Mass spectrum of heavy quarkonium hybrids

Abstract

We have extended the calculation of the correlation functions of heavy quarkonium hybrid operators with various J PC quantum numbers to include QCD condensates up to dimension six. In contrast to previous analyses which were unable to optimize the QCD sum-rules for certain J PC, recent work has shown that inclusion of dimension six condensates stabilizes the hybrid sum-rules and permits reliable mass predictions. In this work we have investigated the effects of the dimension six condensates on the remaining channels. After performing the QCD sum-rule analysis, we update the mass spectra of charmonium and bottomonium hybrids with exotic and non-exotic quantum numbers. We identify that the negative-parity states with J PC = (0, 1, 2)−+ , 1−− form the lightest hybrid supermultiplet while the positive-parity states with J PC = (0, 1)+− , (0, 1, 2)++ belong to a heavier hybrid supermultiplet, confirming the supermultiplet structure found in other approaches. The hybrid with J PC = 0−− has a much higher mass which may suggest a different excitation of the gluonic field compared to other channels. In agreement with previous results, we find that the J PC = 1++ charmonium hybrid is substantially heavier than the X(3872), which seems to preclude a pure charmonium hybrid interpretation for this state.

References

  1. [1]

    S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32 (1985) 189 [INSPIRE].

    ADS  Google Scholar 

  2. [2]

    Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].

    ADS  Google Scholar 

  3. [3]

    E. Klempt and A. Zaitsev, Glueballs, hybrids, multiquarks: experimental facts versus QCD inspired concepts, Phys. Rept. 454 (2007) 1 [arXiv:0708.4016] [INSPIRE].

    ADS  Article  Google Scholar 

  4. [4]

    T. Barnes, F. Close, F. de Viron and J. Weyers, \( Q\overline{Q}G \) hermaphrodite mesons in the MIT bag model, Nucl. Phys. B 224 (1983) 241 [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    M.S. Chanowitz and S.R. Sharpe, Hybrids: mixed states of quarks and gluons, Nucl. Phys. B 222 (1983) 211 [Erratum ibid. B 228 (1983) 588] [INSPIRE].

  6. [6]

    Hadron Spectrum collaboration, L. Liu et al., Excited and exotic charmonium spectroscopy from lattice QCD, JHEP 07 (2012) 126 [arXiv:1204.5425] [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    J.J. Dudek, The lightest hybrid meson supermultiplet in QCD, Phys. Rev. D 84 (2011) 074023 [arXiv:1106.5515] [INSPIRE].

    ADS  Google Scholar 

  8. [8]

    N. Isgur, R. Kokoski and J.E. Paton, Gluonic excitations of mesons: why they are missing and where to find them, Phys. Rev. Lett. 54 (1985) 869 [INSPIRE].

    ADS  Article  Google Scholar 

  9. [9]

    F.E. Close and P.R. Page, The photoproduction of hybrid mesons from CEBAF to HERA, Phys. Rev. D 52 (1995) 1706 [hep-ph/9412301] [INSPIRE].

    ADS  Google Scholar 

  10. [10]

    T. Barnes, F.E. Close and E.S. Swanson, Hybrid and conventional mesons in the flux tube model: numerical studies and their phenomenological implications, Phys. Rev. D 52 (1995) 5242 [hep-ph/9501405] [INSPIRE].

    ADS  Google Scholar 

  11. [11]

    P.R. Page, E.S. Swanson and A.P. Szczepaniak, Hybrid meson decay phenomenology, Phys. Rev. D 59 (1999) 034016 [hep-ph/9808346] [INSPIRE].

    ADS  Google Scholar 

  12. [12]

    F.E. Close and P.R. Page, The production and decay of hybrid mesons by flux tube breaking, Nucl. Phys. B 443 (1995) 233 [hep-ph/9411301] [INSPIRE].

    ADS  Article  Google Scholar 

  13. [13]

    C. McNeile et al., Exotic meson spectroscopy from the clover action at β = 5.85 and 6.15, Nucl. Phys. Proc. Suppl. 73 (1999) 264 [hep-lat/9809087] [INSPIRE].

    ADS  Article  Google Scholar 

  14. [14]

    TXL collaboration, P. Lacock and K. Schilling, Hybrid and orbitally excited mesons in full QCD, Nucl. Phys. Proc. Suppl. 73 (1999) 261 [hep-lat/9809022] [INSPIRE].

    ADS  Article  Google Scholar 

  15. [15]

    C. Bernard et al., Lattice calculation of 1−+ hybrid mesons with improved Kogut-Susskind fermions, Phys. Rev. D 68 (2003) 074505 [hep-lat/0301024] [INSPIRE].

    ADS  Google Scholar 

  16. [16]

    J. Hedditch et al., 1−+ exotic meson at light quark masses, Phys. Rev. D 72 (2005) 114507 [hep-lat/0509106] [INSPIRE].

    ADS  Google Scholar 

  17. [17]

    J. Govaerts, F. de Viron, D. Gusbin and J. Weyers, Exotic mesons from QCD sum rules, Phys. Lett. B 128 (1983) 262 [INSPIRE].

    ADS  Article  Google Scholar 

  18. [18]

    J. Govaerts, F. de Viron, D. Gusbin and J. Weyers, QCD sum rules and hybrid mesons, Nucl. Phys. B 248 (1984) 1 [INSPIRE].

    ADS  Article  Google Scholar 

  19. [19]

    J. Latorre, S. Narison, P. Pascual and R. Tarrach, Hermaphrodite mesons and QCD sum rules, Phys. Lett. B 147 (1984) 169 [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    J.I. Latorre, P. Pascual and S. Narison, Spectra and hadronic couplings of light hermaphrodite mesons, Z. Phys. C 34 (1987) 347 [INSPIRE].

    ADS  Google Scholar 

  21. [21]

    I. Balitsky, D. Diakonov and A. Yung, Exotic mesons with J PC = 1−+ , strange and nonstrange, Z. Phys. C 33 (1986) 265 [INSPIRE].

    ADS  Google Scholar 

  22. [22]

    H. Jin, J. Korner and T.G. Steele, Improved determination of the mass of the 1−+ light hybrid meson from QCD sum rules, Phys. Rev. D 67 (2003) 014025 [hep-ph/0211304] [INSPIRE].

    ADS  Google Scholar 

  23. [23]

    K.G. Chetyrkin and S. Narison, Light hybrid mesons in QCD, Phys. Lett. B 485 (2000) 145 [hep-ph/0003151] [INSPIRE].

    ADS  Article  Google Scholar 

  24. [24]

    S.-L. Zhu, Some decay modes of the 1−+ hybrid meson in QCD sum rules revisited, Phys. Rev. D 60 (1999) 097502 [hep-ph/9903537] [INSPIRE].

    ADS  Google Scholar 

  25. [25]

    E852 collaboration, D. Thompson et al., Evidence for exotic meson production in the reaction π pηπ p at 18 GeV/c, Phys. Rev. Lett. 79 (1997) 1630 [hep-ex/9705011] [INSPIRE].

    ADS  Article  Google Scholar 

  26. [26]

    Crystal Barrel collaboration, A. Abele et al., Exotic ηπ state in \( \overline{p}d \) annihilation at rest into π π 0 ηp spectator, Phys. Lett. B 423 (1998) 175 [INSPIRE].

    ADS  Article  Google Scholar 

  27. [27]

    Crystal Barrel collaboration, A. Abele et al., Evidence for a πη-P-wave in \( \overline{p}p \) -annihilations at rest into π 0 π 0 η, Phys. Lett. B 446 (1999) 349 [INSPIRE].

    ADS  Article  Google Scholar 

  28. [28]

    E862 collaboration, G. Adams et al., Confirmation of a 1−+ exotic meson in the ηπ 0 system, Phys. Lett. B 657 (2007) 27 [hep-ex/0612062] [INSPIRE].

