Advertisement

One-loop operator matching in the static heavy and domain-wall light quark system with O(a) improvement

  • Tomomi IshikawaEmail author
  • Yasumichi Aoki
  • Jonathan M. Flynn
  • Taku Izubuchi
  • Oleg Loktik
Article

Abstract

We discuss perturbative O(g 2 a) matching with static heavy quarks and domain-wall light quarks for lattice operators relevant to B-meson decays and \( {B^0} - {\bar{B}^0} \) mixing. The chiral symmetry of the light domain-wall quarks does not prohibit operator mixing at O(a) for these operators. The O(a) corrections to physical quantities are non-negligible and must be included to obtain high-precision simulation results for CKM physics. We provide results using plaquette, Symanzik, Iwasaki and DBW2 gluon actions and applying APE, HYP1 and HYP2 link-smearing for the static quark action.

Keywords

Lattice QCD Heavy Quark Physics B-Physics 

References

  1. [1]
    N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10 (1963) 531 [SPIRES].ADSCrossRefGoogle Scholar
  2. [2]
    M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49 (1973) 652 [SPIRES].ADSCrossRefGoogle Scholar
  3. [3]
    C.W. Bernard, T. Blum and A. Soni, SU(3) flavor breaking in hadronic matrix elements for B anti-B oscillations, Phys. Rev. D 58 (1998) 014501 [hep-lat/9801039] [SPIRES].ADSGoogle Scholar
  4. [4]
    E. Eichten and B.R. Hill, An effective field theory for the calculation of matrix elements involving heavy quarks, Phys. Lett. B 234 (1990) 511 [SPIRES].ADSGoogle Scholar
  5. [5]
    M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005) 051 [hep-lat/0506008] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    ALPHA collaboration, J. Heitger and R. Sommer, Non-perturbative heavy quark effective theory, JHEP 02 (2004) 022 [hep-lat/0310035] [SPIRES].ADSCrossRefGoogle Scholar
  7. [7]
    C.J. Morningstar and J. Shigemitsu, One-loop matching of lattice and continuum heavy-light axial vector currents using NRQCD, Phys. Rev. D 57 (1998) 6741 [hep-lat/9712016] [SPIRES].ADSGoogle Scholar
  8. [8]
    K.I. Ishikawa, T. Onogi and N. Yamada, O( s) matching coefficients for the ΔB = 2 operators in the lattice static theory, Phys. Rev. D 60 (1999) 034501 [hep-lat/9812007] [SPIRES].ADSGoogle Scholar
  9. [9]
    D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [SPIRES].ADSGoogle Scholar
  10. [10]
    R. Narayanan and H. Neuberger, Infinitely many regulator fields for chiral fermions, Phys. Lett. B 302 (1993) 62 [hep-lat/9212019] [SPIRES].ADSGoogle Scholar
  11. [11]
    Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    O. Loktik and T. Izubuchi, Perturbative renormalization for static and domain-wall bilinears and four-fermion operators with improved gauge actions, Phys. Rev. D 75 (2007) 034504 [hep-lat/0612022] [SPIRES].ADSGoogle Scholar
  13. [13]
    RBC and UKQCD collaborations, C. Albertus et al., B-anti-B mixing with domain wall fermions in the static approximation, PoS(LATTICE 2007)376 [SPIRES].
  14. [14]
    N.H. Christ, T.T. Dumitrescu, O. Loktik and T. Izubuchi, The static approximation to B meson mixing using light domain-wall fermions: perturbative renormalization and ground state degeneracies, PoS(LATTICE 2007)351 [arXiv:0710.5283] [SPIRES].
  15. [15]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [SPIRES].ADSGoogle Scholar
  16. [16]
    A.J. Buras and P.H. Weisz, QCD nonleading corrections to weak decays in dimensional regularization and ’t Hooft-Veltman schemes, Nucl. Phys. B 333 (1990) 66 [SPIRES].ADSCrossRefGoogle Scholar
  17. [17]
    D.J. Broadhurst and A.G. Grozin, Matching QCD and HQET heavy-light currents at two loops and beyond, Phys. Rev. D 52 (1995) 4082 [hep-ph/9410240] [SPIRES].ADSGoogle Scholar
  18. [18]
    J.M. Flynn, O.F. Hernandez and B.R. Hill, Renormalization of four fermion operators determining B anti-B mixing on the lattice, Phys. Rev. D 43 (1991) 3709 [SPIRES].ADSGoogle Scholar
  19. [19]
    X.-D. Ji and M.J. Musolf, Subleading logarithmic mass dependence in heavy meson form-factors, Phys. Lett. B 257 (1991) 409 [SPIRES].ADSGoogle Scholar
  20. [20]
