Advertisement

Journal of High Energy Physics

, 2012:48 | Cite as

η and η′ mesons from N f  = 2 + 1 + 1 twisted mass lattice QCD

  • ETM collaboration
  • Konstantin Ottnad
  • Chris Michael
  • Siebren Reker
  • Carsten Urbach
Article

Abstract

We determine mass and mixing angles of η and η′ states using N f  = 2 + 1 + 1 Wilson twisted mass lattice QCD. We describe how those flavour singlet states need to be treated in this lattice formulation. Results are presented for three values of the lattice spacing, a = 0.061 fm, a = 0.078 fm and a = 0.086 fm, with light quark masses corresponding to values of the charged pion mass in a range of 230 to 500 MeV and fixed bare strange and charm quark mass values. We obtain M η  = 557(15)(45) MeV (first error statistical, second systematic) and ϕ = 44(5)° for a single mixing angle in the quark flavour basis, θ = −10(5)° in the octet-singlet basis.

Keywords

Lattice QCD Lattice Gauge Field Theories Lattice Quantum Field Theory QCD 

References

  1. [1]
    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
  2. [2]
    N. Christ et al., The η and ηmesons from Lattice QCD, Phys. Rev. Lett. 105 (2010) 241601 [arXiv:1002.2999] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    TWQCD collaboration, JLQCD collaboration, T. Kaneko et al., Flavor-singlet mesons in N f = 2 + 1 QCD with dynamical overlap quarks, PoS(LAT2009)107 [arXiv:0910.4648] [INSPIRE].
  4. [4]
    J.J. Dudek et al., Isoscalar meson spectroscopy from lattice QCD, Phys. Rev. D 83 (2011) 111502 [arXiv:1102.4299] [INSPIRE].ADSGoogle Scholar
  5. [5]
    UKQCD collaboration, E.B. Gregory, A.C. Irving, C.M. Richards and C. McNeile, A study of the eta and ηmesons with improved staggered fermions, Phys. Rev. D 86 (2012) 014504 [arXiv:1112.4384] [INSPIRE].ADSGoogle Scholar
  6. [6]
    ETM collaboration, K. Jansen, C. Michael and C. Urbach, The ηmeson from lattice QCD, Eur. Phys. J. C 58 (2008) 261 [arXiv:0804.3871] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    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
  8. [8]
    Y. Iwasaki, Renormalization Group Analysis of Lattice Theories and Improved Lattice Action: Two-Dimensional Nonlinear O(N) σ-model, Nucl. Phys. B 258 (1985) 141 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    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
  10. [10]
    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
  11. [11]
    R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    XLF collaboration, K. Jansen, A. Shindler, C. Urbach and I. Wetzorke, Scaling test for Wilson twisted mass QCD, Phys. Lett. B 586 (2004) 432 [hep-lat/0312013] [INSPIRE].ADSGoogle Scholar
  13. [13]
    XLF collaboration, K. Jansen, M. Papinutto, A. Shindler, C. Urbach and I. Wetzorke, Quenched scaling of Wilson twisted mass fermions, JHEP 09 (2005) 071 [hep-lat/0507010] [INSPIRE].Google Scholar
  14. [14]
    ETM collaboration, R. Baron et al., Light Meson Physics from Maximally Twisted Mass Lattice QCD, JHEP 08 (2010) 097 [arXiv:0911.5061] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    ETM collaboration, B. Blossier et al., Average up/down, strange and charm quark masses with N f = 2 twisted mass lattice QCD, Phys. Rev. D 82 (2010) 114513 [arXiv:1010.3659] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A. Shindler, Twisted mass lattice QCD, Phys. Rept. 461 (2008) 37 [arXiv:0707.4093] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    European Twisted Mass 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].ADSzbMATHCrossRefGoogle Scholar
  18. [18]
    European Twisted Mass collaboration, C. Urbach, Lattice QCD with two light Wilson quarks and maximally twisted mass, PoS(LATTICE 2007)022 [arXiv:0710.1517] [INSPIRE].
  19. [19]
    P. Dimopoulos, R. Frezzotti, C. Michael, G. Rossi and C. Urbach, O(a 2) cutoff effects in lattice Wilson fermion simulations, Phys. Rev. D 81 (2010) 034509 [arXiv:0908.0451] [INSPIRE].ADSGoogle Scholar
  20. [20]
