Semileptonic $B_{c}$ meson decays to S-wave charmonia and $X(3872)$ within the covariant light-front approach

TL;DR

This paper calculates branching ratios and observables for semileptonic $B_c$ decays to various charmonia and $X(3872)$ using the covariant light-front quark model, aiming to test lepton flavor universality and explain the $R_{J/ ext{Psi}}$ anomaly.

Contribution

It provides systematic predictions for decay ratios, polarization fractions, and asymmetries in $B_c$ semileptonic decays within the covariant light-front approach, addressing the $R_{J/ ext{Psi}}$ anomaly.

Findings

Predicted branching ratios for various $B_c$ decay modes.

Calculated $R_X$ ratios to test lepton flavor universality.

Analyzed polarization and asymmetry observables related to the $R_{J/ ext{Psi}}$ anomaly.

Abstract

In this work, we investigate the semileptonic decays of $B_{c}$ meson to $\eta_{c}(1S,2S,3S)$, $\psi(1S,2S,3S)$ and $X(3872)$ within the framework of covariant light-front quark model (CLFQM). We combine the helicity amplitudes via the corresponding form factors to obtain the branching ratios of the semileptonic decays $B_{c}\to \eta_{c}(1S, 2S, 3S)\ell\nu_{\ell}$, $B_{c}\to \psi(1S, 2S, 3S))\ell\nu_{\ell}$ and $B_{c}\to X(3872)\ell\nu_{\ell}$ with $\ell=e,\mu,\tau$. In view of the $R_{J/\Psi}$ anomaly released by the LHCb collaboration, it is necessary to calculate the ratios $R_X$ with $X=\psi(1S,2S,3S),\eta_c(1S,2S,3S),X(3872)$ systematically, which are helpful to check the lepton flavor universality (LFU). Furthermore, we also take into account another two physical observables, one is the longitudinal polarization fraction $f_{L}$ and the other is the forward-backward asymmetry $A_{FB}$, which can provide new clues to understand the $R_{J /\Psi}$ anomaly. Such theoretical predictions are necessary and interesting, which can be tested in the future LHCb experiments.