Leptonic-Decay-Constant Ratio ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}$ from Lattice QCD with Physical Light Quarks

Leptonic-Decay-Constant Ratio $f_{K^{+}} / f_{π^{+}}$ from Lattice QCD with Physical Light Quarks

A. Bazavov, C. Bernard, C. DeTar, J. Foley, W. Freeman, Steven Gottlieb, U. M. Heller, J. E. Hetrick, J. Kim, J. Laiho, L. Levkova, M. Lightman, J. Osborn, S. Qiu, R. L. Sugar, D. Toussaint, R. S. Van de Water, and R. Zhou (MILC Collaboration)

Phys. Rev. Lett. 110, 172003 – Published 26 April 2013

Abstract

A calculation of the ratio of leptonic decay constants $f_{K^{+}} / f_{π^{+}}$ makes possible a precise determination of the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $| V_{us} | / | V_{ud} |$ in the standard model, and places a stringent constraint on the scale of new physics that would lead to deviations from unitarity in the first row of the CKM matrix. We compute $f_{K^{+}} / f_{π^{+}}$ numerically in unquenched lattice QCD using gauge-field ensembles recently generated that include four flavors of dynamical quarks: up, down, strange, and charm. We analyze data at four lattice spacings $a \approx 0.06$ , 0.09, 0.12, and 0.15 fm with simulated pion masses down to the physical value 135 MeV. We obtain $f_{K^{+}} / f_{π^{+}} = 1.1947 (26) (37)$ , where the errors are statistical and total systematic, respectively. This is our first physics result from our $N_{f} = 2 + 1 + 1$ ensembles, and the first calculation of $f_{K^{+}} / f_{π^{+}}$ from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of $f_{K^{+}} / f_{π^{+}}$ , with an error comparable to the current world average. When combined with experimental measurements of the leptonic branching fractions, it leads to a precise determination of $| V_{us} | / | V_{ud} | = 0.2309 (9) (4)$ where the errors are theoretical and experimental, respectively.

Received 30 January 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.172003

Authors & Affiliations

A. Bazavov¹, C. Bernard^2,*, C. DeTar³, J. Foley³, W. Freeman⁴, Steven Gottlieb⁵, U. M. Heller⁶, J. E. Hetrick⁷, J. Kim⁸, J. Laiho^9,10, L. Levkova^3,8, M. Lightman², J. Osborn¹¹, S. Qiu³, R. L. Sugar¹², D. Toussaint^8,†, R. S. Van de Water^13,‡, and R. Zhou⁵ (MILC Collaboration)

¹Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
²Department of Physics, Washington University, St. Louis, Missouri 63130, USA
³Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
⁴Department of Physics, The George Washington University, Washington, DC 20052, USA
⁵Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
⁶American Physical Society, One Research Road, Ridge, New York 11961, USA
⁷Physics Department, University of the Pacific, Stockton, California 95211, USA
⁸Department of Physics, University of Arizona, Tucson, Azusa 85721, USA
⁹SUPA Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland, United Kingdom
¹⁰Department of Physics, Syracuse University, Syracuse, New York 13244, USA
¹¹Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439, USA
¹²Department of Physics, University of California, Santa Barbara, California 93106, USA
¹³Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia 60510, USA