Virtual Photon Emission in Leptonic Decays of Pseudoscalar Mesons

TL;DR

This paper reports a preliminary lattice QCD calculation of form factors for leptonic decays of pseudoscalar mesons involving virtual photon emission, aiming to improve theoretical predictions and compare with experimental data.

Contribution

It introduces a non-perturbative lattice method to compute structure-dependent form factors in meson decays, applicable to any pseudoscalar meson, advancing the theoretical understanding of these processes.

Findings

Reasonable agreement with experimental data

Alignment with next-to-leading order Chiral Perturbation Theory

Method demonstrates potential for broader application

Abstract

We present a preliminary non-perturbative lattice calculation of the form factors entering the processes $K\to \ell\,\nu_\ell\,\ell'^+\,\ell'^-$ and of the corresponding branching ratios. These form factors describe the interaction between the mediating virtual photon and the internal hadronic structure of the meson. By separating them from the point-like contribution to the matrix element we are able to isolate and reconstruct the structure-dependent contribution to the decay width. Our numerical analysis employs only one gauge ensemble and so it is affected by systematic uncertainties due to the missing continuum and physical point extrapolation. Despite this, we already find a reasonable agreement with the experimental data and with the next to leading order Chiral Perturbation Theory predictions. The method is general and can be applied to any pseudoscalar meson, though for heavier mesons the possibility of internal lighter states becomes problematic and still needs a proper study. A non-perturbative, model-independent lattice evaluation of these processes would allow further progress in the theoretical predictions of SM hadronic quantities and in the search of New Physics.