pythia. The treatment of hard gluon

emission in Herwig is improved by matching of the first gluon branching to the three-

jet matrix element (NLO accuracy for high x). In both generators, the parton shower

is terminated when the parton virtualities drop below Qcutoff.

The real difference between Herwig and Pythia is in the implementation of the

hadronization. Herwig exploits a so-called cluster model of hadronization [33] which

is motivated by the preconfinement [23] property of the parton branching. The im-

plementation of the cluster model is the following. At the end of the parton shower,

all gluons are forced to non-perturbatively split into qq pairs. Neighboring qq pairs

then form color-neutral clusters which decay isotropically in their rest frame into

(usually) two hadrons. Special treatment is given to very light clusters, which are

allowed to "decay" into a single hadron, and to very heavy clusters which can decay

into clusters before decaying into hadrons. Baryons are produced from cluster de-

cays into baryon-antibaryon pairs, i.e. clusters themselves always have zero baryon

number. If a cluster contains a quark from the perturbative parton shower (not from










gluon splitting), the hadron formed from this quark "remembers" the original quark's

direction (given by angular probability distribution P(02) e02/20g). The advantage

of the cluster model is its simplicity and that the global event shape and the hadron

momentum spectrum are largely determined by the parameters, A and Qcutoff, gov-

erning the parton shower, and to a lesser extent by the thresholds for clusters of

too high and too low mass. The hadron flavor composition is mainly driven by the

available phase space in cluster decay, in other words, by the cluster mass spectrum

which is asymptotically Q-independent and universal.

The conversion of partons to hadrons in Pythia is accomplished by the Lund

String Model [34]. It is easier to understand the concept of string fragmentation

using an example of the qq pair production in e+e- annihilation. Neglecting for the

moment the soft gluon radiation, the produced quark and antiquark move out in

opposite directions, losing energy to the color field, which collapses into a string-

like configuration between them. The string has a uniform energy per unit length,

corresponding to a linear quark confining potential. The string then breaks up into

hadrons through spontaneous qq pair production in its intense color field. The addi-

tion of gluon radiation results in kinks on the string, each initially carrying localized

energy and momentum equal to that of its parent gluon. During a string breakup in

its rest frame, the (equal and opposite) transverse moment of quarks from a qq pair

are generated according to a Gaussian distribution of width oq. Longitudinal hadron

moment are determined by means of phenomenological fragmentation functions: the

Lund symmetric function for light (u,d,s) quarks, and the Peterson [35] function for

c and b quarks. Baryon production is included by allowing diquark-antiquark pairs

to be created. Meson production in the string between baryon and antibaryon is also

allowed. The string model has a few parameters to describe the energy-momentum

spectra of produced hadrons and many parameters to describe their flavor compo-

sition. The string model was tested extensively in e+e- collisions and showed an







19

excellent agreement with the data. However, it has a complicated structure and the

presence of a large number of phenomenological parameters somewhat shadows the

perturbative information.















CHAPTER 3
STUDIES OF QUARK AND GLUON JETS

This Chapter presents the motivation for measurements of quark and gluon jet

differences at CDF and provides an overview of early experimental results. The

feasibility and strategy of the analysis at CDF are also discussed.

3.1 Physics Motivation

Jet evolution is driven by multi-gluon emission with very small momentum trans-

fers and is governed by soft QCD. Studies of jet fragmentation probe the region where

pQCD calculations are notoriously difficult. They also facilitate investigation of the

transition between the pQCD and non-pQCD domains. One aspect of fragmentation

studies is the measurement of the mean charged particle multiplicities in gluon and

quark jets. As it was discussed in Chapter 2, pQCD has a very definite prediction

about the ratio of these multiplicities, r = Ng/Nq. The difference between quark

and gluon jets is at the heart of QCD. Therefore, not surprisingly, it has sparked

much of experimental interest. Measurements of the multiplicity differences between

quark and gluon jets have a long history. Most of these measurements come from

e+e- colliders. The pQCD calculations imply r~1.4-1.7 in the range of experimen-

tally accessible jet energies. The earliest measurements of the ratio r = Ng/Nq were

consistent with 1 (see [36, 37] and the next section). Over the 10-year LEP era, the

reported values varied from rl1.1 to r--1.5 [36] most of which had small uncertainties

and were significantly below the theoretical predictions, r~1.4-1.7 (see Fig. 3-1). It

should also be pointed out that there is a certain amount of controversy around some

of these measurements related to the difficulties and possible biases arising from the

necessity to identify and manipulate three-jet events-the only source of gluon jets

at LEP (this is left for discussion in the next section). Therefore, the range of e+e









results motivates an independent measurement of r in a different environment such

as pp collisions.

The e+e- experiments have conducted very detailed studies of the fragmentation

in quark jets. These measurements cover a wide range of jet energies from ~5 GeV to

~105 GeV. On the other hand, there are only two model-independent measurements

of gluon jet properties at well defined scales (see next section). This definitely moti-

vates more studies of gluon jets. Finally, jet fragmentation data from the Tevatron

will complement measurements from e+e- and ep experiments, providing a unique

test of the universality of jets.

There is also a practical motivation for studies of quark and gluon jets. Good

understanding of jet fragmentation is important for the success of high-PT physics

programs of Run II at the Tevatron and future LHC experiments. Utilizing the

differences in quark and gluon jet evolution can be an effective tool for reduction of

QCD backgrounds in measurements involving b-jets and/or jets from W-*q'q" and

Z-+qq decays. One of the analyses which can potentially benefit from this is the

study of top quark properties in tt-+bbjjjj channel, where the signal is all quark jets

and the background is many gluon jets.

Many analyses rely on simulation of jets by Monte Carlo event generators (e.g.,

jet energy corrections, acceptance and background estimations). Despite the fact that

both Herwig and Pythia were tuned to reproduce jet fragmentation in e+e- annihi-

lations, it is not clear if they will perform equally well in the much more complicated

and diverse environment of pp collisions. This makes it very important to compare

quark and gluon jet fragmentation in data and Monte Carlo.

3.2 Experimental History

Most early experimental results on the differences between quark and gluon jets

come from e+e- machines. Studying gluon jets in e+e- annihilations is not a trivial










task as one has to look for qqg events and identify which of the three jets is the gluon

jet. A brief review of these measurements is given below.

One of the first quoted results on ratio, r = Ng/Nq, was obtained by the HRS

collaboration. The analysis was based on selecting threefold symmetric e+e -+ qqg

events where the quark and gluon jets were produced at about the same energies

E _10 GeV [38]. The probability for a gluon jet to have higher multiplicity was tested

by assuming the Poissonian multiplicity distribution and independent production of

each of the three jets (very naive assumptions). A value r = 1.2980. was obtained.

The first result from LEP was obtained by the OPAL collaboration [39]. The "Y"

shape events from e+e- -- Z hadrons were selected for the analysis. The ratio

was found to be consistent with unity, r = 1.02 1 0.04(stat.), for jets with energies

about 24 GeV. The analysis was based on a comparison of the multiplicity in different

hemispheres with respect to the plane which was perpendicular to the three-jet event

plane and contained the highest energy jet. The gluon-tagged and normal-mixture

jets were used for the analysis. The results were not corrected for quark and gluon

jets misidentification.

The ratio started climbing up with improvements in the experimental technique.

The "Y" shape events from Zo peak were used in the next OPAL work [40]. The

highest energy jet was assumed to be a quark jet. The lower energy jets were used

to measure multiplicities. The angle between each of the lower energy jets and the

leading jet was 1500100. The so-called kT algorithm [41] was used to reconstruct jets

and assign particles to them. The charged particle multiplicities in quark and gluon

jets were derived from comparison of gluon-tagged jets and mixed jets. Monte Carlo

was used to obtain the flavor composition of the sample. The results were presented

for the energy scale Q = Ejet = 24 GeV. The average charged particle multiplicities

in gluon and quark jets were Ng = 9.100.10 and N(NFM) = 6.860.09 respectively









(here and further, NFM stands for "natural flavor mixture"1 ). The obtained ratio

was r = NgNq(NFM) = 1.326 0.054 0.073. The results were not corrected for

detector acceptance and resolution.

The SLD collaboration used essentially the same technique in their studies of

quark and gluon jets from "Y" type events [42]. The only difference was that gluon

jets were compared to jets originating from light flavor (u, d, s) quarks. The results

were reported for the energy scale Q = Ejet = 24 GeV. The measured ratio was

r = Ng/N, = 1.294 0.064 +0.04

The OPAL measurement [43] essentially repeated the previous [40] study with

only slight improvements. This time, tuned Monte Carlo was used to derive sample

purities and unfold multiplicity. The updated values were Ng = 9.10 0.07 0.09,

Nq(NFM) = 7.27 0.07 0.08 and r = Ng/Nq(NFM) = 1.251 0.024 0.073.

In the next OPAL paper [44], the same approach was used to study differences

between light quark jets and gluon jets. The corresponding results were N, = 9.16

0.07 0.12, Nsd = 6.18 0.06 0.13 and r = N/Nd, = 1.390 0.038 0.032.

The results were reported for the energy scale of Q = Ejet = 24.4 GeV. A novel part

of this work was that all measurements were repeated with the cone jet finder and

multiplicity was measured in the jet cone (R = 300). The corresponding results were

Ng = 6.18 0.06 0.13, Nud8 = 5.44 0.05 0.04 and r = Ng/Nsd = 1.135 0.031

0.029. The reported hardness scale was Q = Ejet = 24.4 GeV.

The ALEPH collaboration has also studied quark and gluon jets from "Y" shape

events at the Zo peak [45] employing the same method as OPAL and SLD. Apart

from light quarks, gluon jets were also compared to c- and b-flavor jets. For the

energy scale Q = Ejet = 24 GeV, ALEPH has reported the following results: N, =



1 According to PDG [14], the fractions of u, d, s, c, b quark jets produced in
Zo-hadrons are 14.5%, 23.3%, 23.79%, 16.79% and 21.62%, respectively.










9.90 0.10 0.27, Nud, = 7.90 0.44 0.26, r = Ng/Nd = 1.249 0.084 0.022

and r = N/Nq(NFM) = 1.194 0.027 0.019.

Various techniques were employed in analysing data from the Zo peak by the

DELPHI collaboration [46]. Quark and gluon jets were studied in symmetric "Y"-

type and "Mercedes"-type events. For both event types, jets from tagged and mixed

samples were used to find multiplicities in quark and gluon jets. In "Y" events, the

highest energy jet was assumed to be a quark. The gluon jet was identified by tagging

one of the lower energy jets as b-quark. The jets from the mixed sample had to fail

heavy flavor tagging. In "Mercedes" events, the angle between jets was 1200 150.

The gluon jet was identified by tagging two other jets as b-quarks. The kT-finder was

used to reconstruct jets and assign tracks. Tuned Monte Carlo was used to derive

sample purities and unfold multiplicity. The ratio from the analysis of "Y"-type

events was measured to be r = Ng/Nds = 1.279 0.021 0.020. The reported ratio

from the analysis of "Mercedes"-type events was r = Ng/Nds = 1.3230.0530.020

for the energy scale Q = Ejet = 30.4 GeV. The results from the analysis of symmetric

qqg and qq7 events were also quoted in the same paper [46]. The method was similar

to the analysis of "Y"-type events. The gluon jet was identified by tagging one of the

lower energy jets as a b-quark. The multiplicity in quark jets of reduced energy was

obtained from qq7 events. The JADE [47] and kT algorithms were used to reconstruct

jets and assign particles. The reported energy scale was Q = Ejt = 26.6 GeV. The

quark jet sample contained 33% of c-quarks and 11% of b-quarks which was slightly

different from the NFM sample. The results obtained with kT and JADE algorithms

were r = Ng/Nudscb = 1.2320.0220.018 and r = Ng/Nudscb = 1.3690.0190.035,

respectively.

All the analyses discussed so far were based on the comparison of jets in twofold

or threefold symmetric 3-jet events. These measurements suffered from one major

problem-the ambiguous assignment of particles to jets in three-jet events which










heavily depended on the details of the particular jet finding algorithm (such jets are

called biased). As a consequence, the results obtained with different algorithms were

very inconsistent. The other basic problem was related to improper choice of the

energy scale for comparison of the data and theory. Thus, the results were reported

for the jet energy as the scale of fragmentation. However, it was later shown in ref.

[48] that it is not the jet energy which describes the fragmentation of jets in three-jet

events. Therefore, the discussed results are biased and cannot be used for comparison

to theory predictions and CDF data.

The problems described above were realized and avoided in the later measure-

ments by CLEO and OPAL. CLEO has obtained the ratio by comparing multiplicity

in T -+ ggy and e+e -+ qq events [49]. The multiplicity in this measurement was

defined inclusively as a number of charged particles in one hemisphere. The quark

sample presented a natural flavor mixture where the fractions of u, d, s, c quarks were

approximately the same. The results were reported for the dijet mass in the range 4

GeV < Mjj < 7 GeV. The reported ratio was r = 1.040.020.05. The energy scale

in this measurement was still too low to clearly see the difference between quark and

gluon jets. In the earlier work [50], the CLEO collaboration has also reported the re-

sults on the charged particle multiplicity in gluon jets at the dijet mass of Mjj = 10.3

GeV: 2N9 = 9.339 0.090 0.045.

The OPAL collaboration returned to studies of "Y" shape events with the sig-

nificantly modified method [51]. A new analysis was based on selecting rare events

where a gluon jet was recoiling against two almost collinear quark jets. Each such

event was divided into two hemispheres by the plane perpendicular to the thrust axis.

A gluon and two tagged b-quark jets were required to be in the opposite hemispheres.

The multiplicity in a gluon jet was then defined inclusively as all charged particles

in a hemisphere. The average gluon jet energy was Ejt = 39.2 GeV. It is important

to note that the jet clustering algorithm was not used to define the gluon jet and









assign particles to it. It was demonstrated in ref. [52] that the properties of gluon

jets selected as described above correspond very closely to the properties of gluon

jets produced from a color singlet source. The multiplicity in quark jets was defined

inclusively as half of the multiplicity in Zo hadrons event. The events had to pass

the light flavor (u, d, s) jet selection criteria. The average energy of quark jets was

Ejet = 45.6 GeV. The multiplicity in quark jets was corrected to account for the differ-

ence in energy compared to gluon jets. Purities of both samples (~80% for gluons, and

~86% for light quarks) and corrections for backgrounds were obtained based on Jet-

set Monte Carlo simulation. The corresponding results were Ng = 14.630.38 0.60,

Nds = 9.50 0.04 0.24 and r = Ng/Nd, = 1.552 0.041 0.060. The reported

energy scale was Q = 2Ejt = 78.4 GeV.

The next OPAL measurements [53, 54] basically repeated with better statistics

the previous analysis [51]. The [53] results were Ng = 14.32 0.23 0.40, N1ds =

10.100.010.18, r = Ng/Nd, = 1.4710.0240.043, with the corresponding energy

scale Q = 2Ejt = 83.6 GeV. The results obtained in [54] were Ng = 14.280.180.31

and r = Ng/Nd, = 1.514 0.019 0.034. The scale was Q = 2Ejt = 80.2 GeV.