    D.J. Broadhurst and A.G. Grozin, Two loop renormalization of the effective field theory of a static quark, Phys. Lett. B 267 (1991) 105 [hep-ph/9908362] [SPIRES].ADSGoogle Scholar
  21. [21]
    V. Giménez, Two loop calculation of the anomalous dimension of four fermion operators with static heavy quarks, Nucl. Phys. B 401 (1993) 116 [SPIRES].ADSCrossRefGoogle Scholar
  22. [22]
    M. Ciuchini, E. Franco and V. Giménez, Next-to-leading order renormalization of the ΔB = 2 operators in the static theory, Phys. Lett. B 388 (1996) 167 [hep-ph/9608204] [SPIRES].ADSGoogle Scholar
  23. [23]
    G. Buchalla, Renormalization of ΔB = 2 transitions in the static limit beyond leading logarithms, Phys. Lett. B 395 (1997) 364 [hep-ph/9608232] [SPIRES].ADSGoogle Scholar
  24. [24]
    D. Becirevic and J. Reyes, HQET with chiral symmetry on the lattice, Nucl. Phys. Proc. Suppl. 129 (2004) 435 [hep-lat/0309131] [SPIRES].ADSCrossRefGoogle Scholar
  25. [25]
    B. Blossier, Lattice renormalisation of O(a) improved heavy-light operators, Phys. Rev. D 76 (2007) 114513 [arXiv:0705.0283] [SPIRES].ADSGoogle Scholar
  26. [26]
    N. Isgur and M.B. Wise, Weak decays of heavy mesons in the static quark approximation, Phys. Lett. B 232 (1989) 113 [SPIRES].ADSGoogle Scholar
  27. [27]
    N. Isgur and M.B. Wise, Weak transition form-factors between heavy mesons, Phys. Lett. B 237 (1990) 527 [SPIRES].ADSGoogle Scholar
  28. [28]
    R. Gupta, Introduction to lattice QCD, hep-lat/9807028 [SPIRES].
  29. [29]
    C. Albertus et al., Neutral B-meson mixing from unquenched lattice QCD with domain-wall light quarks and static b-quarks, Phys. Rev. D 82 (2010) 014505 [arXiv:1001.2023] [SPIRES].ADSGoogle Scholar
  30. [30]
    C.T. Sachrajda, QCD phenomenology from the lattice: renormalization of local operators, Nucl. Phys. Proc. Suppl. 9 (1989) 121 [SPIRES].ADSCrossRefGoogle Scholar
  31. [31]
    S. Aoki, T. Izubuchi, Y. Kuramashi and Y. Taniguchi, Perturbative renormalization factors of quark bilinear operators for domain-wall QCD, Phys. Rev. D 59 (1999) 094505 [hep-lat/9810020] [SPIRES].ADSGoogle Scholar
  32. [32]
    S. Aoki, T. Izubuchi, Y. Kuramashi and Y. Taniguchi, Perturbative renormalization factors in domain-wall QCD with improved gauge actions, Phys. Rev. D 67 (2003) 094502 [hep-lat/0206013] [SPIRES].ADSGoogle Scholar
  33. [33]
    A. Borrelli and C. Pittori, Improved renormalization constants for B decay and B anti-B mixing, Nucl. Phys. B 385 (1992) 502 [SPIRES].ADSCrossRefGoogle Scholar
  34. [34]
    S. Aoki, T. Izubuchi, Y. Kuramashi and Y. Taniguchi, Perturbative renormalization factors of three-and four-quark operators for domain-wall QCD, Phys. Rev. D 60 (1999) 114504 [hep-lat/9902008] [SPIRES].ADSGoogle Scholar
  35. [35]
    E. Eichten and B.R. Hill, Renormalization of heavy-light bilinears and f(B) for Wilson fermions, Phys. Lett. B 240 (1990) 193 [SPIRES].ADSGoogle Scholar
  36. [36]
    A. Hasenfratz and F. Knechtli, Flavor symmetry and the static potential with hypercubic blocking, Phys. Rev. D 64 (2001) 034504 [hep-lat/0103029] [SPIRES].ADSGoogle Scholar
  37. [37]
    APE collaboration, M. Albanese et al., Glueball masses and string tension in lattice QCD, Phys. Lett. B 192 (1987) 163 [SPIRES].ADSGoogle Scholar
  38. [38]
    S. Aoki and Y. Taniguchi, One loop calculation in lattice QCD with domain-wall quarks, Phys. Rev. D 59 (1999) 054510 [hep-lat/9711004] [SPIRES].ADSGoogle Scholar
  39. [39]
    T. Blum, A. Soni and M. Wingate, Calculation of the strange quark mass using domain wall fermions, Phys. Rev. D 60 (1999) 114507 [hep-lat/9902016] [SPIRES].ADSGoogle Scholar
  40. [40]
    J. Noaki and Y. Taniguchi, Scaling property of domain-wall QCD in perturbation theory, Phys. Rev. D 61 (2000) 054505 [hep-lat/9906030] [SPIRES].ADSGoogle Scholar
  41. [41]
    M. Lüscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys. 97 (1985) 59 [Erratum ibid. 98 (1985) 433] [SPIRES].ADSzbMATHCrossRefGoogle Scholar
  42. [42]
    P. Weisz and R. Wohlert, Continuum limit improved lattice action for pure Yang-Mills theory. 2, Nucl. Phys. B 236 (1984) 397 [Erratum ibid. B 247 (1984) 544] [SPIRES].MathSciNetADSCrossRefGoogle 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 [SPIRES].ADSCrossRefGoogle Scholar
