Advertisement

Excited and exotic charmonium spectroscopy from lattice QCD

  • For the Hadron Spectrum collaboration
  • Liuming Liu
  • Graham Moir
  • Michael Peardon
  • Sinéad M. Ryan
  • Christopher E. ThomasEmail author
  • Pol Vilaseca
  • Jozef J. Dudek
  • Robert G. Edwards
  • Bálint Joó
  • David G. Richards
Article

Abstract

We present a spectrum of highly excited charmonium mesons up to around 4.5 GeV calculated using dynamical lattice QCD. Employing novel computational techniques and the variational method with a large basis of carefully constructed operators, we extract and reliably identify the continuum spin of an extensive set of excited states, states with exotic quantum numbers (0+−, 1−+, 2+−) and states with high spin. Calculations are performed on two lattice volumes with pion mass ≈ 400 MeV and the mass determinations have high statistical precision even for excited states. We discuss the results in light of experimental observations, identify the lightest ‘supermultiplet’ of hybrid mesons and comment on the phenomenological implications of the spectrum of exotic mesons.

Keywords

Lattice QCD QCD 

References

  1. [1]
    N. Brambilla et al., Heavy quarkonium: progress, puzzles and opportunities, Eur. Phys. J. C 71 (2011) 1534 [arXiv:1010.5827] [INSPIRE].ADSGoogle Scholar
  2. [2]
    HPQCD, UKQCD collaboration, E. Follana et al., Highly improved staggered quarks on the lattice, with applications to charm physics, Phys. Rev. D 75 (2007) 054502 [hep-lat/0610092] [INSPIRE].ADSGoogle Scholar
  3. [3]
    T. Burch et al., Quarkonium mass splittings in three-flavor lattice QCD, Phys. Rev. D 81 (2010) 034508 [arXiv:0912.2701] [INSPIRE].ADSGoogle Scholar
  4. [4]
    PACS-CS collaboration, Y. Namekawa, Charm quark system on the physical point in 2 + 1 flavor lattice QCD, PoS(LATTICE 2011)132 [arXiv:1111.0142] [INSPIRE].
  5. [5]
    D. Mohler and R. Woloshyn, D and D s meson spectroscopy, Phys. Rev. D 84 (2011) 054505 [arXiv:1103.5506] [INSPIRE].ADSGoogle Scholar
  6. [6]
    C. DeTar, Charmonium spectroscopy from lattice QCD, arXiv:1101.0212 [INSPIRE].
  7. [7]
    J.J. Dudek, R.G. Edwards, N. Mathur and D.G. Richards, Charmonium excited state spectrum in lattice QCD, Phys. Rev. D 77 (2008) 034501 [arXiv:0707.4162] [INSPIRE].ADSGoogle Scholar
  8. [8]
    G. Bali et al., Spectra of heavy-light and heavy-heavy mesons containing charm quarks, including higher spin states for N f = 2 + 1, PoS(LATTICE 2011)135 [arXiv:1108.6147] [INSPIRE].
  9. [9]
    G.S. Bali, S. Collins and C. Ehmann, Charmonium spectroscopy and mixing with light quark and open charm states from n F = 2 lattice QCD, Phys. Rev. D 84 (2011) 094506 [arXiv:1110.2381] [INSPIRE].ADSGoogle Scholar
  10. [10]
    J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards and C.E. Thomas, Highly excited and exotic meson spectrum from dynamical lattice QCD, Phys. Rev. Lett. 103 (2009) 262001 [arXiv:0909.0200] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards and C.E. Thomas, Toward the excited meson spectrum of dynamical QCD, Phys. Rev. D 82 (2010) 034508 [arXiv:1004.4930] [INSPIRE].ADSGoogle Scholar
  12. [12]
    J.J. Dudek et al., Isoscalar meson spectroscopy from lattice QCD, Phys. Rev. D 83 (2011) 111502 [arXiv:1102.4299] [INSPIRE].ADSGoogle Scholar
