Non-perturbative renormalization in QCD+QED and its application to weak decays

TL;DR

This paper introduces a new non-perturbative renormalization method for lattice QCD+QED calculations that accounts for mixed effects, reducing uncertainties and enabling precise determination of weak decay corrections and CKM matrix elements.

Contribution

It presents a systematic strategy for renormalizing lattice operators in QCD+QED, including first order QED corrections and mixed effects, improving accuracy over previous methods.

Findings

First lattice calculation of isospin breaking corrections to leptonic decay rates.

Enhanced precision in matching to the W-regularization scheme.

Updated, more accurate value of |V_{us}|.

Abstract

We present a novel strategy to renormalize lattice operators in QCD+QED, including first order QED corrections to the non-perturbative evaluation of QCD renormalization constants. Our procedure takes systematically into account the mixed non-factorizable QCD+QED effects which were neglected in previous calculations, thus significantly reducing the systematic uncertainty on renormalization corrections. The procedure is presented here in the RI'-MOM scheme, but it can be applied to other schemes (e.g. RI-SMOM) with appropriate changes. We discuss the application of this strategy to the calculation of the leading isospin breaking corrections to the leptonic decay rates $\Gamma(\pi_{\mu 2})$ and $\Gamma(K_{\mu 2})$, evaluated for the first time on the lattice. The precision in the matching to the $W$-regularization scheme is improved to $\mathcal{O}(\alpha_{em}\alpha_s(M_W))$ with respect to previous calculations. Finally, we show the updated precise result obtained for the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|$.