Advertisement

Journal of High Energy Physics

, 2017:153 | Cite as

Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study

  • P. Boyle
  • V. GülpersEmail author
  • J. Harrison
  • A. Jüttner
  • C. Lehner
  • A. Portelli
  • C.T. Sachrajda
Open Access
Regular Article - Theoretical Physics

Abstract

We calculate the strong isospin breaking and QED corrections to meson masses and the hadronic vacuum polarization in an exploratory study on a 64 × 243 lattice with an inverse lattice spacing of a −1 = 1.78 GeV and an isospin symmetric pion mass of m π = 340 MeV. We include QED in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. We find that the electromagnetic correction to the leading hadronic contribution to the anomalous magnetic moment of the muon is smaller than 1% for the up quark and 0.1% for the strange quark, although it should be noted that this is obtained using unphysical light quark masses. In addition to the results themselves, we compare the precision which can be reached for the same computational cost using each method. Such a comparison is also made for the meson electromagnetic mass-splittings.

Keywords

Lattice QCD Lattice Quantum Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 77 (2017) 112 [arXiv:1607.00299] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    T. Blum, T. Doi, M. Hayakawa, T. Izubuchi and N. Yamada, Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions, Phys. Rev. D 76 (2007) 114508 [arXiv:0708.0484] [INSPIRE].ADSGoogle Scholar
  3. [3]
    T. Blum et al., Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED, Phys. Rev. D 82 (2010) 094508 [arXiv:1006.1311] [INSPIRE].
  4. [4]
    Budapest-Marseille-Wuppertal collaboration, S. Borsányi et al., Isospin splittings in the light baryon octet from lattice QCD and QED, Phys. Rev. Lett. 111 (2013) 252001 [arXiv:1306.2287] [INSPIRE].
  5. [5]
    S. Borsányi et al., Ab initio calculation of the neutron-proton mass difference, Science 347 (2015) 1452 [arXiv:1406.4088] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    R. Horsley et al., Isospin splittings of meson and baryon masses from three-flavor lattice QCD + QED, J. Phys. G 43 (2016) 10LT02 [arXiv:1508.06401] [INSPIRE].
  7. [7]
    R. Horsley et al., QED effects in the pseudoscalar meson sector, JHEP 04 (2016) 093 [arXiv:1509.00799] [INSPIRE].ADSGoogle Scholar
  8. [8]
    MILC collaboration, S. Basak et al., Electromagnetic effects on the light pseudoscalar mesons and determination of m u /m d, PoS(LATTICE 2015)259 [arXiv:1606.01228] [INSPIRE].
  9. [9]
    Z. Fodor et al., Up and down quark masses and corrections to Dashen’s theorem from lattice QCD and quenched QED, Phys. Rev. Lett. 117 (2016) 082001 [arXiv:1604.07112] [INSPIRE].
  10. [10]
    RM123 collaboration, G.M. de Divitiis et al., Leading isospin breaking effects on the lattice, Phys. Rev. D 87 (2013) 114505 [arXiv:1303.4896] [INSPIRE].
  11. [11]
    D. Giusti et al., Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions, Phys. Rev. D 95 (2017) 114504 [arXiv:1704.06561] [INSPIRE].ADSGoogle Scholar
  12. [12]
    N. Carrasco et al., QED Corrections to Hadronic Processes in Lattice QCD, Phys. Rev. D 91 (2015) 074506 [arXiv:1502.00257] [INSPIRE].
  13. [13]
    V. Lubicz et al., Electromagnetic corrections to the leptonic decay rates of charged pseudoscalar mesons: lattice results, in Proceedings, 34th International Symposium on Lattice Field Theory (Lattice 2016): Southampton, U.K., July 24-30, 2016, (2016) PoS(LATTICE2016)290 [arXiv:1610.09668] [INSPIRE].
