The ratio of decay widths of X(3872) to $ \psi^{\prime}\gamma $ and $ J/\psi\gamma$ as a test of the X(3872) dynamical structure

TL;DR

This paper investigates the radiative decay ratios of X(3872) using a coupled-channel approach, revealing that the dynamical structure significantly influences decay rates and can distinguish between different models of X(3872).

Contribution

It introduces a coupled-channel method combining relativistic string Hamiltonian and string breaking to analyze X(3872)'s structure and decay ratios, providing new insights into its composition.

Findings

The decay ratio R is significantly reduced from 5 to about 0.8 due to wave function admixture.

The model reproduces the X(3872) mass and decay properties consistent with experimental data.

Wave function admixture enhances the transition rate to J/ψγ by 50-70 keV.

Abstract

Radiative decays of X(3872) with $J^{PC}=1^{++}$ are studied in the coupled-channel approach, where the $c\bar c$ states are described by relativistic string Hamiltonian, while for the decay channels $DD^*$ a string breaking mechanism is used. Within this method a sharp peak and correct mass shift of the $2 {}^3P_1$ charmonium state just to the $D^0D^{*0}$ threshold was already obtained for a prescribed channel coupling to the $DD^*$ decay channels. For the same value of coupling the normalized wave function (w.f.) of X(3872) acquires admixture of the $1 {}^3P_1$ component with the w.f. fraction $c_1=0.153 (\theta=8.8^\circ$), which increases the transition rate $\Gamma(X(3872)\rightarrow J/\psi\gamma)$ up to 50-70 keV, making the ratio $R=\frac{\mathcal{B}(X(3872)\rightarrow \psi^{\prime}\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi \gamma)}=0.8\pm 0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a purely $2 {}^3P_1$ state.