Advertisement

Lattice investigation of the scalar mesons a 0(980) and κ using four-quark operators

  • The ETM collaboration
  • Constantia Alexandrou
  • Jan Oliver Daldrop
  • Mattia Dalla Brida
  • Mario Gravina
  • Luigi Scorzato
  • Carsten Urbach
  • Marc Wagner
Article

Abstract

We carry out an exploratory study of the isospin one a 0(980) and the isospin one-half κ scalar mesons using N f = 2 + 1 + 1 Wilson twisted mass fermions at one lattice spacing. The valence strange quark is included as an Osterwalder-Seiler fermion with mass tuned so that the kaon mass matches the corresponding mass in the unitary N f = 2 + 1 + 1 theory. We investigate the internal structure of these mesons by using a basis of four-quark interpolating fields. We construct diquark-diquark and molecular-type interpolating fields and analyse the resulting correlation matrices keeping only connected contributions. For both channels, the low-lying spectrum is found to be consistent with two-particle scattering states. Therefore, our analysis shows no evidence for an additional state that can be interpreted as either a tetraquark or a tightly-bound molecular state.

Keywords

Lattice QCD Lattice Gauge Field Theories QCD 

References

  1. [1]
    R. Jaffe, Exotica, Phys. Rept. 409 (2005) 1 [hep-ph/0409065] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    C. Amsler and N. Tornqvist, Mesons beyond the naive quark model, Phys. Rept. 389 (2004) 61 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    C.J. Morningstar and M.J. Peardon, The Glueball spectrum from an anisotropic lattice study, Phys. Rev. D 60 (1999) 034509 [hep-lat/9901004] [INSPIRE].ADSGoogle Scholar
  4. [4]
    R.L. Jaffe, Multi-quark hadrons. 1. The phenomenology of (2 quark 2 anti-quark) mesons, Phys. Rev. D 15 (1977) 267 [INSPIRE].ADSGoogle Scholar
  5. [5]
    R.L. Jaffe, Multi-quark hadrons. 2. Methods, Phys. Rev. D 15 (1977) 281 [INSPIRE].ADSGoogle Scholar
  6. [6]
    L. Maiani, F. Piccinini, A. Polosa and V. Riquer, A new look at scalar mesons, Phys. Rev. Lett. 93 (2004) 212002 [hep-ph/0407017] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    A.H. Fariborz, R. Jora and J. Schechter, Toy model for two chiral nonets, Phys. Rev. D 72 (2005) 034001 [hep-ph/0506170] [INSPIRE].ADSGoogle Scholar
  8. [8]
    F. Giacosa, Strong and electromagnetic decays of the light scalar mesons interpreted as tetraquark states, Phys. Rev. D 74 (2006) 014028 [hep-ph/0605191] [INSPIRE].ADSGoogle Scholar
  9. [9]
    D. Parganlija, P. Kovacs, G. Wolf, F. Giacosa and D.H. Rischke, Meson vacuum phenomenology in a three-flavor linear σ-model with (axial-)vector mesons, Phys. Rev. D 87 (2013) 014011 [arXiv:1208.0585] [INSPIRE].ADSGoogle Scholar
  10. [10]
    V. Crede and C. Meyer, The experimental status of glueballs, Prog. Part. Nucl. Phys. 63 (2009) 74 [arXiv:0812.0600] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    E. Klempt and A. Zaitsev, Glueballs, hybrids, multiquarks. Experimental facts versus QCD inspired concepts, Phys. Rept. 454 (2007) 1 [arXiv:0708.4016] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE], and 2011 partial update for the 2012 edition.
  13. [13]
    M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105 (1986) 153 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354 (1991) 531 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    M. Lüscher, Signatures of unstable particles in finite volume, Nucl. Phys. B 364 (1991) 237 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    U. Wiese, Identification of resonance parameters from the finite volume energy spectrum, Nucl. Phys. Proc. Suppl. 9 (1989) 609 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Döring, U. Meissner, E. Oset and A. Rusetsky, Scalar mesons moving in a finite volume and the role of partial wave mixing, Eur. Phys. J. A 48 (2012) 114 [arXiv:1205.4838] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    S. Prelovsek and D. Mohler, A Lattice study of light scalar tetraquarks, Phys. Rev. D 79 (2009) 014503 [arXiv:0810.1759] [INSPIRE].ADSGoogle Scholar
