Journal of High Energy Physics

, 2010:39 | Cite as

HQET at order 1/m: III. Decay constants in the quenched approximation

  • Alpha Collaboration
  • Benoît Blossier
  • Michele Della Morte
  • Nicolas Garron
  • Georg von HippelEmail author
  • Tereza Mendes
  • Hubert Simma
  • Rainer Sommer
Open Access


We report on the computation of the Bs meson decay constant in Heavy Quark Effective Theory on the lattice. The next to leading order corrections in the HQET expansion are included non-perturbatively. We estimate higher order contributions to be very small. The results are extrapolated to the continuum limit, the main systematic error affecting the computation is therefore the quenched approximation used here. The Generalized Eigenvalue Problem and the use of all-to-all propagators are important technical ingredients of our approach that allow to keep statistical and systematic errors under control. We also report on the decay constant \( {f_{{\text{B}}_{s}^{\prime}}} \) of the first radially excited state in the Bs sector, computed in the static limit


Lattice QCD B-Physics Heavy Quark Physics 


  1. [1]
    M. Antonelli et al., Flavor Physics in the Quark Sector, Phys. Rept. 494 (2010) 197 [arXiv:0907.5386] [SPIRES].CrossRefADSGoogle Scholar
  2. [2]
    M. Misiak and J. Urban, QCD corrections to FCNC decays mediated by Z-penguins and W-boxes, Phys. Lett. B 451 (1999) 161 [hep-ph/9901278] [SPIRES].ADSGoogle Scholar
  3. [3]
    G. Buchalla and A.J. Buras, The rare decays \( K \to \pi \nu \bar{\nu } \) , \( B \to X\nu \bar{\nu } \) and B + : An update, Nucl. Phys. B 548 (1999) 309 [hep-ph/9901288] [SPIRES].CrossRefADSGoogle Scholar
  4. [4]
    A.J. Buras, Relations betweenM(s, d) and \( B\left( {s,d} \right) \to \mu \bar{\mu } \) in models with minimal flavor violation, Phys. Lett. B 566 (2003) 115 [hep-ph/0303060] [SPIRES].ADSGoogle Scholar
  5. [5]
    D0 collaboration, V.M. Abazov et al., Search for the rare decay B s 0μ + μ , Phys. Lett. B 693 (2010) 539 [arXiv:1006.3469] [SPIRES].ADSGoogle Scholar
  6. [6]
    K.S. Babu and C.F. Kolda, Higgs mediated B 0μ + μ in minimal supersymmetry, Phys. Rev. Lett. 84 (2000) 228 [hep-ph/9909476] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    LHCb collaboration, P. Perret et al., Prospects for New Physics in CP-violation and Rare Decays at LHCb, arXiv:0901.2856 [SPIRES].
  8. [8]
    M. Della Morte, Standard Model parameters and heavy quarks on the lattice, PoS(LATTICE 2007)008 [arXiv:0711.3160] [SPIRES].
  9. [9]
    E. Gamiz, Heavy avour phenomenology from lattice QCD, PoS(LATTICE 2008)014 [arXiv:0811.4146] [SPIRES].
  10. [10]
    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
  11. [11]
    E. Eichten and B.R. Hill, Static effective field theory: 1/m corrections, Phys. Lett. B 243 (1990) 427 [SPIRES].ADSGoogle Scholar
  12. [12]
    ALPHA collaboration, B. Blossier, M. della Morte, N. Garron and R. Sommer, HQET at order 1/m: I. Non-perturbative parameters in the quenched approximation, JHEP 06 (2010) 002 [arXiv:1001.4783] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    ALPHA collaboration, B. Blossier, M. Della Morte, N. Garron and R. Sommer, Heavy-light decay constant at the 1/m order of HQET, PoS(LATTICE 2007)245 [arXiv:0710.1553] [SPIRES].
  14. [14]
    ALPHA collaboration, 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
  15. [15]
    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
  16. [16]
    C. Michael and I. Teasdale, Extracting glueball masses from lattice QCD, Nucl. Phys. B 215 (1983) 433 [SPIRES].CrossRefADSGoogle Scholar
  17. [17]
    M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [SPIRES].CrossRefADSGoogle Scholar
  18. [18]
    ALPHA collaboration, 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
  19. [19]
    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
  20. [20]
    A. Hasenfratz, R. Hoffmann and F. Knechtli, The static potential with hypercubic blocking, Nucl. Phys. Proc. Suppl. 106 (2002) 418 [hep-lat/0110168] [SPIRES].CrossRefADSGoogle Scholar
  21. [21]
    ALPHA collaboration, M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005) 051 [hep-lat/0506008] [SPIRES].CrossRefGoogle Scholar
  22. [22]
    B. Sheikholeslami and R. Wohlert, Improved Continuum Limit Lattice Action for QCD with Wilson Fermions, Nucl. Phys. B 259 (1985) 572 [SPIRES].CrossRefADSGoogle Scholar
  23. [23]
    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
  24. [24]