  14. [14]
    V. Lubicz, G. Martinelli, C.T. Sachrajda, F. Sanfilippo, S. Simula and N. Tantalo, Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD, Phys. Rev. D 95 (2017) 034504 [arXiv:1611.08497] [INSPIRE].
  15. [15]
    T. Blum, S. Chowdhury, M. Hayakawa and T. Izubuchi, Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD, Phys. Rev. Lett. 114 (2015)012001 [arXiv:1407.2923] [INSPIRE].
  16. [16]
    T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin and C. Lehner, Lattice Calculation of Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment, Phys. Rev. D 93 (2016) 014503 [arXiv:1510.07100] [INSPIRE].
  17. [17]
    T. Blum et al., Connected and Leading Disconnected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment with a Physical Pion Mass, Phys. Rev. Lett. 118 (2017) 022005 [arXiv:1610.04603] [INSPIRE].
  18. [18]
    A. Duncan, E. Eichten and H. Thacker, Electromagnetic splittings and light quark masses in lattice QCD, Phys. Rev. Lett. 76 (1996) 3894 [hep-lat/9602005] [INSPIRE].
  19. [19]
    Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
  20. [20]
    P. Boyle, L. Del Debbio, E. Kerrane and J. Zanotti, Lattice Determination of the Hadronic Contribution to the Muon g − 2 using Dynamical Domain Wall Fermions, Phys. Rev. D 85 (2012) 074504 [arXiv:1107.1497] [INSPIRE].
  21. [21]
    M. Della Morte, B. Jäger, A. Jüttner and H. Wittig, Towards a precise lattice determination of the leading hadronic contribution to (g − 2)μ, JHEP 03 (2012) 055 [arXiv:1112.2894] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  22. [22]
    ETM collaboration, F. Burger, X. Feng, G. Hotzel, K. Jansen, M. Petschlies and D.B. Renner, Four-Flavour Leading-Order Hadronic Contribution To The Muon Anomalous Magnetic Moment, JHEP 02 (2014) 099 [arXiv:1308.4327] [INSPIRE].
  23. [23]
    HPQCD collaboration, B. Chakraborty et al., Strange and charm quark contributions to the anomalous magnetic moment of the muon, Phys. Rev. D 89 (2014) 114501 [arXiv:1403.1778] [INSPIRE].
  24. [24]
    G. Bali and G. Endrődi, Hadronic vacuum polarization and muon g-2 from magnetic susceptibilities on the lattice, Phys. Rev. D 92 (2015) 054506 [arXiv:1506.08638] [INSPIRE].
  25. [25]
    B. Chakraborty, C.T.H. Davies, P.G. de Oliviera, J. Koponen, G.P. Lepage and R.S. Van de Water, The hadronic vacuum polarization contribution to a μ from full lattice QCD, Phys. Rev. D 96 (2017) 034516 [arXiv:1601.03071] [INSPIRE].
  26. [26]
    S. Borsányi et al., Slope and curvature of the hadron vacuum polarization at vanishing virtuality from lattice QCD, arXiv:1612.02364 [INSPIRE].
  27. [27]
    M. Della Morte et al., The hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD, arXiv:1705.01775 [INSPIRE].
  28. [28]
    M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ), Eur. Phys. J. C 71 (2011) 1515 [Erratum ibid. C 72 (2012) 1874] [arXiv:1010.4180] [INSPIRE].
  29. [29]
    K. Hagiwara, R. Liao, A.D. Martin, D. Nomura and T. Teubner, (g − 2)μ and α(M Z2) re-evaluated using new precise data, J. Phys. G 38 (2011) 085003 [arXiv:1105.3149] [INSPIRE].
  30. [30]
    D. Giusti, V. Lubicz, G. Martinelli, F. Sanfilippo and S. Simula, Strange and charm HVP contributions to the muon (g − 2) including QED corrections with twisted-mass fermions, arXiv:1707.03019 [INSPIRE].
  31. [31]
