  \begin{abstract} Nowadays, no dark matter candidates have been discovered. We
consider two possible reasons for that, both related to the approach of on-peak
resonance searching for. As is believed usually, a new particle suits the
conditions that the ratio of the width to the mass is less than $1-3 \%$ and a
narrow width approximation (NWA) is applicable to identify the such type
resonant peak in the invariant mass spectrum of collision products.
  In the present paper, in the framework of generalized Yukawa model, we find
out the properties of 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. We also ascertain the values of particle's parameters when the NWA is
not applicable and estimate the width value when it happens. These estimations
are relevant to interactions between the Standard model and dark matter
particles. Such approach is focused on the role of couplings and mass values
introduced in the model describing interaction of visible and dark matter.
  Key words: dark matter; resonance; narrow width approximation; mixing of
fields.
