Leptonic decay-constant ratio f_{K^+}/f_{pi^+} from lattice QCD with physical light quarks

TL;DR

This paper presents a highly precise lattice QCD calculation of the ratio of leptonic decay constants f_{K^+}/f_{pi^+}, enabling improved determination of CKM matrix element ratios and constraints on new physics.

Contribution

First lattice-QCD calculation of f_{K^+}/f_{pi^+} at the physical point using four-flavor dynamical quarks, achieving unprecedented precision.

Findings

f_{K^+}/f_{pi^+} = 1.1947(26)(37)

|V_{us}|/|V_{ud}| = 0.2309(9)(4)

Most precise lattice determination to date.

Abstract

A calculation of the ratio of leptonic decay constants f_{K^+}/f_{\pi^+} makes possible a precise determination of the ratio of 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_{\pi^+} 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_{\pi^+} = 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_{\pi^+} from lattice-QCD simulations at the physical point. Our result is the most precise lattice-QCD determination of f_{K^+}/f_{\pi^+}, 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.