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Masses of open-flavour heavy-light hybrids from QCD sum-rules

  • J. Ho
  • D. Harnett
  • T. G. Steele
Open Access
Regular Article - Theoretical Physics

Abstract

We use QCD Laplace sum-rules to predict masses of open-flavour heavy-light hybrids where one of the hybrid’s constituent quarks is a charm or bottom and the other is an up, down, or strange. We compute leading-order, diagonal correlation functions of several hybrid interpolating currents, taking into account QCD condensates up to dimension-six, and extract hybrid mass predictions for all J P ∈ {0± , 1±}, as well as explore possible mixing effects with conventional quark-antiquark mesons. Within theoretical uncertainties, our results are consistent with a degeneracy between the heavy-nonstrange and heavy-strange hybrids in all J P channels. We find a similar mass hierarchy of 1+, 1, and 0+ states (a 1+ state lighter than essentially degenerate 1 and 0+ states) in both the charm and bottom sectors, and discuss an interpretation for the 0 states. If conventional meson mixing is present the effect is an increase in the hybrid mass prediction, and we estimate an upper bound on this effect.

Keywords

QCD Phenomenology 

Notes

Open Access

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References

  1. [1]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  2. [2]
    S. Narison, 1−+ light exotic mesons in QCD, Phys. Lett. B 675 (2009) 319 [arXiv:0903.2266] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    C.A. Meyer and E.S. Swanson, Hybrid mesons, Prog. Part. Nucl. Phys. 82 (2015) 21 [arXiv:1502.07276] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    G.-J. Ding and M.-L. Yan, A candidate for 1−− strangeonium hybrid, Phys. Lett. B 650 (2007) 390 [hep-ph/0611319] [INSPIRE].
  5. [5]
    W. Chen, H.-y. Jin, R.T. Kleiv, T.G. Steele, M. Wang and Q. Xu, QCD sum-rule interpretation of X(3872) with J PC = 1++ mixtures of hybrid charmonium and DD molecular currents, Phys. Rev. D 88 (2013) 045027 [arXiv:1305.0244] [INSPIRE].ADSGoogle Scholar
  6. [6]
    S.-L. Zhu, The possible interpretations of Y (4260), Phys. Lett. B 625 (2005) 212 [hep-ph/0507025] [INSPIRE].
  7. [7]
    Belle collaboration, K. Abe et al., Observation of a near-threshold ωJ/ψ mass enhancement in exclusive BKωJ/ψ decays, Phys. Rev. Lett. 94 (2005) 182002 [hep-ex/0408126] [INSPIRE].
  8. [8]
    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].ADSGoogle Scholar
  9. [9]
    B. Ketzer, Hybrid mesons, PoS(QNP2012)025 [arXiv:1208.5125] [INSPIRE].
  10. [10]
    D. Horn and J. Mandula, A model of mesons with constituent gluons, Phys. Rev. D 17 (1978) 898 [INSPIRE].ADSGoogle Scholar
  11. [11]
    T. Barnes, F.E. 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].ADSCrossRefGoogle Scholar
  12. [12]
    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].
  13. [13]
    N. Isgur, R. Kokoski and J. Paton, Gluonic excitations of mesons: why they are missing and where to find them, Phys. Rev. Lett. 54 (1985) 869 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    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].
  15. [15]
    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].
  16. [16]
    J. Govaerts, F. de Viron, D. Gusbin and J. Weyers, Exotic mesons from QCD sum rules, Phys. Lett. B 128 (1983) 262 [Erratum ibid. B 136 (1984) 445] [INSPIRE].
  17. [17]
    J. Govaerts, F. de Viron, D. Gusbin and J. Weyers, QCD sum rules and hybrid mesons, Nucl. Phys. B 248 (1984) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    J.I. Latorre, S. Narison, P. Pascual and R. Tarrach, Hermaphrodite mesons and QCD sum rules, Phys. Lett. B 147 (1984) 169 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J.I. Latorre, P. Pascual and S. Narison, Spectra and hadronic couplings of light hermaphrodite mesons, Z. Phys. 34 (1987) 347.Google Scholar
  20. [20]
    I. Balitsky, D. Diakonov and A.V. Yung, Exotic mesons with J PC = 1−+ , strange and nonstrange, Z. Phys. 33 (1986) 265.Google Scholar
  21. [21]
    H.Y. Jin, J.G. Körner 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].
  22. [22]
    Z.-R. Huang, H.-Y. Jin and Z.-F. Zhang, New predictions on the mass of the 1−+ light hybrid meson from QCD sum rules, JHEP 04 (2015) 004 [arXiv:1411.2224] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    K.G. Chetyrkin and S. Narison, Light hybrid mesons in QCD, Phys. Lett. B 485 (2000) 145 [hep-ph/0003151] [INSPIRE].
  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].
  25. [25]
    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].ADSCrossRefGoogle Scholar
  26. [26]
    W. Chen et al., Mass spectrum of heavy quarkonium hybrids, JHEP 09 (2013) 019 [arXiv:1304.4522] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    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].ADSCrossRefGoogle Scholar
  28. [28]
    S. Perantonis and C. Michael, Static potentials and hybrid mesons from pure SU(3) lattice gauge theory, Nucl. Phys. B 347 (1990) 854 [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    Hadron Spectrum collaboration, L. Liu et al., Excited and exotic charmonium spectroscopy from lattice QCD, JHEP 07 (2012) 126 [arXiv:1204.5425] [INSPIRE].
