Efficient lattice QCD computation of radiative-leptonic-decay form factors at multiple positive and negative photon virtualities

TL;DR

This paper demonstrates an efficient lattice QCD method to compute radiative-leptonic decay form factors across multiple photon virtualities, including both positive and negative values, with high precision and no additional computational cost.

Contribution

The study extends the 3d lattice QCD method to extract form factors at any photon virtuality from the same three-point functions, enhancing computational efficiency and scope.

Findings

Form factors computed for both positive and negative photon virtualities.

Analysis of different time orderings and quark flavor contributions.

Discussion on the behavior of unwanted exponentials and fit model choices.

Abstract

In previous work Phys. Rev. D 107, 074507 (2023), we showed that form factors for radiative leptonic decays of pseudoscalar mesons can be determined efficiently and with high precision from lattice QCD using the ``3d method,'' in which three-point functions are computed for all values of the current-insertion time and the time integral is performed at the data-analysis stage. Here, we demonstrate another benefit of the 3d method: the form factors can be extracted for any number of nonzero photon virtualites from the same three-point functions at no extra cost. We present results for the $D_s\to\ell\nu\gamma^*$ vector form factor as a function of photon energy and photon virtuality, for both positive and negative virtuality. In our analysis, we separately consider the two different time orderings and the different quark flavors in the electromagnetic current. We discuss in detail the behavior of the unwanted exponentials contributing to the three-point functions, as well as the choice of fit models and fit ranges used to remove them for various values of the virtuality. While positive photon virtuality is relevant for decays to multiple charged leptons, negative photon virtuality suppresses soft contributions and is of interest in QCD-factorization studies of the form factors.