The discussed above CLEO [49, 50] and OPAL [51, 53, 54] measurements are

the only model-independent studies of properties of unbiased gluon jets in e+e- an-

nihilations at theoretically well defined energy scales. All so far discussed early ex-

perimental results on the difference between quark and gluon jets are summarized in

Tables 3-1, 3-2 and presented in Fig. 3-1. There are also a few model-dependent and

indirect studies of the multiplicity in gluon jets and the ratio r = Ng/Nq performed

by OPAL and CDF. These measurements are discussed below.

The OPAL collaboration has recently conducted two measurements of the gluon

jet properties. In the first model-dependent study [55], the kT algorithm was tuned to

identify exactly three jets in every event, and only Y-shape events were retained for

the analysis. The multiplicity in a gluon jet was extracted from the multiplicity in a










History of measurements of the ratio of charged
particle multiplicities in Gluon and Quark Jets



LLA, r=CA/CF=2.25

2

M t




Capella et al., 2000 A CLEO 0 DELPHI
Lupia & Ochs, 1998RS ALEPH
Catani et al., 1991 HRS 0 ALEP
0- Mueller, 1984 D OPAL 0 SLD
i
10 100
Q, GeV

Figure 3-1: History of measurements of the ratio of charged particle multiplicities in
gluon and quark jets.


3-jet event by using a theoretical formalism [48] which is valid up to MLLA accuracy.

The multiplicity in unbiased quark jets was obtained from the 3NLO fit [36] to the

inclusive multiplicity in e+e- -+ hadrons events with removed contribution from c, b-

quarks. The reported energy scale was Q = PT,Lu. It was shown in ref. [48] that

PT,LU2 can be used as an energy scale for unbiased gluon jets from 3-jet events. The

results for multiplicity in gluon jets and the ratio, r = Ngluon/Nuds, were reported for

the energy scale in the range from Q=11.1 GeV to Q=30.5 GeV. At Q=30 GeV, the

reported ratio is r = 1.422 0.006 0.051.

In the next measurement [56], gluon jets from 3-jet events were studied by ap-

plying the so-called jet boost algorithm [57] which was motivated by the color dipole




2 PT,Lu = / where sij is the invariant mass of i, j jets. The kinematic limit
for this scale is PT,LU < s/2.
















Table 3-1: The summary of model-independent measurements of the difference be-
tween quark and gluon jets conducted on e+e- machines. The results are obtained
using biased gluon jets. Therefore, they can not be directly compared to theory or
CDF results.

Experiment Hardness, Q Ng1~o, Nquark ratio
HRS[38] Ejet10 GeV 129+
OPAL[39] Ejet-24 GeV 1.020.04(stat.)
OPAL[40] Ejet_24 GeV 9.1010.10 NNFM= N,/NNFM=
6.860.09 1.3260.0540.073
SLD[42] (Ejet)_24 GeV -Ng/Nds =
1.2940.064+0.047
0.064
OPAL[43] NNFM= N,/NNFM=
kT-based Ejet=24.39 GeV 9.1010.070.09 7.270.070.08 1.2510.0240.029
Cone-based Ejet=24.40 GeV 6.2610.060.07 5.710.050.05 1.0960.0230.023
OPAL[44] Nuds= N, lNuds=
kT-based Ejet=24.38 GeV 9.1610.070.12 6.590.060.10 1.3900.0380.032
Cone-based Ejet=24.38 GeV 6.1810.060.13 5.440.050.04 1.1350.0310.029
ALEPH[45] Nuds= Ng/Nuds=
Ejet=24 GeV 9.9010.100.27 7.900.440.26 1.2490.0840.022
NNFM= Ng/NNFM=
8.2860.090.22 1.1940.0270.019
DELPHI[46] Nudscb= N/Nudscb=
kr-based Ejet=10.0 GeV 5.7810.06 5.430.90 1.060.18
kr-based Ejet=15.0 GeV 6.6410.09 5.540.43 1.200.09
kr-based Ejet=20.0 GeV 8.1810.17 7.520.36 1.090.06
kT-based Ejet=25.0 GeV 9.1310.14 7.380.33 1.240.06
kT-based Ejt =30.0 GeV 9.8310.30 7.890.35 1.250.07
kT-based Ejt=35.0 GeV 10.6710.33 8.240.17 1.290.05
kT-based Ejet=40.0 GeV 11.8610.68 8.610.20 1.380.09
kT-based (Ejet)=26.6 GeV -1.2320.0220.018
Jade-based Ejt=10.0 GeV 7.0410.10 5.440.85 1.290.20
Jade-based Ejet=15.0 GeV 7.9510.14 6.730.81 1.180.14
Jade-based Ejet=20.0 GeV 9.3510.19 7.460.53 1.250.09
Jade-based Ejet=25.0 GeV 10.160.43 7.500.33 1.350.06
Jade-based Ejet=30.0 GeV 11.180.47 8.190.19 1.370.07
Jade-based Ejet=35.0 GeV 11.270.74 8.200.23 1.370.10
Jade-based Ejet=40.0 GeV 12.611.32 8.410.16 1.500.16
Jade-based (Ejet)=26.6 GeV -1.3690.0190.035
N/Nuds =
kT-based Ejet=24.2 GeV 1.2790.0210.020
kT-based Ejt =30.4 GeV 1.3230.0530.020
kT-based Ejet=30.4 GeV N,/NNFM=
1.2530.0280.044









model of QCD [58]. According to this technique, the color charge of the gluon in

e+e -+ qqg events can be decomposed into two parts: one equal and opposite to the

color charge of the quark and the other equal and opposite to the color charge of the

antiquark. Therefore, a e+e- qqg event consists of two independent dipoles. For

symmetric 3-jet events, each dipole can be independently boosted to a back-to-back

frame where the dipoles can be combined to yield an event with the color structure of

a gg event from a color singlet. In this measurement, the symmetric Y-shape events

were selected by adjusting the resolution of the kT algorithm to identify exactly three

jets in every event. The results on multiplicity in unbiased gluon were obtained for

the energy scale, Q = 2Et = 2Ejet sin(O/2) (9 is the angle between two lower

energy jets), in the range from 10.5 GeV to 35.4 GeV. To obtain the results on ratio

r = Ngluon/Nuds, the multiplicity in gluon jets was compared to the multiplicity in

unbiased quark jets measured in other e+e- experiments. The reported ratio was

r ~ 1.2 1.5 for Q ~ 10.5-35.4 GeV. Despite the fact that properties of gluon jets

in this analysis were not directly determined by using any theoretical formalism, the

measurement still cannot be considered as direct because 3-jet events resembling the

structure of gg events at specific energy scale were used rather than well defined

gluon jets. Moreover, the ratio was obtained by comparing jets from different event

topologies: gluons from 3-jet events and quarks from 2-jet events.

The CDF collaboration has also obtained results on the ratio r = Ng/Nq in

two model-dependent analyses of jets from dijet events. Both measurements were

performed for events in a wide range of dijet invariant masses, 72 GeV < Mjj <

740 GeV. The analyses were done in the dijet center-of-mass frame, and charged

particles were counted in small cones around the jet directions (0c < 0.47 rad). In

the first measurement [59], the ratio was extracted from the MLLA fits of the mean

multiplicity evolution with the energy scale. The ratio was found to be r=1.70.3.

In the other analysis [60], the ratio was obtained by considering the evolution of the










Table 3-2: The summary of model-independent measurements of the difference be-
tween quark and gluon jets conducted at e+e- machines using unbiased gluon jets.
These results can be directly compared to theory or CDF data.


Experiment Hardness, Q Nglun Nquark ratio
CLEO[49] 4 GeV 2N = 1.0410.0210.05
Mj =4.5 GeV 4.880.10(stat.)
Mjj=5.5 GeV 5.280.10(stat.)
Mjj=6.5 GeV 5.650.12(stat.)
CLEO[50] Mjj=10.3 GeV 2Ng =
9.3390.0900.045 -
OPAL[51] Nuds- NlNds=
2Ejet=78.4 GeV 14.630.380.60 9.500.040.24 1.5520.04110.060
OPAL[53] 2Ejet=83.6 GeV 14.320.230.40 10.100.010.18 1.4710.02410.043
OPAL[54] 2jejt=80.2 GeV 14.280.180.31 1.5140.01910.034


charged particle momentum spectra with the energy scale. The ratio reported in this

analysis was r=1.90.5.

The results of the last four measurements discussed above are summarized in the

Table 3 3.

3.3 Feasibility of Quark and Gluon Jet Studies at CDF

The major advantage of studying differences between quark and gluon jets in pp

collisions as compared to e+e- annihilations is that gluon jets are produced on equal

footing with quark jets. Therefore, there is no need to look for peculiar 3-jet events

to obtain a sample of gluon jets. Moreover, different rates of production of gluon

jets in different subprocesses with similar event topology can be used to statistically

separate quarks from gluons. For instance, one can use for an analysis jets from

dijet and '+jet or Z+jet events (compared to Z+jet sample, '+jet events are more

contaminated by background, but they have an advantage of much higher production

rate).

In order to compare theory predictions with data from hadron collisions, the

analysis has to be performed in the center-of-mass frame of the dijet (or 7/Z+jet)

system where jets (or 7/Z and jet) are back-to-back. Theory also prescribes that























Table 3-3: The summary of model-dependent and indirect measurements of the dif-
ference between gluon jets and light flavor, u-, d-, s-, quark jets.


Hardness, Q2
Q = PT,Lu=30 GeV
11.1 GeV
12.6 GeV
14.1 GeV
15.5 GeV
17.0 GeV
18.4 GeV
19.9 GeV
21.4 GeV
22.9 GeV
24.0 GeV
25.4 GeV
26.7 GeV
27.9 GeV
28.7 GeV
29.6 GeV
30.2 GeV
30.5 GeV


10.60.21.8
11.00.31.7
11.20.31.7
13.00.31.9
13.20.41.8
13.30.41.7
14.40.51.2
14.50.51.1
15.000.520.87
15.530.570.94
15.80.61.5
15.90.61.9
16.50.72.5
17.90.72.0
17.60.72.3
19.10.71.6
18.20.71.9


r = Ng/Nq
1.4220.0060.051
1.310.030.22
1.290.030.20
1.250.030.19
1.390.040.20
1.350.040.19
1.310.040.17
1.380.050.12
1.3440.0460.098
1.3530.0470.079
1.3710.0500.083
1.360.050.13
1.340.050.16
1.370.060.21
1.460.060.16
1.420.060.18
1.530.060.13
1.450.060.15


OPAL[56] Q = 2E*Et = 2Ejet sin(9/2) =
~10.5-35.44 GeV -r ~1.3-1.5
10.50 GeV 9.6060.0600.094
11.96 GeV 10.3800.06010.124 -
13.96 GeV 11.3540.06010.148 -
16.86 GeV 12.5820.06010.180 -
21.84 GeV 14.7560.12410.154 -
28.48 GeV 17.240.260.20
35.44 GeV 19.040.600.66
CDF[59] 72 GeV< Mjj <740 GeV 1.70.3
CDF[60] 72 GeV< Mjj <740 GeV 1.90.5


Experiment
OPAL[55]










particles have to be counted in small cones, 0~, around the jet directions (pQCD

calculations are valid for 0<<1). This, in fact, helps to avoid an ambiguity in assigning

particles to jets (one of the major problems of early e+e- measurements).

Despite all the advantages of studying quark and gluon jets at a hadron collider

such as the Tevatron, there are also factors complicating the analysis. Unlike to e+e-

annihilations, the hard scattering in pp collisions is always accompanied by interac-

tions of proton and anti-proton remnants (the underlying event) whose contribution

has to be properly subtracted. There is also initial state radiation (ISR) from in-

coming partons and color connection between initial and final jets. To reduce the

influence of these effects on measurements, central (at large angles with respect to

beam direction) jets have to be selected for the analysis. The presence of multiple

interactions in the same bunch crossing (secondary events are often referred as "pile-

up") also has to be accounted for. Finally, jet energy measurement in pp collisions is

more complicated because a part of the total energy (associated with the underlying

event) always escapes the detector (in e+e- annihilations, the total energy that would

be deposited in the calorimeter is known a priori).

3.4 Analysis Strategy at CDF

The CDF analysis on fragmentation of quark and gluon jets is largely inde-

pendent of theoretical models of fragmentation. This independence is achieved by

exploiting the difference in quark and gluon jet content of dijet events and 7+jet

events in pp collisions. Dijet events have large gluon content because the gluon com-

ponent in the proton (or anti-proton) is dominant at relatively small XT = 2ET//-V.

In 7+jet events, the jet is usually originating from a quark. This difference in gluon

jet content allows for distinguishing and measuring the properties of gluon and quark

jets on statistical basis. Thus, we do not have to discriminate between quark and

gluon jets when selecting events.









The average charged particle multiplicities per jet in, Nj and Njj, '+jet and

dijet data samples, respectively, can be expressed as functions of the multiplicities in

gluon and quark jets, Ng and Nq:


Njj = fg Ng + (1 fg )N, (3.1)



Nj = fg Ng + (1 f )Nq, (3.2)

where f and f, are fractions of gluon jets in dijet and 7+jet events. To take into

account possible contamination of 7+jet events by fake photons (discussed in Chapter

8), Eq. 3.2 must be modified as follows:


Ny = 56(fg'Ng + (1 fgf)Nq) + (1 S6)Nfj, (3.3)

where S6 is the fraction of real photons among the photon candidates, and Nfj is the

multiplicity in the jet opposite to the fake photon. Eqs. 3.1, 3.3 allow us to extract

the average charged particle multiplicities in gluon and quark jets, Ng and Nq, as well

as their ratio, r = Ng/Nq:

Sa 5r x (a 1) -
r = 1 + -N -- (3.4)
N, f x 6, x f (1 ) x fg xa


rNAP
Ng = 3 1 (3.5)
f (r 1) + 1

N
Nq = -- (3.6)
Sfg'(r 1)+

where we introduced a = Nfj/Njj, to account for possible differences between a jet

from a regular dijet event and a jet opposite to a fake photon.

In summary, we can measure the average charged particle multiplicities in gluon

and quark jets, N, and Nq, as well as their ratio, r = Ng/Nq, by directly measuring or







34

evaluating the following six independent parameters: multiplicity per jet in dijet and

7+jet events, Njj and Nj; fraction of gluon jets in dijet and 7+jet events, f3i and

fY ; purity of the 7+jet sample, 6,; ratio of multiplicities in a jet from a regular dijet

event and a jet opposite to a fake photon, a. These measurements will be described

in Chapter 8.















