Electroweak breaking and Dark Matter from the common scale

Abstract: We propose a classically scale invariant extension of the Standard Model where the electroweak symmetry breaking and the mass of the Dark Matter particle come from the common scale. We introduce $U(1)_X$ gauge symmetry and $X$-charged scalar $\Phi$ and Majorana fermion $N$. Scale invariance is broken via Coleman-Weinberg mechanism providing the vacuum expectation value of the scalar $\Phi$. Stability of the dark matter candidate $N$ is guaranteed by a remnant $Z_2$ symmetry. The Higgs boson mass and the mass of the Dark Matter particle have a common origin, the vacuum expectation value of $\Phi$. Dark matter relic abundance is determined by annihilation $NN \to \Phi\Phi$. We scan the parameter space of the model and find the mass of the dark matter particle in the range from 500 GeV to a few TeV.