    P. Boyle, V. Gülpers, J. Harrison, A. Jüttner, A. Portelli and C. Sachrajda, Electromagnetic Corrections to Meson Masses and the HVP, in Proceedings, 34th International Symposium on Lattice Field Theory (Lattice 2016): Southampton, U.K., July 24-30, 2016, (2016) PoS(LATTICE2016)172 [arXiv:1612.05962] [INSPIRE].
  32. [32]
    M. Hayakawa and S. Uno, QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons, Prog. Theor. Phys. 120 (2008) 413 [arXiv:0804.2044] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  33. [33]
    A. Patella, QED Corrections to Hadronic Observables, in Proceedings, 34th International Symposium on Lattice Field Theory (Lattice 2016): Southampton, U.K., July 24-30, 2016, (2017) PoS(LATTICE2016)020 [arXiv:1702.03857] [INSPIRE].
  34. [34]
    M. Gockeler et al., QED: A Lattice Investigation of the Chiral Phase Transition and the Nature of the Continuum Limit, Nucl. Phys. B 334 (1990) 527 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    M.G. Endres, A. Shindler, B.C. Tiburzi and A. Walker-Loud, Massive photons: an infrared regularization scheme for lattice QCD+QED, Phys. Rev. Lett. 117 (2016) 072002 [arXiv:1507.08916] [INSPIRE].
  36. [36]
    B. Lucini, A. Patella, A. Ramos and N. Tantalo, Charged hadrons in local finite-volume QED+QCD with C boundary conditions, JHEP 02 (2016) 076 [arXiv:1509.01636] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    G.M. de Divitiis et al., Isospin breaking effects due to the up-down mass difference in Lattice QCD, JHEP 04 (2012) 124 [arXiv:1110.6294] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].
  39. [39]
    Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [INSPIRE].
  40. [40]
    RBC-UKQCD collaboration, C. Allton et al., Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory, Phys. Rev. D 78 (2008) 114509 [arXiv:0804.0473] [INSPIRE].
  41. [41]
    RBC and UKQCD collaborations, Y. Aoki et al., Continuum Limit Physics from 2+1 Flavor Domain Wall QCD, Phys. Rev. D 83 (2011) 074508 [arXiv:1011.0892] [INSPIRE].
  42. [42]
    Y. Iwasaki and T. Yoshie, Renormalization Group Improved Action for SU(3) Lattice Gauge Theory and the String Tension, Phys. Lett. B 143 (1984) 449 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    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
  44. [44]
    P.A. Boyle, L. Del Debbio, A. Jüttner, A. Khamseh, F. Sanfilippo and J.T. Tsang, The decay constants f D and f Ds in the continuum limit of N f = 2 + 1 domain wall lattice QCD, arXiv:1701.02644 [INSPIRE].
  45. [45]
    RBC and UKQCD collaborations, T. Blum et al., Domain wall QCD with physical quark masses, Phys. Rev. D 93 (2016) 074505 [arXiv:1411.7017] [INSPIRE].
  46. [46]
    Budapest-Marseille-Wuppertal collaboration, A. Portelli et al., Electromagnetic corrections to light hadron masses, PoS(LATTICE 2010)121 [arXiv:1011.4189] [INSPIRE].
  47. [47]
    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].
  48. [48]
    UKQCD collaboration, C. McNeile and C. Michael, Decay width of light quark hybrid meson from the lattice, Phys. Rev. D 73 (2006) 074506 [hep-lat/0603007] [INSPIRE].
  49. [49]
    P.A. Boyle, A. Jüttner, C. Kelly and R.D. Kenway, Use of stochastic sources for the lattice determination of light quark physics, JHEP 08 (2008) 086 [arXiv:0804.1501] [INSPIRE].Google Scholar
  50. [50]
    Muon g-2 collaboration, G.W. Bennett et al., Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].
  51. [51]
