$B$- and $D$-meson decay constants from three-flavor lattice QCD

$B$ - and $D$ -meson decay constants from three-flavor lattice QCD

A. Bazavov, C. Bernard, C. M. Bouchard, C. DeTar, M. Di Pierro, A. X. El-Khadra, R. T. Evans, E. D. Freeland, E. Gámiz, Steven Gottlieb, U. M. Heller, J. E. Hetrick, R. Jain, A. S. Kronfeld, J. Laiho, L. Levkova, P. B. Mackenzie, E. T. Neil, M. B. Oktay, J. N. Simone, R. Sugar, D. Toussaint, and R. S. Van de Water (Fermilab Lattice and MILC Collaborations)

Phys. Rev. D 85, 114506 – Published 8 June 2012

Abstract

We calculate the leptonic decay constants of $B_{(s)}$ and $D_{(s)}$ mesons in lattice QCD using staggered light quarks and Fermilab bottom and charm quarks. We compute the heavy-light-meson correlation functions on the MILC Asqtad-improved staggered gauge configurations, which include the effects of three light dynamical sea quarks. We simulate with several values of the light valence- and sea-quark masses (down to $\sim m_{s} / 10$ ) and at three lattice spacings ( $a \approx 0.15$ , 0.12, and 0.09 fm) and extrapolate to the physical up and down quark masses and the continuum using expressions derived in heavy-light-meson staggered chiral perturbation theory. We renormalize the heavy-light axial current using a mostly nonperturbative method such that only a small correction to unity must be computed in lattice perturbation theory, and higher-order terms are expected to be small. We use the two finer lattice spacings for our central analysis, and we use the third to help estimate discretization errors. We obtain $f_{B^{+}} = 196.9 (9.1) MeV$ , $f_{B_{s}} = 242.0 (10.0) MeV$ , $f_{D^{+}} = 218.9 (11.3) MeV$ , $f_{D_{s}} = 260.1 (10.8) MeV$ , and the $S U (3)$ flavor-breaking ratios $f_{B_{s}} / f_{B} = 1.229 (26)$ and $f_{D_{s}} / f_{D} = 1.188 (25)$ , where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.

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Received 18 January 2012

DOI:https://doi.org/10.1103/PhysRevD.85.114506

Authors & Affiliations

A. Bazavov¹, C. Bernard², C. M. Bouchard^3,4,5, C. DeTar⁶, M. Di Pierro⁷, A. X. El-Khadra³, R. T. Evans³, E. D. Freeland^3,8, E. Gámiz^4,9, Steven Gottlieb¹⁰, U. M. Heller¹¹, J. E. Hetrick¹², R. Jain³, A. S. Kronfeld⁴, J. Laiho¹³, L. Levkova⁶, P. B. Mackenzie⁴, E. T. Neil⁴, M. B. Oktay⁶, J. N. Simone⁴, R. Sugar¹⁴, D. Toussaint¹⁵, and R. S. Van de Water^1,* (Fermilab Lattice and MILC Collaborations)

¹Physics Department, Brookhaven National Laboratory, Upton, New York, USA
²Department of Physics, Washington University, St. Louis, Missouri, USA
³Physics Department, University of Illinois, Urbana, Illinois, USA
⁴Fermi National Accelerator Laboratory, Batavia, Illinois, USA
⁵Department of Physics, The Ohio State University, Columbus, Ohio, USA
⁶Physics Department, University of Utah, Salt Lake City, Utah, USA
⁷School of Computing, DePaul University, Chicago, Illinois, USA
⁸Department of Physics, Benedictine University, Lisle, Illinois, 60532, USA
⁹CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain
¹⁰Department of Physics, Indiana University, Bloomington, Indiana, USA
¹¹American Physical Society, Ridge, New York, USA
¹²Physics Department, University of the Pacific, Stockton, California, USA
¹³SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
¹⁴Department of Physics, University of California, Santa Barbara, California, USA
¹⁵Department of Physics, University of Arizona, Tucson, Arizona, USA

^*ruthv@bnl.gov

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Vol. 85, Iss. 11 — 1 June 2012

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