One boson exchangeExtract the strange quark form factors from Apyat tree level (one boson exchange)e'(p3)e(p)ZP"(pA)P(p2)(b)(a)<P(p)1J)1 P(P)>=i(p'[F +Fy q'Ju(p)2Mi0< P(p)IJIP(p)>=ü(p)[FZP + F2Z-P+GyusJu(p)92M6
6 One boson exchange , , 1 2 ( ') | | ( ) ( ')[ ] ( ) 2 P P i P p J P p u p F F q u p M = + Extract the strange quark form factors from at tree level (one boson exchange) , , 1 2 5 ( ') | | ( ) ( ')[ ] ( ) 2 Z Z P Z P Z A i P p J P p u p F F q G u p M = + + APV
+ AOBEOBEAOBEG,Q?+Aprz4元α/2 [e(GrP) +t(G%P)]TAOBE=eGEPGrP,= TGKPGMP(1)·福AOBE = -(1- 4sin? Ow))t(1+t)(1-")G′G%-tFr(z),PGr(2)P= Fr(Z),PE2= Fr(Z)P + Fr(z),PGr(Z),PMa7
7 2 1 , 2 , 2 4 2 [ ( ) ( ) ] OBE OBE OBE Z F E M A PV P P E M G Q A A A A G G + + + = − + , , , 2 2 , , ; (1 4sin ) (1 )(1 ) P P E M P M OBE OB Z P Z P E M ZA E E M OBE A W G G G A A G G A G = = = − − + − ( ), ( ), ( ), 1 2 ( ), ( ), ( ), 1 2 Z P Z P Z P E Z P Z P Z P M G F F G F F = − = + (1)
By assuming charge symmetryau,d,s/ p= Ggdus/ p3E.ME,MAnd quark content of proton at tree level:Jem= Q,qrμqr; J=Eq,(g+ghs)qff=u,d,s8
8 By assuming charge symmetry: , , / , , / , , u d s p d u s p G G E M E M = And quark content of proton at tree level: 5 , , ; ( ) em Z f f f f V A f f f f u d s f J Q q q J q g g q = = = +
Results:A+ = A + A, + A,cGr'Gr" +tGh'GMA = -a[(1-4sin’ Qw)-e(GP) +t(GuP)cGI'G: +tGM'GMA =(GP) + t(GP)e'GMG2A, = a(1- 4sin2 Ow)(GP) +t(GhP)a=G,Q2 /4α~2; '=/t(1+t)(1-)9
9 Results: 1 1 2 3 2 1 2 2 2 2 2 2 , , , , , , , 3 2 , , , , , 2 , [(1 4sin ) ] ( ) ( ) ( ) ( ) ' (1 4sin ) ( ) ( ) P n P n E E M M P P E M P P E M P P E M P Z s M A P Z PV W W s M P E M E G G G G G G A A A A A a A a A G G G G G G a G G G G + = + + + = − − − + + = + = − + 2 2 / 4 2; ' = (1+ )(1- ) F a G Q =
One loop level at zero momentumtransferElectro-weak radiative corrections( to Apare welldefined at quark level and can be parame--terized as the 4-fermion effective Hamiltonion(W.J.Marciano, .Sirlin,PRD27,552(1983), PRD29,75(1984); W.-M.Yao,JPG69,1(2006))GHvgE [Cigeyur,eqy"qg+C2gey,eqy"ysg]2q=u,d,sareaustained by matching with the parity -violatingamplitudeofe(p)+q(p2 )→e(p3)+q(p4 )10
10 are obtained by matching with the parity -violating amplitude of One loop level at zero momentum transfer Electro-weak radiative corrections( to ) are well defined at quark level and can be parame- -terized as the 4-fermion effective Hamiltonion (W.J.Marciano, .Sirlin,PRD27,552(1983), PRD29,75(1984); W.-M.Yao, JPG69,1(2006)) 5 1 2 5 , , [ ] 2 e q F PV q q q u d s G H C e eq q C e eq q − = = + 1 2 and C C q q 1 2 3 4 e p q p e p q p ( ) ( ') ( ) ( ') + → + APV