# On lepton flavour universality in semileptonic $B_c \to \eta_c, J/\psi$ decays

## TL;DR

This paper analyzes semileptonic $B_c$ decays to $ a_c$ and $J/\psi$ within the Standard Model and beyond, calculating form factors, branching ratios, and exploring new physics effects on angular observables, highlighting current experimental tensions.

## Contribution

It provides detailed form factor calculations over the full $q^2$ range and investigates new physics impacts on angular distributions in $B_c$ decays, extending the testing framework beyond existing studies.

## Key findings

- Predicted $R_{ a_c}|_{SM} = 0.32 \\pm 0.02$ and $R_{J/\psi}|_{SM} = 0.23 \\pm 0.01.
- Current new physics scenarios cannot fully explain the experimental $R_{J/\psi}$ value.
- New physics can significantly alter angular observables and produce effects absent in the SM.

## Abstract

We discuss $B_c \to \eta_c$ and $B_c \to J/\psi$ semileptonic decays within the Standard Model (SM) and beyond. The relevant transition form factors, being the main source of theoretical uncertainties, are calculated in the sum rule approach and are provided in a full $q^2$ range. We calculate the semileptonic branching fractions and find for the ratios, $R_{\eta_c}|_{\rm SM}= 0.32 \pm 0.02$, $R_{J/\psi}|_{\rm SM} = 0.23 \pm 0.01$. Both predictions are in agreement with other existing calculations and support the current tension in $R_{J/\psi}$ at 2$\sigma$ level with the experiment. To extend the potential of testing the SM in the semileptonic $B_c$ decays, we consider the forward-backward asymmetry and polarization observables. We also study the 4-fold differential distributions of $B_c \rightarrow J/\psi (J/\psi \to \tilde{\ell}^-\tilde{\ell}^+ ) \ell^- \bar{\nu}_\ell$, where $\tilde{\ell} = e, \mu$, in the presence of different new physics scenarios and find that the new physics effects can significantly modify the angular observables and can also produce effects which do not exist in the SM. Using the constraints on the new physics couplings from the recent combined analysis of BaBar, Belle and LHCb data on semileptonic $B \to D^{(\ast)}$ decays, where the effects of new physics could be visible, we find that these different new physics scenarios are not able to simultaneously explain the current experimental value of $R_{J/\psi}$.