Semileptonic Decay of $B_c$ to $\eta_c$ and $J/\psi$ on the Light Front

TL;DR

This paper calculates the semileptonic decay form factors of the $B_c$ meson into charmonia using basis light-front quantization, addressing frame dependence issues and providing decay predictions.

Contribution

It introduces a method to compute $B_c$ decay form factors with basis light-front quantization and proposes preferred frames to reduce unphysical dependencies.

Findings

Calculated decay form factors for $B_c$ to $ a_c$ and $J/\psi$.

Identified frame dependence in form factors due to valence wave functions.

Provided decay widths and branching ratios for multiple charmonium states.

Abstract

We study the semileptonic decay of the $B_c (0^-)$ to charmonia through the bottom-to-charm-quark electroweak current in the framework of basis light-front quantization. Explicitly, we calculate the weak transition form factors for processes of $B_c$ decaying into $\eta_c$ or $J/\psi$ based on the corresponding initial and final valence light-front wave functions both obtained from the basis light-front quantization. We also present the corresponding differential decay width and branching ratios, as well as the branching ratios for decays into the $\eta_c'$ and the $\psi'$. We observe unphysical frame dependence of the calculated form factors, which is attributed to only including the valence light-front wave functions. Based on the analysis of current component, we propose a preferred set of frames to calculate these form factors.