Tentative estimates of $\mathcal{B}(X(3872)\to\pi^0\pi^0\chi_{c1})$ and $\mathcal{B}(X(3872)\to\pi^+\pi^-\chi_{c1})$

TL;DR

This paper estimates the decay rates of X(3872) into specific pion and chi_c1 states using a triangle loop model, predicting similar branching fractions for charged and neutral pion channels and highlighting isospin symmetry violation.

Contribution

The study introduces a triangle loop diagram model to estimate decay rates of X(3872), predicting a ratio of decay branching fractions that significantly violates isotopic symmetry.

Findings

Branching fractions estimated at (0.8-1.7)×10^{-4}.

Predicted ratio R ≈ 1.1, indicating isospin violation.

Narrow peaks in the pi^0 chi_c1 mass spectrum near D^0 D̄^0 threshold.

Abstract

The rates of the $X(3872)\to\pi^0\pi^0\chi_{c1}$ and $X(3872)\to \pi^+\pi^-\chi_{c1}$ decays are estimated in the model of the triangle loop diagrams with charmed $D^*\bar DD$ and $\bar D^*D\bar D$ mesons in the loops. There are the triangle logarithmic singularities in the physical region of the $X(3872)\to\pi^0\pi^0 \chi_{c1}$ decay which manifest themselves as narrow peaks in the $\pi^0\chi_{c1}$ mass spectrum near the $D^0\bar D^0$ threshold. The model predicts approximately the same branching fractions of the $X(3872)\to\pi^0\pi^0 \chi_{c1}$ and $X(3872)\to\pi^+\pi^-\chi_{c1}$ decays at the level of about (0.8-1.7)$\times10^{-4}$. A distinct prediction of the model is the value of the ratio $\mathcal{R}= \mathcal{B}(X(3872)\to\pi^+\pi^-\chi_{c1})/\mathcal{B}(X(3872) \to\pi^0\pi^0\chi_{c1})\approx1.1$. It weakly depends on the $X(3872)$ resonance parameters and indicates a significant violation of the isotopic symmetry according to which one would expect $\mathcal{R}=2$.