Determination of Vus: Recent Input from the Lattice

TL;DR

This paper reviews recent lattice QCD results for key hadronic parameters used to precisely determine the CKM matrix element V_us, highlighting sub-percent accuracy achievements and discussing isospin breaking corrections.

Contribution

It provides updated lattice QCD calculations of f_K+/f_pi+ and f_+(0), demonstrating their precision and relevance for CKM matrix element determinations.

Findings

f_K+/f_pi+ = 1.193(4)

f_+(0)=0.965(3)

Sub-percent accuracy achieved in lattice calculations

Abstract

The two most precise determinations of the CKM matrix element V_us are based on the analyses of leptonic and semileptonic kaon decays. These studies also rely on the lattice QCD calculations of two hadronic parameters, namely the ratio of the kaon and pion decay constants, f_K+/f_pi+, and the kaon semileptonic vector form factor at zero momentum transfer, f_+(0). In this talk, I review the recent lattice results for these quantities, by showing that the sub-percent accuracy required by the phenomenological analyses has been reached by lattice QCD. As best estimates of the lattice calculations I quote f_K+/f_pi+ = 1.193(4) and f_+(0)=0.965(3). I also discuss some recent theoretical progress in the evaluation of the small, but phenomenologically relevant, SU(2) isospin breaking corrections.