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\( \mathcal{O}\left( {{\alpha_s}} \right) \) corrections to J/ψ+ χ cJ production at B factories

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Abstract

We investigate the \( \mathcal{O}\left( {{\alpha_s}} \right) \) corrections to e + e  → J/ψ(ψ′) + χ cJ (J =0, 1, 2) in the NRQCD factorization approach. These next-to-leading order (NLO) corrections are calculated at the level of helicity amplitude. We have made a detailed analysis for both polarized and unpolarized cross sections, and compared our predictions with the measurements at the B factories. We also derive the asymptotic expressions for each of the NLO helicity amplitudes, and confirm the earlier speculation that at NLO in α s , the double logarithm of type \( {\ln^2}\left( {{{s} \left/ {{m_c^2}} \right.}} \right) \) appearing in the NRQCD short-distance coefficient is always associated with the helicity-suppressed channels.

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References

  1. G. Lepage and S.J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22 (1980) 2157 [ inSPIRE].

    ADS  Google Scholar 

  2. V. Chernyak and A. Zhitnitsky, Asymptotic behavior of exclusive processes in QCD, Phys. Rept. 112 (1984) 173 [ inSPIRE].

    Article  ADS  Google Scholar 

  3. M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for B → ππ decays: strong phases and CP-violation in the heavy quark limit, Phys. Rev. Lett. 83 (1999) 1914 [hep-ph/9905312] [ inSPIRE].

    Article  ADS  Google Scholar 

  4. M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for exclusive, nonleptonic B meson decays: General arguments and the case of heavy light final states, Nucl. Phys. B 591 (2000) 313 [hep-ph/0006124] [ inSPIRE].

    Article  ADS  Google Scholar 

  5. Belle Collaboration collaboration, K. Abe et al., Observation of double c anti-c production in e + e annihilation at \( \sqrt {s} \) approximately 10.6 GeV , Phys. Rev. Lett. 89 (2002) 142001 [hep-ex/0205104] [ inSPIRE].

    Article  ADS  Google Scholar 

  6. BABAR Collaboration collaboration, B. Aubert et al., Measurement of double charmonium production in e + e annihilations at \( \sqrt {s} = 10.6 \) GeV, Phys. Rev. D 72 (2005) 031101 [hep-ex/0506062] [ inSPIRE].

    ADS  Google Scholar 

  7. G.T. Bodwin, E. Braaten and G. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum-ibid. D 55 (1997) 5853] [hep-ph/9407339] [ inSPIRE].

  8. E. Braaten and J. Lee, Exclusive double charmonium production from e + e annihilation into a virtual photon, Phys. Rev. D 67 (2003) 054007 [Erratum-ibid. D 72 (2005) 099901] [hep-ph/0211085] [ inSPIRE].

  9. K.-Y. Liu, Z.-G. He and K.-T. Chao, Problems of double charm production in e + e annihilation at \( \sqrt {s} = 10.6 \) GeV, Phys. Lett. B 557 (2003) 45 [hep-ph/0211181] [ inSPIRE].

    ADS  Google Scholar 

  10. K. Hagiwara, E. Kou and C.-F. Qiao, Exclusive J/ψ productions at e + e colliders, Phys. Lett. B 570 (2003) 39 [hep-ph/0305102] [ inSPIRE].

    ADS  Google Scholar 

  11. Y.-J. Zhang, Y.-j. Gao and K.-T. Chao, Next-to-leading order QCD correction to e + e  → J/ψ + η c at \( \sqrt {s} = 10.6 \) GeV, Phys. Rev. Lett. 96 (2006) 092001 [hep-ph/0506076] [ inSPIRE].

    Article  ADS  Google Scholar 

  12. B. Gong and J.-X. Wang, QCD corrections to J/ψ plus η c production in e + e annihilation at \( \sqrt {s} = 10.6 \) GeV, Phys. Rev. D 77 (2008) 054028 [arXiv:0712.4220] [ inSPIRE].

    ADS  Google Scholar 

  13. J. Ma and Z. Si, Predictions for e + e  → J/ψη c with light-cone wave-functions, Phys. Rev. D 70 (2004) 074007 [hep-ph/0405111] [ inSPIRE].

    ADS  Google Scholar 

  14. A. Bondar and V. Chernyak, Is the BELLE result for the cross section σ(e + e  → J/ψ + η c) a real difficulty for QCD?, Phys. Lett. B 612 (2005) 215 [hep-ph/0412335] [ inSPIRE].

    ADS  Google Scholar 

  15. V. Braguta, Double charmonium production at B-factories within light cone formalism, Phys. Rev. D 79 (2009) 074018 [arXiv:0811.2640] [ inSPIRE].

    ADS  Google Scholar 

  16. Y.-J. Zhang, Y.-Q. Ma and K.-T. Chao, Factorization and NLO QCD correction in e + e  → J/ψ(ψ(2S)) + χ (c0) at B Factories, Phys. Rev. D 78 (2008) 054006 [arXiv:0802.3655] [ inSPIRE].

    ADS  Google Scholar 

  17. Belle Collaboration collaboration, P. Pakhlov et al., Measurement of the \( {e^{+} }{e^{-} } \to {{J} \left/ {\psi } \right.}c\bar{c} \) cross section at \( \sqrt {s} \,10.6 \) GeV , Phys. Rev. D 79 (2009) 071101 [arXiv:0901.2775] [ inSPIRE].

    ADS  Google Scholar 

  18. Y. Jia, J.-X. Wang and D. Yang, Bridging light-cone and NRQCD approaches: asymptotic behavior of B c electromagnetic form factor, arXiv:1012.6007 [ inSPIRE].

