Semileptonic Decay of $B_c$ to $\hat{I}{\cdot }_c$ and $J/\ddot{I}ˆ$ on the Light Front

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 $\hat{I}{\cdot }_c$ or $J/\ddot{I}ˆ$ 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 $\hat{I}{\cdot }_c^{\prime }$ and the $\ddot{I}{ˆ}^{\prime }$. 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.