Form factors and phenomenology of $\boldsymbol{B_{(s)}}$ and $\boldsymbol{D_{(s)}}$ semileptonic decays to $\boldsymbol{\eta}$ and $\boldsymbol{\eta^\prime}$

TL;DR

This paper employs advanced parametrizations and recent data to analyze form factors in $B_{(s)}$ and $D_{(s)}$ decays to $ ext{eta}$ and $ ext{eta'}$, extracting CKM elements and testing lepton universality with good agreement to experimental results.

Contribution

It introduces state-of-the-art form factor parametrizations fitted to latest sum rule results, enabling precise extraction of CKM elements and mixing angles from semileptonic decay data.

Findings

Good agreement between computed branching ratios and experimental data.

Extraction of CKM elements $|V_{ub}|$, $V_{cs}$, $V_{cd}$ with improved precision.

Tests of lepton flavour universality show consistency with the Standard Model.

Abstract

Motivated by more precise recent measurements of the $B \to \eta \ell \nu$ and $D_{(s)} \to \eta^{(\prime)}\ell \nu$ decays, we employ state-of-the-art parametrizations to describe the $B_{(s)}, D_{(s)} \to \eta^{(\prime)}$ form factors across the full $q^2$ range, fitting them to the latest light-cone sum rule results. Using these results, we compute the branching ratios for all relevant decays and compare them with experimental data, finding good agreement. Additionally, we examine the validity and precision of the extracted $\eta$-$\eta'$ mixing angle in the context of heavy meson decays. By combining our predictions for the $B, D, D_s \to \eta^{(\prime)}$ form factors with recent semileptonic decay measurements, we extract the CKM elements $|V_{ub}|$, $V_{cs}$, and $V_{cd}$. We also provide tests of the lepton flavour universality in the $B, D, D_s \to \eta^{(\prime)} \ell \nu$ decays and present results for the forward-backwards asymmetries in these decays. Our findings indicate that the extracted values are becoming comparable in precision to those obtained from more conventional semileptonic decay analyses.