Constraints on mass dimension one fermionic dark matter from the Yukawa interaction

We study the loop corrections to the scalar propagator and the fermionic self-energy for the mass dimension one fermionic dark matter with the Yukawa interaction. We find, in the former case, there is a nonvanishing Lorentz-violating term while the latter is Lorentz-invariant. Our study of the fermionic loop correction shows that unitarity demands the fermionic mass must be at least half of the bosonic mass and that the Lorentz-violating term makes a nontrivial correction to the bosonic propagator. We discuss what these results mean in the context of the standard model and the possibility of bypassing the unitarity constraint. In the simplest scenario, within the framework of standard quantum field theory, by identifying the scalar boson to be the Higgs boson with a mass of 125 GeV, the mass of the fermion must be at least 62.5 GeV.

Figure 1

Loop correction to the scalar propagator.

Figure 2

The plot of $F(p)/g_{\varphi }^2$ obtained by Monte Carlo integration with $5.8\times 10^7$ sample points that represents the angular distribution in the $\theta -\varphi$ plane. We considered $m_{\mathrm{\Lambda }}=62.5\mathrm{GeV}$, $m_{\mathrm{\Lambda }}=500\mathrm{GeV}$ with an effective cutoff ${\mu }_{\mathrm{eff}}=1.2209\times 10^{19}\mathrm{GeV}$ at the Planck scale.

Figure 3

Fermionic self-energy.