1. Exclusive charmonium production within Light 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 The amplitude is divided into two parts:Hadronization Twist-2 2-distribution amplitudes Twist-3 4-distribution amplitudes … … Light cone formalism is designed to study hard exclusive processes

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

6. Relativistic corrections LCFNRQCD DA resums relativististic corrections to the amplitude.

7. Leading logarithmic radiative corrections Exclusive quarkonium production Inclusive 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 a n 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 -  V( 3 S 1 ) P( 1 S 0 ) This formula was first derived in Bondar, Chernyak, Phys. Lett. B612, 215 (2005)

22. Twist-3 distribution amplitudes are unknown 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: Problems: 1. Violation of velocity scaling rules at larger scales 2. v 2 correction can be large for 1S and 2S states

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

26. The results of the calculation Why LO NRQCD predictions are much smaller than the experimental results? a E. Braaten, J. Lee b K.Y. Liu, Z.G. He, K.T. Chao 1. Relativistic corrections K~2.5-6 2. 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 logarithmic radiative corrections are very important