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Annihilation rate of 2−+ charmonium and bottomonium

  • Tianhong Wang
  • Guo-Li Wang
  • Wan-Li Ju
  • Yue Jiang
Article

Abstract

The 11 D 2 \( \left( {c\overline{c}} \right) \) state is the ground state of spin-singlet D-wave charmonia. Although it has not been found yet, the experimental data accumulate rapidly. This charmonium attracts more and more attention, especially when the BaBar Collaboration finds that the X(3872) particle has negative parity. In this paper we calculate the double-gamma and double-gluon annihilation processes of 1 D 2 charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. We find the relativistic corrections make the decay widths of 11 D 2 \( \left( {c\overline{c}} \right) \) 2~5 times smaller than the non-relativistic results. If this state is below the D 0 D 0∗ threshold, we can use the sum of annihilation widths and EM transition widths to estimate the total decay width. Our result for 11 D 2 \( \left( {c\overline{c}} \right) \) with m = 3820 GeV is Γ = 432 keV. The dominant decay channel 11 D 2 \( \left( {c\overline{c}} \right) \)h c γ, whose branching ratio is about 90%, can be used to discover this state.

Keywords

Phenomenological Models Heavy Ion Phenomenology 

References

  1. [1]
    Y. Fan, Z.-G. He, Y.-Q. Ma and K.-T. Chao, Predictions of light hadronic decays of heavy quarkonium 1 D 2 states in NRQCD, Phys. Rev. D 80 (2009) 014001 [arXiv:0903.4572] [INSPIRE].ADSGoogle Scholar
  2. [2]
    Y. Jia, W.L. Sang and J. Xu, Is the J P = 2 assignment for the X(3872) compatible with the radiative transition data?, arXiv:1007.4541 [INSPIRE].
  3. [3]
    H.-W. Ke and X.-Q. Li, What do the radiative decays of X(3872) tell us, Phys. Rev. D 84 (2011) 114026 [arXiv:1107.0443] [INSPIRE].ADSGoogle Scholar
  4. [4]
    Y. Kalashnikova and A. Nefediev, X(3872) as a 1 D 2 charmonium state, Phys. Rev. D 82 (2010) 097502 [arXiv:1008.2895] [INSPIRE].ADSGoogle Scholar
  5. [5]
    T. Burns, F. Piccinini, A. Polosa and C. Sabelli, The 2−+ assignment for the X(3872), Phys. Rev. D 82 (2010) 074003 [arXiv:1008.0018] [INSPIRE].ADSGoogle Scholar
  6. [6]
    Belle collaboration, J.S. Lange, Results on charmonium(-like) and bottomonium(-like) states from Belle and BaBar, AIP Conf. Proc. 1374 (2011) 115 [arXiv:1010.2331] [INSPIRE].Google Scholar
  7. [7]
    Y. Fan, J.-Z. Li, C. Meng and K.-T. Chao, B-meson semi-inclusive decay to 2−+ charmonium in NRQCD and X(3872), Phys. Rev. D 85 (2012) 034032 [arXiv:1112.3625] [INSPIRE].ADSGoogle Scholar
  8. [8]
    T. Wang et al., Electromagnetic decay of X(3872) as the 1 1 D 2(2−+) charmonium , J. Phys. G 40 (2013) 035003 [arXiv:1205.5725] [INSPIRE].ADSGoogle Scholar
  9. [9]
    BABAR collaboration, P. del Amo Sanchez et al., Evidence for the decay X(3872) → J/ψω, Phys. Rev. D 82 (2010) 011101 [arXiv:1005.5190] [INSPIRE].ADSGoogle Scholar
  10. [10]
    E.J. Eichten, K. Lane and C. Quigg, B meson gateways to missing charmonium levels, Phys. Rev. Lett. 89 (2002) 162002 [hep-ph/0206018] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    T. Barnes and S. Godfrey, Charmonium options for the X(3872), Phys. Rev. D 69 (2004) 054008 [hep-ph/0311162] [INSPIRE].ADSGoogle Scholar
  12. [12]
    E. Ackleh and T. Barnes, Two photon widths of singlet positronium and quarkonium with arbitrary total angular momentum, Phys. Rev. D 45 (1992) 232 [INSPIRE].ADSGoogle Scholar
  13. [13]
    C.R. Münz, Two-photon decays of mesons in a relativistic quark model, Nucl. Phys. B 609 (1996) 364 [hep-ph/9601206] [INSPIRE].Google Scholar
  14. [14]
    C. Kim, T. Lee and G.-L. Wang, Annihilation rate of heavy 0−+ quarkonium in relativistic Salpeter method, Phys. Lett. B 606 (2005) 323 [hep-ph/0411075] [INSPIRE].ADSGoogle Scholar
  15. [15]
    G.-L. Wang, Annihilation rate of 2++ charmonium and bottomonium, Phys. Lett. B 674 (2009) 172 [arXiv:0904.1604] [INSPIRE].ADSGoogle Scholar
  16. [16]
    G.-L. Wang, Annihilation rate of heavy 0++ P-wave quarkonium in relativistic Salpeter method, Phys. Lett. B 653 (2007) 206 [arXiv:0708.3516] [INSPIRE].ADSGoogle Scholar
  17. [17]
    E. Salpeter and H. Bethe, A relativistic equation for bound state problems, Phys. Rev. 84 (1951) 1232 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  18. [18]
    E.E. Salpeter, Mass corrections to the fine structure of hydrogen-like atoms, Phys. Rev. 87 (1952) 328 [INSPIRE].ADSMATHCrossRefGoogle Scholar
  19. [19]
    C.S. Kim and G.-L. Wang, Average kinetic energy of heavy quark \( \left( {\mu_{\pi}^2} \right) \) inside heavy meson of 0 state by Bethe-Salpeter method, Phys. Lett. B 584 (2004) 285 [Erratum ibid. B 634 (2006) 564] [hep-ph/0309162] [INSPIRE].
  20. [20]
    S. Mandelstam, Dynamical variables in the Bethe-Salpeter formalism, Proc. R. Soc. Lond. 233 (1955) 248.MathSciNetADSMATHCrossRefGoogle Scholar
  21. [21]
    S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32 (1985) 189 [INSPIRE].ADSGoogle Scholar
  22. [22]
    V.A. Novikov et al., Charmonium and gluons: basic experimental facts and theoretical introduction, Phys. Rep. 41 (1978) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    H.W. Crater, C.-Y. Wong and P. Van Alstine, Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons, Phys. Rev. D 74 (2006) 054028 [hep-ph/0603126] [INSPIRE].ADSGoogle Scholar
  24. [24]
    P. Volkovitsky, On pp decay widths of heavy quarkonium states, Phys. Lett. B 308 (1993) 100 [INSPIRE].ADSGoogle Scholar
  25. [25]
    Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Tianhong Wang
    • 1
  • Guo-Li Wang
    • 1
  • Wan-Li Ju
    • 1
  • Yue Jiang
    • 1
  1. 1.Department of PhysicsHarbin Institute of TechnologyHarbinChina

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