  Recently, CMS and ATLAS collaborations at LHC announced a Higgs like particle
with mass near $125$GeV. Regarding this, to explore its intrinsic properties,
different observables are needed to be measured precisely at the LHC for
various decay channels of the Higgs. In this context, we calculate the final
state lepton polarization asymmetries, namely, single lepton polarization
asymmetries ($P_i$) and double lepton polarization asymmetries ($P_{ij}$) in
the SM for radiative semileptonic Higgs decay $H\to\gamma\tau^+\tau^-$. In the
phenomenological analysis of these lepton polarization asymmetries both tree
and loop level diagrams are considered and it is found that these diagrams give
important contributions in the evaluation of said asymmetries. Interestingly,
it is found that in $P_{ij}$ the tree level diagrams contribute separately,
which however, are missing in the calculations of $P_i$ and the lepton
forward-backward asymmetries ($A_{FB}$). Similar to the other observables such
as the decay rate and the lepton forward-backward asymmetries, the
$\tau$-lepton polarization asymmetries would be interesting observables. The
experimental study of these observables will provide a fertile ground to
explore the intrinsic properties of the SM Higgs boson and its dynamics as well
as help us to extract the signatures of the possible new physics beyond the SM.
