Determination of $|{V}_{us}|$ from a Lattice QCD Calculation of the $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ Semileptonic Form Factor with Physical Quark Masses

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Determination of $| V_{u s} |$ from a Lattice QCD Calculation of the $K \to π ℓ ν$ Semileptonic Form Factor with Physical Quark Masses

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, Jongjeong Kim, A. S. Kronfeld, J. Laiho, L. Levkova, P. B. Mackenzie, E. T. Neil, M. B. Oktay, Si-Wei Qiu, J. N. Simone, R. Sugar, D. Toussaint, R. S. Van de Water, and Ran Zhou (Fermilab Lattice and MILC Collaborations)

Phys. Rev. Lett. 112, 112001 – Published 17 March 2014

Abstract

We calculate the kaon semileptonic form factor $f_{+} (0)$ from lattice QCD, working, for the first time, at the physical light-quark masses. We use gauge configurations generated by the MILC Collaboration with $N_{f} = 2 + 1 + 1$ flavors of sea quarks, which incorporate the effects of dynamical charm quarks as well as those of up, down, and strange. We employ data at three lattice spacings to extrapolate to the continuum limit. Our result, $f_{+} (0) = 0.9704 (32)$ , where the error is the total statistical plus systematic uncertainty added in quadrature, is the most precise determination to date. Combining our result with the latest experimental measurements of $K$ semileptonic decays, one obtains the Cabibbo-Kobayashi-Maskawa matrix element $| V_{u s} | = 0.22290 (74) (52)$ , where the first error is from $f_{+} (0)$ and the second one is from experiment. In the first-row test of Cabibbo-Kobayashi-Maskawa unitarity, the error stemming from $| V_{u s} |$ is now comparable to that from $| V_{u d} |$ .

Received 5 December 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.112001

Authors & Affiliations

A. Bazavov^1,2, C. Bernard³, C. M. Bouchard⁴, C. DeTar⁵, Daping Du⁶, A. X. El-Khadra^6,7, J. Foley⁵, E. D. Freeland⁸, E. Gámiz^9,*, Steven Gottlieb¹⁰, U. M. Heller¹¹, Jongjeong Kim¹², A. S. Kronfeld⁷, J. Laiho^13,14, L. Levkova⁵, P. B. Mackenzie⁷, E. T. Neil^7,15,16, M. B. Oktay⁵, Si-Wei Qiu⁵, J. N. Simone⁷, R. Sugar¹⁷, D. Toussaint¹², R. S. Van de Water⁷, and Ran Zhou^10,7 (Fermilab Lattice and MILC Collaborations)

¹Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
²Department of Physics and Astronomy, University of Iowa, Iowa 52242, USA
³Department of Physics, Washington University, St. Louis, Missouri 63130, USA
⁴Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
⁵Physics Department, University of Utah, Salt Lake City, Utah 84112, USA
⁶Physics Department, University of Illinois, Urbana, Illinois 61801, USA
⁷Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
⁸Liberal Arts Department, School of the Art Institute of Chicago, Chicago, Illinois 60603, USA
⁹CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, E-18071 Granada, Spain
¹⁰Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
¹¹American Physical Society, Ridge, New York 11961, USA
¹²Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
¹³SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
¹⁴Department of Physics, Syracuse University, Syracuse, New York 13244, USA
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

^*megamiz@ugr.es

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Vol. 112, Iss. 11 — 21 March 2014

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Physical Review Letters

Determination of |Vus| from a Lattice QCD Calculation of the K→πℓν Semileptonic Form Factor with Physical Quark Masses

Phys. Rev. Lett. 112, 112001 – Published 17 March 2014

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Determination of $| V_{u s} |$ from a Lattice QCD Calculation of the $K \to π ℓ ν$ Semileptonic Form Factor with Physical Quark Masses