  The paper formulates a principal positions of non-Hermitian models with
$\gamma_5$-mass extensions, which often be ignored in some investigations for
this subject. In fact in this case Hamiltonians contain not only Hermitian
masses $m_1$, but also contribution from anti-Hermitian components of fermion
masses $m_2$. Main misunderstanding a number of papers is consist in using of
this 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 a
simple 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 $M$ becomes
infinite 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 a
number of new fermions masses which are equal to the masses of particles
Standard Model(SM) but when they have the non-Hermitian characteristics. In
this case the paradox of the "two masses" takes place and its solution may be
done only in suggested model with a maximal mass. Appearing particles can be
considered as some new particles arising beyond SM. The unusual properties of
these particles allow also to consider their as possible candidates in
structure of dark matter.
