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F. S. N. , M. Nielsen

Charm hadronic form factors with QCD sum rules. Motivation. QCDSR. Results on form factors. Application: charmonium production. Conclusion. F. S. N. , M. Nielsen. IFUSP (São Paulo) BRAZIL. interactions at RHIC and LHC. Lin,Ko nucl-th/0210014. Charm form factors.

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F. S. N. , M. Nielsen

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  1. Charm hadronic form factors with QCD sum rules Motivation QCDSR Results on form factors Application: charmonium production Conclusion F. S. N. , M. Nielsen IFUSP (São Paulo) BRAZIL

  2. interactions at RHIC and LHC Lin,Ko nucl-th/0210014 Charm form factors

  3. Charmonium decays in B factories X (3872) X (3872) Liu, Zhang, Zhu, hep-ph/0610278

  4. interactions at FAIR Haidenbauer, Krein, Meissner, Sibirtsev arXiv:0704.3668 [nucl-th]

  5. Form factors in QCD sum rules (data)

  6. 1) Write the three-point correlation function: The QCD side (Operator Product Expansion side): 2) Choose the currents: 3) Insert the currents in and make the contractions:

  7. 4) Perform the OPE: The hadronic side (phenomenological side): 5) Insert hadronic states in + higher resonances

  8. 6) Use the matrix elements: 7) Use an effective Lagrangian to compute the amplitude: 8) Write

  9. On both sides: 9) Decompose in tensor structures and choose one of them: 10) Write a double dispersion relation: double discontinuity 11) Identify 12) Apply a double Borel transform:

  10. 13) Write the sum rule: 14) Numerical analysis: or Borel masses: Continuum thresholds : Numbers :

  11. 15) Check Borel stability and OPE convergence: off-shell total perturbative gluon condensate

  12. 16) Fix M , plot fit and extrapolate to the meson pole: Exp. off-shell off-shell

  13. Correlated extrapolation of the three form factors J/Psi D D*

  14. Varying M and M´ independently: off-shell Good stability !

  15. off-shell Dependence on the continuum threshold 0.6 0.5 0.4 0.6 0.5 0.4

  16. Couplings

  17. Parametrizations:

  18. Comments Coupling D*-D-pion compatible with data and with lattice QCD: lattice data Becirevic, Charles, Le Yaouanc, L.Olivier, Pene, Raynal, (2003) Compatibilitywith HQET relations : Oh, Lee, Song, PRC (2000) =

  19. Application Charmonium production and absorption in nuclear matter Oh, Lee, Song, PRC (2000)

  20. Application Charmonium production and absorption in nuclear matter “Charmonium regeneration”

  21. without with with without

  22. Conclusion Charm form factors are still very usefull for phenomenology Charm form factors change calculations by one order of magnitude We can calculate them with QCDSR (finished the first round) The obtained coupling constants are of the same order of magnitude The numbers roughly agree with previous phenomenological estimates The form factors were used in one phenomenological application

  23. References M.E. Bracco et al., Phys. Lett. B521, 1 (2001) R.D. Matheus et al., Phys. Lett. B541, 265 (2002) F.S. Navarra et al., Phys. Rev. D65, 037502 (2002) M.E. Bracco et al., Phys. Lett. B605, 326 (2005) F. Carvalho et al., Phys. Rev. C72, 024902 (2005) R.D. Matheus et al., Int. J. Mod. Phys. E14, 555 (2005) M.E. Bracco et al., Phys. Lett. B659, 559 (2008) B. Osorio Rodrigues et al., arXiv:1003.2604 [hep-ph]

  24. Three different particles off-shell in the vertex J/Psi D D*

  25. Pole versus continuum off-shell off-shell

  26. Errors Truncation of the OPE corrections Choice of tensor structure Pole + continuum Ansatz ~ 20 % Continuum threshold parameters Values of masses and condensates Choice of Borel mass Medium effects Extrapolation to the mass shell ?

  27. Borel stability in different structures:

  28. 14 tensor structures Choose

  29. Form factors in different structures :

  30. versus

  31. Couplings with vector mesons not very compatible with VDM estimates : Matinyann, Muller, PRC (1998) Oh, Lee, Song, PRC (2000)

  32. P1

  33. P3

  34. P3

  35. P4

  36. P4

  37. P4

  38. P5

  39. P5

  40. P5 Sergei G. Matinyann, Berndt Muller Phys.Rev.C58:2994-2997,1998. nucl-th/9806027

  41. P6

  42. P6

  43. Kodjamirian

  44. P7

  45. P8

  46. P10

  47. Frequent questions Higher dimension condensates ? Infinities ? Killed by Imaginary Corr + Cutkosky + Borel + s0 / QHD Differences between on and off-shell ? Only Borel ? Compatible with SU(4) ? HQET ? VMD? Pole versus continuum (well defined ?) changes with Q2 ? Extension to quartic couplings ? Why the restrictions in the Q2 region ? Why not smaller Q2 ? Final errors ? Observable applications ?

  48. Back ups

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