Dark matter polarization operator in the generalized Yukawa model

Nowadays, no dark matter candidates have been discovered. We consider the possible reason for that which is related to the approach of on-peak resonance searching for. As is believed usually, a new particle has small width and a narrow width approximation is applicable to identify such type resonant peak in the invariant mass spectrum of collision products. In the present paper, in the framework of the generalized Yukawa model, we find out the propertiesof the searched particle when its width is larger than a maximal one expected during experiments and so this state could be missed as a noise. Usually, the new particle width is considered as an arbitrary parameter. Here, we obtain the width of the dark matter particle from an imaginary part of polarization operators. Then the width is analyzed as explicit function of the couplings and masses in the underlying model of the dark matter. The corresponding constraints on the model parameters are obtained. Role of the one-loop mixing of visible and dark matter fields is investigated and constraint on the mixing angle value is derived. These estimations are quite general and, in particular, relevant to interactions between the particles of the Standard model and dark matter.