Advertisement

The kaon semileptonic form factor in N f = 2 + 1 domain wall lattice QCD with physical light quark masses

  • The RBC/UKQCD collaboration
  • P. A. Boyle
  • N. H. Christ
  • J. M. Flynn
  • N. Garron
  • C. Jung
  • A. JüttnerEmail author
  • R. D. Mawhinney
  • D. Murphy
  • C. T. Sachrajda
  • F. Sanfilippo
  • H. Yin
Open Access
Regular Article - Theoretical Physics

Abstract

We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f + K π (0) = 0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K → π decays for a determination of the CKM-matrix element for which we predict |V us | = 0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.

Keywords

Kaon Physics Lattice QCD Standard Model 

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]
    N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    FlaviaNet Working Group on Kaon Decays collaboration, M. Antonelli et al., An Evaluation of |V u s| and precise tests of the Standard Model from world data on leptonic and semileptonic kaon decays, Eur. Phys. J. C 69 (2010) 399 [arXiv:1005.2323] [INSPIRE].Google Scholar
  4. [4]
    A. Bazavov et al., Determination of |V us| from a lattice-QCD calculation of the Kπν semileptonic form factor with physical quark masses, Phys. Rev. Lett. 112 (2014) 112001 [arXiv:1312.1228] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    P.A. Boyle et al., K(l3) semileptonic form-factor from 2+1 flavour lattice QCD, Phys. Rev. Lett. 100 (2008) 141601 [arXiv:0710.5136] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    RBC-UKQCD collaboration, P.A. Boyle et al., Kπ form factors with reduced model dependence, Eur. Phys. J. C 69 (2010) 159 [arXiv:1004.0886] [INSPIRE].Google Scholar
  7. [7]
    P.A. Boyle et al., The kaon semileptonic form factor with near physical domain wall quarks, JHEP 08 (2013) 132 [arXiv:1305.7217] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Bazavov et al., Kaon semileptonic vector form factor and determination of |V us| using staggered fermions, Phys. Rev. D 87 (2013) 073012 [arXiv:1212.4993] [INSPIRE].ADSGoogle Scholar
  9. [9]
    ETM collaboration, V. Lubicz, F. Mescia, S. Simula and C. Tarantino, Kπlν Semileptonic Form Factors from Two-Flavor Lattice QCD, Phys. Rev. D 80 (2009) 111502 [arXiv:0906.4728] [INSPIRE].ADSGoogle Scholar
  10. [10]
    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
  11. [11]
    S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 74 (2014) 2890 [arXiv:1310.8555] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    G. Amelino-Camelia et al., Physics with the KLOE-2 experiment at the upgraded DAϕNE, Eur. Phys. J. C 68 (2010) 619 [arXiv:1003.3868] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    H. Na, C.T.H. Davies, E. Follana, G.P. Lepage and J. Shigemitsu, The DK, lν Semileptonic Decay Scalar Form Factor and |V cs| from Lattice QCD, Phys. Rev. D 82 (2010) 114506 [arXiv:1008.4562] [INSPIRE].ADSGoogle Scholar
  14. [14]
    P.A. Boyle, A. Juttner, 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
  15. [15]
    P.A. Boyle, J.M. Flynn, A. Jüttner, C.T. Sachrajda and J.M. Zanotti, Hadronic form factors in Lattice QCD at small and vanishing momentum transfer, JHEP 05 (2007) 016 [hep-lat/0703005] [INSPIRE].Google Scholar
  16. [16]
    P.F. Bedaque and J.-W. Chen, Twisted valence quarks and hadron interactions on the lattice, Phys. Lett. B 616 (2005) 208 [hep-lat/0412023] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    G.M. de Divitiis, R. Petronzio and N. Tantalo, On the discretization of physical momenta in lattice QCD, Phys. Lett. B 595 (2004) 408 [hep-lat/0405002] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    C.T. Sachrajda and G. Villadoro, Twisted boundary conditions in lattice simulations, Phys. Lett. B 609 (2005) 73 [hep-lat/0411033] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    RBC, UKQCD collaboration, T. Blum et al., Domain wall QCD with physical quark masses, arXiv:1411.7017 [INSPIRE].
