  The decay rates of $Q \bar Q$ mesons ($Q \varepsilon {c, b}$) are studied in
the NRQCD formalism in terms of their short distance and long distance
coefficients. The long distance coefficients are obtained through
phenomenological potential model description of the mesons. The model
parameters that reproduces the mass spectrum of the $c \bar c$, $b \bar b$ and
$c \bar b$ mesons are employed to study the decay widths of these mesons. We
extract the mass spectrum as well as the reproduces the respective radial wave
functions from the different potential models as well as from non-relativistic
phenomenological quark antiquark potential of the type
$V(r)=-\frac{\alpha_c}{r}+A r^{\nu}$, with $\nu$ varying from 0.5 to 2. The
spin hyperfine and spin-orbit interactions are employed to obtain the masses of
the pseudoscalar and vector mesons. The decay constants with QCD corrections
are computed in this model as well as in the case of other potential models for
comparison. The digamma and dileptonic decays of $c \bar c$, and $b \bar b$
mesons are investigated using some of the known potential models without and
with radiative corrections up to the lowest order. These decay width are also
computed within the NRQCD formalism up to $O(v^4)$ by making uses of the
respective spectroscopic parameters of the models. Our theoretical predictions
of the decays of the $c \bar c$, and $b \bar b$ mesons and the results obtained
from some of the other potential schemes are compared with the experimental
values. The partial widths and life time of the $B_c$ meson are also computed
using the model parameters and are found to be in good accordance with the
experimental values.
