The decay property of the $X(3842)$ as the ${\psi }_{{}_3}(1^3{D}_{{}_3})$ state

Abstract

In this paper, the new particle $X(3842)$ discovered by the LHCb Collaboration is identified to be the ${\psi }_{{}_3}(1^3{D}_{{}_3})$ state. We study its strong decays with the combination of the Bethe-Salpeter method and the ${}^3{P}_{{}_0}$ model. Its electromagnetic (EM) decay is also calculated by the Bethe-Salpeter method within Mandelstam formalism. The strong decay widths are {$\Gamma [X(3842)\to D^0{\bar{D}}^0]=1.28$ MeV}, $\Gamma [X(3823)\to D^{+}{D}^{-}]=1.08$ MeV, and the ratio $\mathcal{B}[X(3842)\to D^{+}{D}^{-}]/\mathcal{B}[X(3823)\to D^0{\bar{D}}^0]=0.84$. The EM decay width is $\Gamma [X(3842)\to {\chi }_{{}_{c2}}\gamma ]=0.29$ 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.

Comments: 19 pages, 3 figures, 3 tables