Common Origin of $3.55$ keV X-ray line and Gauge Coupling Unification with Left-Right Dark Matter

Abstract: We present a minimal left-right dark matter framework that can simultaneously explain the recently observed 3.55 keV X-ray line from several galaxy clusters and gauge coupling unification at high energy scale. Adopting a minimal dark matter strategy, we consider both left and right handed triplet fermionic dark matter candidates which are stable by virtue of a remnant $\mathcal{Z}_2\simeq (-1)^{B-L}$ symmetry arising after the spontaneous symmetry breaking of left-right gauge symmetry to that of the standard model. A scalar bitriplet field is incorporated whose first role is to allow radiative decay of right handed triplet dark matter into the left handed one and a photon with energy 3.55 keV. The other role this bitriplet field at TeV scale plays is to assist in achieving gauge coupling unification at a high energy scale within a non-supersymmetric $SO(10)$ model while keeping the scale of left-right gauge symmetry around the TeV corner. Apart from solving the neutrino mass problem and giving verifiable new contributions to neutrinoless double beta decay and charged lepton flavour violation, the model with TeV scale gauge bosons can also give rise to interesting collider signatures like diboson excess, dilepton plus two jets excess reported recently in the large hadron collider data.