CHAPTER 4
ACCELERATOR AND DETECTOR

The Fermi National Accelerator Laboratory (FNAL, Fermilab) is the leading

facility in the experimental particle physics. Fermilab is the home of a hadron collider

called the Tevatron. The Tevatron is the worlds most powerful accelerator. It was

the site of the bottom and the top quark discoveries. There is a chance we can even

witness a discovery of the long-hypothesized Higgs boson during the Run 2 of the

Tevatron.

The Collider Detector at Fermilab (CDF) is one of the two (the other one is

DO) multipurpose detectors built at collision points of the Tevatron. The analysis

presented in this dissertation is based on the data sample collected by CDF during

the 1993-1995 running period of the Tevatron.

4.1 Tevatron during the 1993-1995 Running Period

The Fermilab accelerator complex is shown on a schematic drawing on Fig. 4-1.

The pp collisions at the center-of-mass energy of 1.8 TeV were produced by a

sequence of five individual accelerators. First, a Cocroft-Walton accelerator boosted

negative hydrogen ions to 750 KeV energy. Then, the ions were directed to the second

stage of the process provided by the Linac. The Linac is a 145 m long, two-stage linear

accelerator that further increased the energy of ions up to 401.5 MeV. To produce

the protons before the next stage, the ions were stripped of their electrons by passing

through a carbon foil. Protons leaving the Linac entered the Booster. The Booster

is a synchrotron accelerator of about 150 m in diameter. It was used to accelerate

protons up to 8 GeV. Next, protons were injected into another circular accelerator

called the Main Ring. The Main Ring is a 1 km radius machine which consists of a

total of 774 dipole and 240 quadrupole superconducting magnets used to keep protons









Main Ring
Antiproton Storage Ring





Antiprotons Protons




/ Booster

Tevatron CDF Linac
Cockroft- Walton

Figure 4-1: Overview of the Fermilab accelerator complex. The pp collisions at
the center-of-mass energy of 1.8 TeV are produced by a sequence of five individual
accelerators: the Cockroft-Walton, Linac, Booster, Main Ring, and Tevatron.


in a stable circular orbit. The Main Ring served two functions. It provided a source

of 120 GeV protons which were used to produce anti-protons and boosted protons

and anti-protons up to 150 GeV before injecting them into the Tevatron.

In order to produce anti-protons, protons of 120 GeV energy were transported

from the Main Ring to a tungsten target. The produced sprays of secondary particles

contained anti-protons. Those anti-protons were selected and stored into the De-

buncher ring where they were stochastically cooled to reduce the momentum spread.

At the end of this process, the anti-protons were stored in an Accumulator, until they

were needed in the Tevatron. The Tevatron is located 65 cm below the Main Ring in

the same tunnel. It is a synchrotron accelerator that uses a total of 774 dipole and

216 quadrupole superconducting magnets cooled down to 4.6 K by liquid helium.

Finally, 150 GeV protons and anti-protons were injected into the Tevatron where

they were simultaneously accelerated to 900 GeV. Therefore, the center-of-mass en-

ergy of colliding beams was 1.8 TeV. The Tevatron counter-circulated six bunches

of protons and anti-protons which were collided every 3.5 ps. The proton bunches







37

contained approximately 2x 1011 protons, and the anti-proton bunches had 2-9 x1010

anti-protons. During the Run 1B, the collision volume was approximately circular in

the x y plane with an average radius of 25 pum and had a Gaussian distribution

with a sigma of 30 cm in z direction.

The instantaneous luminosity of the Tevatron is given by

N, NPf
finst (4.1)


where Np and Np are the numbers of protons and anti-protons per bunch, f is the

frequency of bunch crossings and A is the effective area of the crossing beams. For

the Run 1B, the average initial luminosity was inst 1.6x1031 cm2s-1. The instan-

taneous luminosity exponentially decreases with time due to transverse spreading of

the beam and losses of protons and anti-protons from collisions. The period of time

when the same proton and anti-proton bunches continue to collide is called a store.

The typical store duration during the Run 1B was about 8-18 hours. The luminosity

decreases by approximately an order of magnitude during the lifetime of a store.

4.2 CDF Design and Overview

The CDF is a multipurpose collider detector located at one of the two colliding

beam interaction points. It is designed to study a wide range of processes occurring in

pp collisions. The CDF allows to observe and measure the properties of jets, photons,

electrons, muons and charged hadrons.

A schematic drawing of the CDF detector can be found on Fig. 4-2. The CDF

is approximately cylindrically symmetric about the beam direction. It is about 10 m

high, extends about 27 m from end to end, and weighs over 5000 ton. The CDF uses

a right-handed Cartesian coordinate system with its origin in the nominal interaction

point (center of the detector). The positive z-axis points in the proton beam direction,

positive y-axis points vertically upward, and the positive x-axis points toward the

center of the Tevatron ring. The azimuthal angle 0 is measured around the beam



























Figure 4-2: Drawing of the CDF detector. One quarter view.


axis from the positive x-axis. The polar angle 0 is defined as the angle measured from

the positive z-axis. It is more often that the pseudo-rapidity, rq=- ln(tan(0/2)), is

used in place of the polar angle. The pseudo-rapidity can be defined with respect to

the actual position of the interaction vertex (event ry) and with respect to the center

of the detector (detector rjd)

The major components of the CDF detector are listed below:

Silicon Vertex Detector (SVX). The SVX was designed for precise measurement

of the position of the interaction vertex in the r 0 plane.

Vertex Time Projection Chamber (VTX). It measures the z-position of the

interaction vertex.

Central Tracking Chamber (CTC). The CTC provides measurements of momen-

tum and spatial parameters of particle's trajectories (tracks) in the magnetic

field (B=1.4 T).

Calorimetry (central, plug and forward calorimeters). Two types of calorime-

ters, electromagnetic (EM) and hadronic (HA), are used to measure the energy

of photons, electrons and jets of particles.










Central Preradiator detector (CPR) and Central Electromagnetic Strip Cham-

ber (CES). The CPR and CES are important components of the photon and

electron identification.

Muon System (made of layers of drift chambers and scintillators). The Muon

System is positioned (partially) behind a special protective steel wall, which

absorbs all particles that may escape the calorimeter except for muons.

Beam-Beam Counters (BBC). The BBC provides measurement of the instan-

taneous luminosity.

The CDF detector is described in ref. [61] and references therein. In the rest of

this chapter we will discuss in more details the sub-detectors directly related to this

analysis.

4.2.1 Vertex Detectors (VTX and SVX)

The Silicon Microstrip Detector (SVX) surrounds the beryllium beam pipe. The

SVX is about 60 cm long and covers the radial region from 3.0 cm to 7.9 cm. It consists

of 4 layers of silicon strips parallel to the beam line. The SVX covers rl]d < 1.0 region

and has acceptance of ~60% in this range. Its single hit resolution in the transverse

plane is ~10 pm. The SVX is a part of the tracking system along with VTX and

CTC. It provides a very precise measurement of the transverse position of the event

vertex.

Directly outside of the SVX is the Vertex Time Projection Chamber (VTX)

detector. The VTX is 2.8 m long in z direction and extends from an inner radius 8

cm out to a radius of 22 cm from the beam pipe. It is made of 8 octagonal modules

divided into 8 separate wedges. The chambers are filled with a mixture of 50% argon

and 50% ethane gases. The VTX provides r z tracking information which is used

to determine the position of the interaction vertex in z direction with the resolution

of ~1 mm.


























554 00 mm I D


2760.00 mm O.D.



Figure 4-3: The CTC end plate view.


Both SVX and VTX are the critical components of the CDF detector used in

many analyses. They allow to precisely determine the primary interaction position

as well as to identify events with multiple interactions.

4.2.2 Central Tracking Chamber (CTC)

The Central Tracking Chamber (CTC) extends from a radius of 31 cm up to a

radius of 132 cm from the beam pipe. It provides an angular coverage up to Tral < 1.5,

however, it is most efficient in the region of r]dl < 1.0. The CTC is a gas drift chamber

of cylindrical shape. It has 9 super-layers of wires. The super-layers are divided on 5

axial and 4 stereo super-layers. Every axial layer has 12 sense wires arranged along

the beam line. The role of axial super-layers is to provide r 0 information. Each

of stereo layers has 6 sense wires which are tilted 3 with respect to the beam axis.

The stereo layers provide r z information about particle's trajectory. The wires

in both stereo and axial layers are arranged in planes which make a 450 angle with

respect to radial direction to compensate for the drift of ions caused by the 1.4 T










Table 4-1: Selected parameters of the CDF Central Tracking Chamber.

Number of sense wires 30,504
Number of layers 84
Number of super-layers 9 (5 axial + 4 stereo)
Drift field -1350 V/cm
Resolution (Sro) <200 /m per wire
Efficiency >98% per hit
Double track resolution <5 mm or 100 ns
Maximum drift distance 40 mm
Maximum hits per wire >7
Axial (z) resolution ~4 mm
Momentum resolution SPT/pT 0.002 pr
Rmin, Rmax 31 cm and 132 cm
Magnetic field, B 1.4 T


magnetic field. Fig. 4-3 shows the end plate view of the CTC, and some of the

essential parameters of the CTC are summarized in Table 4-1.

The CTC is used to measure the momentum and spatial parameters of particle's

trajectory by arranging hits produced by a passing detector particle into segments

of hits in same layer and then linking into a full trajectory. The Tracking Algorithm

then fits the obtained hits to a helix (particle's trajectory in the magnetic field). The

momentum resolution of the CTC alone is better than SpT/pr 0.002 pr. The

resolution improves if the information from VTX, SVX and CTC is combined.

4.2.3 Preshower and Shower Maximum Detectors, Calorimetry

The Central Preradiator Detector (CPR) is positioned between the supercon-

ducting solenoid and the central calorimeter. The solenoid serves as a radiator that

converts ~60% of the photons into electron-positron showers that are detected in the

CPR. The CPR is an array of 24 multi-wire proportional chambers (one per azimuthal

wedge of the central calorimeter). Each chamber is a rectangular cell 37.3 cm wide

(150 in q) and 2.86 cm high that contains 32 sense wires. The sense wires are read

out in pairs, thus providing an effective spatial resolution of 1.11 cm in r q view










(or 0.0065 radians in 0). There are four CPR cylinders of 124 cm long which cover

the region between z=-248 cm and z=248 cm (or |rUd < 1.0 angular region).

The Central Electromagnetic Strip chamber (CES) is located in the central elec-

tromagnetic calorimeter at depth of about 5.9 radiation lengths which corresponds

to the point where maximum electromagnetic shower development occurs. The CES

determines the shower position and transverse shower development by measuring the

charge deposited on orthogonal strips and wires. Cathode strips are arranged in the

azimuthal direction providing z-view information, while anode wires are arranged in

the z direction providing the r b view information. The CES is located 184 cm

from the beam line. There are 24 strip chambers corresponding to each wedge of the

calorimeter. There are two strip and wire sections per wedge. The decision between

sections is located at |z =121.2 cm. In the first section, there are 69 strips of 1.67 cm

wide which fill the region between 6.2 and 121.2 cm. In the second section, there are

59 strips of 2.01 cm wide which fill the region between 121.2 and 239.6 cm. There are

also 62 wire cells in each half section. The segmentation of the CES detector provides

a shower position resolution of ~2 mm in each direction for 50 GeV electrons.

The CPR and CES detectors are the most important elements in the photon

identification. The information from these detectors is used to suppress the neutral

meson background as well as to determine the purity of the photon sample. The

measurement of the fraction of real photons among the photon candidates is based

on evaluating the y-conversion probability in the CPR. It also uses the transverse

profile of the electromagnetic shower measured by the CES detector.

The CDF calorimetry contains seven calorimeter systems: CEM (Central Elec-

tromagnetic), PEM (Plug Electromagnetic), FEM (Forward Electromagnetic),CHA

(Central Hadronic), WHA (Wall Hadronic), PHA (Plug Hadronic) and FHA (For-

ward Hadronic). The CDF calorimeter system provides full 27 azimuthal coverage,

and it extends up to 4.2 in pseudo-rapidity. The segmentation and rapidity coverage









of each of the calorimeter components are given in Table 4-2. We will further consider

in more details the CEM, CHA and WHA calorimeters because they are directly used

in this analysis.

The CDF calorimeter system has a projective geometry, i.e. all towers point to

the center of the detector. Each tower of the center calorimeter has a few alternating

layers of absorber (lead in CEM and iron in CHA and WHA) and active (polystyrene

scintillator in CEM and acrylic scintillator in CHA and WHA) media. When a particle

passes through the dense absorber media it interacts with its material loosing some

energy and producing a shower of secondary particles. Then, secondary particles

interact with the active media and produce light which is collected and converted

into the energy measurement. The electromagnetic shower develops spatially faster

than hadronic shower, therefore the electromagnetic calorimeter is positioned closer

to the interaction point. The CEM extends from the radius of 173 cm up to 208 cm

from the beam line. A total thickness of the CEM material is equivalent to about 18

radiation lengths. The CHA is located right after the CEM. Both CHA and WHA

have a total material depth of about 4.5 interaction lengths. The energy resolution

of the CEM for electrons (and photons) between 10 and 100 GeV is

a(E) 13.5%
S( =1- 1.7% (CEM), (4.2)
E JEP

where ET is the transverse energy of the electron (photon), and the symbol D indicates

that two independent terms are added in quadrature. The energy resolution of the

CHA and WHA for charged pions between 10 and 150 GeV is

a(E) 50%
-= g 3% (CHA), (4.3)

a(E) 75%
=) e4% (WHA),
E VI-

respectively. The initial calibration of the electromagnetic and hadronic calorimeters

was performed with 50 GeV electrons and charged pions during the test beam.










Table 4-2: The CDF Calorimeter System coverage and detector segmentation.

Detector Pseudorapidity, ld rid -- segmentation
CEM 0.0-1.1 0.11 x 150
Central Calorimeter CHA 0.0-0.9 0.1 x 150
WHA 0.7-1.3 0.11 x 150
PEM 1.1-2.4 0.09 x 50
Forward Calorimeter PHA 1.3-2.4 0.09 x 5"
FEM 2.2-4.2 0.1 x 50
FEM 2.3-4.2 0.1 x 5"


In this analysis the calorimeter was used to determine the momentum and direc-

tion of photons and jets.

4.3 CDF Trigger System

The inelastic pp cross section at vs = 1.8 TeV is about 50 mb (~50x10-27

cm2). For a typical instantaneous luminosity Lint = 1.6 x 1031 cm-2/s we have

about 800,000 inelastic collisions per second at CDF. The CDF readout electronics

and event storage system are not physically capable to write events at such a high

rate (CDF Run 1 storage media can write a few events per second). Moreover, most

of these events do not present a significant interest for the CDF physics program.

Another concern for the data acquisition system (DAQ) is to minimize the dead-time

that occurs when a particular event is being read out of the detector electronics and

processed. To reduce the readout rate and effectively process only events interesting

in terms of physics, the CDF developed a sophisticated on-line three-level (Level 1,

Level 2 and Level 3) trigger system [62]. Each next trigger level examines fewer

events but in greater details. The Level 1 and Level 2 triggers present fast hardware

implemented algorithms, while the Level 3 trigger is implemented in software running

on the commercial computers. The individual trigger path can be prescaled which

means only a fraction of events satisfying the trigger requirements is accepted. It is

done to keep the trigger rates manageable and still have data samples for wide variety

of processes.










