The role of electromagnetic interaction in the $X(3872)$ and its analogs

Abstract

We investigate the role of the electromagnetic interaction in the formation and decay of the $X(3872)$. The binding properties of the $X(3872)$ are studied by assuming the molecular nature and considering the $S$-$D$ wave mixing, isospin breaking, and coupled channel effects, and in particular the correction from the electromagnetic interaction. The radiative decays can better reflect the difference between the charged and neutral $D{\bar{D}}^{\ast }$ components, since the electromagnetic interaction explicitly breaks the isospin symmetry. We further study the radiative decay widths with the obtained wave functions for different $D{\bar{D}}^{\ast }$ channels. We also explore other similar hidden-charm molecular states. The electromagnetic interaction can make the molecule tighter. Our result of the radiative decay width for $X(3872)\to \gamma J/\psi$ is in agreement with the experiment. The branching ratio $R_{\gamma \psi }$ is less than 1 in our framework, which supports the Belle and BESIII measurements.

arXiv comment17 pages, 8 figures, 7 tables

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• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Masses and radiative decay widths of the $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\prime }(2460)$ and their bottom analogs
• Molecular pentaquarks composed of a ground-state octet baryon and a $P-$wave anticharmed meson
• Electromagnetic probes revealing the inner structure of the ${\Lambda }_c(2940)$