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 $\mathbb{ Z}_2\times \mathbb{ Z}^\prime_2$ 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 ${ \mathbb{ Z}_2^{ \prime\prime}}$, provided $u\leq 10$ 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 $\chi_{ { }_{ { }_3}}\rightarrow\gamma \gamma$) by the XMM-Newton observatory.
Categories: hep-ph