  30. [30]
    G. Moir, Excited D and D s meson spectroscopy from lattice QCD, PoS(Confinement X)139.
  31. [31]
    J.J. Dudek, The lightest hybrid meson supermultiplet in QCD, Phys. Rev. D 84 (2011) 074023 [arXiv:1106.5515] [INSPIRE].ADSGoogle Scholar
  32. [32]
    T. Huang, H.-y. Jin and A.-l. Zhang, The spectrum and strong couplings of heavy-light hybrids, Phys. Rev. D 61 (2000) 034016 [hep-ph/9906494] [INSPIRE].
  33. [33]
    D0 collaboration, V.M. Abazov et al., Evidence for a B s0 π ± state, Phys. Rev. Lett. 117 (2016) 022003 [arXiv:1602.07588] [INSPIRE].
  34. [34]
    LHCb collaboration, Search for structure in the B s0 π ± invariant mass spectrum, Phys. Rev. Lett. 117 (2016) 152003 [arXiv:1608.00435] [INSPIRE].
  35. [35]
    W. Chen, H.-X. Chen, X. Liu, T.G. Steele and S.-L. Zhu, Decoding the X(5568) as a fully open-flavor \( su\overline{b}\overline{d} \) tetraquark state, Phys. Rev. Lett. 117 (2016) 022002 [arXiv:1602.08916] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    W. Chen, T.G. Steele and S.-L. Zhu, Masses of the bottom-charm hybrid \( \overline{b} Gc \) states, J. Phys. G 41 (2014) 025003 [arXiv:1306.3486] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    J. Govaerts, L.J. Reinders and J. Weyers, Radial excitations and exotic mesons via QCD sum rules, Nucl. Phys. B 262 (1985) 575 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    J. Govaerts, L.J. Reinders, H.R. Rubinstein and J. Weyers, Hybrid quarkonia from QCD sum rules, Nucl. Phys. B 258 (1985) 215 [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    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].ADSCrossRefGoogle Scholar
  40. [40]
    T. Hilger and A. Krassnigg, Quasi-exotic open-flavor mesons, arXiv:1605.03464 [INSPIRE].
  41. [41]
    E. Bagán, M.R. Ahmady, V. Elias and T.G. Steele, Plane-wave, coordinate-space, and moment techniques in the operator-product expansion: equivalence, improved methods, and the heavy quark expansion, Z. Phys. 61 (1994) 157.Google Scholar
  42. [42]
    P. Pascual and R. Tarrach, QCD: renormalization for the practitioner. Springer, (1984).Google Scholar
  43. [43]
    D. Binosi and L. Theussl, JaxoDraw: a graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
  44. [44]
    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].
  45. [45]
    O.V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension, Phys. Rev. D 54 (1996) 6479 [hep-th/9606018] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  46. [46]
    O.V. Tarasov, Generalized recurrence relations for two loop propagator integrals with arbitrary masses, Nucl. Phys. B 502 (1997) 455 [hep-ph/9703319] [INSPIRE].
  47. [47]
    M.S. Chanowitz, M. Furman and I. Hinchliffe, The axial current in dimensional regularization, Nucl. Phys. B 159 (1979) 225 [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, QCD and resonance physics. theoretical foundations, Nucl. Phys. B 147 (1979) 385 [INSPIRE].
  49. [49]
    S. Narison and E. de Rafael, On QCD sum rules of the Laplace transform type and light quark masses, Phys. Lett. B 103 (1981) 57 [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    M. Gell-Mann, R.J. Oakes and B. Renner, Behavior of current divergences under SU 3 × SU 3, Phys. Rev. D 175 (1968) 2195.ADSCrossRefGoogle Scholar
  51. [51]
    S. Narison, QCD as a theory of hadrons: from partons to confinement. Cambridge University Press, (2004).Google Scholar
  52. [52]
    J.L. Rosner, S. Stone and R.S. Van de Water, Leptonic decays of charged pseudoscalar mesons — 2015, Submitted to: Particle Data Book (2015) [arXiv:1509.02220] [INSPIRE].
  53. [53]
    B. Chakraborty et al., High-precision quark masses and QCD coupling from n f = 4 lattice QCD, Phys. Rev. D 91 (2015) 054508 [arXiv:1408.4169] [INSPIRE].ADSGoogle Scholar
  54. [54]
    G. Launer, S. Narison and R. Tarrach, Nonperturbative QCD vacuum from e + e I = 1 hadron data, Z. Phys. C 26 (1984) 433 [INSPIRE].ADSGoogle Scholar
  55. [55]
    S. Narison, Gluon condensates and c, b quark masses from quarkonia ratios of moments, Phys. Lett. B 693 (2010) 559 [Erratum ibid. B 705 (2011) 544] [arXiv:1004.5333] [INSPIRE].
  56. [56]
    S. Narison, Beautiful mesons from QCD spectral sum rules, Phys. Lett. B 210 (1988) 238 [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    S. Narison, Open charm and beauty chiral multiplets in QCD, Phys. Lett. B 605 (2005) 319 [hep-ph/0307248] [INSPIRE].
  58. [58]
    S. Narison, Decay constants of heavy-light mesons from QCD, Nucl. Part. Phys. Proc. 270-272 (2016) 143 [arXiv:1511.05903] [INSPIRE].CrossRefGoogle Scholar
  59. [59]
    S. Narison, Improved \( {f_{D\ast}}_{{}_{\left(\mathrm{s}\right)}} \) , \( {f_{B\ast}}_{{}_{\left(\mathrm{s}\right)}} \) and \( {f_B}_{{}_c} \) from QCD Laplace sum rules, Int. J. Mod. Phys. A 30 (2015) 1550116 [arXiv:1404.6642] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of Physics and Engineering PhysicsUniversity of SaskatchewanSaskatoonCanada
  2. 2.Department of PhysicsUniversity of the Fraser ValleyAbbotsfordCanada

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