Kaon semileptonic decays with $N_f=2+1+1$ HISQ fermions and physical light-quark masses

TL;DR

This paper improves the precision of kaon semileptonic decay form factor calculations using HISQ fermions on $N_f=2+1+1$ configurations, analyzing finite-volume effects and implications for CKM unitarity and $ ext{V}_{us}$ tensions.

Contribution

It introduces enhanced statistical analysis, new lattice data at finer spacings, and a study of finite-volume effects, advancing the accuracy of form factor computations.

Findings

Reduced errors in $f_+^{K o \pi}(0)$ calculations.

Implications for CKM matrix unitarity.

Insights into $ ext{V}_{us}$ tension with leptonic determinations.

Abstract

We discuss the reduction of errors in the calculation of the form factor $f_+^{K \pi}(0)$ with HISQ fermions on the $N_f=2+1+1$ MILC configurations from increased statistics on some key ensembles, new data on ensembles with lattice spacings down to 0.042 fm and the study of finite-volume effects within staggered ChPT. We also study the implications for the unitarity of the CKM matrix in the first row and for current tensions with leptonic determinations of $\vert V_{us}\vert$.