### Abstract

We compute the leptonic decay constants fD+, fDs, and fK+ and the quark-mass ratios mc/ms and ms/ml in unquenched lattice QCD using the experimentally determined value of fπ+ for normalization. We use the MILC highly improved staggered quark ensembles with four dynamical quark flavors - up, down, strange, and charm - and with both physical and unphysical values of the light sea-quark masses. The use of physical pions removes the need for a chiral extrapolation, thereby eliminating a significant source of uncertainty in previous calculations. Four different lattice spacings ranging from a≈0.06 to 0.15 fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are fD+=212.6(0.4)(+1.0-1.2)MeV, fDs=249.0(0.3)(+1.1-1.5)MeV, and fDs/fD+=1.1712(10)(+29-32), where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately 2-4 times smaller than those of the most precise previous lattice calculations. We also obtain fK+/fπ+=1.1956(10)(+26-18), updating our previous result, and determine the quark-mass ratios ms/ml=27.35(5)(+10-7) and mc/ms=11.747(19)(+59-43). When combined with experimental measurements of the decay rates, our results lead to precise determinations of the Cabibbo-Kobayashi-Maskawa matrix elements |Vus|=0.22487(51)(29)(20)(5), |Vcd|=0.217(1)(5)(1) and |Vcs|=1.010(5)(18)(6), where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of |Vus|, the uncertainty in |Vud|, respectively.

Original language | English (US) |
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Article number | 074509 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 90 |

Issue number | 7 |

DOIs | |

State | Published - Oct 30 2014 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*90*(7), [074509]. https://doi.org/10.1103/PhysRevD.90.074509