Lattice inputs to Flavor Physics

TL;DR

This paper reviews recent lattice QCD results for quark masses and hadronic parameters essential for flavor physics, highlighting progress, challenges, and future directions in incorporating electromagnetic effects and hadronic decays.

Contribution

It provides a comprehensive overview of lattice computations in flavor physics, emphasizing the FLAG initiative and recent advances in electromagnetic corrections and decay amplitude calculations.

Findings

High precision in light-quark quantities enhances confidence in averages.

Heavy-light sector computations are still limited, except for decay constants.

Electromagnetic corrections are increasingly relevant for precise flavor physics analyses.

Abstract

We review recent lattice results for quark masses and low-energy hadronic parameters relevant for flavor physics. We do that by describing the FLAG initiative, with emphasis on its scope and rating criteria. The emerging picture is that while for light quantities a large number of computations using different approaches exist, and this increases the overall confidence on the final averages/estimates, in the heavy-light case the field is less advanced and, with the exception of decay constants, only a few computations are available. The precision reached for the light quantities is such that electromagnetic (EM) corrections, beyond the point-like approximation, are becoming relevant. We discuss recent computations of the spectrum based on direct simulations of QED+QCD. We also present theoretical developments for including EM effects in leptonic decays. We conclude describing recent results for the $K \to \pi \pi$ transition amplitudes and prospects for tackling hadronic decays on the lattice.