Exclusive charmonium production within Light Cone Formalism.

1. Exclusive charmoniumproductionwithinLight Cone Formalism. V.V. Braguta Institute for High Energy Physics Protvino, Russia

2. Outline: • Introduction • Charmonium Distribution Amplitudes (DA) • Exclusive charmonium production within light cone formalism: • Conclusion

3. Introduction

4. Light Cone Formalism Light cone formalism is designed to study hard exclusive processes The amplitude is divided into two parts: Hadronization Twist-2 2-distribution amplitudesTwist-3 4-distribution amplitudes … …

5. Comparison of LCF and NRQCD The cross section is double series LCF Power corrections: NRQCD Relativisitic corrections: Radiative corrections:

6. Relativistic corrections LCF NRQCD DA resums relativististic corrections to the amplitude.

7. Leading logarithmic radiative corrections Inclusive quarkonium production Exclusive quarkonium production DA resums leading logarithmic radiative corrections.

8. Distribution Amplitudes are the key ingredient of Light Cone Formalism

9. Charmonium Distribution Amplitudes

10. The models of leading twist DAs 1S states 2S states • V.V. Braguta, A.K. Likhoded, A.V. Luchinsky, Phys.Lett.B646:80-90,2007 • V.V. Braguta, Phys.Rev.D75:094016,2007 • V.V. Braguta, arXiv:0709.3885 [hep-ph]

11. The model of DAs within NRQCD At leading order approximation is the only parameter

12. The violation of NRQCD scaling rules At larger scales the fine tuning of the coefficients an is broken and NRQCD scaling rules are violated NRQCD velocity scaling rules are violated in hard processes

13. Improvement of the model for DA The evolution of the second moment The accuracy of the model for DA is better at larger scales

14. Exclusive charmonium production within light cone formalism

15. The processes:

16. The diagrams Fragmentation diagrams Nonfragmentation diagrams

17. The cross section at NLO

18. Relativistic and leading logarithmic radiative corrections Interference of fragmentation and nonfragmentation diagrams The role of corrections

19. The results of the calculation a Bodwin, Braaten, Lee, Phys. Rev. D74

20. The processes:

21. e+e-gV(3S1) P(1S0) This formula was first derived in Bondar, Chernyak, Phys. Lett. B612, 215 (2005)

22. Twist-3 distribution amplitudes Problem:The scale dependences of some twist-3 DAs are unknown

23. First modification of BC formula Propagators:

24. Second modification of BC formula Problems:1. Violation of velocity scaling rules at larger scales2. v2 correction can be large for 1S and 2S states

25. The constants needed in the calculation The values of the constants(preliminary results)

26. The results of the calculation a E. Braaten, J. Leeb K.Y. Liu, Z.G. He, K.T. Chao Why LO NRQCD predictions are much smaller than the experimental results? 1. Relativistic corrections K~2.5-62. Leading logarithmic radiative corrections K~1.5-2.5

27. Conclusion • The processes considered in the report: • Within the error of the calculation the results are in agreement with the experiments • In hard exclusive processes (e+e- annihilation, bottomonium decays) relativistic and leading logarithmicradiative corrections are very important