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Изучение процессов двойного рождения чармониев на B-фабриках и волновые функции чармониев

Изучение процессов двойного рождения чармониев на B-фабриках и волновые функции чармониев. В.В. Брагута Институт Физики Высоких Энергий. Content:. Introduction Charmonia Distribution Amplitudes Properties of Charmonia Distribution Amplitudes Double Charmonium Production at B-factories

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Изучение процессов двойного рождения чармониев на B-фабриках и волновые функции чармониев

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  1. Изучение процессов двойного рождения чармониев на B-фабриках и волновые функции чармониев В.В. Брагута Институт Физики Высоких Энергий

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

  3. Introduction

  4. Factorization

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

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

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

  8. Charmonia Distribution Amplitudes

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

  10. The twist-3 distribution amplitudes If one ignores the contribution of the higher Fock states, EOM unambiguously fix twist-3 distribution amplitudes P.Ball, et.al., Nucl.Phys. B529 P. Ball, JHEP 9901:010

  11. Properties of distribution amplitudes

  12. 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

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

  14. 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

  15. Double charmonium production at B-factories

  16. The processes:

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

  18. The results of the calculation [1] E. Braaten, J. Lee[2] K.Y. Liu, Z.G. He, K.T. Chao[21] D. Ebert, R.N.Faustov, V.O.Galkin, A.P. Martynenko[26] Z.G. He, Y.Fan, K.T. Chao[27] G.T. Bodwin, J. Lee, C.Yu [ ] A.E. Bondar, V.L. Chernyak Why LO NRQCD predictions are much smaller than the experimental results? 1. Relativistic corrections K~3-142. Leading logarithmic radiative corrections K~1.3-2.3

  19. NRQCD results NRQCD results are overestimated

  20. Conclusion • Light cone formalism is natural approach to hard exclusive processes • Within the accuracy of the calculation one can reach the agreement between the experimental results and light cone predictions for the double charmonium production • In hard exclusive processes (e+e- annihilation, bottomonium decays) relativistic and leading logarithmicradiative corrections are very important

  21. Спасибо за внимание

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