  20. [20]
    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].Google Scholar
  21. [21]
    Y. Aoki et al., Continuum Limit of B K from 2+1 Flavor Domain Wall QCD, Phys. Rev. D 84 (2011) 014503 [arXiv:1012.4178] [INSPIRE].ADSGoogle Scholar
  22. [22]
    RBC, UKQCD collaboration, Y. Aoki et al., Continuum Limit Physics from 2+1 Flavor Domain Wall QCD, Phys. Rev. D 83 (2011) 074508 [arXiv:1011.0892] [INSPIRE].Google Scholar
  23. [23]
    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
  24. [24]
    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
  25. [25]
    R.C. Brower, H. Neff and K. Orginos, Mobius fermions: Improved domain wall chiral fermions, Nucl. Phys. Proc. Suppl. 140 (2005) 686 [hep-lat/0409118] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    R.C. Brower, H. Neff and K. Orginos, Mobius fermions, Nucl. Phys. Proc. Suppl. 153 (2006) 191 [hep-lat/0511031] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    R.C. Brower, H. Neff and K. Orginos, The Móbius Domain Wall Fermion Algorithm, arXiv:1206.5214 [INSPIRE].
  28. [28]
    D.B. Kaplan, A Method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    T. Blum, T. Izubuchi and E. Shintani, New class of variance-reduction techniques using lattice symmetries, Phys. Rev. D 88 (2013) 094503 [arXiv:1208.4349] [INSPIRE].ADSGoogle Scholar
  31. [31]
    T. Blum et al., Kππ ΔI = 3/2 decay amplitude in the continuum limit, Phys. Rev. D 91 (2015) 074502 [arXiv:1502.00263].ADSGoogle Scholar
  32. [32]
    Particle Data Group collaboration, K. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001.Google Scholar
  33. [33]
    M. Ademollo and R. Gatto, Nonrenormalization Theorem for the Strangeness Violating Vector Currents, Phys. Rev. Lett. 13 (1964) 264 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    J. Gasser and H. Leutwyler, Low-Energy Expansion of Meson Form-Factors, Nucl. Phys. B 250 (1985) 517 [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    J. Bijnens and P. Talavera, K(l3) decays in chiral perturbation theory, Nucl. Phys. B 669 (2003) 341 [hep-ph/0303103] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    K. Ghorbani and H. Ghorbani, Kaon semi-leptonic form factor at zero momentum transfer in finite volume, Eur. Phys. J. A 49 (2013) 134 [arXiv:1301.0919] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    G.M. de Divitiis, P. Dimopoulos, R. Frezzotti, V. Lubicz, G. Martinelli 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]
    N. Tantalo, Lattice calculation of isospin corrections to Kl2 and Kl3 decays, arXiv:1301.2881 [INSPIRE].
  39. [39]
    A. Portelli, Review on the inclusion of isospin breaking effects in lattice calculations, PoS(KAON13)023 [arXiv:1307.6056] [INSPIRE].
  40. [40]
    N. Carrasco et al., QED Corrections to Hadronic Processes in Lattice QCD, arXiv:1502.00257.

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • The RBC/UKQCD collaboration
  • P. A. Boyle
    • 1
  • N. H. Christ
    • 2
  • J. M. Flynn
    • 3
  • N. Garron
    • 4
  • C. Jung
    • 5
  • A. Jüttner
    • 3
    Email author
  • R. D. Mawhinney
    • 2
  • D. Murphy
    • 2
  • C. T. Sachrajda
    • 3
  • F. Sanfilippo
    • 3
  • H. Yin
    • 2
    • 6
  1. 1.School of Physics & AstronomyUniversity of EdinburghEdinburghUK
  2. 2.Physics DepartmentColumbia UniversityNew YorkUSA
  3. 3.School of Physics and AstronomyUniversity of SouthamptonSouthamptonUK
  4. 4.School of Computing and Mathematics and Centre for Mathematical SciencePlymouth UniversityPlymouthUK
  5. 5.Brookhaven National LaboratoryUptonUSA
  6. 6.Mountain ViewUSA

Personalised recommendations