    ADS  Article  Google Scholar 

  29. [29]

    D. Horn and J. Mandula, A model of mesons with constituent gluons, Phys. Rev. D 17 (1978) 898 [INSPIRE].

    ADS  Google Scholar 

  30. [30]

    J. Govaerts, L.J. Reinders, H.R. Rubinstein and J. Weyers, Hybrid quarkonia from QCD sum rules, Nucl. Phys. B 258 (1985) 215 [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    J. Govaerts, L.J. Reinders and J. Weyers, Radial excitations and exotic mesons via QCD sum rules, Nucl. Phys. B 262 (1985) 575 [INSPIRE].

    ADS  Article  Google Scholar 

  32. [32]

    J. Govaerts, L.J. Reinders, P. Francken, X. Gonze and J. Weyers, Coupled QCD sum rules for hybrid mesons, Nucl. Phys. B 284 (1987) 674 [INSPIRE].

    ADS  Article  Google Scholar 

  33. [33]

    S.-L. Zhu, Hybrid quarkonium masses up to the order of 1/m Q , Phys. Rev. D 60 (1999) 031501 [hep-ph/9812469] [INSPIRE].

    ADS  Google Scholar 

  34. [34]

    C.-F. Qiao, L. Tang, G. Hao and X.-Q. Li, Determining 1−− heavy hybrid masses via QCD sum rules, J. Phys. G 39 (2012) 015005 [arXiv:1012.2614] [INSPIRE].

    ADS  Article  Google Scholar 

  35. [35]

    D. Harnett, R.T. Kleiv, T.G. Steele and H.-y. Jin, Axial vector J PC = 1++ charmonium and bottomonium hybrid mass predictions with QCD sum-rules, J. Phys. G 39 (2012) 125003 [arXiv:1206.6776] [INSPIRE].

    ADS  Article  Google Scholar 

  36. [36]

    R. Berg, D. Harnett, R.T. Kleiv and T.G. Steele, Mass predictions for pseudoscalar J PC = 0−+ charmonium and bottomonium hybrids in QCD sum-rules, Phys. Rev. D 86 (2012) 034002 [arXiv:1204.0049] [INSPIRE].

    ADS  Google Scholar 

  37. [37]

    S. Perantonis and C. Michael, Static potentials and hybrid mesons from pure SU(3) lattice gauge theory, Nucl. Phys. B 347 (1990) 854 [INSPIRE].

    ADS  Article  Google Scholar 

  38. [38]

    K.J. Juge, J. Kuti and C.J. Morningstar, Ab initio study of hybrid \( \overline{b}gb \) mesons, Phys. Rev. Lett. 82 (1999) 4400 [hep-ph/9902336] [INSPIRE].

    ADS  Article  Google Scholar 

  39. [39]

    Y. Liu and X.-Q. Luo, Estimate of the charmed 0−− hybrid meson spectrum from quenched lattice QCD, Phys. Rev. D 73 (2006) 054510 [hep-lat/0511015] [INSPIRE].

    ADS  Google Scholar 

  40. [40]

    X.-Q. Luo and Y. Liu, Gluonic excitation of non-exotic hybrid charmonium from lattice QCD, Phys. Rev. D 74 (2006) 034502 [Erratum ibid. D 74 (2006) 039902] [hep-lat/0512044] [INSPIRE].

  41. [41]

    L. Liu, S.M. Ryan, M. Peardon, G. Moir and P. Vilaseca, Charmonium spectroscopy from an anisotropic lattice study, PoS(Lattice 2011)140 [arXiv:1112.1358] [INSPIRE].

  42. [42]

    P. Guo, A.P. Szczepaniak, G. Galata, A. Vassallo and E. Santopinto, Heavy quarkonium hybrids from Coulomb gauge QCD, Phys. Rev. D 78 (2008) 056003 [arXiv:0807.2721] [INSPIRE].