    TrinLat collaboration, J. Foley et al., Practical all-to-all propagators for lattice QCD, Comput. Phys. Commun. 172 (2005) 145 [hep-lat/0505023] [SPIRES].CrossRefADSGoogle Scholar
  25. [25]
    ALPHA collaboration, B. Blossier et al., HQET at order 1/m: II. Spectroscopy in the quenched approximation, JHEP 05 (2010) 074 [arXiv:1004. 2661] [SPIRES].CrossRefADSGoogle Scholar
  26. [26]
    ALPHA collaboration, M. Guagnelli, R. Sommer and H. Wittig, Precision computation of a low-energy reference scale in quenched lattice QCD, Nucl. Phys. B 535 (1998) 389 [hep-lat/9806005] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    ALPHA collaboration, J. Garden, J. Heitger, R. Sommer and H. Wittig, Precision computation of the strange quark’s mass in quenched QCD, Nucl. Phys. B 571 (2000) 237 [hep-lat/9906013] [SPIRES].CrossRefADSGoogle Scholar
  28. [28]
    S. Güsken et al., Nonsinglet axial vector couplings of the baryon octet in Lattice QCD, Phys. Lett. B 227 (1989) 266 [SPIRES].ADSGoogle Scholar
  29. [29]
    APE collaboration, M. Albanese et al., Glueball Masses and String Tension in Lattice QCD, Phys. Lett. B 192 (1987) 163 [SPIRES].ADSGoogle Scholar
  30. [30]
    S. Basak et al., Combining Quark and Link Smearing to Improve Extended Baryon Operators, PoS( LAT2005) 076 [hep-lat/0509179] [SPIRES].
  31. [31]
    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
  32. [32]
    ALPHA collaboration, J. Heitger, A. Jüttner, R. Sommer and J. Wennekers, Non-perturbative tests of heavy quark effective theory, JHEP 11 (2004) 048 [hep-ph/0407227] [SPIRES].CrossRefADSGoogle Scholar
  33. [33]
    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
  34. [34]
    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
  35. [35]
    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
  36. [36]
    M.A. Shifman and M.B. Voloshin, On Annihilation of Mesons Built from Heavy and Light Quark and \( {\bar{B}^0} - {B^0} \) Oscillations, Sov. J. Nucl. Phys. 45 (1987) 292 [SPIRES].Google Scholar
  37. [37]
    H.D. Politzer and M.B. Wise, Leading Logarithms of Heavy Quark Masses in Processes with Light and Heavy Quarks, Phys. Lett. B 206 (1988) 681 [SPIRES].ADSGoogle Scholar
  38. [38]
    T. Burch, C. Hagen, C.B. Lang, M. Limmer and A. Schäfer, Excitations of single-beauty hadrons, Phys. Rev. D 79 (2009) 014504 [arXiv:0809.1103] [SPIRES].ADSGoogle Scholar
  39. [39]
    V. Morénas, A. Le Yaouanc, L. Oliver, O. Pène and J.C. Raynal, Decay constants in the heavy quark limit in models à la Bakamjian and Thomas, Phys. Rev. D 58 (1998) 114019 [hep-ph/9710298] [SPIRES].ADSGoogle Scholar
  40. [40]
    D. Ebert, V.O. Galkin and R.N. Faustov, Mass spectrum of orbitally and radially excited heavy-light mesons in the relativistic quark model, Phys. Rev. D 57 (1998) 5663 [hep-ph/9712318] [SPIRES].ADSGoogle Scholar
  41. [41]
    D. Ebert, R.N. Faustov and V.O. Galkin, Decay constants of heavy-light mesons in the relativistic quark model, Mod. Phys. Lett. A 17 (2002) 803 [hep-ph/0204167] [SPIRES].ADSGoogle Scholar
  42. [42]
    A.M. Badalian, B.L.G. Bakker and Y.A. Simonov, Decay constants of the heavy-light mesons from the field correlator method, Phys. Rev. D 75 (2007) 116001 [hep-ph/0702157] [SPIRES].ADSGoogle Scholar
  43. [43]
    L. Del Debbio, H. Panagopoulos and E. Vicari, Theta dependence of SU(N) gauge theories, JHEP 08 (2002) 044 [hep-th/0204125] [SPIRES].CrossRefADSGoogle Scholar
  44. [44]
    L. Del Debbio, G.M. Manca and E. Vicari, Critical slowing down of topological modes, Phys. Lett. B 594 (2004) 315 [hep-lat/0403001] [SPIRES].ADSGoogle Scholar
  45. [45]
    S. Schaefer, R. Sommer and F. Virotta, Investigating the critical slowing down of QCD simulations, PoS(LAT2009)032 [arXiv:0910.1465] [SPIRES].

Copyright information

© The Author(s) 2010

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
  • Georg von Hippel
    • 2
    • 5
    Email author
  • Tereza Mendes
    • 5
    • 6
  • Hubert Simma
    • 5
  • Rainer Sommer
    • 5
  1. 1.Laboratoire de Physique ThéoriqueCNRS et Université Paris-Sud XIOrsay CedexFrance
  2. 2.Institut für KernphysikJohannes-Gutenberg-Universität MainzMainzGermany
  3. 3.Departamento de Física Teórica and Instituto de Física Teórica IFT - UAM/CSICUniversidad Autónoma de MadridMadridSpain
  4. 4.SUPA, School of Physics and AstronomyUniversity of EdinburghEdinburghU.K.
  5. 5.NIC, DESYZeuthenGermany
  6. 6.IFSC, University of São PauloSão Carlos SPBrazil

Personalised recommendations