  13. [13]
    J. Bulava et al., Nucleon, Δ and Ω excited states in N f = 2 + 1 lattice QCD, Phys. Rev. D 82 (2010) 014507 [arXiv:1004.5072] [INSPIRE].ADSGoogle Scholar
  14. [14]
    R.G. Edwards, J.J. Dudek, D.G. Richards and S.J. Wallace, Excited state baryon spectroscopy from lattice QCD, Phys. Rev. D 84 (2011) 074508 [arXiv:1104.5152] [INSPIRE].ADSGoogle Scholar
  15. [15]
    J.J. Dudek and R.G. Edwards, Hybrid baryons in QCD, Phys. Rev. D 85 (2012) 054016 [arXiv:1201.2349] [INSPIRE].ADSGoogle Scholar
  16. [16]
    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].
  17. [17]
    A.X. El-Khadra, A.S. Kronfeld and P.B. Mackenzie, Massive fermions in lattice gauge theory, Phys. Rev. D 55 (1997) 3933 [hep-lat/9604004] [INSPIRE].ADSGoogle Scholar
  18. [18]
    R.G. Edwards, B. Joo and H.-W. Lin, Tuning for three-flavors of anisotropic clover fermions with Stout-link smearing, Phys. Rev. D 78 (2008) 054501 [arXiv:0803.3960] [INSPIRE].ADSGoogle Scholar
  19. [19]
    Hadron Spectrum collaboration, H.-W. Lin et al., First results from 2 + 1 dynamical quark flavors on an anisotropic lattice: light-hadron spectroscopy and setting the strange-quark mass, Phys. Rev. D 79 (2009) 034502 [arXiv:0810.3588] [INSPIRE].ADSGoogle Scholar
  20. [20]
    C. Morningstar and M.J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69 (2004) 054501 [hep-lat/0311018] [INSPIRE].ADSGoogle Scholar
  21. [21]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 , and 2011 partial update for the 2012 edition [INSPIRE].ADSGoogle Scholar
  22. [22]
    Hadron Spectrum collaboration, M. Peardon et al., A Novel quark-field creation operator construction for hadronic physics in lattice QCD, Phys. Rev. D 80 (2009) 054506 [arXiv:0905.2160] [INSPIRE].ADSGoogle Scholar
  23. [23]
    R. Morrin, A.O. Cais, M. Peardon, S.M. Ryan and J.-I. Skullerud, Dynamical QCD simulations on anisotropic lattices, Phys. Rev. D 74 (2006) 014505 [hep-lat/0604021] [INSPIRE].ADSGoogle Scholar
  24. [24]
    J.J. Dudek, R.G. Edwards and C.E. Thomas, S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD, arXiv:1203.6041 [INSPIRE].
  25. [25]
    C. Michael, Adjoint sources in lattice gauge theory, Nucl. Phys. B 259 (1985) 58 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    Z. Davoudi and M.J. Savage, Restoration of rotational symmetry in the continuum limit of lattice field theories, arXiv:1204.4146 [INSPIRE].
  28. [28]
    L. Levkova and C. DeTar, Charm annihilation effects on the hyperfine splitting in charmonium, Phys. Rev. D 83 (2011) 074504 [arXiv:1012.1837] [INSPIRE].ADSGoogle Scholar
  29. [29]
    M. Lüscher, S. Sint, R. Sommer, P. Weisz and U. Wolff, Nonperturbative O(a) improvement of lattice QCD, Nucl. Phys. B 491 (1997) 323 [hep-lat/9609035] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    J.J. Dudek and E. Rrapaj, Charmonium in lattice QCD and the non-relativistic quark-model, Phys. Rev. D 78 (2008) 094504 [arXiv:0809.2582] [INSPIRE].ADSGoogle Scholar
  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]
    F.-K. Guo and U.-G. Meissner, Light quark mass dependence in heavy quarkonium physics, arXiv:1203.1116 [INSPIRE].
  33. [33]
    S.-L. Zhu, The possible interpretations of Y (4260), Phys. Lett. B 625 (2005) 212 [hep-ph/0507025] [INSPIRE].ADSGoogle Scholar
