Semileptonic decays of heavy mesons with artificial neural networks

TL;DR

This paper introduces a novel method using artificial neural networks trained on experimental data to predict semileptonic form factors of heavy mesons, enabling more accurate extraction of CKM matrix elements with quantified uncertainties.

Contribution

It proposes a neural network-based approach to model semileptonic form factors, reducing model dependency and improving the precision of CKM matrix element extraction.

Findings

Neural networks can effectively predict form factor shapes.

Uncertainty quantification improves CKM element bounds.

Comparison with traditional models highlights advantages of the neural network approach.

Abstract

Experimental checks of the second row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix involve extractions of the matrix element $V_{cd}$, which may be obtained from semileptonic decay rates of $D$ to $\pi$. These decay rates are proportional to hadronic form factors which parameterize how the quark $c \to d$ transition is realized in $D \to \pi$ meson decays. The form factors can not yet be analytically computed over the whole range of available momentum transfer $q^2$, but can be parameterized with a varying degree of model dependency. We propose using artificial neural networks trained from experimental pseudo-data to predict the shape of these form factors with a prescribed uncertainty. We comment on the parameters of several commonly-used model parameterizations of semileptonic form factors. We extract shape parameters and use unitarity to bound the form factor at a given $q^2$, which then allows us to bound the CKM matrix element $|V_{cd}|$.