A simple extension of SM that can explain the $(g-2{)}_{\mu }$ anomaly, small neutrino mass and a dark-matter

In this work we propose a simple extension of standard-model (SM) by adding eleven new particles to it. Three heavy leptons ($f_e,f_{\mu },f_{\tau }$) singlet under the $SU(3{)}_c\times SU(2{)}_L$ carrying respective Lepton-Numbers, charged under the $U(1{)}_Y$ with $Y=-2$ and transforming under a discrete symmetry as $f_i\to -f_i$. One scalar (${\varphi }_2$), singlet under all the SM gauge groups and transforming under the discrete symmetry as ${\varphi }_2\to -{\varphi }_2$ which does not develops a non zero vacuum-expectation-value (VEV). One more scalar (${\varphi }_3$), singlet under all the SM gauge groups and invariant under the discrete symmetry which develops a non zero VEV ($v_3$) and gives masses to $f_i$s, ${\varphi }_2$ and neutrinos. Three right-handed neutrinos (${\nu }_{iR}$) and three left-handed Majorana neutrinos ($s_{iL}$). With these new additional particles added to SM we have been able to give explanations to the long standing muon (g -2) anomaly as well as the smallness of neutrino masses by the inverse see-saw mechanism. And also in this model we have a very suitable scalar dark-matter (DM) candidate in ${\varphi }_2$ with allowed mass as high as 53 GeV, although due to large Yukawa coupling required to explain the muon (g-2), its contribution to the DM relic density turn out to be too small and so it can account only a small fraction of the DM relic density of the universe.