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2005 International Conference on QCD and Hadronic Physics, Peking University

Pion Electromagnetic Form Factor in the K T Factorization Formulae. Xing-Gang Wu (IHEP). In colarboration with Prof. Tao Huang. 2005 International Conference on QCD and Hadronic Physics, Peking University. Background.

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2005 International Conference on QCD and Hadronic Physics, Peking University

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  1. Pion Electromagnetic Form Factor in the KT Factorization Formulae Xing-Gang Wu (IHEP) In colarboration with Prof. Tao Huang 2005 International Conference on QCD and Hadronic Physics, Peking University

  2. Background • Higher helicity components’ Contributions to the pion ---electromagnetic form factor • Higher twist structures’ Contributions to the pion ---electromagnetic form factor • Summary

  3. I.Background soft regions up to 1.6GeV2 PRL26,1713(2001) by JLAB A 12 GeV upgrade to CEBAF will offer the possibility to measure pion form factor to good precision out to Q2= 36GeV2 for the first time. This offers the best possibility to study the transition between the dominance of `soft’ and `hard’ processes in the dynamics, and to learn where the pQCD limit may be reached, and also to check the pQCD results.

  4. Pion form factor in the large momentum transfer: LO results: Twist-2 Improved to LL: G.R. Farrar and D.R. Jackson, PRL23,246,1979

  5. To short the gap between the theoretical prediction and the experimental, two ways are tried: 1) Non-perturbative contributions A.P. Bakulev etal. PHYS.REV.D70, 033014(2004); O.C. Jacob and L.S. Kisslinger, Phys.Rev.Lett. 56, 225(1986); L.S. Kisslinger etal. Phys.Rev.D63,113005(2001); V.M. Braun etal. Phys.Rev.D61,073004(2000); F. Schlumpf, Phys.Rev.D50, 6895(1994) 2) Power corrections to the LO pion form factor: • higher helicity contributions • higher-twist effect • higher order in alpha_s

  6. Wigner Rotation: II. Higher helicity components’ Contributions to the pion form factor 1. Background and the reason for it Instant Form The right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the kT depen-dence in the hard amplitude, and that the kT dependence in LC wave function affects the hard and soft contributions substantially.

  7. PQCD result: PRD54, 5890(1996) S.W. Wang and L.S. Kisslinger PQCD result: J.Phys.G21, 765(1995) B.Q. Ma and T. Huang Enhancement Suppression LC PQCD result: PRD55, 7107(1997) T.Huang etal. Qualitative analysis Need a quantitative results to clarify the situation!

  8. 2. LC pQCD calculations Six LO time-ordered Feynman Diagrams

  9. Instantaneous diagram Upper three

  10. Lower three

  11. The higher helicty components will contribute zero at the order of Q2. To do numerical calculation: energy flow To ensure the gluon is hard enough Model dependence: Wigner rotation BHL

  12. separation After integration over the azimuth angle, one may find that contributions from the higher helicity states will also provide a negative sign!

  13. Typical Q4- behavior 3. Conclusion The right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the kT depen-dence in the hard amplitude, and that the kT dependence in LC wave function affects the hard and soft contributions substantially.

  14. 4. A discussion on the soft part Higher helicity components

  15. hard Combined twist-2 contribution NLO, Twist-3 ? Higher Fock states ? soft

  16. III. pionic twist-3 contributions 1) The pionic wave function： T. Huang etal. PRD70,014013(2004), QCD sum rule for the wave function of pion

  17. Gegenbauer polynomial expansion BHL The present obtained twist-3 contribution to the pion form factor is comparable or even larger than that of the leading twist in a wide intermediate energy region, Q2 (2-40) GeV2 So, and improved form for the twist-3 wave functions must be introduced to suppress the end-point singularity. New Model

  18. our present DAs V.M. Braun, I.E. Filyanov and P. Ball T. Huang etal.

  19. 2) pion electro-magnetic form factor in the b-space PRD70,093013(2004) For usual helicity component

  20. For all the helicity components

  21. Twsit-3 3) considering the model dependence of the twist-3 contributions Only for usual helicity components

  22. 2(0.320,0.370) Moments mp0=1.3GeV

  23. 4) comparison among different calculations Conclusion: The transverse momentum dependence has been included. A new form of twist-3 wave function has been adopted. The present obtained twist-3 indeed ispower suppressed. Twist-3 NLO Twist-2 F.G.Cao etal. Z.T.Wei and M.Z.Yang EPJC11,501(1998) PRD67,094013(2003)

  24. IV.Summary 1) Higher helicity structure and twist-3 contributions to the pion electro-magnetic form factor have been discussed. Q2-suppressed 2) The kTfactorization approach, where the transverse momentum dependence in the wave function and the hard scattering kernel have been kept, ensures these two are really power suppressed. 3) Both two can give sizeable contributions in the intermediate energy regions. Taking both into consideration, the present experimental data can be roughly explained. 4) The coming CEBAF results shall test the PQCD calculations more precisely.

  25. Thanks !

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