Leptonic decay-constant ratio $f_K/f_\pi$ from clover-improved $N_f=2+1$ QCD

TL;DR

This paper presents a lattice-QCD calculation of the ratio of decay constants $f_K/f_$ using $N_f=2+1$ dynamical fermions, providing precise systematic uncertainty analysis and implications for CKM matrix elements.

Contribution

The study introduces a high-precision lattice-QCD computation of $f_K/f_$ with systematic error quantification, including physical point simulations and chiral perturbation theory input.

Findings

Calculated $f_K/f_$ ratio with controlled uncertainties.

Quoted $f_{K^\u00b1}/f_{^}$ ratio using chiral perturbation theory.

Estimated CKM matrix element $V_{us}$ from decay constants and nuclear beta decays.

Abstract

The leptonic decay-constant ratio $f_K/f_\pi$ is calculated from lattice-QCD simulations using $N_f=2+1$ dynamical fermion flavors in the clover-improved formulation and 2-HEX smearing. The simulations were performed for a range of mass-degenerate light quarks including the physical point and at various lattice couplings and volumes, allowing to quantify all relevant sources of systematic uncertainties for our final number of the decay-constant ratio. Utilizing input from chiral perturbation theory, we also quote the charged decay-constant ratio $f_{K^\pm}/f_{\pi^\pm}$. With further input from super-allowed nuclear $\beta$-decays, eventually we obtain an estimate for the CKM-matrix element $V_{\rm us}$.