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Study of charmonium distribution amplitudes.

Study of charmonium distribution amplitudes. V.V. Braguta Institute for High Energy Physics Protvino, Russia. Content:. Introduction Study of 1S and 2S charmonium distribution amplitudes ( Potential models, NRQCD, QCD sum rules approaches ) Properties of distribution amplitudes

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Study of charmonium distribution amplitudes.

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  1. Study of charmonium distribution amplitudes. V.V. Braguta Institute for High Energy Physics Protvino, Russia

  2. Content: • Introduction • Study of 1S and 2S charmonium distribution amplitudes ( Potential models, NRQCD, QCD sum rules approaches) • Properties of distribution amplitudes • Application: double charmonium production at B-factories

  3. The results were obtained in papers: • “The study of leading twist light cone wave functions of eta_c meson” V.V. Braguta, A.K. Likhoded, A.V. LuchinskyPhys.Lett.B646:80-90,2007 • “The study of leading twist light cone wave functions of J/Psi meson” V.V. BragutaPhys.Rev.D75:094016,2007 • “The study of leading twist light cone wave functions of 2S state charmonium mesons” V.V. Braguta, to be published in Phys. Rev. D

  4. Introduction

  5. Light cone formalism The amplitude is divided into two parts: Hadronization can be describedby distribution amplitudes

  6. Definitions of leading twist DA

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

  8. DA of nonrelativistic system

  9. Study of charmonium 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. Property of DA DA of nS state has 2n+1 extremums

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

  14. Model for 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. Application: Double charmonium production at B-factories

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

  22. Thank You.

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