    Fermilab E989 collaboration, G. Venanzoni, The New Muon g-2 experiment at Fermilab, Nucl. Part. Phys. Proc. 273-275 (2016) 584 [arXiv:1411.2555] [INSPIRE].
  52. [52]
    E34 collaboration, M. Otani, Status of the Muon g-2/EDM Experiment at J-PARC (E34), JPS Conf. Proc. 8 (2015) 025008 [INSPIRE].
  53. [53]
    T. Blum, Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 91 (2003) 052001 [hep-lat/0212018] [INSPIRE].
  54. [54]
    J. Green, O. Gryniuk, G. von Hippel, H.B. Meyer and V. Pascalutsa, Lattice QCD calculation of hadronic light-by-light scattering, Phys. Rev. Lett. 115 (2015) 222003 [arXiv:1507.01577] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    N. Asmussen, J. Green, H.B. Meyer and A. Nyffeler, Position-space approach to hadronic light-by-light scattering in the muon g − 2 on the lattice, PoS(LATTICE2016)164 [arXiv:1609.08454] [INSPIRE].
  56. [56]
    RBC/UKQCD collaboration, T. Blum et al., Lattice calculation of the leading strange quark-connected contribution to the muon g − 2, JHEP 04 (2016) 063 [Erratum ibid. 05 (2017) 034] [arXiv:1602.01767] [INSPIRE].
  57. [57]
    D. Bernecker and H.B. Meyer, Vector Correlators in Lattice QCD: Methods and applications, Eur. Phys. J. A 47 (2011) 148 [arXiv:1107.4388] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    C. Aubin, T. Blum, M. Golterman and S. Peris, Model-independent parametrization of the hadronic vacuum polarization and g-2 for the muon on the lattice, Phys. Rev. D 86 (2012) 054509 [arXiv:1205.3695] [INSPIRE].
  59. [59]
    F. Jegerlehner and A. Nyffeler, The Muon g-2, Phys. Rept. 477 (2009) 1 [arXiv:0902.3360] [INSPIRE].
  60. [60]
    V. Gülpers, A. Francis, B. Jäger, H. Meyer, G. von Hippel and H. Wittig, The leading disconnected contribution to the anomalous magnetic moment of the muon, PoS(LATTICE2014)128 [arXiv:1411.7592] [INSPIRE].
  61. [61]
    B. Chakraborty, C.T.H. Davies, J. Koponen, G.P. Lepage, M.J. Peardon and S.M. Ryan, Estimate of the hadronic vacuum polarization disconnected contribution to the anomalous magnetic moment of the muon from lattice QCD, Phys. Rev. D 93 (2016) 074509 [arXiv:1512.03270] [INSPIRE].
  62. [62]
    T. Blum et al., Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 116 (2016) 232002 [arXiv:1512.09054] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    M. Della Morte and A. Jüttner, Quark disconnected diagrams in chiral perturbation theory, JHEP 11 (2010) 154 [arXiv:1009.3783] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  64. [64]
    J. Bijnens and J. Relefors, Connected, Disconnected and Strange Quark Contributions to HVP, JHEP 11 (2016) 086 [arXiv:1609.01573] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    V. Furman and Y. Shamir, Axial symmetries in lattice QCD with Kaplan fermions, Nucl. Phys. B 439 (1995) 54 [hep-lat/9405004] [INSPIRE].
  66. [66]
    T. Blum et al., Quenched lattice QCD with domain wall fermions and the chiral limit, Phys. Rev. D 69 (2004) 074502 [hep-lat/0007038] [INSPIRE].
  67. [67]
    M.E. Matzelle and B.C. Tiburzi, Finite-Volume Corrections to Electromagnetic Masses for Larger-Than-Physical Electric Charges, Phys. Rev. D 95 (2017) 094510 [arXiv:1702.01296] [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.School of Physics and AstronomyUniversity of EdinburghEdinburghUnited Kingdom
  2. 2.School of Physics and AstronomyUniversity of SouthamptonSouthamptonUnited Kingdom
  3. 3.Physics Department, Brookhaven National LaboratoryUptonU.S.A.

Personalised recommendations