$B\ensuremath{\rightarrow}D\ensuremath{\ell}\ensuremath{\nu}$ form factors at nonzero recoil and $|{V}_{cb}|$ from $2+1$-flavor lattice QCD

$B \to D ℓ ν$ form factors at nonzero recoil and $| V_{c b} |$ from $2 + 1$ -flavor lattice QCD

Jon A. Bailey, A. Bazavov, C. Bernard, C. M. Bouchard, C. DeTar, Daping Du, A. X. El-Khadra, J. Foley, E. D. Freeland, E. Gámiz, Steven Gottlieb, U. M. Heller, J. Komijani, A. S. Kronfeld, J. Laiho, L. Levkova, P. B. Mackenzie, E. T. Neil, Si-Wei Qiu, J. Simone, R. Sugar, D. Toussaint, R. S. Van de Water, and Ran Zhou (Fermilab Lattice and MILC Collaborations)

Phys. Rev. D 92, 034506 – Published 10 August 2015

Abstract

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay $\bar{B} \to D ℓ \bar{ν}$ at nonzero recoil. We carry out numerical simulations on 14 ensembles of gauge-field configurations generated with $2 + 1$ flavors of asqtad-improved staggered sea quarks. The ensembles encompass a wide range of lattice spacings (approximately 0.045 to 0.12 fm) and ratios of light (up and down) to strange sea-quark masses ranging from 0.05 to 0.4. For the $b$ and $c$ valence quarks we use improved Wilson fermions with the Fermilab interpretation, while for the light valence quarks we use asqtad-improved staggered fermions. We extrapolate our results to the physical point using rooted staggered heavy-light meson chiral perturbation theory. We then parametrize the form factors and extend them to the full kinematic range using model-independent functions based on analyticity and unitarity. We present our final results for $f_{+} (q^{2})$ and $f_{0} (q^{2})$ , including statistical and systematic errors, as coefficients of a series in the variable $z$ and the covariance matrix between these coefficients. We then fit the lattice form-factor data jointly with the experimentally measured differential decay rate from BABAR to determine the CKM matrix element, $| V_{c b} | = (39.6 \pm 1. 7_{QCD + \exp} \pm 0. 2_{QED}) \times 10^{- 3}$ . As a byproduct of the joint fit we obtain the form factors with improved precision at large recoil. Finally, we use them to update our calculation of the ratio $R (D)$ in the Standard Model, which yields $R (D) = 0.299 (11)$ .

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Received 3 April 2015

DOI:https://doi.org/10.1103/PhysRevD.92.034506

Authors & Affiliations

Jon A. Bailey¹, A. Bazavov^2,*, C. Bernard³, C. M. Bouchard^4,5, C. DeTar^6,†, Daping Du^7,8, A. X. El-Khadra⁷, J. Foley⁶, E. D. Freeland⁹, E. Gámiz¹⁰, Steven Gottlieb¹¹, U. M. Heller¹², J. Komijani³, A. S. Kronfeld^13,14, J. Laiho⁸, L. Levkova⁶, P. B. Mackenzie¹³, E. T. Neil^15,16, Si-Wei Qiu^6,‡, J. Simone¹³, R. Sugar¹⁷, D. Toussaint¹⁸, R. S. Van de Water¹³, and Ran Zhou^11,13 (Fermilab Lattice and MILC Collaborations)

¹Department of Physics and Astronomy, Seoul National University, Seoul 151-742, South Korea
²Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
³Department of Physics, Washington University, St. Louis, Missouri 63130, USA
⁴Physics Department, College of William and Mary, Williamsburg, Virginia 23187, USA
⁵Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
⁶Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
⁷Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
⁸Department of Physics, Syracuse University, Syracuse, New York 13244, USA
⁹Liberal Arts Department, School of the Art Institute of Chicago, Chicago, Illinois 60603, USA
¹⁰CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada E-18002, Spain
¹¹Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
¹²American Physical Society, Ridge, New York 11961, USA
¹³Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
¹⁴Institute for Advanced Study, Technische Universität München, 85748 Garching, Germany
¹⁵Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
¹⁶RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA
¹⁷Department of Physics, University of California, Santa Barbara, California 93106, USA
¹⁸Department of Physics, University of Arizona, Tucson, Arizona 85721, USA

^*Present address: Department of Physics and Astronomy, University of Iowa, Iowa City, IA, USA.
^†detar@physics.utah.edu
^‡Present address: Laboratory of Biological Modeling, NIDDK, NIH, Bethesda, Maryland, USA. qiu@physics.utah.edu

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Vol. 92, Iss. 3 — 1 August 2015

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Physical Review D

covering particles, fields, gravitation, and cosmology

$B \to D ℓ ν$ form factors at nonzero recoil and $| V_{c b} |$ from $2 + 1$ -flavor lattice QCD

Phys. Rev. D 92, 034506 – Published 10 August 2015

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Physical Review D

covering particles, fields, gravitation, and cosmology

B→Dℓν form factors at nonzero recoil and |Vcb| from 2+1-flavor lattice QCD

Phys. Rev. D 92, 034506 – Published 10 August 2015

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$B \to D ℓ ν$ form factors at nonzero recoil and $| V_{c b} |$ from $2 + 1$ -flavor lattice QCD