Chiral phases for massive fermions and spinor classifications

Abstract

We explore the physics of regular spinors in the Lounesto classification. These spinors are constructed by introducing two chiral phases. One is a degree of freedom present in choosing the $\gamma^{\mu}$ matrices that leaves the Lorentz generators invariant. Another is a degree of freedom allowed by the massive spin-half field that is unconstrained by Poincar\'{e} symmetry and locality. By choosing appropriate values of the two phases, we obtain all the classes of regular spinors. For the Dirac fermions, both phases are equal. We argue that the chiral phase of the Standard Model fermions is a new set of physical parameter. We find, the lepton chiral phases cannot be measured within the weak interaction. For quarks, their phases are conjectured to be identical. In general, to measure the phases between different fermionic generations would require interactions beyond the Standard Model.