    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].
  21. [21]
    R. Sommer, A New way to set the energy scale in lattice gauge theories and its applications to the static force and α s in SU(2) Yang-Mills theory, Nucl. Phys. B 411 (1994) 839 [hep-lat/9310022] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    G. Colangelo et al., Review of lattice results concerning low energy particle physics, Eur. Phys. J. C 71 (2011) 1695 [arXiv:1011.4408] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Skouroupathis and H. Panagopoulos, Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice, Phys. Rev. D 76 (2007) 094514 [Erratum ibid. D 78 (2008) 119901] [arXiv:0707.2906] [INSPIRE].ADSGoogle Scholar
  24. [24]
    C. Michael and I. Teasdale, Extracting glueball masses from Lattice QCD, Nucl. Phys. B 215 (1983) 433 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    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
  26. [26]
    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
  27. [27]
    ETM collaboration, B. Blossier et al., Renormalisation constants of quark bilinears in lattice qcd with four dynamical wilson quarks, in preparation.Google Scholar
  28. [28]
    ETM collaboration, B. Blossier et al., Renormalisation constants of quark bilinears in lattice QCD with four dynamical Wilson quarks, PoS(Lattice 2011)233 [arXiv:1112.1540] [INSPIRE].
  29. [29]
    T. Feldmann, Quark structure of pseudoscalar mesons, Int. J. Mod. Phys. A 15 (2000) 159 [hep-ph/9907491] [INSPIRE].ADSGoogle Scholar
  30. [30]
    H. Leutwyler, On the 1/N expansion in chiral perturbation theory, Nucl. Phys. Proc. Suppl. 64 (1998) 223 [hep-ph/9709408] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    ETM collaboration, P. Boucaud et al., Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details, Comput. Phys. Commun. 179 (2008) 695 [arXiv:0803.0224] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    ALPHA collaboration, U. Wolff, Monte Carlo errors with less errors, Comput. Phys. Commun. 156 (2004) 143 [Erratum ibid. 176 (2007) 383] [hep-lat/0306017] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  33. [33]
    C. Urbach, K. Jansen, A. Shindler and U. Wenger, HMC algorithm with multiple time scale integration and mass preconditioning, Comput. Phys. Commun. 174 (2006) 87 [hep-lat/0506011] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    UKQCD collaboration, C. McNeile and C. Michael, The eta and eta-prime mesons in QCD, Phys. Lett. B 491 (2000) 123 [Erratum ibid. B 551 (2003) 391] [hep-lat/0006020] [INSPIRE].ADSGoogle Scholar
  35. [35]
    C. Di Donato, G. Ricciardi and I. Bigi, η - ηMixingFrom electromagnetic transitions to weak decays of charm and beauty hadrons, Phys. Rev. D 85 (2012) 013016 [arXiv:1105.3557] [INSPIRE].ADSGoogle Scholar
  36. [36]
    K. Jansen and C. Urbach, tmLQCD: A program suite to simulate Wilson Twisted mass Lattice QCD, Comput. Phys. Commun. 180 (2009) 2717 [arXiv:0905.3331] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  37. [37]
    A. Deuzeman, S. Reker and C. Urbach, Lemon: an MPI parallel I/O library for data encapsulation using LIME, Comput. Phys. Commun. 183 (2012) 1321 [arXiv:1106.4177] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    R Development Core Team, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna Austria, (2005), ISBN 3-900051-07-0.Google Scholar
  39. [39]
    F. Farchioni et al., Pseudoscalar decay constants from N f = 2 + 1 + 1 twisted mass lattice QCD, PoS(Lattice 2010)128 [arXiv:1012.0200] [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • ETM collaboration
  • Konstantin Ottnad
    • 1
  • Chris Michael
    • 2
  • Siebren Reker
    • 3
  • Carsten Urbach
    • 1
  1. 1.Helmholtz Institut für Strahlen- und KernphysikUniversität BonnBonnGermany
  2. 2.Theoretical Physics Division, Department of Mathematical SciencesThe University of LiverpoolLiverpoolU.K.
  3. 3.Centre for Theoretical PhysicsUniversity of GroningenGroningenThe Netherlands

Personalised recommendations