# Nonleptonic $B_c$ decay rates from model independent relations

## TL;DR

This paper analyzes nonleptonic B_c decays to P-wave charmonia and light mesons using a model-independent approach, providing predictions for branching ratios and exploring the production of exotic states like _{c1}(3872).

## Contribution

It introduces a universal form factor framework for B_c to P-wave charmonia transitions at leading order, enabling model-independent predictions of decay rates.

## Key findings

- Predicted ratios of branching fractions for various decay modes.
- Estimated production rates for the exotic _{c1}(3872) state.
- Identification of universal functions governing form factors.

## Abstract

Nonleptonic $B_c$ decays to $P$-wave charmonia and light $\pi^+$, $K^+$, and $\rho^+$, $K^{*+}$ mesons are analysed using factorization. The hadronic form factors parametrizing the $B_c \to \chi_{cJ}(h_c)$ matrix elements are expressed in terms of universal functions at the leading order of an expansion in the relative velocity of the heavy quarks in the $B_c$ rest-frame and in $1/m_Q$. Several ratios of branching fractions are evaluated, and when experimental information can be used, single branching fractions are presented. Both the $1P$ and $2P$ charmonia are considered. If the exotic candidate state $\chi_{c1}(3872)$ corresponds to $\chi_{c1}(2P)$, it should be produced in nonleptonic $B_c$ decays with predicted abundances with respect to the other states in the charmonium $2P$ spin four-plet.