The CDF Level 1 trigger examines every bunch crossing and makes a trigger

decision within 3.5 ps between bunch crossings, thus it has no dead-time. The Level

1 uses the information about energy of calorimeter towers or hits in the muon system.

It reduces the rate from ~280 kHz down to 1 kHz.

The Level 2 trigger requires about 25-35 ps to process an event arrived from the

Level 1 trigger and can incur dead-time of a few percent. The Level 2 output rate is

limited to about 40-45 Hz. The Level 2 algorithm uses the information about high

momentum tracks and clustered calorimeter energy. If the accept decision is made by

the trigger, then the information from all subsystems is read out and passed on Level

3.

The Level 3 trigger consists of on-line software filters based on simplified versions

of the offline reconstruction code. All events which pass the Level 3 trigger are written

on disk or tape with a typical output rate of 8 Hz.















CHAPTER 5
JETS AT CDF

Jets at CDF are defined using a cone clustering algorithm based on the Snowmass

convention [63]. Jets are reconstructed using calorimeter energies and the position of

the primary vertex. The jet algorithm is implemented in the standard CDF routine

JETCLU. The clustering is done in three steps: preclustering, clustering, and merg-

ing. A set of corrections is applied to raw jet energies in the cone to compensate for

detector and physics effects.

Jet reconstruction begins by creating a list of calorimeter towers with ET >

1 GeV which are called seed towers. The seeds are stored in order of decreasing

ET. Preclusters are formed by combining seed towers within a cone of radius R =

/(A)2+ (A) in r7-0 space. A seed tower is added to the precluster if it is within
a radius R from a seed tower which is already assigned to the precluster. Jets are

typically clustered using three cone sizes R=0.4, 0.7, and 1.0. In this analysis, jets

are defined using the radius R=0.7 (standard for many QCD analyses at CDF).

The jet clustering is performed using the ET weighted centroid of a precluster



Ell -, ETj
77c Z En (5.1)
En Ei










where the sums are carried out over all seed towers in the precluster. The tower

centroid (ri, 0i) is obtained by

EEM EM + EHA HA
Ti i ETi i ( )

EEM EM + EHA HA
e E Te, i a T,i Ei
ET

where EEM and Ef are transverse energies deposited in the electromagnetic and

(EM) and hadronic (HA) parts of the ith calorimeter tower, (rfiE, OfM) and (r7HA, 0HA)

are the centroids of the electromagnetic and hadronic components of the tower cal-

culated with respect to the event vertex (not the same as the geometric center of the

CDF detector).

A cone of radius R is formed around the centroid of a precluster. All towers with

ET > 100 MeV are merged to form a cluster if their centroids are within the cone. A

new cluster centroid is re-calculated using all the towers within the cone, and a new

cone is formed. The process continues until the cone centroid becomes stable. This

procedure is repeated for all preclusters.

After the clustering stage, there can be some towers which are shared by two

or more clusters. If one cluster is entirely within the other one, then the smaller

cluster is dropped. If two clusters partially overlap, an overlap fraction is calculated

by summing the ET of shared towers and dividing the sum by ET of the smaller

cluster. The two clusters are merged if this fraction is above 0.75. If the fraction is

less than 0.75, the clusters are kept unchanged and the towers are assigned to the

nearest cluster in rq-0 space. After all the towers are uniquely assigned to clusters,

the clustering and merging procedures are repeated until all clusters remain stable.

After all jets are reconstructed, a set of corrections [64] is applied to the raw jet

energy in the cone: to compensate for the non-linearity and non-uniformity of the

energy response of the calorimeter; to subtract the energy deposited in the jet cone

by sources other than the initial parton (underlying event, multiple interactions etc.);







48

and to add the energy radiated by the initial parton out of the jet cone (out-of-cone

correction).















CHAPTER 6
PHOTONS AT CDF

Photon identification at CDF is based on three basic properties of prompt pho-

tons originating from hard scattering. The prompt photons are expected to be ob-

served as localized and isolated deposits of electromagnetic energy in the calorimeter

with no high momentum charged tracks associated with them. The last statement is

not always true, however. A photon can convert into an electron-positron pair prior

to entering the tracking chamber, or it can accidentally overlap with a track from

the underlying event. Nonetheless, this is one of the basic criteria which allows to

distinguish a photon from an electron.

The photon identification and reconstruction is based on information from the

calorimeter, shower max detector (CES), and tracking chamber (COT). The energy

and direction of the photon are calculated with respect to the event vertex.

The offline photon reconstruction begins by selecting the clusters of one to three

towers adjacent in ry (electromagnetic showers are usually contained in one tower

with small leakage into neighboring towers). These clusters are required to carry at

least 5 GeV of total energy and have less than 12.5% of this energy observed in the

hadronic calorimeter (energetic electromagnetic objects can loose a small fraction of

their energy in the hadronic portion of the calorimeter due to a late development of

the shower).

The selected electromagnetic clusters are required to be isolated. That is, extra

transverse energy (other than candidate energy) in calorimeter towers within a cone

of radius R=0.4 around the candidate has to be below a certain threshold (usually

1 GeV in most of the CDF analyses involving photons). This requirement helps to

suppress photons due to bremsstrahlung from an initial or final state quarks. These









photons tend to be collinear with the quark, and therefore the jet, and usually ac-

companied by other debris from jet fragmentation. This requirement also helps to

reduce contamination due to background photons from energetic 7r's and ri's pro-

duced during jet fragmentation.

The photon candidates are required to have no high momentum tracks pointing

to the electromagnetic cluster. This requirement is primarily used to distinguish

between photons and electrons.

The position (i.e. direction) of the photon candidate is determined based on

the location of the shower maximum as it is measured by the CES chamber. The

additional requirements on the shape of the electromagnetic shower and presence of

other CES clusters can be applied to further reduce the multi-meson backgrounds.

The CES shower profile, X2, is usually required to be consistent with that of a single

photon. The quantity X2 is defined by the following equation [65]:

2 Xv~2+X2
X2 X= (6.1)

where the individual contributions from the strips (wires) X (w) are given by


Xs(w) = (~ i)2/fr (6.2)


o = 4[0.0262 + 0.0962y,](10 GeV/E)0.747


The pi are measured strip (wire) pulse heights (normalized to a total pulse hight

of unity) and yi are the expected pulse heights. The forms for the yi and ao were

determined empirically from test beam data.















CHAPTER 7
ANALYSIS TOOLS

Monte Carlo event generators have become an invaluable tool in high energy

physics. They are used for a large variety of tasks which include, but are not limited

to, geometrical acceptance estimation, event selection optimization and efficiency

estimation, background studies, corrections for detector effects, etc.

The Monte Carlo event generators incorporate certain theoretical models and

allow to simulate a wide range of physics processes. Given a set of initial conditions for

a specific process, they return a list of final particles and their moment. In practice,

the data obtained in real measurements always suffers from detector inefficiencies

and resolution effects. As a result, a fraction of particles can be lost altogether while

those particles which are detected can be reconstructed with distorted parameters. To

reproduce these detector effects, the output of the event generator is passed through

a detector simulation program which converts the generated particles into a set of

observable in the detector quantities.

In order to simulate a specific hard scattering process ab -+ cd (e.g., qq -* yg) in

pp collisions, the Monte Carlo generator has to use the information about densities of

partons a and b inside of a proton and anti-proton. This information is provided in

the form of Parton Distribution Functions (PDF's). Two partons which take part in

the hard scattering will each carry some fraction Xa and xb of the initial proton and

anti-proton moment. The square of the center-of-mass energy in the hard scattering

process, 9, is related to the square of the energy in the proton and anti-proton center-

of-mass, s, by X = XaXbs. Finally, the cross section for hard scattering process ab -+ cd

will depend on scale Q2 and on the momentum fraction distribution of the partons

seen by the probe at this scale, f(x, Q2).










In this analysis, Herwig 5.6 [30] and Pythia 6.115 [31] Monte Carlo generators are

used. For QCD hard scattering, both generators use Leading Order QCD calculations

and can be linked to different parton distribution functions. For jet fragmentation,

Herwig and Pythia incorporate various color coherence effects and use re-summed

Leading Log Approximation calculations. Hadronization in Herwig is done by means

of the cluster model while Pythia utilizes the string model. The fragmentation and

hadronization models of both generators have been already discussed in details in

Section 2.3. Herwig is probably the most advanced generator in terms of handling

the color coherence effects. This is the primary reason for choosing Herwig as a

baseline Monte Carlo generator in this analysis.

At CDF, the detector simulation is done by a special package called QFL [66].

QFL takes a properly formated list of particles and their parameters from a Monte

Carlo event generator and propagates them through the detector. This propagation

of particles includes all the appropriate effects such as multiple scattering, decays

of short-lived particles, photon conversions and other interactions of particles in the

material. QFL also simulates the response of individual detector components to

passing particles as well as the geometrical and instrumental inefficiencies.















CHAPTER 8
MEASUREMENTS

This chapter presents a detailed discussion of the measurements. It starts with

the description of data samples and event selection cuts followed by the explanation

of how all the independent parameters introduced in Section 3.4 are measured. The

corrections applied to data are also discussed.

8.1 Data Samples

This analysis is based on events produced in pp collisions with center-of-mass

energy v7=1.8 TeV and recorded by CDF during the 1993-1995 run period (Run

1B). The total integrated luminosity is 957 pb-1.

The dijet sample is accumulated by using the inclusive jet trigger with ET thresh-

old 20 GeV (Jet20 trigger). The trigger is pre-scaled by 1000. Its detailed description

can be found in ref. [67]. There are also Jet50, Jet70 and Jet100 triggers, but events

from the corresponding jet samples are not used in the analysis.

The 7+jet sample is collected using the inclusive photon triggers with thresholds

of 23 and 50 GeV on ET. To reduce the contamination from fake photons in the

lower energy 7+jet sample, the 23 GeV trigger requires photon isolation, i.e. extra

transverse energy (other than candidate energy) in neighboring calorimeter towers

around the candidate has to be less than 4 GeV. More detailed information about

photon triggers can be found in ref. [68].

8.2 Event Selection Cuts

In this measurement, the jets are defined by a cone algorithm with cone radius

R = V(A)2 + (A)2 = 0.7 and the jet energy is corrected to the parton level using

the standard JTC96X.CDF routine (also see Chapter 5).

The following cuts are applied in the offline to select the dijet events:









1. Good run required (this means that all the sub-detectors and components of

the CDF detector were functioning properly during the entire run).

2. Number of leading jets is 2 (to avoid a bias toward narrow jets, we also allowed

for third and fourth extra jets if their raw energies were below 7 GeV because

sometimes a single astray track can be identified as a jet).

3. Both leading jets are required to be in the central region, r7jetl,2| < 0.9. There

are three reasons for this: in this region ET is of the order of E (theoretically

motivated), efficient track reconstruction in CTC, and complementary cones

can be defined only for jets in the central region (see Section 8.5.b for more

information).

4. The jets have to be well balanced: ET, + ET2/(ET, + ET2) < 0.15, which

corresponds to about 2a cut to remove events with large missing ET.

5. Number of good primary vertices is no more than 2 (selecting only single vertex

events would have unnecessarily reduced the statistics).

6. The z-position of the primary vertex has to be within Zvyx < 60 cm to insure

that vertex detectors are fully efficient.

7. For events with two primary interactions, all tracks are associated with vertices

by their proximity. The separation between vertices is required to be zXl1 -

zvx2I > 12 cm (corresponding to ~12oz for tracks) to allow for unambiguous

assignment of tracks. The vertex that has the largest EPT of tracks from cones

with R=0.7 around the jet directions is taken to be the one associated with the

hard collision.

The /+jet events must pass exactly the same cuts (treating the photon as one of

two jets) and satisfy specific photon identification requirements. To identify photons,

we used standard PH094.CDF routine with the following cuts:









1. Cut on the fraction of cluster energy observed in the hadronic calorimeter:

HA/EMtotai < 0.125 (this cut is applied in the offline clustering, it suppresses

hadron background).

2. Exactly one photon candidate with ET >20 GeV.

3. To remove events where photon hits near the edge of the calorimeter wedges

(and, therefore, its energy is poorly measured or cannot be measured at all),
the following fiducial cuts on (x, z)-coordinates of the electromagnetic shower

profile center are applied: IXCESl < 17.5 cm and 14 cm < ZCES < 217 cm.

4. Photon isolation cut of 1 GeV on the extra transverse energy in a cone R = 0.4

around the photon candidate (to remove fake photon content due to regular

jets).

5. No 3D CTC reconstructed tracks pointing to the EM cluster associated with

a photon candidate (to remove electrons and further suppress jet associated

background).

6. Energy in the second CES cluster in the same wedge as the photon (if present)

<1 GeV (to reduce the single and multiple meson background).

7. The electromagnetic transverse shower profile measured by the CES has to be

consistent with that of a single photon: X2ES < 20.

The selected events are then subdivided into two bins according to invariant

mass, which is defined as M=\V(El + E2)2/4 (_A1 +122/c2, where E and Pi are

the jet or photon energy and momentum and jets are treated as massless objects.

The bins have width A In M=0.3, which is chosen to be greater than the dijet mass

spread due to calorimeter resolution, ~--10%. In the lower bin (72-94 GeV/c2),

our sample consists of 3602 dijet and 2526 7+jet events with an average invariant

mass of 82 GeV/c2. The other bin (94-120 GeV/c2) has 1768 dijet and 910 7+jet

events with an average invariant mass of 105 GeV/c2. The choice of invariant mass

range, 72 GeV < M < 120 GeV, has two explanations. Dijet events with M < 72











0.08
0.07
S0.06 Bin 1, = 81.9 GeV/2 Bin 2, M= 105.1 GeV/c2
0.06
Z 0.05
0.04
z 0 3Dijet sample
0.03

0.01
0
75 80 85 90 95 100 105 110 115 120
Mjj GeV/c2
0.08
0.07
r" Bin 1. N1 =SO GcV'2 Bin 2. N1 =1046 .cV'c2
2 0.06 .1
Z 0.05
S0.04
z0.03 Photon-jet sample

0.02
0.01
0
75 80 85 90 95 100 105 110 115 120
MyJ GeV/c2


Figure 8-1: Invariant mass spectrum of dijet and photon+jet events which pass event
selection cuts.


GeV cannot be used in the analysis because properties of jets from these events are

biased by trigger requirements (trigger is not fully efficient for jets with energies close

to the trigger threshold). At high energies (M > 120 GeV), the 7+jet sample has

insufficient statistics. The invariant mass and ET spectra for both data samples can

be found on Fig. 8-1,8-2.