    ADS  Google Scholar 

  43. [43]

    N. Brambilla et al., Heavy quarkonium: progress, puzzles and opportunities, Eur. Phys. J. C 71 (2011) 1534 [arXiv:1010.5827] [INSPIRE].

    ADS  Google Scholar 

  44. [44]

    M. Nielsen, F.S. Navarra and S.H. Lee, New charmonium states in QCD sum rules: a concise review, Phys. Rept. 497 (2010) 41 [arXiv:0911.1958] [INSPIRE].

    ADS  Article  Google Scholar 

  45. [45]

    E.S. Swanson, The new heavy mesons: a status report, Phys. Rept. 429 (2006) 243 [hep-ph/0601110] [INSPIRE].

    ADS  Article  Google Scholar 

  46. [46]

    S.-L. Zhu, New hadron states, Int. J. Mod. Phys. E 17 (2008) 283 [hep-ph/0703225] [INSPIRE].

    Article  Google Scholar 

  47. [47]

    J.L. Rosner, Heavy quark spectroscopytheory overview, J. Phys. Conf. Ser. 69 (2007) 012002 [hep-ph/0612332] [INSPIRE].

    ADS  Article  Google Scholar 

  48. [48]

    S.-L. Zhu, The possible interpretations of Y (4260), Phys. Lett. B 625 (2005) 212 [hep-ph/0507025] [INSPIRE].

    ADS  Google Scholar 

  49. [49]

    F.E. Close and P.R. Page, Gluonic charmonium resonances at BaBar and Belle?, Phys. Lett. B 628 (2005) 215 [hep-ph/0507199] [INSPIRE].

    ADS  Article  Google Scholar 

  50. [50]

    F.E. Close and S. Godfrey, Charmonium hybrid production in exclusive B meson decays, Phys. Lett. B 574 (2003) 210 [hep-ph/0305285] [INSPIRE].

    ADS  Article  Google Scholar 

  51. [51]

    M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, QCD and resonance physics. Theoretical foundations, Nucl. Phys. B 147 (1979) 385 [INSPIRE].

    ADS  Article  Google Scholar 

  52. [52]

    L.J. Reinders, H. Rubinstein and S. Yazaki, Hadron properties from QCD sum rules, Phys. Rept. 127 (1985) 1 [INSPIRE].

    ADS  Article  Google Scholar 

  53. [53]

    P. Colangelo and A. Khodjamirian, QCD sum rules, a modern perspective, in At the frontier of particle physics / Handbook of QCD, M. Shifman ed., World Scientific, Singapore (2001) [hep-ph/0010175] [INSPIRE].

    Google Scholar 

  54. [54]

    R. Mertig and R. Scharf, TARCER: a Mathematica program for the reduction of two loop propagator integrals, Comput. Phys. Commun. 111 (1998) 265 [hep-ph/9801383] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  55. [55]

    O. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, Phys. Rev. D 54 (1996) 6479 [hep-th/9606018] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  56. [56]

    O. Tarasov, Generalized recurrence relations for two loop propagator integrals with arbitrary masses, Nucl. Phys. B 502 (1997) 455 [hep-ph/9703319] [INSPIRE].

    ADS  Article  Google Scholar 

  57. [57]

    E. Boos and A.I. Davydychev, A method of evaluating massive Feynman integrals, Theor. Math. Phys. 89 (1991) 1052 [INSPIRE].

    MathSciNet  Article  Google Scholar 

  58. [58]

    A.I. Davydychev, General results for massive N point Feynman diagrams with different masses, J. Math. Phys. 33 (1992) 358 [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  59. [59]

    D.J. Broadhurst, J. Fleischer and O. Tarasov, Two loop two point functions with masses: asymptotic expansions and Taylor series, in any dimension, Z. Phys. C 60 (1993) 287 [hep-ph/9304303] [INSPIRE].

    ADS  Google Scholar 

  60. [60]

    W. Chen and S.-L. Zhu, The possible J PC = 0−− charmonium-like state, Phys. Rev. D 81 (2010) 105018 [arXiv:1003.3721] [INSPIRE].

