Abstract
We present a lattice QCD determination of the b quark mass and of the B and B s decay constants, performed with N f = 2 twisted mass Wilson fermions, by simulating at four values of the lattice spacing. In order to study the b quark on the lattice, two methods are adopted in the present work, respectively based on suitable ratios with exactly known static limit and on the interpolation between relativistic data, evaluated in the charm mass region, and the static point, obtained by simulating the HQET on the lattice. The two methods provide results in good agreement. For the b quark mass in the \( \overline {\text{MS}} \) scheme and for the decay constants we obtain \( {\overline m_b}\left( {{{\overline m }_b}} \right) \) = 4.29(14) GeV, f B = 195(12) MeV, f Bs = 232(10) MeV and f Bs /f B = 1.19(5). As a byproduct of the analysis we also obtain the results for the f D and f Ds decay constants: f D = 212(8) MeV, f Ds = 248(6) MeV and f Ds /f D = 1.17(5).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
UTfit collaboration, http://www.utfit.org.
UTfit collaboration, M. Bona et al., An improved standard model prediction of BR(B → τν) and its implications for new physics, Phys. Lett. B 687 (2010) 61 [arXiv:0908.3470] [INSPIRE].
C. Aubin, Lattice studies of hadrons with heavy flavors, PoS(LAT2009)007 [arXiv:0909.2686] [INSPIRE].
ETM collaboration, B. Blossier et al., A Proposal for B-physics on current lattices, JHEP 04 (2010) 049 [arXiv:0909.3187] [INSPIRE].
ETM collaboration, B. Blossier et al., f (B) and f (B)(s) with maximally twisted Wilson fermions, PoS(LAT2009)151 [arXiv:0911.3757] [INSPIRE].
C. Allton, C.T. Sachrajda, V. Lubicz, L. Maiani and G. Martinelli, A lattice computation of the decay constant of the B meson, Nucl. Phys. B 349 (1991) 598 [INSPIRE].
ETM collaboration, M. Constantinou et al., Non-perturbative renormalization of quark bilinear operators with N f = 2 (tmQCD) Wilson fermions and the tree-level improved gauge action, JHEP 08 (2010) 068 [arXiv:1004.1115] [INSPIRE].
ETM collaboration, B. Blossier et al., Pseudoscalar decay constants of kaon and D-mesons from N f = 2 twisted mass lattice QCD, JHEP 07 (2009) 043 [arXiv:0904.0954] [INSPIRE].
P. Weisz, Continuum limit improved lattice action for pure Yang-Mills theory. 1, Nucl. Phys. B 212 (1983) 1 [INSPIRE].
Alpha collaboration, R. Frezzotti et al., Lattice QCD with a chirally twisted mass term, JHEP 08 (2001) 058 [hep-lat/0101001] [INSPIRE].
ETM collaboration, R. Baron et al., Light meson physics from maximally twisted mass lattice QCD, JHEP 08 (2010) 097 [arXiv:0911.5061] [INSPIRE].
ETM collaboration, P. Boucaud et al., Dynamical twisted mass fermions with light quarks, Phys. Lett. B 650 (2007) 304 [hep-lat/0701012] [INSPIRE].
ETM collaboration, P. Boucaud et al., Dynamical twisted mass fermions with light quarks: simulation and analysis details, Comput. Phys. Commun. 179 (2008) 695 [arXiv:0803.0224] [INSPIRE].
ETM collaboration, C. Urbach, Lattice QCD with two light Wilson quarks and maximally twisted mass, PoS(LATTICE 2007)022 [arXiv:0710.1517] [INSPIRE].
ETM collaboration, P. Dimopoulos et al., Scaling and chiral extrapolation of pion mass and decay constant with maximally twisted mass QCD, PoS(LATTICE 2008)103 [arXiv:0810.2873] [INSPIRE].
R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].
R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. II. Four-quark operators, JHEP 10 (2004) 070 [hep-lat/0407002] [INSPIRE].
ETM collaboration, B. Blossier et al., Average up/down, strange and charm quark masses with N f = 2 twisted mass lattice QCD, Phys. Rev. D 82 (2010) 114513 [arXiv:1010.3659] [INSPIRE].
K. Chetyrkin, Quark mass anomalous dimension to O \( \left( {\alpha_s^4} \right) \), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [INSPIRE].
J. Vermaseren, S. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett. B 405 (1997) 327 [hep-ph/9703284] [INSPIRE].
K. Chetyrkin and A. Retey, Renormalization and running of quark mass and field in the regularization invariant and MS-bar schemes at three loops and four loops, Nucl. Phys. B 583 (2000) 3 [hep-ph/9910332] [INSPIRE].
N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Three loop relation of quark (modified) MS and pole masses, Z. Phys. C 48 (1990) 673 [INSPIRE].
