# Decays of $X(3872)$ to $\chi_{cJ}\pi^0$ and $J/\psi\pi^+\pi^-$

## TL;DR

This paper models the decay processes of the $X(3872)$ particle, predicting decay rates to various charmonium states and comparing them to experimental data, using an extended Friedrichs scheme.

## Contribution

It introduces a novel application of the extended Friedrichs scheme to calculate decay rates of $X(3872)$ to $ ext{\chi}_{cJ}\pi^0$ and $J/\psi\pi^+\pi^-$, providing insights into its structure.

## Key findings

- Decay widths to $\chi_{cJ}\pi^0$ are similar for J=0,1,2.
- Decay to $\chi_{c1}\pi^0$ is significantly smaller than to $J/\psi\pi^+\pi^-$.
- Model aligns with experimental observations of decay rate hierarchies.

## Abstract

By describing the $X(3872)$ using the extended Friedrichs scheme, in which $D\bar D^*$ is the dominant component, we calculate the decay rates of the $X(3872)$ to $\pi^0$ and a $P$-wave charmonium $\chi_{cJ}$ state with $J=0,1$, or $2$, and its decays to $J/\psi\pi^+\pi^-$ where $\pi^+\pi^-$ are assumed to be produced via an intermediate $\rho$ state. The decay widths of $X(3872)\to\chi_{cJ}\pi^0$ for $J=0,1,2$ are of the same order. However, this model calculation exhibits that the decay rate of $X(3872)$ to $\chi_{c1}\pi^0$ is one order of magnitude smaller than its decay rate to $J/\psi\pi^+\pi^-$.