  19. [19]
    ETM collaboration, K. Jansen, C. McNeile, C. Michael and C. Urbach, Meson masses and decay constants from unquenched lattice QCD, Phys. Rev. D 80 (2009) 054510 [arXiv:0906.4720] [INSPIRE].ADSGoogle Scholar
  20. [20]
    S. Prelovsek et al., Lattice study of light scalar tetraquarks with I = 0, 2, 1/2, 3/2: are σ and κ tetraquarks?, Phys. Rev. D 82 (2010) 094507 [arXiv:1005.0948] [INSPIRE].ADSGoogle Scholar
  21. [21]
    C. Alexandrou and G. Koutsou, The static tetraquark and pentaquark potentials, Phys. Rev. D 71 (2005) 014504 [hep-lat/0407005] [INSPIRE].ADSGoogle Scholar
  22. [22]
    F. Okiharu, H. Suganuma and T.T. Takahashi, Detailed analysis of the tetraquark potential and flip-flop in SU(3) lattice QCD, Phys. Rev. D 72 (2005) 014505 [hep-lat/0412012] [INSPIRE].ADSGoogle Scholar
  23. [23]
    ETM collaboration, M. Wagner, Static-static-light-light tetraquarks in lattice QCD, Acta Phys. Polon. Supp. 4 (2011) 747 [arXiv:1103.5147] [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    P. Bicudo and M. Wagner, Lattice QCD signal for a bottom-bottom tetraquark, arXiv:1209.6274 [INSPIRE].
  25. [25]
    M. Kalinowski and M. Wagner, Strange and charm meson masses from twisted mass lattice QCD, arXiv:1212.0403 [INSPIRE].
  26. [26]
    ETM collaboration, R. Baron et al., Status of ETMC simulations with N f = 2 + 1 + 1 twisted mass fermions, PoS(LATTICE 2008)094 [arXiv:0810.3807] [INSPIRE].
  27. [27]
    ETM collaboration, R. Baron et al., First results of ETMC simulations with N f = 2 + 1 + 1 maximally twisted mass fermions, PoS(LAT2009)104 [arXiv:0911.5244] [INSPIRE].
  28. [28]
    ETM collaboration, R. Baron et al., Light hadrons from lattice QCD with light (u, d), strange and charm dynamical quarks, JHEP 06 (2010) 111 [arXiv:1004.5284] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    ETM collaboration, R. Baron et al., Light hadrons from N f = 2 + 1 + 1 dynamical twisted mass fermions, PoS(LATTICE 2010)123 [arXiv:1101.0518] [INSPIRE].
  30. [30]
    J.O. Daldrop et al., Lattice investigation of the tetraquark candidates a 0(980) and κ, PoS(LATTICE 2012)161 [arXiv:1211.5002] [INSPIRE].
  31. [31]
    Y. Iwasaki, Renormalization group analysis of lattice theories and improved lattice action: two-dimensional nonlinear \( \mathcal{O} \)(N) σ-model, Nucl. Phys. B 258 (1985) 141 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Alpha collaboration, R. Frezzotti, P.A. Grassi, S. Sint and P. Weisz, Lattice QCD with a chirally twisted mass term, JHEP 08 (2001) 058 [hep-lat/0101001] [INSPIRE].Google Scholar
  33. [33]
    R. Frezzotti and G. Rossi, Twisted mass lattice QCD with mass nondegenerate quarks, Nucl. Phys. Proc. Suppl. 128 (2004) 193 [hep-lat/0311008] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    T. Chiarappa et al., Numerical simulation of QCD with u, d, s and c quarks in the twisted-mass Wilson formulation, Eur. Phys. J. C 50 (2007) 373 [hep-lat/0606011] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. 1. \( \mathcal{O} \)(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    ETM collaboration, R. Baron et al., Computing K and D meson masses with N f = 2 + 1 + 1 twisted mass lattice QCD, Comput. Phys. Commun. 182 (2011) 299 [arXiv:1005.2042] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  37. [37]
    ETM collaboration, R. Baron et al., Kaon and D meson masses with N f = 2 + 1 + 1 twisted mass lattice QCD, arXiv:1009.2074 [INSPIRE].
  38. [38]
    C. Alexandrou, P. de Forcrand and B. Lucini, Evidence for diquarks in lattice QCD, Phys. Rev. Lett. 97 (2006) 222002 [hep-lat/0609004] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    ETM collaboration, M. Wagner and C. Wiese, The static-light baryon spectrum from twisted mass lattice QCD, JHEP 07 (2011) 016 [arXiv:1104.4921] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    S.R. Sharpe and J.M. Wu, Twisted mass chiral perturbation theory at next-to-leading order, Phys. Rev. D 71 (2005) 074501 [hep-lat/0411021] [INSPIRE].ADSGoogle Scholar