  44. [44]
    Y. Iwasaki, Renormalization group analysis of lattice theories and improved lattice action. 2. Four-dimensional nonabelian SU(N) gauge model, UTHEP-118, University of Tsukuba, Tsukuba Japan (1983) [SPIRES].
  45. [45]
    QCD-TARO collaboration, P. de Forcrand et al., Renormalization group flow of SU(3) lattice gauge theory: numerical studies in a two coupling space, Nucl. Phys. B 577 (2000) 263 [hep-lat/9911033] [SPIRES].CrossRefGoogle Scholar
  46. [46]
    G.P. Lepage and P.B. Mackenzie, On the viability of lattice perturbation theory, Phys. Rev. D 48 (1993) 2250 [hep-lat/9209022] [SPIRES].ADSGoogle Scholar
  47. [47]
    O.F. Hernandez and B.R. Hill, Tadpole improved perturbation theory for heavy-light lattice operators, Phys. Rev. D 50 (1994) 495 [hep-lat/9401035] [SPIRES].ADSGoogle Scholar
  48. [48]
    R. Horsley, H. Perlt, P.E.L. Rakow, G. Schierholz and A. Schiller, Perturbative determination of cSW for plaquette and Symanzik gauge action and stout link clover fermions, Phys. Rev. D 78 (2008) 054504 [arXiv:0807.0345] [SPIRES].ADSGoogle Scholar
  49. [49]
    A. Hasenfratz and P. Hasenfratz, The connection between the Λ parameters of lattice and continuum QCD, Phys. Lett. B 93 (1980) 165 [SPIRES].ADSGoogle Scholar
  50. [50]
    A. Hasenfratz and P. Hasenfratz, The scales of Euclidean and Hamiltonian lattice QCD, Nucl. Phys. B 193 (1981) 210 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  51. [51]
    P. Weisz, Continuum limit improved lattice action for pure Yang-Mills theory. 1, Nucl. Phys. B 212 (1983) 1 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  52. [52]
    Y. Iwasaki and S. Sakai, The Λ parameter for improved lattice gauge actions, Nucl. Phys. B 248 (1984) 441 [SPIRES].ADSCrossRefGoogle Scholar
  53. [53]
    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 [SPIRES].ADSGoogle Scholar
  54. [54]
    S. Sakai, T. Saito and A. Nakamura, Anisotropic lattice with improved gauge actions. I: study of fundamental parameters in weak coupling regions, Nucl. Phys. B 584 (2000) 528 [hep-lat/0002029] [SPIRES].ADSCrossRefGoogle Scholar
  55. [55]
    S. Aoki and Y. Kuramashi, The lattice Λ parameter in domain wall QCD, Phys. Rev. D 68 (2003) 034507 [hep-lat/0306008] [SPIRES].ADSGoogle Scholar
  56. [56]
    W.-J. Lee and S.R. Sharpe, One-loop matching coefficients for improved staggered bilinears, Phys. Rev. D 66 (2002) 114501 [hep-lat/0208018] [SPIRES].ADSGoogle Scholar
  57. [57]
    W.-J. Lee, Perturbative improvement of staggered fermions using fat links, Phys. Rev. D 66 (2002) 114504 [hep-lat/0208032] [SPIRES].ADSGoogle Scholar
  58. [58]
    RBC collaboration, Y. Aoki et al., Continuum limit physics from 2 + 1 flavor domain wall QCD, arXiv:1011.0892 [SPIRES].
  59. [59]
    K.G. Chetyrkin, Quark mass anomalous dimension to O(α s 4 ), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [SPIRES].ADSGoogle Scholar
  60. [60]
    J.A.M. Vermaseren, S.A. Larin and T. van Ritbergen, The 4-loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett. B 405 (1997) 327 [hep-ph/9703284] [SPIRES].ADSGoogle Scholar
  61. [61]
    T.A. DeGrand, One loop matching coefficients for a variant overlap action and some of its simpler relatives, Phys. Rev. D 67 (2003) 014507 [hep-lat/0210028] [SPIRES].ADSGoogle Scholar
  62. [62]
    G.P. Lepage, A new algorithm for adaptive multidimensional integration, J. Comput. Phys. 27 (1978) 192 [SPIRES].ADSzbMATHCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Tomomi Ishikawa
    • 1
    • 2
    Email author
  • Yasumichi Aoki
    • 2
    • 6
  • Jonathan M. Flynn
    • 3
  • Taku Izubuchi
    • 2
    • 4
  • Oleg Loktik
    • 5
  1. 1.Physics DepartmentUniversity of ConnecticutStorrsU.S.A.
  2. 2.RIKEN BNL Research CenterBrookhaven National LaboratoryUptonU.S.A.
  3. 3.School of Physics and AstronomyUniversity of SouthamptonHighfieldU.K.
  4. 4.Physics DepartmentBrookhaven National LaboratoryUptonU.S.A.
  5. 5.Physics DepartmentColumbia UniversityNew YorkU.S.A.
  6. 6.Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI)Nagoya UniversityNagoyaJapan

Personalised recommendations