A Phenomenological analysis on isospin-violating decay of $X(3872)$

Abstract

In a molecular scenario, we investigate the isospin-breaking hidden charm decay processes of $X(3872)$, i.e., $X(3872) \to π^+ π^- J/ψ$, $X(3872) \to π^+ π^- π^0 J/ψ$, and $X(3872)\to π^0χ_{cJ}$. We assume that the source of the strong isospin violation comes from the different coupling strengths of $X(3872)$ to its charged components $D^{\ast +} D^-$ and neutral components $D^{\ast 0 } \bar{D}^0$ as well as the interference between the charged meson loops and neutral meson loops. The former effect could fix our parameters by using the measurement of the ratio $Γ[X(3872) \to π^+ π^- π^0 J/ψ]/Γ[X(3872) \to π^+ π^- J/ψ]$. With the determined parameter range, we find that the estimated ratio $Γ[X(3872) \to π^0 χ_{c1}/Γ[X(3872) \to π^+ π^- J/ψ]$ is well consistent with the experimental measurement from the BESIII collaboration. Moreover, the partial width ratio of $π^0 χ_{cJ}$ for $J=0,1,2$ is estimated to be $1.77\sim1.65:1:1.09\sim1.43$, which could be tested by further precise measurements of BESIII and Belle II.