  We perform a detailed study of the signal rate of the lightest Higgs boson in
the diphoton channel ($\mu_{\gamma \gamma}$), recently analyzed by both the
ATLAS and CMS collaborations at the Large Hadron Collider, in the framework of
$U(1)_R-$ lepton number model with a right handed neutrino superfield. The
corresponding neutrino Yukawa coupling, `$f$', plays a very important role in
the phenomenology of this model. A large value of $f\sim\mathcal O(1)$ provides
an additional tree level contribution to the lightest Higgs boson mass along
with a very light (mass $\sim$ a few hundred MeV) bino like neutralino and a
small tree level mass of one of the active neutrinos that is compatible with
various experimental results. In the presence of this light neutralino, the
invisible decay width of the Higgs boson can become important. We studied this
scenario in conjunction with the recent LHC results. The signal rate
$\mu_{\gamma\gamma}$ obtained in this scenario is compatible with the recent
results from both the ATLAS and the CMS collaborations at 1$\sigma$ level. A
small value of `$f$', on the other hand, is compatible with a sterile neutrino
acting as a 7 keV dark matter that can explain the observation of a
mono-energetic X-ray photon line by the XMM-Newton X-ray observatory. We also
study the impact of $\mu_{\gamma\gamma}$ in this case.
