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In this paper, the new particle $X(3842)$ discovered by the LHCbCollaboration is identified to be the $\psi_{_3}(1^3D_{_3})$ state. We studyits strong decays with the combination of the Bethe-Salpeter method and the$^3P_{_0}$ model. Its electromagnetic (EM) decay is also calculated by theBethe-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 ${\calB}[X(3842)\rightarrow D^{+}D^{-}]/{\cal B}[X(3823)\rightarrowD^{0}\bar{D}^{0}]=0.84$. The EM decay width is$\Gamma[X(3842)\rightarrow\chi_{_{c2}}\gamma]=0.29$ MeV. We also estimate thetotal width to be 2.87 MeV, which is in good agreement with the experimentaldata $2.79^{+0.86}_{-0.86}$ MeV. Since the used relativistic wave functionsinclude different partial waves, we also study the contributions of differentpartial waves in electromagnetic decay.

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