HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation

  • ALPHA Collaboration
  • Benoît Blossier
  • Michele Della Morte
  • Nicolas GarronEmail author
  • Rainer Sommer
Open Access


We determine non-perturbatively the parameters of the lattice HQET Lagrangian and those of the time component of the heavy-light axial-vector current in the quenched approximation. The HQET expansion includes terms of order 1/m b. Our results allow to compute, for example, the heavy-light spectrum and B-meson decay constants in the static approximation and to order 1/m b in HQET. The determination of the parameters is separated into universal and non-universal parts. The universal results can be used to determine the parameters for various discretizations. The computation reported in this paper uses the plaquette gauge action and the “HYP1/2” action for the b-quark described by HQET. The parameters of the current also depend on the light-quark action, for which we choose non-perturbatively O(a)-improved Wilson fermions.


Lattice QCD B-Physics Heavy Quark Physics 


  1. [1]
    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
  2. [2]
    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
  3. [3]
    H. Georgi, An effective field theory for heavy quarks at low energies, Phys. Lett. B 240 (1990) 447 [SPIRES].ADSGoogle Scholar
  4. [4]
    E. Eichten and B.R. Hill, Static effective field theory: 1/m corrections, Phys. Lett. B 243 (1990) 427 [SPIRES].ADSGoogle Scholar
  5. [5]
    B. Grinstein, The static quark effective theory, Nucl. Phys. B 339 (1990) 253 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  6. [6]
    ALPHA collaboration, J. Heitger and J. Wennekers, Effective heavy-light meson energies in small-volume quenched QCD, JHEP 02 (2004) 064 [hep-lat/0312016] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    M. Della Morte, P. Fritzsch, J. Heitger and R. Sommer, Non-perturbative quark mass dependence in the heavy-light sector of two-flavour QCD, PoS(LATTICE 2008)226 [arXiv:0810.3166] [SPIRES].
  8. [8]
    M. Antonelli et al., Flavor Physics in the Quark Sector, arXiv:0907.5386 [SPIRES].
  9. [9]
    ALPHA collaboration, M. Kurth and R. Sommer, Heavy Quark Effective Theory at one-loop order: An explicit example, Nucl. Phys. B 623 (2002) 271 [hep-lat/0108018] [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    J. Heitger and A. Juttner, Lattice cutoff effects for FDs with improved Wilson fermions - a final lesson from the quenched case, JHEP 05 (2009) 101 [arXiv:0812.2200] [SPIRES].ADSGoogle Scholar
  11. [11]
    A.S. Kronfeld, Heavy quarks and lattice QCD, Nucl. Phys. Proc. Suppl. 129 (2004) 46 [hep-lat/0310063] [SPIRES].CrossRefADSGoogle Scholar
  12. [12]
    N. Garron, Status of heavy quark physics from the lattice, Nucl. Phys. Proc. Suppl. 174 (2007) 193 [hep-ph/0612155] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    M. Della Morte, Standard Model parameters and heavy quarks on the lattice, PoS(LATTICE 2007)008 [arXiv:0711.3160] [SPIRES].
  14. [14]
    E. Gamiz, Heavy flavour phenomenology from lattice QCD, PoS(LATTICE 2008)014 [arXiv:0811.4146] [SPIRES].
  15. [15]
    C. Aubin, Lattice studies of hadrons with heavy flavors, arXiv:0909.2686 [SPIRES].
  16. [16]
    ALPHA collaboration, J. Heitger and R. Sommer, Non-perturbative heavy quark effective theory, JHEP 02 (2004) 022 [hep-lat/0310035] [SPIRES].CrossRefADSGoogle Scholar
  17. [17]
    M. Della Morte, N. Garron, M. Papinutto and R. Sommer, Heavy quark effective theory computation of the mass of the bottom quark, JHEP 01 (2007) 007 [hep-ph/0609294] [SPIRES].CrossRefADSGoogle Scholar
  18. [18]
    M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005) 051 [hep-lat/0506008] [SPIRES].CrossRefGoogle Scholar
  19. [19]
    ALPHA collaboration, M. Kurth and R. Sommer, Renormalization and O(a)-improvement of the static axial current, Nucl. Phys. B 597 (2001) 488 [hep-lat/0007002] [SPIRES].CrossRefADSGoogle Scholar
  20. [20]
    M. Bochicchio, L. Maiani, G. Martinelli, G.C. Rossi and M. Testa, Chiral Symmetry on the Lattice with Wilson Fermions, Nucl. Phys. B 262 (1985) 331 [SPIRES].CrossRefADSGoogle Scholar
  21. [21]
    M. Lüscher, S. Sint, R. Sommer and H. Wittig, Non-perturbative determination of the axial current normalization constant in O(a) improved lattice QCD, Nucl. Phys. B 491 (1997) 344 [hep-lat/9611015] [SPIRES].CrossRefADSGoogle Scholar