8.3 Fraction of Gluon Jets

The fractions of gluon jets in dijet events, f13, and pure photon+jet events,

fY, are determined from Herwig 5.6 and Pythia 6.115 Monte Carlo generators with

parton distribution function sets CTEQ4M, CTEQ4A2, and CTEQ4A4 [69]. The

results obtained with Herwig+CTEQ4M are taken as default. Fig. 8-3 shows the

evolution of the gluon jet content with dijet or photon+jet invariant mass. The results

on gluon jet fractions are presented in Table 8-1. The PDFs are very stable and well












Mass bin 82 GeV
0 :M1 an 38.61 :
0.1
0.075 Dijet

0.05
0.025
0 1--. I --I--I-I 3 =-
20 30 40 50 60
GeV
jet ET
LU
Z 0.1
0.075 Photon-jet
> 0.075
Z 0.05
0.025
0
20 30 40 50 60
jet ET GeV


Mass bin 105 GeV


30 40 50 60 30 40 50 60 70
photon ET GeV photon ET GeV


Figure 8-2: Transverse energy spectrum of jets and photons from dijet and pho-
ton+jet events after event selection cuts.


known in the region of relatively small XT = 2ETr/xs corresponding to jet energies

used in the analysis.

8.4 Fraction of Real Photons

Generally, the photon+jet sample is contaminated by dijet events with one of the

jets fragmented in such a way as to pass photon selection criteria (e.g., one prompt 70

accompanied by a few very soft 7r, 7's; see ref. [68] for more details). Requirement

of the photon isolation in the calorimeter usually reduces the fraction of fakes by a

large factor. However, the much larger dijet QCD production cross section results in

a noticeable fraction of fake photons in the final sample.

There are two statistical methods to determine the remaining fraction of fake

photons [68]. The conversion method is based on determining the number of pho-

ton conversions in the solenoid material by using the Central Preradiator Detector








58

Gluon fraction in Dijet and y+jet samples
1.0

0.9 0 Dijet, CTEQ4M
0 Dijet, CTEQ4A4
0.8 y+jet, CTEQ4M

0.7 v y+jet, CTEQ4A4

0.6 0

0.5
C
0.4 -
0 0.4

0.3 -

0.2 -

0.1

0.0 -
70 80 90 100 110 120 130
Mjj (detector level), GeV


Figure 8-3: Fractions of gluon jets in dijet and 7+jet samples.


(CPR). The profile method exploits the difference in the transverse profile of the elec-

tromagnetic showers in the Central Electromagnetic Strip chambers (CES) caused by

prompt single photons and background. The conversion method has an advantage of

much smaller systematic uncertainties at high PT's and an unlimited PT range, while

the profile method better separates signal from background in the low PT region (it

becomes inefficient at PT>30 GeV). In our analysis, we consider photons with PT>30

GeV and, therefore, use the conversion method implemented in the standard routine

GETCPRWEIGHT.CDF.

The conversion method is based on evaluating the probability of conversions in

the CPR right in front of the tower with electromagnetic cluster. Real photons have

a conversion probability p, = 1 e-7/9X (X is the amount of material in radiation

lengths in front of the CPR), while fakes, being mostly 7rs, i.e. two photons, have

higher conversion probability pB 1 (1 )2= 2 (see ref. [68] for more

details). The typical values of p, and [B are ~0.6 and ~0.8, respectively. Therefore,










Table 8-1: Fractions of gluon jets in dijet events and in 100% pure 7-jet events
obtained using Herwig and Pythia along with various sets of parton distribution
functions.

PDF set Dijet 100% pure y-jet
41 GeV 52.5 GeV 41 GeV 52.5 GeV
Herwig+CTEQ4M (Default) 0.6150.006 0.5880.008 0.2160.009 0.2560.015
Herwig+CTEQ4A2 0.6230.006 0.5950.008 0.2180.009 0.2530.015
Herwig+CTEQ4A4 0.6130.006 0.5760.008 0.2180.009 0.2620.015
Pythia+CTEQ4M 0.6230.006 0.5980.008 0.1970.009 0.2500.015


if one has N photon candidates, out of which /pN had conversions, the numbers of

real photons and background can be estimated from the two equations: N = NB + N-

and pN = pN. + PIBNB.

The fractions of real photons, 6,, in two mass bins are 75% (82 GeV/c2) and 90%

(105 GeV/c2). As a cross-check we developed another empirical method of evaluating

the fraction of fakes among photon candidates. It is described in Chapter 9. The

method gave results consistent with the CPR weights.

8.5 Multiplicity Measurements

The analysis is carried out in the dijet (or photon+jet) center-of-mass frame, so

that Ejet=Mc2/2. Multiplicities of charged particles associated with jets in dijet and

photon+jet events (Njj and Nj) are measured for particles (tracks) falling into a

restricted cone of 0c = 0.28, 0.36, 0.47 rad, where 0~ is the angle between the jet axis

and the cone side (opening angle). The multiplicities are normalized "per jet".

There are three major sources of uncertainties we have to deal with when mea-

suring the multiplicity of charged particles in jets from both data samples:

1. tracks from 7-conversions, K and A decays (background correlated with jet

direction);

2. secondary interactions, underlying event and accelerator induced backgrounds

(background not correlated with jet direction);

3. CTC track reconstruction inefficiency.













4
o



o














-8 -6 -4 -2 0 2
Log(PT) vs. Log(dl) Logd), d in cm

Figure 8-4: Example of the distribution of logpT versus log d for tracks within a cone
of 0c=0.47 rad around the jet direction. Here, pr is the transverse momentum of a
track and d is the impact parameter. The default cut on the impact parameter is
shown by the solid line, while the cut shown by the dashed line is used to estimate
the systematic uncertainty.


8.5.1 Track Cuts

We apply vertex cuts to suppress tracks due to secondary interactions, V-conversions,

Ko and A decays, or other backgrounds.

The first cut is on the track impact parameter, d, defined as the shortest distance
(in r plane) between the interaction point as measured by the SVX detector and

the particle trajectory as obtained by the CTC tracking algorithm fit.

Fig. 8-4 shows the distribution of log (pT) versus log (d) for the dijet events

from the first bin (Mjj=82 GeV), where the large cluster of points corresponds to

particles produced at the interaction point, and the straight line of correlated points

to the right of the main region corresponds to y-conversions happening in the cables
K ndA ecys o oterbakgouds
Th irtcu s nte rckipatpaaeer eindasteshres-isac

(i r-








R p/eB
d 2-R R1 1 r2 -R r2 eBr2
2 R2 2R 2p

logd log er) -log p
2







YR












log Pr log (0. 152 g 8.1)
Figure 85: Illustration of correlatiers, the magn e particle momentum, PT,
and impact parameter, r, for electrons and positions produced in c-conversions.

between)-plane, are to the CTC chambers. It can be straithown (see Fig. 8 5) that for

electrons and positions produced in 7-conversions at radius r fffereom the beam line, Pz
and d have the following correlation:

logPT -- log (0.15r2B) log Id|, (8.1)

where r and d are measured in meters, the magnetic field B in Tesla, and PT in

GeV/c.

The default cut on the impact parameter selects only tracks which, on the (log |dl,

logPT)-plane, are to the left of the strait line segments defined by the equations:
log |d| = -1 and log(lPrd|) = 0 (solid lines on Fig. 8-4).

The second vertex cut used is on Az, defined as the difference between the z

position of the track at the point of its closest approach to the beam-line and the

position of the primary vertex as measured by the vertex detector (see Fig. 8-6).










1600
S/ndf 56.68 37
Constant 1246. 9.419
S1400 Mean 08101E-01 Ol 7143E-02
Sigmia 1.074 0.7465E-02

4- 1200

S1000

800

default cut default cut
600

400

200


-10 -7.5 -5 -2.5 0 2.5 5 7.5 10
Az=Iz-zvtxl, cm


Figure 8-6: Example of the Az distribution for tracks from events with only one
vertex (primary interaction). Tracks are counted within a cone of 0c=0.47 rad around
the jet direction.


This cut helps to remove tracks from the secondary interactions. The default value

of this cut is: |Azl < 6.0 cm (~ 60rAz).

After applying vertex cuts, there is still a small number of correlated background

tracks remaining, mostly due to y-conversions. These are estimated by turning

on/off conversions in the QFL detector simulation package. This fraction is found to

be around 3.5%.

8.5.2 Background Tracks Removal

Tracks coming from the underlying event, multiple interactions in the same bunch

crossing (with unresolved z-vertices), and any other uncorrelated backgrounds can be

easily subtracted on average using complementary cones. A pair of complementary

cones is defined such that their axis is in the plane normal to the dijet direction

and at the same polar angle as the dijet axis (Fig. 8-7 shows the orientation of

the complementary cones). Note that such cones can only be defined for jets in the

region 450 < 0cm < 1350 (corresponds to I|jetl,2| < 0.9). These cones are expected























Figure 8-7: Illustration of the definition of complementary cones. The unlabeled
arrows are the axes of cones complementary to jets 1 and 2.

to collect statistically the same uncorrelated background as the cones around the

jets. However, there still could be a small fraction of tracks associated with jets

which found their way into the complementary cones. There are several indications

of that. In photon+jet events, the multiplicity in the half cone on the photon side of

the complementary cone is about 7-9% less than that on the jet side. Finally, there

is a small correlation between the multiplicity in the complementary cones and the

multiplicity in cones around jets (see Fig. 8-8). To estimate the true contribution

of the uncorrelated background, we made a linear fit of the dependence of mean

complementary cone multiplicity on mean multiplicity in jets for events from dijet

and photon+jet samples. The extrapolation of this function to zero was taken as an

estimate of the uncorrelated background contribution in the jet cone (0.55 and 0.46

tracks per cone of 0c =0.47 rad in dijet and photon+jet events, respectively).

8.5.3 Tracking Efficiency

We also corrected the measured multiplicities for the CTC track reconstruction

inefficiency. We use the results of the method developed in ref. [70]. This method

is based on embedding tracks at the CTC hit level into real events and re-running

the full CTC track reconstruction. For this purpose, a track selected from one of the

jets in dijet event is rotated 1800 in the center-of-mass frame, and embedded into the












5
/5 ndf 65.62 / 42
4.5
4 AO: 1.092 0.1601E-01
35 Al 0.7498E-02 0.8175E-03
3.5
3 I
2.5di t m a .. r .an.r _o -- ;4 Co .W ? I

5 1.5

S0.5
0
0 5 10 15 20 25 30 35 40 45 50
o dijet :i i.1il 'i.. ii.
5
5 X/ndf 18.37 / 24
4 AI 1.15$ 0.6180E-01
- 3.5 Al 0.7482E-02 0.4230E-02
8 diet ass range: 72-120 GeV/c2

1.5

0.5
0
0 5 10 15 20 25 30 35 40 45 50
dijet :ii. 1 i l. i .. il .


Figure 8-8: The correlation between multiplicity in complementary cones (per event)
and dijet multiplicity (per event). The results of linear fit, ncompl.cone = Po +PI x ndijet
are shown. We do not fit the dependence in the region ndijet < 5, because the
contribution of uncorrelated background tracks can dominate in the dijet multiplicity
in this region. The expected multiplicity of uncorrelated background tracks in a cone
around the jet direction is estimated as Po The results of the fit are almost the
same (within statistical errors) for events with very different dijet mass which implies
a very small dependence of the complementary cone multiplicity on the jet energy.





Table 8-2: Efficiencies of the track selection cuts for jets with the average energy
Ejet=41 GeV. Stages of multiplicity measurements: raw multiplicity in cone, Stepl;
cut on |dz|, Step2; cut on impact parameter, d, and logPT, Step3; CTC efficiency
corrections, Step4; correction for remaining 7-conversions, Step5; complementary cone
subtraction, Step6.

cone 0c = 0.28 cone 0c = 0.36 cone 0c = 0.47
Dijet --jet Dijet 7-jet Dijet 7-jet
Stepl 5.11 (100%) 4.71 (100%) 6.18 (100%) 5.65 (100%) 7.43 (100%) 6.74 (100%)
Step2 4.92 (96.4%) 4.50 (95.5%) 5.90 (95.5%) 5.33 (94.5%) 6.99 (94.1%) 6.29 (93.3%)
Step3 4.53 (88.7%) 4.03 (85.5%) 5.42 (87.7%) 4.76 (84.3%) 6.41 (86.3%) 5.61 (83.3%)
Step4 4.80 (94.1%) 4.28 (90.8%) 5.77 (93.4%) 5.07 (89.8%) 6.80 (91.6%) 5.95 (88.4%)
Step5 4.67 (91.4%) 4.16 (88.3%) 5.59 (90.4%) 4.91 (87.0%) 6.55 (88.2%) 5.74 (85.2%)
Step6 4.48 (87.7%) 4.01 (85.1%) 5.29 (85.6%) 4.64 (82.2%) 6.05 (81.5%) 5.31 (78.8%)










Table 8-3: Efficiencies of the track selection cuts for jets with the average energy
Ejet=52.5 GeV. Stages of multiplicity measurements: raw multiplicity in cone, Stepl;
cut on |dz|, StepS; cut on impact parameter, d, and logPT, Step3; CTC efficiency
corrections, Step4; correction for remaining 7-conversions, Step5; complementary cone
subtraction, Step6.

cone 0 = 0.28 cone 0 = 0.36 cone 0 = 0.47
Dijet ~y-jet Dijet 7-jet Dijet y-jet
Stepl 5.82 (100%) 5.29 (100%) 6.98 (100%) 6.29 (100%) 8.33 (100%) 7.49 (100%)
Step2 5.61 (96.3%) 5.06 (95.5%) 6.66 (95.4%) 5.95 (94.5%) 7.85 (94.1%) 6.99 (93.3%)
Step3 5.16 (88.7%) 4.48 (84.7%) 6.11 (87.5%) 5.29 (84.0%) 7.19 (86.3%) 6.20 (82.7%)
Step4 5.54 (95.2%) 4.82 (91.1%) 6.56 (94.0%) 5.69 (90.4%) 7.72 (92.7%) 6.67 (89.0%)
Step5 5.38 (92.5%) 4.68 (88.4%) 6.35 (91.0%) 5.50 (87.4%) 7.44 (89.2%) 6.42 (85.7%)
Step6 5.19 (89.2%) 4.53 (85.6%) 6.05 (86.7%) 5.23 (83.2%) 6.94 (83.3%) 5.99 (80.0%)


other jet. Then, the parameters of the reconstructed tracks are compared with their

original values before embedding. Corrections obtained this way take into account

the efficiency dependence on jet energy, particle momentum, and particle angle with

respect to the jet axis. The size of these corrections on average multiplicities is 6-8%,

depending on jet energy and cone size Oc.

The results of multiplicity measurements with default set of cuts and corrections

can be found in Tables 8-2,8-3.

