  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.