  22. [22]
    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] [SPIRES].Google Scholar
  23. [23]
    ALPHA collaboration, J. Heitger, M. Kurth and R. Sommer, Non-perturbative renormalization of the static axial current in quenched QCD, Nucl. Phys. B 669 (2003) 173 [hep-lat/0302019] [SPIRES].CrossRefADSGoogle Scholar
  24. [24]
    ALPHA collaboration, J. Heitger, A. Juttner, R. Sommer and J. Wennekers, Non-perturbative tests of heavy quark effective theory, JHEP 11 (2004) 048 [hep-ph/0407227] [SPIRES].CrossRefADSGoogle Scholar
  25. [25]
    K.G. Chetyrkin and A.G. Grozin, Three-loop anomalous dimension of the heavy-light quark current in HQET, Nucl. Phys. B 666 (2003) 289 [hep-ph/0303113] [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    S. Bekavac et al., Matching QCD and HQET heavy-light currents at three loops, Nucl. Phys. B 833 (2010) 46 [arXiv:0911.3356] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    M. Della Morte, P. Fritzsch and J. Heitger, Non-perturbative renormalization of the static axial current in two-flavour QCD, JHEP 02 (2007) 079 [hep-lat/0611036] [SPIRES].Google Scholar
  28. [28]
    M. Della Morte et al., Heavy-strange meson decay constants in the continuum limit of quenched QCD, JHEP 02 (2008) 078 [arXiv:0710.2201] [SPIRES].Google Scholar
  29. [29]
    M. Lüscher, P. Weisz and U. Wolff, A Numerical method to compute the running coupling in asymptotically free theories, Nucl. Phys. B 359 (1991) 221 [SPIRES].CrossRefADSGoogle Scholar
  30. [30]
    A. Grimbach, D. Guazzini, F. Knechtli and F. Palombi, O(a) improvement of the HYP static axial and vector currents at one-loop order of perturbation theory, JHEP 03 (2008) 039 [arXiv:0802.0862] [SPIRES].Google Scholar
  31. [31]
    M. Lüscher, S. Sint, R. Sommer, P. Weisz and U. Wolff, Non-perturbative O(a) improvement of lattice QCD, Nucl. Phys. B 491 (1997) 323 [hep-lat/9609035] [SPIRES].CrossRefADSGoogle Scholar
  32. [32]
    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
  33. [33]
    B. Blossier et al., Spectroscopy and Decay Constants from Nonperturbative HQET at Order 1/m, arXiv:0911.1568 [SPIRES].
  34. [34]
    M. Lüscher, R. Narayanan, P. Weisz and U. Wolff, The Schrödinger functional: A Renormalizable probe for nonAbelian gauge theories, Nucl. Phys. B 384 (1992) 168 [hep-lat/9207009] [SPIRES].CrossRefADSGoogle Scholar
  35. [35]
    S. Sint, On the Schrödinger functional in QCD, Nucl. Phys. B 421 (1994) 135 [hep-lat/9312079] [SPIRES].CrossRefADSGoogle Scholar
  36. [36]
    Alpha collaboration, G. de Divitiis et al., Universality and the approach to the continuum limit in lattice gauge theory, Nucl. Phys. B 437 (1995) 447 [hep-lat/9411017] [SPIRES].CrossRefADSGoogle Scholar
  37. [37]
    ALPHA collaboration, A. Bode, P. Weisz and U. Wolff, Two loop computation of the Schroedinger functional in lattice QCD, Nucl. Phys. B 576 (2000) 517 [hep-lat/9911018] [SPIRES].CrossRefADSGoogle Scholar
  38. [38]
    ALPHA collaboration, M. Della Morte et al., Computation of the strong coupling in QCD with two dynamical flavours, Nucl. Phys. B 713 (2005) 378 [hep-lat/0411025] [SPIRES].ADSGoogle Scholar
  39. [39]
    P. Hasenfratz, The theoretical background and properties of perfect actions, hep-lat/9803027 [SPIRES].
  40. [40]
    S. Sint and P. Weisz, Further results on O(a) improved lattice QCD to one-loop order of perturbation theory, Nucl. Phys. B 502 (1997) 251 [hep-lat/9704001] [SPIRES].CrossRefADSGoogle Scholar
  41. [41]
    M. Lüscher, S. Sint, R. Sommer and P. Weisz, Chiral symmetry and O(a) improvement in lattice QCD, Nucl. Phys. B 478 (1996) 365 [hep-lat/9605038] [SPIRES].CrossRefADSGoogle Scholar

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

Authors and Affiliations

  • ALPHA Collaboration
  • Benoît Blossier
    • 1
  • Michele Della Morte
    • 2
  • Nicolas Garron
    • 3
    • 4
    Email author
  • Rainer Sommer
    • 5
  1. 1.Laboratoire de Physique ThéoriqueUniversité Paris XIOrsay CedexFrance
  2. 2.Institut für KernphysikUniversity of MainzMainzGermany
  3. 3.Departamento de Física Teórica and Instituto de Física Teórica IFT-UAM/CSICUniversidad Autónoma de MadridMadridSpain
  4. 4.School of Physics and AstronomyUniversity of EdinburghEdinburghU.K.
  5. 5.NIC, DESYZeuthenGermany

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