Abstract
We formulate principal positions of a non-Hermitian model with a γ5-extension of the fermion mass, which are often neglected in investigating this subject. A consistent approach to this problem requires the constraint m ≤ M, where M bounds the entire fermion mass spectrum. An analogous approach was proposed in the geometric model, which can be regarded as the first PT-symmetric non-Hermitian fermion model with a γ5-extension of mass. Exotic particles appear in both these theories. A detailed consideration of the properties of these particles allows conjecturing that they are possible candidates in the structure of dark matter. We also discuss a simple estimate for determining the maximum admissible value of the fermion mass M.
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