    ADS  Google Scholar 

  61. [61]

    W. Chen and S.-L. Zhu, The vector and axial-vector charmonium-like states, Phys. Rev. D 83 (2011) 034010 [arXiv:1010.3397] [INSPIRE].

    ADS  Google Scholar 

  62. [62]

    W. Chen, Z.-X. Cai and S.-L. Zhu, The tensor charmonium and bottomonium states with J PC = 2−−, arXiv:1107.4949 [INSPIRE].

  63. [63]

    M.-L. Du, W. Chen, X.-L. Chen and S.-L. Zhu, Exotic \( QQ\overline{qq} \) , \( QQ\overline{qs} \) and \( QQ\overline{ss} \) states, Phys. Rev. D 87 (2013) 014003 [arXiv:1209.5134] [INSPIRE].

    ADS  Google Scholar 

  64. [64]

    K.G. Chetyrkin et al., Charm and bottom quark masses: an update, Phys. Rev. D 80 (2009) 074010 [arXiv:0907.2110] [INSPIRE].

    ADS  Google Scholar 

  65. [65]

    S. Narison, Gluon condensates and \( {{\overline{m}}_b}\left( {{{\overline{m}}_b}} \right) \) from QCD-exponential moments at higher orders, Phys. Lett. B 707 (2012) 259 [arXiv:1105.5070] [INSPIRE].

    ADS  Article  Google Scholar 

  66. [66]

    S. Narison, Gluon condensates and c, b quark masses from quarkonia ratios of moments, Phys. Lett. B 693 (2010) 559 [Erratum ibid. 705 (2011) 544] [arXiv:1004.5333] [INSPIRE].

  67. [67]

    J.H. Kuhn, M. Steinhauser and C. Sturm, Heavy quark masses from sum rules in four-loop approximation, Nucl. Phys. B 778 (2007) 192 [hep-ph/0702103] [INSPIRE].

    ADS  Article  Google Scholar 

  68. [68]

    S. Narison and R. Tarrach, Higher dimensional renormalization group invariant vacuum condensates in quantum chromodynamics, Phys. Lett. B 125 (1983) 217 [INSPIRE].

    ADS  Article  Google Scholar 

  69. [69]

    S. Narison, QCD as a theory of hadrons from partons to confinement, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 17 (2002) 1 [hep-ph/0205006] [INSPIRE].

    Google Scholar 

  70. [70]

    L.S. Kisslinger, D. Parno and S. Riordan, Hybrid charmonium and the ρπ puzzle, Adv. High Energy Phys. 2008 (2008) 982341 [arXiv:0805.1943] [INSPIRE].

    Google Scholar 

  71. [71]

    Belle collaboration, K. Abe et al., Experimental constraints on the possible J PC quantum numbers of the X(3872), hep-ex/0505038 [INSPIRE].

  72. [72]

    CDF collaboration, A. Abulencia et al., Analysis of the quantum numbers J PC of the X(3872), Phys. Rev. Lett. 98 (2007) 132002 [hep-ex/0612053] [INSPIRE].

    ADS  Article  Google Scholar 

  73. [73]

    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].

    ADS  Google Scholar 

  74. [74]

    LHCb collaboration, Determination of the X(3872) meson quantum numbers, Phys. Rev. Lett. 110 (2013) 222001 [arXiv:1302.6269] [INSPIRE].

    Article  Google Scholar 

  75. [75]

    A. Erdélyi ed., Higher transcendental functions, Bateman Manuscript Project, vol. 1., McGraw-Hill, New York U.S.A. (1953).

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to T. G. Steele.

Additional information

ArXiv ePrint: 1304.4522

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chen, W., Kleiv, R.T., Steele, T.G. et al. Mass spectrum of heavy quarkonium hybrids. J. High Energ. Phys. 2013, 19 (2013). https://doi.org/10.1007/JHEP09(2013)019

Download citation

Keywords

  • Sum Rules
  • QCD