  The mathematical model of multiple microscopic particles potentials
corresponds to a fourth order symmetric tensor with a particular structure in
particle physics. In this paper, we mainly dedicate to the study of
copositivity for a class of tensors defined by the scalar dark matter with the
standard model Higgs and an inert doublet and a complex singlet. With the help
of its structure, we obtain the necessary and sufficient conditions, which
attains the analytic conditions required by the physical problems. At the same
time, this analytic expression provides how to determine a unique solution of
the corresponding tensor complementarity problem with a parameter.
