Chiral symmetry breaking as a geometrical process

TL;DR

This paper introduces a geometric mechanism for chiral symmetry breaking using a formalism that relates linear dynamics in curved space to nonlinear dynamics in Minkowski space, offering an alternative view on neutrino chirality.

Contribution

It extends the Dynamical Bridge formalism to spinor fields, revealing a geometric process that causes chiral symmetry breaking without mass, potentially explaining undetected right-handed neutrinos.

Findings

Chiral symmetry breaking arises from geometric effects in the formalism.

Right-handed neutrinos are trapped by a NJL-type potential.

Left-handed components obey the Dirac equation in flat space.

Abstract

This article expands for spinor fields the recently developed Dynamical Bridge formalism which relates a linear dynamics in a curved space to a nonlinear dynamics in Minkowski space. Astonishingly, this leads to a new geometrical mechanism to generate a chiral symmetry breaking without mass, providing an alternative explanation for the undetected right-handed neutrinos. We consider a spinor field obeying the Dirac equation in an effective curved space constructed by its own currents. This way, both chiralities of the spinor field satisfy the same dynamics in the curved space. Subsequently, the dynamical equation is re-expressed in terms of the flat Minkowski space and then each chiral component behaves differently. The left-handed part of the spinor field satisfies the Dirac equation while the right-handed part is trapped by a Nambu-Jona-Lasinio (NJL) type potential.