Dipion transitions from $X(3872)$ to ${\chi }_{cJ}(J=0,1,2)$

Abstract

In this work, we investigate the dipion transition processes $X(3872)\to \pi \pi {\chi }_{cJ}(J=0,1,2)$ within the framework of heavy hadron chiral perturbation theory, treating $X(3872)$ as a molecular state composed of $D{\bar{D}}^{\ast }$+ H.c. components. By analyzing the box and triangle loop diagrams with the nonrelativistic effective field theory power-counting rule, we demonstrate that box diagrams dominate these dipion transition processes. Branching ratios are calculated as functions of the mixing angle $\theta$, which parametrizes the neutral and charged meson compositions of the $X(3872)$. Our results indicate that the branching fractions for $X(3872)\to \pi \pi {\chi }_{c0}$, $X(3872)\to \pi \pi {\chi }_{c1}$, and $X(3872)\to \pi \pi {\chi }_{c2}$ are of the orders of $10^{-4}$, $10^{-3}$, and $10^{-5}$, respectively. We also predict the ratios $\mathcal{B}[X(3872)\to \pi \pi {\chi }_{c0/2}]/\mathcal{B}[X(3872)\to \pi \pi {\chi }_{c1}]$ and $\mathcal{B}[X(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{cJ}]/\mathcal{B}[X(3872)\to {\pi }^0{\pi }^0{\chi }_{cJ}]$. The latter deviates from isospin-symmetry expectations, revealing various degrees of isospin violation. By studying the ${\pi }^{+}{\pi }^{-}$ and ${\pi }^{+}{\chi }_{cJ}$ invariant mass spectra, we find a double-bump structure in the ${\pi }^{+}{\pi }^{-}$ invariant mass distributions of the process $X(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{c1}$ and ${\pi }^{+}{\chi }_{c0}$ invariant mass distribution of the process $X(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{c0}$, which could be tested by future experimental measurements.

Comments: 10 pages, 5 figures, 1 table, matches published version