8.6 Effect of Fake Photons

We use Monte Carlo (HERWIG and PYTHIA along with detector simulation) to

study the fake 7+jet events To obtain the fake 7+jet sample, we generated regular

dijet events and selected only events passing the photon cuts. To get statistically

meaningful sample of fake 7+jet events (~ 3 103 events), we had to generate

~ 3 107 dijet events (numbers are quoted for Pythia). Therefore, we found that the

probability for a jet to fake a photon is on the order of _10-4. Fake photons, based

on these studies, appear to be regular jets with usually a single 7r faking a photon.

It turns out that this ro, on average, carries only about 90-93% of the original jet

energy (see Fig. 8-9). The remaining 10% of the energy is carried by other particles

from the original jet. This effect results in a mis-measurement of the dijet mass of










Table 8-4: The a-correction due to difference in multiplicities between a regular jet
and a jet opposite to a fake photon. The opening angles are Oc = 0.28, 0.36, 0.47.

Ejet, GeV Cone, Oc Q=EjetOc, GeV HERWIG PYTHIA "Shifted" data
0.28 11.5 1.0420.018 1.0870.019 1.0240.011
41 0.36 14.7 1.0250.016 1.0750.017 1.0250.010
0.47 19.2 1.0320.015 1.0840.016 1.0300.009
0.28 14.7 1.0400.031 1.0560.029 1.0260.014
52.5 0.36 18.9 1.0230.028 1.0560.029 1.0350.013
0.47 24.7 1.00.026 1.0550.027 1.0370.012


fake 7+jet events by about 3-5% (see Fig. 8-10). Therefore, fake 7+jet, on average,

have higher true invariant mass than the reconstructed one. Consequently, the 7+jet

mass bins are actually populated with fake 7+jet events of higher true Myj values

than the same mass bins in the case of dijet events. Thus, one can assume that the

higher true energy may result in a higher multiplicity in the jet opposite to the fake

photon (simply fake later in text) as compared to a regular jet from a dijet event.

We found that multiplicities in jets opposite to fakes, Nfj, are typically a few percent

higher than those in jets from regular dijet events, Njj. Table 8-4 presents the results

for the ratio a=Nfj/Njj obtained in these studies.

Assuming that jet fragmentation occurs independently in each of the jets, one

can also obtain a from the dijet data sample by artificially shifting the energy of one

of the jets (fake) by the same 7-10%. This crosscheck gives similar results to what

we have obtained from Monte Carlo simulations. As a default estimate of a, we take

the average results obtained from HERWIG, PYTHIA, and "shifted" dijet data.

There is one more interesting observation which we can make with the Monte

Carlo studies of fake 7+jet events. It turns out that only about 3-6% (Herwig

predicts smaller fraction than Pythia) fakes are gluon jets. As we show in these

studies, quark jets have, on average, lower particle multiplicity then the gluon jets

and it is, therefore, conceivable that it is easier for a quark jet to fluctuate into a

single high energy pion.


















9 MeR 09023 Meai 09292
SRMS .2sE-1 RMS .7471E-01
8 8
7 82 GeV mass bin 105 GeV mass bin
6 fake y-jet events 6 fake yjret events
5 5
4 4
3 3
2 2
1 1
0 0
0.6 0.7 0.8 0.9 1 1.1 0.6 0.7 0.8 0.9 1 1.1
A = ET(QFL)/E(Herwig)


A = ET(QFL)/ET(Pythia)


Figure 8-9: The ratio of the measured energy of a fake photon (detector level) to the

real energy of a parent jet (MC parton level).


8 ndf 18.91 25 8ndf 1894 20
stan t 4.848 02012 Cnstant 1 4.764 0.3906
7 M --- 49r--2734E-02 7 --- -al 68 ,i-2E
Slgma 0.805E01 0.200E-02 Sigm 0 870E-l 0.428E-02
6 82 GeVmass bin 6 105 GeV mas n

S5 ake y-jet e
z4 4 4
3 3
2 2
1 1
0 0
0.8 1 1.2 0.8 1 1.2
A =mass(QFL)/mass(Herwig)


/ndf 2679
Constant 4
Silgma 08666E
82 GeV mas Pin

fake yet







0.8 1


28 : 8 n
A17 02328 tonst
01 1 0.2925E-02 : Sig-
6 o5 GeV

5 ac ,1e[
4
3
2
1
0
1.2 0.8
A= mass(QFL)/mass(Pythia)


f 5665 / 10
nt 5106 0.4926
0.7500E-011 0449E-02
as 1in









1 1.2


Figure 8-10: The ratio of the measured invariant mass of a fake 7+jet event (detector

level) to the real invariant mass (MC parton level).










Table 8-5: Results of the measurements with the default set of cuts. The multiplicities
in dijet events, Njj, and in photon+jet events, Nj, do not include corrections for
remaining particles from K and A decays and losses of low PT tracks.

Ejet 41 GeV 52.5 GeV
0c 0.28 rad 0.36 rad 0.47 rad 0.28 rad 0.36 rad 0.47 rad
Q=EjetOc 11.5 GeV 14.7 GeV 19.2 GeV 14.7 GeV 18.9 GeV 24.7 GeV
Njj 4.4760.025 5.2870.027 6.0520.029 5.190.04 6.050.04 6.940.04
Nrj 4.010.04 4.640.04 5.310.05 4.530.07 5.230.08 6.000.08
fyq 0.6150.006 same same 0.5880.008 same same
f~y3 0.2160.009 same same 0.2560.015 same same
6, 0.750.04 same same 0.900.07 same same
a 1.0400.016 1.0350.014 1.0410.015 1.0320.012 1.0360.011 1.0340.011


8.7 Final Corrections and Results

Now that we measured or evaluated Njj, Nj, f J, fyj, 6, and a (see Table 8-5),

we can calculate Ng, Nq and r = Ng/Nq, using Eqs. 3.4-3.6. In order to obtain the

final results, two corrections must be applied. These corrections are derived from

Monte Carlo and are expected to be different for quarks and gluons, which makes it

natural for them to be applied in the last order.

The production rates of KF and A's depend on jet type. The fraction of these

particles is enhanced in jets originating from s- and c-type quarks compared to

gluon jets or jets originating from u and d quarks. Therefore, including their decay

products can bias the measurement of the ratio of charged particle multiplicities.

One of the purposes of the vertex cuts is to suppress tracks due to K1 and A decays.

However, there is still a considerable fraction of charged particles from these decays

which pass the cuts. In order to evaluate and remove this contribution the following

study was performed. We compared two Monte Carlo samples: one sample with

7-conversions, K1 and A decays switched "OFF", and another sample with only 7-

conversions switched "OFF". Comparing the MC level multiplicities, we were able to

find the fraction of particles coming from K and A decays. From comparison with

the detector level (MC+QFL) multiplicities, we found what fraction of these particles

passed the cuts. Given these numbers, we obtained multiplicity correction factors:










Table 8-6: Effect of KF and A decays on the charged particle multiplicity within
a cone of the opening angle 0c=0.47. The results presented in the Table are based
on Herwig. Multiplicity correction factors are essentially the same for Pythia and
smaller opening angles, 0c=0.28, 0.36.

Jet type Fraction of ch. particles Fraction of ch. particles Multiplicity
from K and A decays from decays which passed cuts corr. factor
Gluon 8% 47% 0.96
u, d-quarks 9% 46% 0.96
s-quark 15% 56% 0.92
c-quark 10% 44% 0.96
all quarks 10% 49% 0.95


Table 8-7: Charged particle multiplicities in small cones around gluon and quark jet
directions and their ratio, N,, Nq and r = Ng/Nq respectively. Multiplicities do not
include charged particles from K' and A decays.

E 0, Q=EtOc Ng Nq r=
0.28 11.5 GeV 4.9810.070.52 3.280.1110.37 1.5210.080.13
41 GeV 0.36 14.7 GeV 6.02-0.080.55 3.700.11-0.40 1.63-0.090.14
0.47 19.2 GeV 6.9410.080.58 4.230.1210.47 1.6410.090.14
0.28 14.7 GeV 5.9410.120.69 3.700.1710.43 1.6010.120.19
52.5 GeV 0.36 18.9 GeV 7.0210.130.72 4.220.1810.49 1.6610.130.20
0.47 24.7 GeV 8.0810.140.72 4.860.1910.57 1.6610.130.18


~0.96 for gluon jets and -0.95 for quark jets. Results of these studies can be found

in Table 8-6.

Finally, the measured multiplicities were corrected for losses of low PT tracks

due to curling in the magnetic field of the solenoid (the efficiency for reconstructing

tracks with PT < 300 MeV is practically zero). To make this correction, we estimate

the fraction of Monte Carlo tracks (before detector simulation) with PT < 300 MeV

(below this threshold PT distribution of charged tracks after QFL simulation is falling

sharply). The correction is small: -2% for gluon jets and ~1% for quark jets.

The final results (including the described above corrections) on N,, Nq and r =

Ng/Nq, are presented in Table 8-7.















CHAPTER 9
SYSTEMATIC UNCERTAINTIES AND CROSS-CHECKS

The sources of systematic uncertainties are discussed in the following sections

and are summarized in Tables 9-1,9-2, 9-3.

9.1 Event Selection

Ideally, the results of an analysis should not depend on the event selection. In

practice, the event selection cuts always introduce certain biases in properties of

objects being studied. It is important to choose the cuts such that these biases are

minimal or could be corrected by a simple procedure.

The systematic uncertainties due to the event selection cuts include effects re-

lated to the choice of r9-cut on jets, presence of the second vertex, and difference

in the energy balance between dijet and photon+jet events. We do not include in

this list effects related to photon identification and jet reconstruction because the

uncertainties associated with these effects will be discussed separately.

There are two reasons why the multiplicity in jets may depend on rjet: detector

effect associated with a decrease in tracking efficiency in the forward region, and

a real physics effects associated with the initial-to-final state color coherence. The

first effect is accounted for by the CTC efficiency corrections [70]. The second effect

is expected to make almost no impact on the inclusive properties of jets such as

multiplicities if particles are counted in small cones around the centrally produced

jets (these two conditions are met in our analysis). To confirm that the initial-to-final

color coherence effects are negligible at the conditions of the analysis, the following

test was conducted. The coherence effects, if present, should reveal themselves in the

angular distribution, dn/d/, of particles around jets (see [71, 72]). The radial or polar

angle 3 is defined in (r7, 4/)-plane as follows: A9 = ARcos/, A0 = ARsin/ where Aq,











3 X/h 27.92 19 3 /hdf 10.86 / 19
A A2.021 0.9322E-62 AO 2.20 0.1411E-61
2.5 i- 2.5 -

-o 2 P-E-3%0539k- 0013E 2
C
1.5 1.5
dijet events dijet events
S1 Eet=41 GeV 1 et= 52.5GeV
0. 0,=0.47 rad 0 =0.47 rad
0.5 0.5 -

0 0
0 1 2 3 0 1 2 3
3, rad 3, rad
S //df 2084 / 19 /hdf 24.76 / 19
A0 1.3 3 0.1437E- 1 AO 1.940 0.2494E- 1
2.5 2.5 -

2 2

S1.5 i i 1.5
S "photon"+jet events "photon"+jet events
1 Ejet41 GeV 1 Eet= 52.5 GeV
Jet= 4 1 5GV
o 0.5 =0.47 rad 0.5 ,=0.47 rad

0 0
0 1 2 3 0 1 2 3
3, rad 3, rad

Figure 9-1: The angular distribution of particles in cone 0.47 around jet direction. No
signature of the color coherence effects is observed (distributions are fairly flat). The
color coherence effects would reveal themselves in the increased density of particles
in the preferred direction (p = 7/2 for y+jet events and = 0, 7r for dijet events).


A0, and AR = / 2 + A2 correspond to an angular distance between a particle

and a jet. Fig. 9-1 shows that the angular distribution is fairly flat. Therefore, the

coherence effects are negligible because otherwise we would see an increase in particle

production in certain preferred directions (see ref. [72] for more details).

The default set of event selection cuts allows up to two primary vertices in an

event. The fraction of N,,=2 events in our data set is ~ 17%. One of the reasons we

keep such events is that the CPR method was tuned on an inclusive sample of photons

with some fraction of events with multiple vertices (mostly N,,=l and N,,=2 events,

with a small fraction of N,, >3 events). On the other hand, the presence of the second

vertex introduces some ambiguities in assigning tracks to vertices which results in a

4-6% difference in particle multiplicity in jets from one and two vertex events. To









estimate the systematic uncertainty associated with this effect, we repeat the analysis

conservatively assuming that multiplicities in jets from Nvx12=1 and Nvx12=2 events

are the same (i.e., use NN7j 1 instead of N N<2). The effect on the multiplicities in

quark and gluon jets is found to be ~1-2%. The corresponding value of uncertainty

on the ratio r is ~2-4%.

An energy balance cut is applied to select events with well measured jets. The

dijet and photon+jet events are required to pass exactly the same cut: ET +

ET2 /(ET1 +ET2) < 0.15. It is important that jets in selected dijet and real photon+jet

events have the same properties. However, applying the same energy balance cut to

events from both samples can lead to a small bias. The photon energy resolution is

much better than that of jets. Therefore, from this naive point of view, i-jet balance

is expected to be better (or narrower) than jet-jet one. At the same, time there are

factors which can lead to a broadening of the 7-jet balance (in fact, we see in data

that 7-jet and jet-jet are almost the same; see Fig. 9-2). One of these factors is the

presence of fakes which energies are ~10% less than energies of jets recoiling against

them. The other factor is a small relative offset (~ 4% according to MC) in the en-

ergy scales of quarks and gluons (because jet corrections are obtained for an average

jet from dijet sample). Therefore, it leads to a natural offset in balance of 7-g and

7-q pairs which, in turn, results in broadening of a generic y-jet balance. Because all

these effects described above are quite small and there is no a clear way to correct

for them, we simply assign a systematic uncertainty associated with the effect of the

energy balance cut. To evaluate this effect we use a tighter cut (motivated by MC

studies; see Fig. 9-3) for photon+jet events: P~T + PT2 /(PT + PT2) < 0.125. The

corresponding uncertainties turn out to be ~3% for the ratio r and ~1-2% for the

measured multiplicties, Nq and N,.










73


10/df 23.52 / 17 10 df 2065 / 16
S Consnt .366 0.1352 Constant 561 j 0.2016
S Man -0.2336E-03 0 193E_02 Mean 0.429E-02 0.3184E 02
8 0S.ga 7979E-01 0.3354 E-02 8 0L gma 776E-01 ..05Q9 7E-02
S82 GeV mass bin 105 GeV maqs bin





2- i A 2 7- e
6 "6



3 3
2 2

S0 0o
-0.2 0 0.2 -0.2 0 0.2
z Dijet sample

S10 /df 1546 / 10 /nd 25 14
z Contat 5161 01514 Constant 6291 03018
Man 246E-02 0903E-02 Mean 1862E02 0.3216E02
Sg a U 812E-01 0.4744E -02 Sigma 6249E 01 j 0 0424E -02
82 GeV mass bin 105 GeV bin
6 6
5 5
4 4
3 3
2 4 4 2
0 1 0
0 0
-0.2 0 0.2 -0.2 0 0.2
"Photon"+jet sample, ISO < 1GeV

A=(E1x,y+E2x,y) ( Etl + Et2)


Figure 9-2: Energy balance in data: ET1 + ET I/(ET, + ET).


