Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10 (1963) 531 [SPIRES].

    Article  ADS  Google Scholar 

  2. M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49 (1973) 652 [SPIRES].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  5. M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005) 051 [hep-lat/0506008] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. ALPHA collaboration, J. Heitger and R. Sommer, Non-perturbative heavy quark effective theory, JHEP 02 (2004) 022 [hep-lat/0310035] [SPIRES].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  8. K.I. Ishikawa, T. Onogi and N. Yamada, O(aα s ) matching coefficients for the ΔB = 2 operators in the lattice static theory, Phys. Rev. D 60 (1999) 034501 [hep-lat/9812007] [SPIRES].

    ADS  Google Scholar 

  9. D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [SPIRES].

    ADS  Google Scholar 

  10. R. Narayanan and H. Neuberger, Infinitely many regulator fields for chiral fermions, Phys. Lett. B 302 (1993) 62 [hep-lat/9212019] [SPIRES].

    ADS  Google Scholar 

  11. Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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. 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. Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [SPIRES].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  19. X.-D. Ji and M.J. Musolf, Subleading logarithmic mass dependence in heavy meson form-factors, Phys. Lett. B 257 (1991) 409 [SPIRES].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  24. D. Becirevic and J. Reyes, HQET with chiral symmetry on the lattice, Nucl. Phys. Proc. Suppl. 129 (2004) 435 [hep-lat/0309131] [SPIRES].

    Article  ADS  Google Scholar 

  25. B. Blossier, Lattice renormalisation of O(a) improved heavy-light operators, Phys. Rev. D 76 (2007) 114513 [arXiv:0705.0283] [SPIRES].

    ADS  Google Scholar 

  26. N. Isgur and M.B. Wise, Weak decays of heavy mesons in the static quark approximation, Phys. Lett. B 232 (1989) 113 [SPIRES].

    ADS  Google Scholar 

  27. N. Isgur and M.B. Wise, Weak transition form-factors between heavy mesons, Phys. Lett. B 237 (1990) 527 [SPIRES].

    ADS  Google Scholar 

  28. R. Gupta, Introduction to lattice QCD, hep-lat/9807028 [SPIRES].

  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].

    ADS  Google Scholar 

  30. C.T. Sachrajda, QCD phenomenology from the lattice: renormalization of local operators, Nucl. Phys. Proc. Suppl. 9 (1989) 121 [SPIRES].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  33. A. Borrelli and C. Pittori, Improved renormalization constants for B decay and B anti-B mixing, Nucl. Phys. B 385 (1992) 502 [SPIRES].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  37. APE collaboration, M. Albanese et al., Glueball masses and string tension in lattice QCD, Phys. Lett. B 192 (1987) 163 [SPIRES].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  41. M. Lüscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys. 97 (1985) 59 [Erratum ibid. 98 (1985) 433] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  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. 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].

    Article  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  49. A. Hasenfratz and P. Hasenfratz, The connection between the Λ parameters of lattice and continuum QCD, Phys. Lett. B 93 (1980) 165 [SPIRES].

    ADS  Google Scholar 

  50. A. Hasenfratz and P. Hasenfratz, The scales of Euclidean and Hamiltonian lattice QCD, Nucl. Phys. B 193 (1981) 210 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. P. Weisz, Continuum limit improved lattice action for pure Yang-Mills theory. 1, Nucl. Phys. B 212 (1983) 1 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  52. Y. Iwasaki and S. Sakai, The Λ parameter for improved lattice gauge actions, Nucl. Phys. B 248 (1984) 441 [SPIRES].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  55. S. Aoki and Y. Kuramashi, The lattice Λ parameter in domain wall QCD, Phys. Rev. D 68 (2003) 034507 [hep-lat/0306008] [SPIRES].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  57. W.-J. Lee, Perturbative improvement of staggered fermions using fat links, Phys. Rev. D 66 (2002) 114504 [hep-lat/0208032] [SPIRES].

    ADS  Google Scholar 

  58. RBC collaboration, Y. Aoki et al., Continuum limit physics from 2 + 1 flavor domain wall QCD, arXiv:1011.0892 [SPIRES].

  59. K.G. Chetyrkin, Quark mass anomalous dimension to O(α s 4 ), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [SPIRES].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  62. G.P. Lepage, A new algorithm for adaptive multidimensional integration, J. Comput. Phys. 27 (1978) 192 [SPIRES].

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Yasumichi Aoki

    Present address: Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602, Japan

Authors and Affiliations

  1. Physics Department, University of Connecticut, Storrs, CT, 06269-3046, U.S.A.

    Tomomi Ishikawa

  2. RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY, 11973, U.S.A.

    Tomomi Ishikawa, Yasumichi Aoki & Taku Izubuchi

  3. School of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, U.K.

    Jonathan M. Flynn

  4. Physics Department, Brookhaven National Laboratory, Upton, NY, 11973, U.S.A.

    Taku Izubuchi

  5. Physics Department, Columbia University, New York, NY, 10027, U.S.A.

    Oleg Loktik

Authors
  1. Tomomi Ishikawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yasumichi Aoki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jonathan M. Flynn
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Taku Izubuchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Oleg Loktik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomomi Ishikawa.

Additional information

ArXiv ePrint: 1101.1072

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ishikawa, T., Aoki, Y., Flynn, J.M. et al. One-loop operator matching in the static heavy and domain-wall light quark system with O(a) improvement. J. High Energ. Phys. 2011, 40 (2011). https://doi.org/10.1007/JHEP05(2011)040

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP05(2011)040

Keywords

Search

Navigation