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The paper formulates a principal positions of non-Hermitian models with$\gamma_5$-mass extensions, which often be ignored in some investigations forthis subject. In fact in this case Hamiltonians contain not only Hermitianmasses $m_1$, but also contribution from anti-Hermitian components of fermionmasses $m_2$. Main misunderstanding a number of papers is consist in using ofthis model for any values of fermion masses for fixed values of $m_1$ and$m_2$. However the basis appearing of two parameters masses may be undertaken asimple estimation for determination maximal permissible value of fermion mass$M={m_1}^2/2m_2$ which may be used for this model. Easy to see that $M$ becomesinfinite and hence experimentally does not observable only in Dirac's limit,when the non-Hermitian mass fully is disappearing. In particular the equality$m_1=m_2$ can be realized only in two cases when $m_1=m_2=0$ and $m_1=m_2=2M$.Moreover in the second case the question is about the possibility existence anumber of new fermions masses which are equal to the masses of particlesStandard Model(SM) but when they have the non-Hermitian characteristics. Inthis case the paradox of the "two masses" takes place and its solution may bedone only in suggested model with a maximal mass. Appearing particles can beconsidered as some new particles arising beyond SM. The unusual properties ofthese particles allow also to consider their as possible candidates instructure of dark matter.

An upper limit on fermion mass spectrum in non-Hermitian models and its implications for studying of dark matter