10 /ndf 225 / 17 10 /df 2511 16
S Constant i 5.168 0.7085E-01 9 Constant i 5,496 .756E-01
Mean .1238E-02 0.137E-02 Man -1410E-02 0.1362E-02
8 &s- H-8503E-01 021 -175E-02 80 0_76830E-01 0 2080E-02
7 82GeV mass bin 7 105GeV mass bin
6 6

4 4
3 3
2 2 4
: A 4x
<1 1 1 ,
0 0
-0.2 0 0.2 -0.2 0 0.2
MC dijet sample
) 10 10 8df i1n 2 13
: 1 I /ndf 8.404 / 15 1 :--- I-- 77n -f 6.172 1 13 --
S Constant 5.706 0.1055 Constant 6318 0.1155
M n -0.6300E-03- .1OE-02 Man 0.1332E-02 0. 1228 E-02
8 Sga 745E- 01 0 50E -02 8- 0648E01. 01838E0
S82 GeV mass bin 7 105 GeV mass bin
6 6
5 5
4 4
3 3
ii 2414


0 0
-0.2 0 0.2 -0.2 0 0.2
MC photon+jet sample, ISO < 1GeV
A= ( Elx,y + E2x,y) / ( Et + Et2)


Figure 9-3: Energy balance in Herwig Monte Carlo: ET, + ET2 /(ET, + ET2).










9.2 Jet Reconstruction and Energy Corrections

There are four effects associated with jet reconstruction and energy corrections:

jet algorithm bias, mis-measurement of the jet direction, uncertainty in the jet energy

scale, and migration of events between mass bins. These effects and their correspond-

ing uncertainties are discussed below.

In theory, there are only two initial partons or jets. In practice, the number of

reconstructed jets depends on the resolution parameters of the clustering algorithm.

Therefore, the properties of jets will depend in some way on the jet clustering al-

gorithm. To estimate this potential bias, the following study was conducted. We

compare the properties of Monte Carlo jets reconstructed with three different jet

clustering cones: R=0.4, R=0.7 (default in our analysis) and R=1.0. The events are

selected using the standard set of cuts. To disentangle effects related to jet algorithm

and energy corrections, the comparison is done for jets of the same energy at MC gen-

erator level (true energy of outgoing partons). Charged particles are counted in cones

of various sizes around the true direction of the outgoing parton and the direction

of the reconstructed jet. This procedure allows for an estimate of the potential bias

due to selecting jets with specific properties and the bias due to mis-measurement

of the jet direction. The results of the study can be found in Figs. 9-4, 9-5. From

these plots one can make two conclusions: the bias due to the size of a clustering

cone depends on the opening angle 0~ and a flavor of a jet (it is bigger for gluon jets

than for quark jets). Thus, the effect of the jet algorithm is found to be negligible

for the results obtained with the opening angle 0~=0.47. However, it becomes one of

the leading systematic uncertainties for multiplicities in quark and gluon jets mea-

sured in smaller opening angles, 0~=0.28 and Oc=0.36. The corresponding bias in the

measurements of the ratio r turns out to be small (1-3%) for all three opening angles.

To understand the effect of the jet clustering algorithm, it is helpful to consider

how the cluster merging procedure of the cone algorithm works. In general, a jet has










a subject structure in the angular distribution of particles. These subjects, or clusters,

can be merged by the jet finder in one jet or reconstructed as separate jets. The chance

for two clusters to be merged depends on the clustering cone size and on the fraction of

energy they share. For instance, two clusters of about the same energy and separation

AR=0.6 will be reconstructed as two R=0.4 jets in about 80% of the cases and as one

R=0.7 jet in about 80%-90% of the cases. Based on this example, one can conclude

that cone R=0.4 jets will have much fewer subjects than cone R=1.0 jets which has

two consequences for jet direction resolution. First, it results in a better jet direction

resolution for smaller clustering cones (see Fig. 9-6). Second, there are situations

when the reconstructed jet direction does not coincide with the direction of any of

the subjects. It happens more frequently for cone R=1.0 jets than for cone R=0.4

jets. Therefore, for small opening angles 0c one may count particles in the region

between subjects where the density of particles is small. This explains the multiplicity

behavior in cones with small opening angle: NR=0.4 jet > NR=0.7 jet > N R1.0 jet. The

situation changes for large opening angles. It was shown above that the chance for

a cone R=1.0 jet to consist of two clusters (or subjects) is greater than for a cone

R=0.4 jet. It is also known that N(E1) + N(E2) > N(Eo = El + E2), where N(E)

is the multiplicity in a jet (or subject) with energy E. Therefore, it is more likely

for large opening angle cones to contain most tracks from both clusters (or subjects .

All this explains why the multiplicity behavior at large opening angles is reversed:

NR=0.4 jet < NR=0.7 jet < NR=1.0 jet-

The systematic uncertainty due to imprecise knowledge of the actual jet direction

is evaluated by using Monte Carlo quark and gluon jets. The difference between the

multiplicity in a cone around the reconstructed jet direction and the multiplicity in

a cone around the true direction of an initial parton is taken to be an estimate of the

corresponding systematic uncertainty. The effect appears to be negligible.












MC jet direction, Gluon jet
:Mass bir 1


S N 0N.4 NJ
,1 2 ......... .. .. .. ..... ......... ............... .......


M : a : b :
S Nje.7 Jt 1.0 1
oi



: a s : :b :






E ii
S .g.................. .. ....................... .





ENJei 0.7tNJdt 1.0:




02 a3 04 05 0G O7 0
opening angle
i ...I..... i ....i l^ei O~i '.i J i~ oi


2 QFL jet direction, Qlun jet
S :Mass bid 1


NJet 0.4 NJet 1.0
2 0 .. .. ..* ........ .. ....... ......... ......... ....
S NJei 0.7 NJ :

s .. .. i . i
-10
o


02 03 04 05 O 07 0
opening angle


QFL jet direction, Quark jet
1 Mass bin 1


NJe 0. et 1.0i
I -,,........ ... ... ...... .................. .......





02 O n 04 0 0g O7 0
opening angle


Figure 9-4: Difference in charged particle multiplicities between jets reconstructed
with different clustering cone sizes. The multiplicity ratios, NR=0.4 jet/NR= .o jet and

NR=o.7 jet/N= 1.0 jet, are presented as functions of the opening angle Oc. Results are
obtained by counting particles around the true parton direction and the reconstructed
jet direction (QFL jets). MC data from mass bin 1 is presented.



The overall uncertainty on the jet energy scale is 5%. To evaluate its effect

on the measurements, we use the standard CDF routine JTC96X to vary the jet

energy around the measured value. It includes both systematic up and down shifts

in the absolute energy scale and the relative, rT-dependent, scale. After each shift

in the jet energy scale, the entire data set is re-processed and events are re-selected

with default cuts. The maximum variation in results is taken as an estimate of the

corresponding systematic uncertainty. Imprecise knowledge on the jet energy scale

is one of the leading sources of systematic uncertainties in the analysis. The size of

this uncertainty is 2-5% for the multiplicities in quark and gluon jets and 4-9% for

the ratio, r = Ng/N,.

There is another effect closely related to the jet energy measurement. It is a

migration of events between mass bins. Given the ~ 10% jet energy resolution, a

jet's measured energy can fluctuate to significantly lower or higher values compared














MC jet direction, Gluon jet









02 N 0 0 i 0

opening angle


MC jet direction, Quark jet!
Mass bin 2



N:0 0. NJet 1
, .... .. ..... ....... ..... ..... .. ...... .. ..... .



S ...... I......... .. .... ........................ ..


02 03 04 05 0G 07 O
opening angle


OFL lel direction. Gluon lel
Mass bin 2


I I



02 as 0 45 Jm 7- .
N0 I N

" -.. ... ............ ......... !... I .. ..... .... ....



opening angle


OFL let direction. Ouark lel
Mass bin 2


- ,, NJet 0.4 INet 10.
i 105 i... i.. ..... ....... .... .

0 i i N

..op i n .. .......g[ ......... ......... ...... ... .


o02 a03 01 0 7 4a 0
opening angle


Figure 9-5: Difference in charged particle multiplicities between jets reconstructed

with different clustering cone sizes. The multiplicity ratios, NR=0.4 jet/NR=1.o jet and

NR=o.7 jet/N= 1.o jet, are presented as functions of the opening angle 0O. Results are
obtained by counting particles around the true parton direction and the reconstructed

jet direction (QFL jets). MC data from mass bin 2 is presented.


Angle, e, between outgoing parton and reconstructed jet
in center-of-mass frame


15 Mea 0127.01
RMS .54s7E01
10

5 Cone 0.4 Gluon jet


0
0 0.1 0.2 0.3 0.4 0.5


15 Mear 072 01
RMS O.5949E01
z 10

Cone 0.7, Gluon jet
z 5


0 0.1 0.2 0.3 0.4 0.5


15 Ma, 0.666E1
RMS 9| 778E.01
10

C ne 1.0, Gluon jet


0 0.1 0.2 0.3 0.4 0.5


15i M 0, 11
RMS P .78E.01
10

5 Cone 0.4, Quark jet

0
0 0.1 0.2 0.3 0.4 0.5


15 Mea 063E01
RMS 0.467E-01
10

Cone 0.7, Quark jet


0 0.1 0.2 0.3 0.4 0.5


15
RMS .6717E-01
10

Cone 1.0, Quark jet


0 0.1 0.2 0.3 0.4 0.5


e, rad


Figure 9-6: Angle between the direction of an outgoing parton and the direction of

a reconstructed jet.













MC Dijet, Bin 1 MC Dijet, Bin 2
0.08 0.08
0.08 M smear= 79.8 GeV/c2 Musmear = 102.2 GeV/c2
0.07 -0.07
7 iM = 81.1 GeV/c2 smear=104.8 GeV/c2
0.06 1 0.06
0.05 0.05
S0.04 0.04
c 0.03 j v 0.03
z
S0.02 0.02
0.01 0.01 i
0 0
40 60 80 100 120 140 50 75 100 125 150
M GeV/c2
MCy-jet, Bin 1I MC y-jet, Bin 2 Ge
0.08 0.08
00 smear. 79.1 GeV/c2m 102.1 eVc2
"s-eal. : Mnmear.-- 102
0.07 0.07
0.0 = 81.1 GeV/c2 mear.== 104.8 GeV/c2
0.06 0.06
S0.05 0.05
Z 0.04 0.04
Z 0.03 2 0.03
0.02 0.02
0.01 0.01
0 0
40 60 80 100 120 140 50 75 100 125 150
M y GeV/c2


Figure 9-7: Invariant mass spectrum of Monte Carlo dijet and 7+jet samples. The
solid line histogram is the detector level (smeared) distribution. The dashed line
histogram is the unsmeared distribution.



to its true energy. This can also propagate into the measured invariant mass of an

entire event so that it can fall into a wrong mass bin. Taking into account that

the invariant mass spectrum is close to a falling exponential, it leads to an average

effective migration of the events to the higher masses (see Fig. 9-7). As a result of

this migration, the unsmeared invariant mass is about 2% less than the measured


(smeared) one. Given the fact that the multiplicity depends on the logarithm of the

energy and that this smearing effect is smaller than the uncertainty on the jet energy

scale, we decided not to apply any unsmearing correction to the data. But to be

conservative, we assign the corresponding systematic uncertainty which is estimated

by comparing the default results with the results obtained by applying the unsmearing

procedure and taking into account a small difference in invariant mass distributions

of dijet and photon+jet events. The effect of the smearing correction turns out to be

negligible for both mass bins.










9.3 Presence of Fake Photons

The photon identification cuts obviously do not affect the properties of jets in

pure photon+jet events because a photon and a jet are independent objects in these

events. On the other hand, the photon selection cuts have a direct impact on the

purity of the sample and the properties of fake 7+jet events. In the analysis, the

presence of fake photons is accounted for by two parameters, 6, and a. Below we will

discuss the systematic uncertainties associated with the evaluation of these parame-

ters.

We use the conversion method to determine the real photon content in the pho-

ton+jet data sample as described in Section 8.4. This method was developed by the

CDF photon group and implemented in the standard routine GETCPRWEIGHT.CDF.

This routine also provides means of estimating the systematic uncertainties associated

with the conversion method.

The main backgrounds for prompt photons are single 7r's and 7r's decaying into

two 7's. There are smaller backgrounds from other multi-r0 states (rl TrOoo,

KS -+ Tror0 and jets with 27r) which, obviously, give more photons. The conver-

sion probability for background photons is re-calculated using the measured rlT/7

and K/Tr0 production rates. All these corrections are implemented in the standard

GETCPRWEIGHT.CDF routine. The deviation from a simple two-photon model is

taken to be the systematic uncertainty. The GETCPRWEIGHT.CDF routine also

provides estimates of the systematic uncertainties due to back-scattered electromag-

netic showers and the presence of CPR hits from the underlying event. All these

individual sources of uncertainties in the determination of the real photon content,

65, are summarized in Table 9-4. We repeat all the measurements using these deviated

values of 6, to evaluate the corresponding effect on the final results. The uncertainty

in the fraction of real photons, 6,, leads to a significant uncertainty, 4-6%, in the

measurements of the ratio, r = Ng/N,.










We rely on Monte Carlo simulation of the fake 7+jet events. To make sure

that MC provides an adequate description of these events, we conduct the following

test which is based on the difference in shape of the isolation energy distributions

for real photons and fakes. Thus, the additional (isolation) energy in cones R =0.4

around real photons is mostly due to the underlying event and its distribution has

an approximately exponential shape with typical average value of 0.65 GeV per cone

R=0.4 [73, 74]. At the same time, the isolation energy in cones around fake photons

is dominated by contributions from jet debris. According to Monte Carlo simulation,

the isolation energy in cones around fakes has a fairly flat distribution (see Fig. 9-8).

From Fig. 9-8, we can also notice that the distribution in photon+jet data looks

very much like a weighted sum of the exponential (which is how the underlying event

contribution should look) and a "shelf-like" contribution due to fakes. If true, the

weights can be extracted and used as a direct measurement of the photon content in

a data sample. We can try to use this to discriminate between the two in attempt

to estimate the fraction of real photons in the data sample and also to predict such

fraction for any given isolation cut. Thus, we perform a very simple calculation. We

estimate the area under the real data curve in the region from ISO=3 GeV to ISO=4

GeV (see Fig. 9-8). Assuming that this region is dominated by fakes, we can then use

the number of fakes per unit of ISO to predict the fraction of fakes (or real photons)

in a sample with arbitrary cut on isolation. Fig. 9-9 shows the comparison of this

proposed method to the standard CPR based results. One can see that even with

our "back of the envelope" calculations, we obtain an impressively good agreement.

