At zero momentum transfer approximation areainbtcdependent on momentum, and the corrections at quarklevel can by applied to hadron level directly whichresults inApv(p,x) = A + A, + ACGPGr"+TGYPGrnA =-ap[(1-4k sin’ ew)-(GrP) + t(GMP)(2)EGIPG +TGMPGMA =ape(GrP) +t(GrP)e'GPGZA, = a(1- 4sin 0w)e(GP) + t(GrP)?41+ sin' w); Cia = p(,-2 sin' 0n)lu = p(-)-232Usually used to extract the strange quark formfactors fromexperiment data (HAPPEX, A4)11
11 At zero momentum transfer approximation are not dependent on momentum, and the corrections at quark level can by applied to hadron level directly which results in 1 2 and C C q q 1 2 3 2 , , , , , , , , , , 1 2 2 2 2 2 2 , 2 , 3 2 , ( , ) [(1 4 sin ) ] ( ) ( ) ( ) ( ) ' (1 4sin ) ( ) ( ) P n P n E E M M P P E M P P E M P P E M P Z M A P P E M s PV W s E M W A A A A A a A a G G G G G G G G G G G G G A a G = + + + = − − − + + = + = − + 2 2 1 1 1 4 1 2 ( sin ); ( sin ) 2 3 2 3 C C u W d W = − + = − Usually used to extract the strange quark form factors from experiment data (HAPPEX, A4). (2)
Experiment DataSAMPLE CollaborationPRL78,3824(1997)Q2 ~ 0.1GeV2, 130° <0<1700A = -6.34±1.45±0.53 ppmG%(Q2 = 0.1GeV2)= 0.34±0.09±0.04±0.05PLB583,79(2004)A(Q2 = 0.1)= -5.61±0.67±0.88 ppmA(Q2 = 0.1) = -5.56±3.37G ±1.54Ge(T=l) ppmG(Q2 =0.1)= 0.37±0.20±0.26±0.07fitting method: useG =(1-4sin2Ow)(1+R,)G-(1+R")G" -G% + (1)12others form : Science 90,2117(2000)
12 Experiment Data SAMPLE Collaboration PLB583,79(2004) 2 2 o 0 2 2 0.1 , 130 170 6.34 1.45 0.53 ppm ( 0.1 ) 0.34 0.09 0.04 0.05 Z M Q GeV A G Q GeV = − = = others form : Science 90,2117(2000) PRL78,3824(1997) 2 2 ( 1) 2 ( 0.1) 5.61 0.67 0.88 ppm ( 0.1) 5.56 3.37 1.54 ppm ( 0.1) 0.37 0.20 0.26 0.07 s e T M A s M A Q A Q G G G Q = = = − = = − = = 2 fitting method: use (1 4sin )(1 ) (1 ) + (1) s P P n n Z G R G R G G M W V M V M M = − + − + −
HAPPEX Collaboration by Zhu et.al PRD62,033008(2000)TPRC69,065501(2004)Q2 = 0.477, 0=12.3°A= -15.05±0.98(stat)±0.56(syst)ppmG:+0.392G=0.014±0.020±0.010PLB635,275(2006)Q2 = 0.099, 0=6.00A = -1.14±0.24(stat)±0.06(syst)ppmG +0.080G = 0.030±0.025(stat)±0.006(sys)±0012(FF)PRL98,032301(2007)fitting method: use (2)Q2 =0.109, 0=6.0°A=-1.58±0.12(stat)±0.04(syst)ppmG: +0.09GM = 0.007±0.011(stat)±0.006(sys)13
13 HAPPEX Collaboration PLB635,275(2006) PRL98,032301(2007) PRC69,065501(2004) 2 o 0.477, =12.3 15.05 0.98(stat) 0.56(syst)ppm 0.392 0.014 0.020 0.010 s s E M Q A G G = = − + = by Zhu et.al PRD62,033008(2000) Z GA 2 o 0.099, =6.0 1.14 0.24(stat) 0.06(syst)ppm 0.080 0.030 0.025(stat) 0.006(sys) 0012(FF) s s E M Q A G G = = − + = 2 o 0.109, =6.0 1.58 0.12(stat) 0.04(syst)ppm 0.09 0.007 0.011(stat) 0.006(sys) s s E M Q A G G = = − + = fitting method: use (2)
A4 CollaborationPRL93,022002(2004)Q2 =0.23, 0=30°- 40°A =-5.44±0.54(stat)±0.26(syst)ppmG +0.225G% = 0.039±0.034PRL94,152001(2005)Q2=0.108, 0=30°-40°A = -1.36 ±0.29(stat)±0.13(syst)ppmG+0.106G%=0.071±0.036fitting method: use (2)14
14 A4 Collaboration PRL93,022002(2004) PRL94,152001(2005) 2 o 0.23, =30 40 5.44 0.54(stat) 0.26(syst)ppm 0.225 0.039 0.034 o s s E M Q A G G = − = − + = 2 o 0.108, =30 40 1.36 0.29(stat) 0.13(syst)ppm 0.106 0.071 0.036 o s s E M Q A G G = − = − + = fitting method: use (2)
Go CollaborationPRL95,092001(2005),Nucl.Phys.Proc.Suppl.159,121(2006)0.20.15GOHAPPEX0.1Q2 = 0.12 -1 GeV20.050=52°-78°Nltao00.05fitting method: use (1)0and radiative-0.0350.40.60.20.81.00corrections areQ (Gev2)includedaserrorbarFurther: Q? = 0.23,0.63 GeV2; 0 ~ 108°15
15 G0 Collaboration PRL95,092001(2005), Nucl.Phys.Proc.Suppl.159,121(2006) 2 2 0.12 1 GeV 52 78 o o Q = − = − 2 2 o Further: 0.23,0.63 GeV ; 108 Q = fitting method: use (1) and radiative corrections are included as error bar