The and -Z Exchange Corrections to Parity Violating Elastic Scattering

1. The and -Z Exchange Corrections to Parity Violating Elastic Scattering 周海清/东南大学物理系 based on PRL99,262001(2007) in collaboration with C.W.Kao, S.N.Yang 2008/4/27

2. Outline • Introduction • One boson exchange • Two boson exchange correction • Extraction from experimental data • Conclusion

3. Introduction Motivation: To extract the strange quark form factors of proton more precisely by parity violating elastic electron-proton scattering, one-loop corrections should be considered more carefully, especially the corrections from box diagrams. The importance of these corrections has been indicated in elastic ep scattering (to extract the electromagnetic form factors of proton).

4. Proton : constructed by u, d, s, c…quarks, one of the most important QCD bound state and component of the world. Strange quark form factors of proton:

5. Parity violating elastic electron-proton scattering:

6. One boson exchange Extract the strange quark form factors from at tree level (one boson exchange)

8. (1)

9. By assuming charge symmetry: And quark content of proton at tree level:

10. Results:

11. 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)) are obtained by matching with the parity -violating amplitude of

12. 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 (2) Usually used to extract the strange quark form factors from experiment data (HAPPEX, A4).

13. Experiment Data SAMPLE Collaboration PRL78,3824(1997) PLB583,79(2004) others form : Science 90,2117(2000)

14. HAPPEX Collaboration PRC69,065501(2004) PLB635,275(2006) PRL98,032301(2007) fitting method: use (2)

15. A4 Collaboration PRL93,022002(2004) PRL94,152001(2005) fitting method: use (2)

16. G0 Collaboration PRL95,092001(2005), Nucl.Phys.Proc.Suppl.159,121(2006) fitting method: use (1) and radiative corrections are included as error bar

17. Summary Ex: precision about 0.1 ppm , or about 10%, 5% Theoretic approximation: Zero momentum transfer Charge symmetry Deuteron form factors …..

18. Two boson exchange correction Go beyond zero momentum transfer approximation. Among the one loop correction, the box diagrams are most important. Hinted by the un-polarized elastic electron-proton scattering. cross diagrams are implied

19. Two model dependent methods are applied to calculated the TPE diagrams’ contribution in unpolarized ep scattering. A: Hadronic mechanism (hadron level). P. G. Blunden et al.PRL91,142304(2003) The correction to unpolarized cross section is calculated. Furthermore, its effects to electromagnetic form factors of proton are analyzed and found to be large. cross diagram is implied Properties: Consistent with effective interaction by zero momentum transfer approximation . The results are model-independent by soft photon approximation.

20. B: General parton distributions (quark level). Y. C. Chen et al. PRL93,122301(2004), A. V. Afanasev et al. PRL94,212301(2005) Also the correction to unpolarized cross section is calculated and the effects to electromagnetic form factors of proton are analyzed. Corrections to from TPE at high are discussed. The two results are consistent for unpolarized cross section.

21. We applied the first method to calculated the exchange contributions to . Input parameters: Using elastic intermediate state approximation, take the form factors as the effective vertexes. This results in no new input except the tree level form factors.

22. Practical calculation, two forms of the form factors are chose. A) Monopole form B) Dipole form

23. Parameters: Usual dipole form (Ref HAPPEX, A4) For comparing choose four case x, y, z (E. J. Beise etc Prog.Part.Nucl. Phys 54,289(2005)) Then calculating the diagrams…and IR divergence emerges…

24. IR divergence Bremsstrahlung contribution should be considered to cancel the IR divergence of the cross sections from box diagrams. Separate the corrections in the soft photon approximation is factorized correction in soft photon approximation and is model independent and R,L independent.

25. What we calculated.

26. Results

33. Properties: • The total corrections are not sensitive to the input • parameters. • The dependence of correction is evidently. • Not very small: 1-2%. • 4. Corrections from respectively • are a little sensitive to parameters. • (Argument in recent paper J.A.Tjon etc PRL 100, 082003 (2008))

34. Extraction from experimental data HAPPEX and A4 To avoid double counting of box diagrams, the contributions at zero momentum transfer should be subtracted. M is strong interaction parameter, chosen as 1GeV. Then

35. Define Result

36. The values of for HAPPEX and A4 experiments. I,II and III refer to HAPPEX data in 2004, 2006, and 2007(K.A. Aniol et al. PRC 69, 065501(2004), PLB 635, 275 (2006); A. Acha et al, PRL98, 032301 (2007)), And IV and V correspond to A4 data in 2004 and 2005(F.E. Maas et al ,PRL93, 022002(2004); PRL94, 152001 (2005)).

37. large

38. SAMPLE: 1: At backward where the correction is larger. 2: is extracted from of deuteron in some case . The box diagrams corrections of latter have not been well estimated theoretically, so the result is not certain.

39. the weak charge of proton Now experimentally, 4% uncertainty in , corresponding to 2.2% uncertainty in

40. Not small.

41. Conclusion 1: exchange corrections to in ep scattering are calculated. 2: The corrections to the current experimental data on strange quark form factor are found to be not small. Even reach to -40% in some case. 3: The corrections to is also analyzed and find to reach about -6.65%.

42. Further Work 1: Correction to the precise measurement of from beta decay of neutron. 2: PV in BESⅢ and the structure of nucleons. 3: Corrections in e-d scattering. Thanks!

43. APPENDIX