Nonthermal Two Component Dark Matter Model for Fermi-LAT $gamma$-ray excess and 3.55 keV X-ray Line

A two component model of nonthermal dark matter is formulated to simultaneously explain the Fermi-LAT results indicating a $gamma$-ray excess observed from our Galactic Centre in the 1-3 GeV energy range and the detection of an X-ray line at 3.55 keV from extragalactic sources. Two additional Standard Model singlet scalar fields $S_2$ and $S_3$ are introduced. These fields couple among themselves and with the Standard Model Higgs doublet $H$. The interaction terms among the scalar fields, namely $H$, $S_2$ and $S_3$, are constrained by the application of a discrete $mathbb{Z}_2times mathbb{Z}^prime_2$ symmetry which breaks softly to a remnant $mathbb{Z}^{prime prime}_2$ symmetry. This residual discrete symmetry is then spontaneously broken through an MeV order vacuum expectation value $u$ of the singlet scalar field $S_3$. The resultant physical scalar spectrum has the Standard Model like Higgs as $chi_{{}_{{}_1}}$ with $M_{chi_{{}_{{}_1}}}sim 125$ GeV, a moderately heavy scalar $chi_{{}_{{}_2}}$ with $50 ,,{rm GeV} leq M_{chi_{{}_{{}_2}}}leq 80,,{rm GeV}$ and a light $chi_{{}_{{}_3}}$ with $M_{chi_{{}_{{}_3}}} sim 7$ keV. There is only tiny mixing between $chi_{{}_{{}_1}}$ and $chi_{{}_{{}_2}}$ as well as between $chi_{{}_{{}_1}}$ and $chi_{{}_{{}_3}}$. The lack of importance of domain wall formation in the present scenario from the spontaneous breaking of the discrete symmetry ${mathbb{Z}_2^{primeprime}}$, provided $uleq 10$ MeV, is pointed out. We find that our proposed two component dark matter model is able to explain successfully both the above mentioned phenomena $-$ the Fermi-LAT observed $gamma$-ray excess (from the $chi_{{}_{{}_2}} rightarrow {rm b} bar{rm b}$ decay mode) and the observation of the X-ray line (from the decay channel $chi_{{}_{{}_3}}rightarrowgamma gamma$) by the XMM-Newton observatory.