  41. [41]
    R. Frezzotti, G. Martinelli, M. Papinutto and G. Rossi, Reducing cutoff effects in maximally twisted lattice QCD close to the chiral limit, JHEP 04 (2006) 038 [hep-lat/0503034] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    ETM collaboration, B. Blossier et al., Light quark masses and pseudoscalar decay constants from N f = 2 Lattice QCD with twisted mass fermions, JHEP 04 (2008) 020 [arXiv:0709.4574] [INSPIRE].Google Scholar
  43. [43]
    C. Lang, L. Leskovec, D. Mohler and S. Prelovsek, K pi scattering for isospin 1/2 and 3/2 in lattice QCD, Phys. Rev. D 86 (2012) 054508 [arXiv:1207.3204] [INSPIRE].ADSGoogle Scholar
  44. [44]
    S. Gusken, A study of smearing techniques for hadron correlation functions, Nucl. Phys. Proc. Suppl. 17 (1990) 361 [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    ETM collaboration, C. Alexandrou et al., Light baryon masses with dynamical twisted mass fermions, Phys. Rev. D 78 (2008) 014509 [arXiv:0803.3190] [INSPIRE].ADSGoogle Scholar
  46. [46]
    APE collaboration, M. Albanese et al., Glueball masses and string tension in lattice QCD, Phys. Lett. B 192 (1987) 163 [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    ETM collaboration, K. Jansen, C. Michael, A. Shindler and M. Wagner, The static-light meson spectrum from twisted mass lattice QCD, JHEP 12 (2008) 058 [arXiv:0810.1843] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    UKQCD collaboration, M. Foster and C. Michael, Quark mass dependence of hadron masses from lattice QCD, Phys. Rev. D 59 (1999) 074503 [hep-lat/9810021] [INSPIRE].ADSGoogle Scholar
  49. [49]
    B. Blossier, M. Della Morte, G. von Hippel, T. Mendes and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, JHEP 04 (2009) 094 [arXiv:0902.1265] [INSPIRE].Google Scholar
  50. [50]
    W. Detmold, K. Orginos, M.J. Savage and A. Walker-Loud, Kaon Condensation with Lattice QCD, Phys. Rev. D 78 (2008) 054514 [arXiv:0807.1856] [INSPIRE].ADSGoogle Scholar
  51. [51]
    M. Wagner et al., Scalar mesons and tetraquarks by means of lattice QCD, arXiv:1212.1648 [INSPIRE].
  52. [52]
    P.F. Bedaque, Aharonov-Bohm effect and nucleon nucleon phase shifts on the lattice, Phys. Lett. B 593 (2004) 82 [nucl-th/0402051] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104 (1986) 177 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  54. [54]
    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
  55. [55]
    M. Lage, U.-G. Meissner and A. Rusetsky, A method to measure the antikaon-nucleon scattering length in lattice QCD, Phys. Lett. B 681 (2009) 439 [arXiv:0905.0069] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    V. Bernard, M. Lage, U.-G. Meissner and A. Rusetsky, Scalar mesons in a finite volume, JHEP 01 (2011) 019 [arXiv:1010.6018] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    E. Oset, M. Döring, U. Meißner and A. Rusetsky, Chiral unitary theory of scalar mesons in a finite volume, arXiv:1108.3923 [INSPIRE].
  58. [58]
    M. Döring, U.-G. Meißner, E. Oset and A. Rusetsky, Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector, Eur. Phys. J. A 47 (2011) 139 [arXiv:1107.3988] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • The ETM collaboration
  • Constantia Alexandrou
    • 1
    • 2
  • Jan Oliver Daldrop
    • 3
  • Mattia Dalla Brida
    • 4
  • Mario Gravina
    • 1
  • Luigi Scorzato
    • 5
  • Carsten Urbach
    • 3
  • Marc Wagner
    • 6
  1. 1.Department of PhysicsUniversity of CyprusNicosiaCyprus
  2. 2.Computation-based Science and Technology Research Center, Cyprus InstituteNicosiaCyprus
  3. 3.Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  4. 4.School of Mathematics, Trinity College DublinDublin 2Ireland
  5. 5.ECT⋆TrentoItaly
  6. 6.Goethe-Universität Frankfurt am Main, Institut für Theoretische PhysikFrankfurt am MainGermany

Personalised recommendations