### 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≈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.

Original language | English (US) |
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Article number | 172003 |

Journal | Physical review letters |

Volume | 110 |

Issue number | 17 |

DOIs | |

State | Published - Apr 26 2013 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

_{K}

^{+}/f

_{π}

^{+}from lattice QCD with physical light quarks.

*Physical review letters*,

*110*(17), [172003]. https://doi.org/10.1103/PhysRevLett.110.172003