  New resonance X(3915) was identified as the charmonium $\chi_{c0}(2P)$ by
BABAR Collaboration, but there seems still open question of this assignment:
why its full width is so narrow? To answer this question, we calculate the
Okubo-Zweig-Iizuka (OZI) allowed strong decays $X(3915)\to D \bar D$, where
X(3915) is assigned as a $\chi_{c0}(2P)$ state, and estimate its full width in
the cooperating framework of $^3/!P_0^{}$ model and the Bethe-Salpeter (BS)
method using the Mandelstam Formalism, during which non-perturbative QCD
effects of the hadronic matrix elements are well considered by overlapping
integral over the relativistic Salpeter wave functions of the initial and
finial states. We find the node structure of $\chi_{c0}(2P)$ wave function
resulting in the narrow width of X(3915) and show the dependence of the decay
width on the variation of the initial mass of X(3915). We point out that the
rate of $\frac{\Gamma(X(3915)\to D^+ D^-)}{\Gamma(X(3915)\to D^0 \bar D^0)}$ is
crucial to confirm whether X(3915) is the $\chi_{c0}(2P)$ state or not.
