Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD

TL;DR

This paper derives universal finite-volume corrections for leptonic decay widths in lattice QED, enabling more precise calculations of decay amplitudes by accounting for volume effects independent of meson structure.

Contribution

It extends existing techniques to include external momentum dependence, providing a universal correction framework for decay amplitudes at order alpha in lattice QCD.

Findings

Universal finite-volume effects are independent of meson structure.

Leading non-universal corrections are of order 1/L^2.

The methods can be applied to semileptonic decays for improved precision.

Abstract

We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(\alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.\,\cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(\alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics.