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

TL;DR

This paper investigates the copositivity of a specific class of fourth order symmetric tensors arising from scalar dark matter models, providing necessary and sufficient conditions and solutions for related tensor complementarity problems.

Contribution

It introduces explicit analytic conditions for copositivity of tensors linked to scalar dark matter, connecting mathematical tensor analysis with physical particle models.

Findings

Derived necessary and sufficient copositivity conditions

Provided a method to solve the tensor complementarity problem

Linked tensor properties to physical dark matter models

Abstract

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.