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Recently, CMS and ATLAS collaborations at LHC announced a Higgs like particlewith mass near $125$GeV. Regarding this, to explore its intrinsic properties,different observables are needed to be measured precisely at the LHC forvarious decay channels of the Higgs. In this context, we calculate the finalstate lepton polarization asymmetries, namely, single lepton polarizationasymmetries ($P_i$) and double lepton polarization asymmetries ($P_{ij}$) inthe SM for radiative semileptonic Higgs decay $H\to\gamma\tau^+\tau^-$. In thephenomenological analysis of these lepton polarization asymmetries both treeand loop level diagrams are considered and it is found that these diagrams giveimportant 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 leptonforward-backward asymmetries ($A_{FB}$). Similar to the other observables suchas the decay rate and the lepton forward-backward asymmetries, the$\tau$-lepton polarization asymmetries would be interesting observables. Theexperimental study of these observables will provide a fertile ground toexplore the intrinsic properties of the SM Higgs boson and its dynamics as wellas help us to extract the signatures of the possible new physics beyond the SM.

Lepton Polarization Asymmetries of $H\to\gamma\tau^+\tau^-$ Decays in Standard Model