Singlet fermionic dark matter and naturalness

We reexamine a renormalizable model of a fermionic dark matter with a gauge singlet Dirac fermion and a real singlet scalar which ensure the cancellation of one-loop quadratic divergence to the Higgs mass. We constrain the model parameters from the fine-tuning problem originating from the radiative corrections to the Higgs mass using the Veltman condition (VC), and show the allowed region of new physics parameters satisfying the recent measurement of relic abundance. With the obtained parameter set, we predict the elastic scattering cross section of the singlet fermion into target nuclei for a direct detection of the dark matter. We also perform the analysis with arbitrary set of parameters without the VC as a comparison, and discuss the implication of the constraints by the VC.