  In the traditional non-relativistic bound state calculation, the two-photon
decay amplitudes of the $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ states depend
on the derivative of the wave function at the origin which can only be obtained
from potential models. However by neglecting the relative quark momenta, the
decay amplitude can be written as the matrix element of a local heavy quark
field operator which could be obtained from other processes or computed with
QCD sum rules technique or lattice simulation. Following the same line as in
recent work for the two-photon decays of the $S$-wave $\eta_{c}$ and $\eta_{b}$
quarkonia, we show that the effective Lagrangian for the two-photon decays of
the $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ is given by the heavy quark
energy-momentum tensor local operator or its trace, the $\bar{Q}Q$ scalar
density and that the expression for $\chi_{c0}$ two-photon and two-gluon decay
rate is given by the $f_{\chi_{c0}}$ decay constant and is similar to that of
$\eta_{c}$ which is given by $f_{\eta_{c}}$. From the existing QCD sum rules
value for $f_{\chi_{c0}}$, we get $5\rm keV$ for the $\chi_{c0}$ two-photon
width, somewhat larger than measurement, but possibly with large uncertainties.