D.J. Broadhurst, N. Gray and K. Schilcher, Gauge invariant on-shell Z(2) in QED, QCD and the effective field theory of a static quark, Z. Phys. C 52 (1991) 111 [INSPIRE].
K. Chetyrkin and M. Steinhauser, Short distance mass of a heavy quark at order \( \alpha_s^3 \), Phys. Rev. Lett. 83 (1999) 4001 [hep-ph/9907509] [INSPIRE].
K. Melnikov and T.v. Ritbergen, The three loop relation between the MS-bar and the pole quark masses, Phys. Lett. B 482 (2000) 99 [hep-ph/9912391] [INSPIRE].
K. Chetyrkin and A. Grozin, Three loop anomalous dimension of the heavy light quark current in HQET, Nucl. Phys. B 666 (2003) 289 [hep-ph/0303113] [INSPIRE].
J. Goity, Chiral perturbation theory for SU(3) breaking in heavy meson systems, Phys. Rev. D 46 (1992) 3929 [hep-ph/9206230] [INSPIRE].
B. Grinstein, E.E. Jenkins, A.V. Manohar, M.J. Savage and M.B. Wise, Chiral perturbation theory for f D(s) /f D and B B(s) /B B , Nucl. Phys. B 380 (1992) 369 [hep-ph/9204207] [INSPIRE].
S.R. Sharpe and Y. Zhang, Quenched chiral perturbation theory for heavy-light mesons, Phys. Rev. D 53 (1996) 5125 [hep-lat/9510037] [INSPIRE].
Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].
H. Ohki, H. Matsufuru and T. Onogi, Determination of B*Bπ coupling in unquenched QCD, Phys. Rev. D 77 (2008) 094509 [arXiv:0802.1563] [INSPIRE].
D. Becirevic, B. Blossier, E. Chang and B. Haas, g(B*Bπ)-coupling in the static heavy quark limit, Phys. Lett. B 679 (2009) 231 [arXiv:0905.3355] [INSPIRE].
ETM collaboration, K. Jansen et al., The static-light meson spectrum from twisted mass lattice QCD, JHEP 12 (2008) 058 [arXiv:0810.1843] [INSPIRE].
ETM collaboration, C. Michael et al., The continuum limit of the static-light meson spectrum, JHEP 08 (2010) 009 [arXiv:1004.4235] [INSPIRE].
M. Della Morte, A. Shindler and R. Sommer, On lattice actions for static quarks, JHEP 08 (2005) 051 [hep-lat/0506008] [INSPIRE].
A. Hasenfratz and F. Knechtli, Flavor symmetry and the static potential with hypercubic blocking, Phys. Rev. D 64 (2001) 034504 [hep-lat/0103029] [INSPIRE].
ALPHA collaboration, M. Della Morte et al., Lattice HQET with exponentially improved statistical precision, Phys. Lett. B 581 (2004) 93 [Erratum ibid. B 612 (2005) 313-314] [hep-lat/0307021] [INSPIRE].
B. Blossier, Lattice renormalisation of O(a) improved heavy-light operators: an addendum, Phys. Rev. D 84 (2011) 097501 [arXiv:1106.2132] [INSPIRE].
HPQCD collaboration, E. Gamiz et al., Neutral B meson mixing in unquenched lattice QCD, Phys. Rev. D 80 (2009) 014503 [arXiv:0902.1815] [INSPIRE].
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] [INSPIRE].
R. Baron et al., Light hadrons from lattice QCD with light (u, d), strange and charm dynamical quarks, JHEP 06 (2010) 111 [arXiv:1004.5284] [INSPIRE].
ETM collaboration, R. Baron et al., Computing K and D meson masses with N f = 2 + 1 + 1 twisted mass lattice QCD, Comput. Phys. Commun. 182 (2011) 299 [arXiv:1005.2042] [INSPIRE].
M. Gremm, A. Kapustin, Z. Ligeti and M.B. Wise, Implications of the B → X lepton anti-lepton-neutrino lepton spectrum for heavy quark theory, Phys. Rev. Lett. 77 (1996) 20 [hep-ph/9603314] [INSPIRE].
C. Davies, Standard Model flavor physics on the lattice, plenary talk at the XXIX International Symposium on Lattice Field Theory (LATTICE2011), July 10-16, Squaw Valley, Lake Tahoe, California, U.S.A. (2011), http://tsailab.chem.pacific.edu/lat11/plenary/davies.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1107.1441
Heisenberg Fellow. (A. Shindler)
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Dimopoulos, P., Frezzotti, R., Herdoiza, G. et al. Lattice QCD determination of m b , f B and f Bs with twisted mass Wilson fermions. J. High Energ. Phys. 2012, 46 (2012). https://doi.org/10.1007/JHEP01(2012)046
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2012)046