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

Abstract

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 $f_{i} \rightarrow -f_{i}$. One scalar ($\phi_{2}$), singlet under all the SM gauge groups and transforming under the discrete symmetry as $\phi_{2} \rightarrow -\phi_{2}$ which does not develops a non zero vacuum-expectation-value (VEV). One more scalar ($\phi_{3}$), 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, $\phi_{2}$ 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 $\phi_{2}$ 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.