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

Abstract

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.