Weak productions of new charmonium in semi-leptonic decays of B_c

TL;DR

This paper investigates the weak production of various heavy mesons, including exotic states, in semi-leptonic B_c decays using light-cone QCD sum rules, aiming to clarify their internal structures through future experiments.

Contribution

It provides theoretical predictions for production rates of heavy and exotic charmonium states in B_c decays, considering different quantum number assignments and mixing scenarios.

Findings

Different interpretations of X(3940) lead to significant differences in production rates.

Predicted large production rates for X(3872) and Y(3940) in B_c decays.

Small decay rate predicted for B_c to Y(4260).

Abstract

We study the weak productions of novel heavy mesons, such as $\eta_c^{\prime}$, $h_c$, $h_c^{\prime}$, $\chi_{c0}^{\prime}$, X(3940), Y(3940), X(3872), and Y(4260), in the semi-leptonic $B_c$ decays. Since there is still no definite answer for the components of X(3940), Y(3940), X(3872), Y(4260) so far, we will assign them as excited charmonium states with the possible quantum numbers constrained by the current experiments. As for the weak transition form factors, we calculate them in the framework of light-cone QCD sum rules approach, which is proved to be a powerful tool to deal with the non-perturbative hadronic matrix element. Our results indicate that different interpretations of X(3940) can result in remarkable discrepancy of the production rate in the $B_c$ decays, which would help to clarify the inner structure of the X(3940) with the forthcoming LHC-b experiments. Besides, the predicted large weak production rates of X(3872) and Y(3940) in $B_c$ decays and the small semi-leptonic decay rate for $B_c \to Y(4260)$ all depend on their quantum number $J^{PC}$ assignments. Moreover, the $S-D$ mixing of various vector charmonium states in the weak decay of $B_c$ is also discussed in this work. The future experimental measurements of these decays will test the inner structures of these particles, according to our predictions here.