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

Why X(3915) is so narrow as a $\chi_{c0}(2P)$ state