Semileptonic decays of heavy mesons with artificial neural networks

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 $|V_{cd}|$.