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Double charmonium production in exclusive processes.

Double charmonium production in exclusive processes. V.V. Braguta Institute for High Energy Physics Protvino, Russia. Content:. Introduction Charmonia Distribution Amplitudes Properties of Charmonia Distribution Amplitudes Double Charmonia Production at B-factories

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Double charmonium production in exclusive processes.

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  1. Double charmoniumproductionin exclusive processes. V.V. Braguta Institute for High Energy Physics Protvino, Russia

  2. Content: • Introduction • Charmonia Distribution Amplitudes • Properties of Charmonia Distribution Amplitudes • Double Charmonia Production at B-factories • Conclusion

  3. Introduction

  4. Processes to be discussed

  5. Factorization

  6. Nonperturbative effects At given order approximation in 1/s expansion some operators can be omitted

  7. The leading twist distribution amplitude Properties of distribution amplitudes • Resume infinite series of operators • Resume leading logarithmic radiative corrections

  8. Evolution of DA • DA can be parameterized through the coefficients of conformal expansion an : • Alternative parameterization through the moments:

  9. Charmonia Distribution Amplitudes

  10. Different approaches to the study of DA 1. Functional approach - Bethe-Salpeter equation 2. Operator approach - NRQCD - QCD sum rules

  11. Potential models Brodsky-Huang-Lepage procedure: • Solve Schrodinger equation • Get wave function in momentum space: • Make the substitution in the wave function: • Integrate over transverse momentum:

  12. The moments within NRQCD

  13. Model for DA within NRQCD At leading order approximation is the only parameter

  14. DA within QCD sum rules Advantage: The results are free from the uncertainty due to the relativistic corrections Disadvantage: The results are sensitive to the uncertainties in QCD sum rules parameters: QCD sum rules is the most accurate approach

  15. The results of the calculation The results for 1S states The results for 2S states

  16. Models of DAs 1S states 2S states

  17. Properties of distribution amplitudes

  18. Relativistic tail • At DA is suppressed in the region • This suppression can be achieved if there is fine tuning of an • Fine tuning is broken at due to evolution

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

  20. Property of DA DA of nS state has 2n+1 extremums

  21. Pion distribution amplitude Distinction from pion distribution amplitude • Much better knowledge of DAs (even for higher twist and excited states) • Improvement of the accuracy of models Rather accurate predictions for exclusive charmonia production

  22. Application: Double charmonium production at B-factories

  23. The processes:

  24. 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

  25. Conclusion • One can get rather good knowledge of charmonia distribution amplitudes • One can get rather good description of hard exclusive processes • In hard exclusive processes (e+e- annihilation, bottomonium decays) relativistic and leading logarithmicradiative corrections are very important

  26. Thank You.

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