  19. M. Jacob and G. Wick, On the general theory of collisions for particles with spin, Annals Phys. 7 (1959) 404 [ inSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. H.E. Haber, Spin formalism and applications to new physics searches, hep-ph/9405376 [ inSPIRE].

  21. S.J. Brodsky and G. Lepage, Helicity selection rules and tests of gluon spin in exclusive QCD processes, Phys. Rev. D 24 (1981) 2848 [ inSPIRE].

    ADS  Google Scholar 

  22. J.H. Kuhn, J. Kaplan and E.G.O. Safiani, Electromagnetic annihilation of e + e into quarkonium states with even charge conjugation, Nucl. Phys. B 157 (1979) 125 [ inSPIRE].

    Article  ADS  Google Scholar 

  23. G.T. Bodwin and A. Petrelli, Order v 4 corrections to S-wave quarkonium decay, Phys. Rev. D 66 (2002) 094011 [hep-ph/0205210] [ inSPIRE].

    ADS  Google Scholar 

  24. J. Kublbeck, M. Böhm and A. Denner, Feyn arts: computer algebraic generation of Feynman graphs and amplitudes, Comput. Phys. Commun. 60 (1990) 165 [ inSPIRE].

    Article  ADS  Google Scholar 

  25. T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [ inSPIRE].

    Article  ADS  MATH  Google Scholar 

  26. R. Mertig, M. Böhm and A. Denner, Feyn calc: computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [ inSPIRE].

    Article  ADS  Google Scholar 

  27. M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [ inSPIRE].

    Article  ADS  Google Scholar 

  28. G.T. Bodwin, X. Garcia i Tormo and J. Lee, Factorization theorems for exclusive heavy-quarkonium production, Phys. Rev. Lett. 101 (2008) 102002 [arXiv:0805.3876] [ inSPIRE].

    Article  ADS  Google Scholar 

  29. Z.-z. Song and K.-T. Chao, Problems of QCD factorization in exclusive decays of B meson to charmonium, Phys. Lett. B 568 (2003) 127 [hep-ph/0206253] [ inSPIRE].

    ADS  Google Scholar 

  30. Z.-Z. Song, C. Meng, Y.-J. Gao and K.-T. Chao, Infrared divergences of B meson exclusive decays to P wave charmonia in QCD factorization and nonrelativistic QCD, Phys. Rev. D 69 (2004) 054009 [hep-ph/0309105] [ inSPIRE].

    ADS  Google Scholar 

  31. M. Beneke and L. Vernazza, B → χ cJ K decays revisited, Nucl. Phys. B 811 (2009) 155 [arXiv:0810.3575] [ inSPIRE].

    Article  ADS  Google Scholar 

  32. A. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [ inSPIRE].

    Article  ADS  Google Scholar 

  33. T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [ inSPIRE].

    Article  ADS  Google Scholar 

  34. Y. Jia and D. Yang, Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production, Nucl. Phys. B 814 (2009) 217 [arXiv:0812.1965] [ inSPIRE].

    Article  ADS  Google Scholar 

  35. Y. Jia, Exclusive double charmonium production from Υ decay, Phys. Rev. D 76 (2007) 074007 [arXiv:0706.3685] [ inSPIRE].

    ADS  Google Scholar 

  36. B. Gong, Y. Jia and J.-X. Wang, Exclusive ηb decay todouble J/ψ at next-to-leadingorder in α s , Phys. Lett. B 670 (2009) 350 [arXiv:0808.1034] [ inSPIRE].

    ADS  Google Scholar 

  37. G. Lepage and S.J. Brodsky, Exclusive processes in quantum chromodynamics: evolution equations for hadronic wave functions and the form-factors of mesons, Phys. Lett. B 87 (1979) 359 [ inSPIRE].

    ADS  Google Scholar 

  38. A. Efremov and A. Radyushkin, Factorization and asymptotical behavior of pion form-factor in QCD, Phys. Lett. B 94 (1980) 245 [ inSPIRE].

    ADS  Google Scholar 

  39. G.T. Bodwin, J. Lee and C. Yu, Resummation of relativistic corrections to e + e  → J/ψ + η c , Phys. Rev. D 77 (2008) 094018 [arXiv:0710.0995] [ inSPIRE].

    ADS  Google Scholar 

  40. E.J. Eichten and C. Quigg, Quarkonium wave functions at the origin, Phys. Rev. D 52 (1995) 1726 [hep-ph/9503356] [ inSPIRE].

    ADS  Google Scholar 

  41. W. Buchmüller and S. Tye, Quarkonia and quantum chromodynamics, Phys. Rev. D 24 (1981) 132 [ inSPIRE].

    ADS  Google Scholar 

  42. Belle Collaboration collaboration, K. Abe et al., Study of double charmonium production in e + e annihilation at \( \sqrt {s} \,10.6 \) GeV, Phys. Rev. D 70 (2004) 071102 [hep-ex/0407009] [ inSPIRE].

    ADS  Google Scholar 

  43. K. Wang, Y.-Q. Ma and K.-T. Chao, QCD corrections to e + e  → J/ ψ(ψ(2S)) + χ cJ (J =0, 1, 2) at B factories, Phys. Rev. D 84 (2011) 034022 [arXiv:1107.2646] [ inSPIRE].

    ADS  Google Scholar 

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Correspondence to Feng Feng.

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ArXiv ePrint: 1107.4351

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Dong, HR., Feng, F. & Jia, Y. \( \mathcal{O}\left( {{\alpha_s}} \right) \) corrections to J/ψ+ χ cJ production at B factories. J. High Energ. Phys. 2011, 141 (2011). https://doi.org/10.1007/JHEP10(2011)141

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