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

Chiral phases for massive fermions and spinor classifications