The weak decay $B_c$ to $Z(3930)$ and $X(4160)$ by Bethe-Salpeter method

TL;DR

This paper calculates the decay rates of Bc mesons into Z(3930) and X(4160) states using an improved Bethe-Salpeter approach, including relativistic effects, to aid in their experimental discovery and understanding.

Contribution

It introduces an improved Bethe-Salpeter method to compute form factors and branching ratios for Bc decays into specific charmonium-like states, considering relativistic corrections.

Findings

Predicted branching ratios for Bc decays to Z(3930) and X(4160).

Provided theoretical guidance for experimental searches of these states.

Enhanced understanding of relativistic effects in meson decay calculations.

Abstract

Considering $Z(3930)$ and $X(4160)$ as $\chi_{c2}(2P)$ and $\chi_{c2}(3P)$ states, the semileptonic and nonleptonic of $B_c$ decays to $Z(3930)$ and $X(4160)$ are studied by the improved Bethe-Salpeter(B-S) Method. The form factors of decay are calculated through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The influence of relativistic corrections are considered in the exclusive decays. Branching ratios of $B_c$ weak decays to $Z(3930)$ and $X(4160)$ are predicted. Some of the branching ratios are: $Br(B_c^+\to Z(3930)e^+\nu_e)$$=(3.03^{+0.09}_{-0.16})\times 10^{-4}$ and $Br(B_c^+\to X(4160)e^+\nu_e)$$=(3.55^{+0.83}_{-0.35})\times 10^{-6}$. These results may provide useful information to discover $Z(3930)$ and $X(4160)$ and the necessary information for the phenomenological study of $B_c$ physics.