This test gives us confidence that Monte Carlo correctly reproduces main properties

of fake photons.

Finally, we estimate the systematic uncertainty associated with the a-correction.

This correction depends on the Monte Carlo simulation of fake photons which relies

on a particular fragmentation model. The fragmentation models implemented in















0.8 -
ISO cut
0.6

0.4

0.2

0
-0.5 0 0.5 1 1.5 2 2.5
Isolation


-0.5 0 0.5 1 1.5 2 2.5
Isolation


3 3.5 4 4.5
GeV


3 3.5 4 4.5
GeV


Figure 9-8: Isolation energy distribution in photon+jet data and Monte Carlo fake
7+jet events. The Monte Carlo distributions are scaled to be the same as data in the
region ISO > 3.0 GeV (mostly populated by fakes).


0 -
o
" 0.9

c 0.8



a
0_0.7

r 0.6

0.5

0.4

0.3

0.2

0.1

0


0.5 1 1.5 2 2.5 3
Isolation, GeV


Figure 9-9: The predicted real photon content as a function of the cut on isolation
energy in a cone around photon candidate (dots-prediction based on the shape of
the isolation energy distributions in data and Monte Carlo fakes, band-real photon
fraction and its uncertainty based on the standard conversion method). The results
are presented for events from both mass bins


CDF PRELIMINARY










Herwig and Pythia are very different. We repeat the measurements using the Herwig

and Pythia based values of the a-parameter. The difference between results is taken

to be a systematic uncertainty associated with the dependence on the Monte Carlo

fragmentation model in the evaluation of the a-parameter. The effect turns out to

be small.

9.4 PDF Uncertainties

As mentioned in Section 8.3, the fractions of gluon jets in dijet events, f 3, and

pure 7-jet events, fYJ, are determined from Herwig and Pythia Monte Carlo gener-

ators with PDF sets CTEQ4M, CTEQ4A2, and CTEQ4A4. The results obtained

with Herwig+CTEQ4M are taken as default. The largest variations in results (typi-

cally 1-3%) obtained with different Monte Carlo generators and PDFs are treated as

estimates of the corresponding systematic uncertainties.

9.5 Uncertainties in Multiplicity Measurements

The choice of the impact parameter cut is motivated by the distribution of corre-

lated points on the (log |dl,logPr)-plane (see discussion in Section 8.5 and Fig. 8-4).

The position of the straight line on the Fig. 8-4 corresponds to roughly 6ad of the

impact parameter resolution. Moving this cut further to the left would remove more

background tracks, but would also start eliminating some signal tracks from the tails

of the impact parameter resolution. The natural point of closest approach is around

3a.d Thus, the position of the deviated cut is set to eliminate all tracks outside the

region of 3(impact (dashed line on the Fig. 8-4). For all measured values, the differ-

ence in results is assigned to the systematic uncertainty associated with the impact

parameter requirements.

The parameter Az is used to exclude tracks due to secondary interactions in the

same bunch crossing. Fig. 8-6 shows Az distribution for tracks from dijet events with

only one vertex. The |Az < 6.0 cm criterion motivated the requirement IZl z2 <

12.0 cm on the spatial separation of primary vertices in two-vertex events used in the









event selection described earlier. To estimate the systematics due to a choice of Az

cut, we repeat all the measurements with tightened cut of |Azl < 4.0 cm which is

three times less than the distance between two vertices.

The background track removal by means of cuts on Az and impact parameters

is the leading source of systematic uncertainty (typical value is 5-8%) in the mea-

surement of multiplicity in quark and gluon jets. At the same time, these cuts have

a small effect (typically less than 3%) on the measurement of the ratio, r = Ng/Nq.

For the 7-conversions remaining after the vertex cuts, the correction based on

Monte Carlo studies is applied. We conservatively estimate the associated uncertainty

to be equal to the correction itself (typical value is ~3.5%).

The results are also corrected for the remaining (after vertex cuts) decay prod-

ucts of K' and A. The correction procedure is based on Monte Carlo studies. The

associated systematic uncertainty is conservatively taken to be equal to the correction

itself (typical value is ~4-5%).

The contribution of uncorrelated background to multiplicity in jet cone is de-

termined using the complementary cone technique. The multiplicity of tracks (0.55

tracks per cone of 0c=0.47 rad in dijet events and 0.46 tracks in photon+jet events

for both mass bins) from complementary cones associated with this source of back-

ground is extracted from fitting procedure described in Section 8.5. To estimate the

systematic uncertainty due to uncorrelated background subtraction, we repeat all the

measurements with the average (not extrapolated) complementary cone multiplicity.

As mentioned earlier, the jet multiplicity is corrected for CTC inefficiency. This

correction is the same for dijet and photon+jet data samples. The default correction

is equal to 6.3% for events with jet energy of Ejet=41 GeV and 7.5% for Ejet=52.5

GeV (both corrections are quoted for 0c=0.47). To estimate the systematic effect

of CTC corrections on the ratio r, we repeat all the measurements with no CTC

correction and with both "',lin-,.;li,"" and "pessimistic" CTC correction scenarios







84

(see ref. [60, 70]). The variations in r appear to be negligible. In the case of charged
particle multiplicities in quark and gluon jets, the difference in the results obtained

with "o'/li'/,lil/-" and "pessimistic" scenarios is assigned to be the corresponding

systematic uncertainty (<2%).

Another source of systematic uncertainty is the losses of low PT tracks because

of curling in the magnetic field of the solenoid. We evaluate the fraction of lost tracks

from Herwig. The correction turns out to be small (<2%), so we conservatively

estimate the associated uncertainty to be equal to correction itself.

















Table 9-1: The summary of systematic uncertainties in the measurements of Ng, Nq,
and r = Ng/Nq obtained for the opening angle Oc = 0.47. The errors are rounded.

Default cuts & Syst. uncertainty Ejet=41 GeV Ejet=52.5 GeV
corrections evaluation method ANg AN, Ar = N-g ANg ANq Ar- N
N,1 Ng
correction for use NJ-1721
Nv12=2 events -0.04 0.06 -0.03 -0.07 0.11 -0.05
Jet energy scale: max. dev. using DMYY PDYY
JTC96X option: MDYY, PDYY,
DDYY DMYY & DPYY 0.20 -0.09 0.09 -0.31 0.15 -0.11
Jet energy balance: < 0.125
-l +-2 < 0.15 (photon+jet only) -0.06 0.04 -0.05 0.06 -0.09 0.05

Inv. mass spec.
correction: N/A Applied -0.01 0.0 0.0 0.0 0.0 0.0
Jet algorithm: MC comparison of,
Cone R=0.7 jets R=0.4, 0.7, 1.0 jets 0.13 0.07 0.0 0.14 0.05 0.01
Impact param.:
Idl < 6oad dl < 3od -0.30 -0.28 0.03 -0.32 -0.35 0.06
|Az| < 6 cm |Azl < 4 cm -0.13 -0.10 0.01 -0.14 -0.15 0.02
remaining 7-conv.
corr.: MC-based no correction 0.23 0.15 0.0 0.28 0.17 0.0
KO and A decays
corr.: MC-based no correction 0.28 0.22 -0.02 0.33 0.25 -0.01
uncorrelated bckg.:
extrapolated compl. measured compl.
cone multiplicity cone multiplicity -0.07 -0.08 0.02 -0.15 -0.01 -0.03
Default CTC no eff. correction N/A N/A 0.0 N/A N/A 0.01
efficiency corr. "optimistic" corr. -0.01 -0.01 0.0 -0.04 -0.03 0.0
"pessimistic" corr. 0.02 0.01 0.0 0.05 0.02 0.0
PT <300 MeV trks.:
MC correction no correction -0.13 -0.06 -0.01 -0.16 -0.05 -0.01
Jet direction: MC comparison:
reconstructed jet QFL jet vs. MC jet 0.06 0.04 0.0 0.06 0.04 0.0
fraction of gl. jets: CTEQ4A2+Herwig -0.04 0.0 -0.01 -0.05 0.03 -0.02
CTEQ4M+Herwig CTEQ4A4+Herwig 0.01 -0.01 0.01 0.12 -0.07 0.05
fraction of CPR hit rate -0.06 0.09 -0.05 -0.06 0.09 -0.04
real photons: Back-scattering 0.07 -0.12 0.06 0.11 -0.15 0.07
default CPR r/x0 rate 0.02 -0.03 0.01 0.01 -0.01 0.0
method Ks/I rate -0.02 0.03 -0.01 -0.01 0.01 0.0
a-correction: difference between
average of all meth. Herwig & Pythia 0.01 -0.08 0.03 -0.06 -0.01 -0.01

















Table 9-2: The summary of systematic uncertainties in the measurements of Ng, Nq,
and r = Ng/Nq obtained for the opening angle Oc = 0.36. The errors are rounded.

Default cuts & Syst. uncertainty Ejt=41 GeV Ejt=52.5 GeV
corrections evaluation method ANg AN, Ar = Ng ANg ANq Ar=-
correction for use N-{j2-1
Nv12=2 events -0.05 0.07 -0.04 -0.09 0.14 -0.07
Jet energy scale: max. dev. using DMYY PDYY
JTC96X option: MDYY, PDYY,
DDYY DMYY & DPYY 0.14 -0.07 0.07 -0.34 0.18 -0.14
Jet energy balance: < 0.125
l1T < 0.15 (photon+jet only) -0.07 0.10 -0.06 0.02 -0.03 0.02
Inv. mass spec.
correction: N/A Applied 0.0 0.01 0.0 -0.01 0.0 0.0
Jet algorithm: MC comparison of,
Cone R=0.7 jets R=0.4, 0.7, 1.0 jets 0.25 0.11 0.02 0.31 0.10 0.03
Impact param.:
Idl < 6ad |d| < 3od -0.28 -0.23 0.02 -0.30 -0.27 0.04
|Az| < 6 cm |Azl < 4 cm -0.10 -0.08 0.01 -0.11 -0.11 0.02
remaining 7-conv.
corr.: MC-based no correction 0.18 0.10 0.0 0.21 0.12 0.0
KO and A decays
corr.: MC-based no correction 0.24 0.18 0.02 0.28 0.21 0.02
uncorrelated bckg.:
extrapolated comply. measured compl.
cone multiplicity cone multiplicity 0.07 -0.04 0.03 -0.11 0.06 -0.05
Default CTC no eff. correction N/A N/A 0.0 N/A N/A 0.01
efficiency corr. "optimistic" corr. -0.06 -0.03 0.0 -0.09 -0.05 0.0
"pessimistic" corr. 0.05 0.03 0.0 0.09 0.05 0.0
PT <300 MeV trks.:
MC correction no correction -0.08 -0.04 -0.01 -0.11 -0.03 -0.01
Jet direction: MC comparison:
reconstructed jet QFL jet vs. MC jet 0.09 0.05 0.0 0.11 0.06 0.0
fraction of gl. jets: CTEQ4A2+Herwig -0.03 0.0 -0.01 -0.05 0.03 -0.02
CTEQ4M+Herwig CTEQ4A4+Herwig 0.01 -0.02 0.01 0.10 -0.06 0.05
fraction of CPR hit rate -0.05 0.07 -0.05 -0.05 0.07 -0.04
real photons: Back-scattering 0.06 -0.10 0.06 0.09 -0.13 0.08
default CPR r/Or0 rate 0.01 -0.02 0.02 0.01 -0.01 0.01
method Ks/I rate -0.02 0.02 -0.02 0.0 0.01 0.0
a-correction: difference between
average of all meth. Herwig & Pythia 0.01 -0.05 0.02 -0.06 0.02 -0.02












Table 9-3: The summary of systematic uncertainties in the measurements of Ng, Nq,
and r = Ng/Nq obtained for the opening angle Oc = 0.28. The errors are rounded.

Default cuts & Syst. uncertainty Ejet=41 GeV Ejt=52.5 GeV
corrections evaluation method ANg AN, Ar = N ANg ANq Ar= N
correction for use Njv 121
Ni12=2 events -0.03 0.05 -0.03 -0.06 0.09 -0.05
Jet energy scale: max. dev. using DMYY PDYY
JTC96X option: MDYY, PDYY,
DDYY DMYY & DPYY 0.14 -0.07 0.07 -0.32 0.15 -0.14
Jet energy balance: < 0.125
(t^ < 0.15 (photon+jet only) -0.07 0.11 -0.07 0.0 -0.01 0.01
Inv. mass spec.
correction: N/A Applied 0.0 0.01 0.0 0.01 0.01 0.0
Jet algorithm: MC comparison of,
Cone R=0.7 jets R=0.4, 0.7, 1.0 jets 0.32 0.15 0.03 0.41 0.15 0.05
Impact param.:
Idl < 6od |d| < 3od -0.25 -0.19 0.01 -0.27 -0.23 0.03
|Az| < 6 cm |AzI < 4 cm -0.07 -0.06 0.01 -0.08 -0.08 0.02
remaining 7-conv.
corr.: MC-based no correction 0.13 0.09 0.0 0.16 0.10 0.0
K' and A decays
corr.: MC-based no correction 0.20 0.16 -0.01 0.24 0.18 -0.01
uncorrelated bckg.:
extrapolated compl. measured compl.
cone multiplicity cone multiplicity -0.01 -0.02 0.0 -0.03 -0.01 0.0
Default CTC no eff. correction N/A N/A 0.0 N/A N/A 0.01
efficiency corr. "optimistic" corr. -0.04 -0.03 0.0 -0.07 -0.04 0.0
"pessimistic" corr. 0.05 0.03 0.0 0.07 0.05 0.0
PT <300 MeV trks.:
MC correction no correction -0.05 -0.03 0.0 -0.07 -0.02 0.0
Jet direction: MC comparison:
reconstructed jet QFL jet vs. MC jet 0.11 0.06 -0.01 0.13 0.07 0.0
fraction of gl. jets: CTEQ4A2+Herwig -0.02 0.0 -0.01 -0.04 0.02 -0.02
CTEQ4M+Herwig CTEQ4A4+Herwig 0.01 -0.01 0.01 0.06 -0.04 0.05
fraction of CPR hit rate -0.03 0.05 -0.04 -0.04 0.06 -0.03
real photons: Back-scattering 0.05 -0.07 0.05 0.07 -0.10 0.07
default CPR /xr rate 0.01 -0.02 0.01 0.0 0.0 0.0
method Ks/lr rate -0.01 0.01 -0.01 -0.01 0.01 0.0
a-correction: difference between
average of all meth. Herwig & Pythia 0.02 -0.05 0.03 -0.06 0.03 -0.02



Table 9-4: Fraction of real photons in the photon+jet sample and its associ-
ated systematic uncertainties. Results are based on CPR weights calculated by
GETCPRWEIGHT.CDF routine.

Jet Energy (GeV) Default CPR hit rate Back-scattering r/x0u Ks/IT
41 0.7510.04 0.780.04 0.700.04 0.7310.04 0.7510.04
52.5 0.9010.07 0.940.07 0.850.07 0.9010.07 0.9010.07