Chiral phases for massive fermions and spinor classifications

TL;DR

This paper investigates the role of chiral phases in regular spinors within the Lounesto classification, revealing new physical parameters for fermions and implications for Standard Model particles and beyond.

Contribution

It introduces two chiral phases in spinor construction, showing how they classify all regular spinors and proposing the lepton and quark phases as potentially new physical parameters.

Findings

All classes of regular spinors can be obtained by tuning two chiral phases.

The chiral phase of Standard Model fermions is a new physical parameter.

Lepton phases are unmeasurable within the weak interaction.

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.