1. 1 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

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

3. 3 I.Background soft regions up to 1.6GeV 2 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 Q 2 = 36GeV 2 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. 4 Pion form factor in the large momentum transfer: LO results: Improved to LL: G.R. Farrar and D.R. Jackson, PRL23,246,1979 Twist-2

5. 5 2) Power corrections to the LO pion form factor: 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) a)higher helicity contributions b)higher-twist effect c)higher order in alpha_s

6. 6 The right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the k T depen-dence in the hard amplitude, and that the k T dependence in LC wave function affects the hard and soft contributions substantially. Wigner Rotation: Instant Form II. Higher helicity components ’ Contributions to the pion form factor 1. Background and the reason for it

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

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

9. 9 Upper three Instantaneous diagram

10. 10 Lower three

11. 11 To do numerical calculation: To ensure the gluon is hard enough BHL The higher helicty components will contribute zero at the order of Q 2. Model dependence: energy flow Wigner rotation

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

13. 13 Typical Q 4 - behavior The right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the k T depen- dence in the hard amplitude, and that the k T dependence in LC wave function affects the hard and soft contributions substantially. 3. Conclusion

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

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

16. 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. 17 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, Q 2  (2-40) GeV 2 So, and improved form for the twist-3 wave functions must be introduced to suppress the end-point singularity. Gegenbauer polynomial expansionBHL New Model

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

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

20. 20 For all the helicity components

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

22. 22 Moments m p 0 =1.3GeV  2  (0.320,0.370)

23. 23 F.G.Cao etal. Z.T.Wei and M.Z.Yang 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 is power suppressed. EPJC11,501(1998) PRD67,094013(2003) Twist-2 NLO Twist-3

24. 24 IV.Summar y 1) Higher helicity structure and twist-3 contributions to the pion electro-magnetic form factor have been discussed. Q 2 -suppressed 2) The k T factorization 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. 25 Thanks !