  34. [34]
    F.E. Close and P.R. Page, Gluonic charmonium resonances at BaBar and BELLE?, Phys. Lett. B 628 (2005) 215 [hep-ph/0507199] [INSPIRE].ADSGoogle Scholar
  35. [35]
    E. Kou and O. Pene, Suppressed decay into open charm for the Y (4260) being an hybrid, Phys. Lett. B 631 (2005) 164 [hep-ph/0507119] [INSPIRE].ADSGoogle Scholar
  36. [36]
    CLEO collaboration, T. Pedlar et al., Observation of the h c (1P using e+e collisions Above threshold, Phys. Rev. Lett. 107 (2011) 041803 [arXiv:1104.2025][INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    J.J. Dudek, R.G. Edwards, M.J. Peardon, D.G. Richards and C.E. Thomas, The phase-shift of isospin-2 π-π scattering from lattice QCD, Phys. Rev. D 83 (2011) 071504 [arXiv:1011.6352] [INSPIRE].ADSGoogle Scholar
  38. [38]
    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].ADSCrossRefGoogle Scholar
  39. [39]
    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].ADSCrossRefGoogle Scholar
  40. [40]
    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].ADSGoogle Scholar
  41. [41]
    N. Isgur and J.E. Paton, A flux tube model for hadrons in QCD, Phys. Rev. D 31 (1985) 2910 [INSPIRE].ADSGoogle Scholar
  42. [42]
    M. Lüscher, Signatures of unstable particles in finite volume, Nucl. Phys. B 364 (1991) 237 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    K. Rummukainen and S.A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice, Nucl. Phys. B 450 (1995) 397 [hep-lat/9503028] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    C. Kim, C. Sachrajda and S.R. Sharpe, Finite-volume effects for two-hadron states in moving frames, Nucl. Phys. B 727 (2005) 218 [hep-lat/0507006] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    N.H. Christ, C. Kim and T. Yamazaki, Finite volume corrections to the two-particle decay of states with non-zero momentum, Phys. Rev. D 72 (2005) 114506 [hep-lat/0507009] [INSPIRE].ADSGoogle Scholar
  46. [46]
    SciDAC, LHPC, UKQCD collaboration, R.G. Edwards and B. Joo, The Chroma software system for lattice QCD, Nucl. Phys. Proc. Suppl. 140 (2005) 832 [hep-lat/0409003] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    M. Clark, R. Babich, K. Barros, R. Brower and C. Rebbi, Solving lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181 (2010) 1517 [arXiv:0911.3191] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  48. [48]
    R. Babich, M.A. Clark and B. Joo, Parallelizing the QUDA library for multi-GPU calculations in lattice quantum chromodynamics, in International Conference for High Performance Computing, Networking, Storage and Analysis, November 13-19, New Orleans, U.S.A. (2010), arXiv:1011.0024 [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • For the Hadron Spectrum collaboration
  • Liuming Liu
    • 1
  • Graham Moir
    • 1
  • Michael Peardon
    • 1
  • Sinéad M. Ryan
    • 1
  • Christopher E. Thomas
    • 1
    Email author
  • Pol Vilaseca
    • 1
  • Jozef J. Dudek
    • 2
    • 3
  • Robert G. Edwards
    • 2
  • Bálint Joó
    • 2
  • David G. Richards
    • 2
  1. 1.School of MathematicsTrinity CollegeDublin 2Ireland
  2. 2.Jefferson LaboratoryNewport NewsU.S.A.
  3. 3.Department of PhysicsOld Dominion UniversityNorfolkU.S.A.

Personalised recommendations