The decay property of the $X(3842)$ as the $\psi_{_3}(1^3D_{_3})$ state

TL;DR

This paper identifies the new particle X(3842) as the $ ext{ψ}_3(1^3D_3)$ state, analyzing its decay properties using Bethe-Salpeter and $^3P_0$ models, and finds results consistent with experimental data.

Contribution

It provides a detailed theoretical analysis of X(3842)'s decay modes and confirms its identification as the $ ext{ψ}_3(1^3D_3)$ state with consistent decay width predictions.

Findings

Decay widths match experimental data

Electromagnetic decay contributions analyzed

Partial wave contributions studied

Abstract

In this paper, the new particle $X(3842)$ discovered by the LHCb Collaboration is identified to be the $\psi_{_3}(1^3D_{_3})$ state. We study its strong decays with the combination of the Bethe-Salpeter method and the $^3P_{_0}$ model. Its electromagnetic (EM) decay is also calculated by the Bethe-Salpeter method within Mandelstam formalism. The strong decay widths are {$\Gamma[X(3842)\rightarrow D^{0}\bar{D}^{0}]=1.28$ MeV}, $\Gamma[X(3823)\rightarrow D^{+}D^{-}]=1.08$ MeV, and the ratio ${\cal B}[X(3842)\rightarrow D^{+}D^{-}]/{\cal B}[X(3823)\rightarrow D^{0}\bar{D}^{0}]=0.84$. The EM decay width is $\Gamma[X(3842)\rightarrow\chi_{_{c2}}\gamma]=0.29$ MeV. We also estimate the total width to be 2.87 MeV, which is in good agreement with the experimental data $2.79^{+0.86}_{-0.86}$ MeV. Since the used relativistic wave functions include different partial waves, we also study the contributions of different partial waves in electromagnetic decay.