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 $$\mathbb{Z}$2\times $\mathbb{Z}$^\prime_2$symmetrywhichbreakssoftlytoaremnant$$\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,amoderatelyheavyscalar$\chi{{}{{}2}}$with$50 ,,{\rm GeV} \leq M{\chi_{{}{{}2}}}\leq 80,,{\rm GeV}$andalight$\chi{{}{{}3}}$with$M{\chi_{{}{{}3}}} \sim 7$keV\mathrm{.}Thereisonlytinymixingbetween$\chi{{}{{}1}}$and$\chi{{}{{}2}}$aswellasbetween$\chi{{}{{}1}}$and$\chi{{}{{}3}}$. The lack of importance of domain wall formation in the present scenario from the spontaneous breaking of the discrete symmetry ${\mathbb{Z}}_2^{\mathrm{\prime }\mathrm{\prime }}$, provided $u\le 10$ 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 $\chi{{}{{}2}} \rightarrow {\rm b} \bar{\rm b}$decaymode)andtheobservationoftheX-rayline(fromthedecaychannel$\chi{{}_{{}_3}}\rightarrow\gamma \gamma$) by the XMM-Newton observatory.