Radiative decays of the spin-\(2\) partner of \(X(3872)\)

• Published in: arXiv.org 2023-06
• Main Authors: Pan-Pan, Shi, Dias, Jorgivan M, Feng-Kun, Guo
• Format: Article
• Language: English
• Subjects: Decay; Invariants; Mass distribution; Photons; Quantum numbers
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2302.13017

It has been generally expected that the \(X(3872)\) has a spin-2 partner, \(X_2\), with quantum numbers \(J^{PC}=2^{++}\). In the hadronic molecular model, its mass was predicted to be below the \(D^*\bar D^*\) threshold, and the new structure reported in the \(\gamma \psi(2S)\) invariant mass distribution by the Belle Collaboration with mass \(M= (4014.3 \pm 4.0 \pm 1.5)\) MeV and decay width \(\Gamma= (4 \pm 11 \pm 6)\) MeV, with a global significance of 2.8 \(\sigma\), is a nice candidate for it. We consider the radiative decay widths for the \(X_{2}\to \gamma\psi\) with \(\psi=J/\psi, \psi(2S)\) treating the \(X_2\) as a \(D^*\bar{D}^*\) shallow bound state, and estimate the events of \(X_2\) in two-photon collisions that can be collected in the \(\gamma J/\psi\to\gamma\ell^+\ell^-\) (\(\ell=e,\mu\)) final states at Belle. Based on the upper limit for the ratio of decay widths of \(X(3872)\to \gamma \psi(2S)\) and \(X(3872)\to \gamma J/\psi\) measured by BESIII, we predict the similar ratio \(\Gamma(X_2\to \gamma \psi(2S))/\Gamma(X_2\to \gamma J/\psi)\) to be smaller than \(1.0\). We suggest searching for the \(X_2\) signal in the \(\gamma J/\psi\) invariant mass distribution via two-photon fusions. The results will lead to insights into both the \(X(3872)\) and the new structure observed by Belle.