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The mathematical model of multiple microscopic particles potentialscorresponds to a fourth order symmetric tensor with a particular structure inparticle physics. In this paper, we mainly dedicate to the study ofcopositivity for a class of tensors defined by the scalar dark matter with thestandard model Higgs and an inert doublet and a complex singlet. With the helpof its structure, we obtain the necessary and sufficient conditions, whichattains the analytic conditions required by the physical problems. At the sametime, this analytic expression provides how to determine a unique solution ofthe corresponding tensor complementarity problem with a parameter.

Copositivity for a class of fourth order symmetric tensors given by scalar dark matter