Systematic analysis of the form factors of $B_{c}$ to $P$-wave charmonia and corresponding weak decays

TL;DR

This paper calculates form factors for $B_c$ decays to P-wave charmonia using QCD sum rules, then predicts decay widths and branching ratios for semileptonic and nonleptonic decays, aiding understanding of heavy quark dynamics.

Contribution

It provides the first systematic analysis of $B_c$ to P-wave charmonia form factors and decay properties within the QCD sum rules framework.

Findings

Calculated form factors for $B_c$ to P-wave charmonia.

Predicted decay widths and branching ratios for various decay modes.

Enhanced understanding of $B_c$ meson and P-wave charmonia properties.

Abstract

In this article, the vector, axial vector and tensor form factors of $B_{c}\to \chi_{cJ}$ ($J=0,1,2$) and $B_{c}\to h_{c}$ are analyzed within the framework of three-point QCD sum rules. With the calculated vector and axial vector form factors, we directly study the decay widths and branching ratios of semileptonic decays $B_{c}^{-}\to \chi_{cJ}l \bar{\nu}_l, h_{c}l \bar{\nu}_l$ $(l=e, \mu$ and $\tau)$ and analyze the nonleptonic decays $B_{c}^{-}\to \chi_{cJ}\pi^{-}, \chi_{cJ}K^{-}, \chi_{cJ}\rho^{-}, \chi_{cJ}K^{*-}$, $B_{c}^{-}\to h_{c}\pi^{-}, h_{c}K^{-}, h_{c}\rho^{-}, h_{c}K^{*-}$ by using the naive factorization approach (NFA). These results can provide more information to understand the properties of $B_{c}$ meson and $P$-wave charmonia and to study the heavy quark dynamics.