Interaction of massless Dirac field with a Poincar\'e gauge field

TL;DR

This paper explores how massless Dirac fields interact differently with a Poincaré gauge field modeled as a gravitational and Yang-Mills field, revealing chiral asymmetries not present in standard Reissner-Nordström black holes.

Contribution

It introduces a Poincaré gauge theory model where gravitational and Yang-Mills fields are unified and analyzes the unique interaction effects on massless Dirac fields, highlighting chiral differences.

Findings

Left-handed and right-handed Dirac fields behave differently in the presence of the gauge fields.

The interaction causes observable differences in scattering by a Reissner-Nordström type black hole.

Chiral asymmetry arises from direct coupling with the Yang-Mills field, unlike in standard geometries.

Abstract

In this paper we consider a model of Poincar\'e gauge theory (PGT) in which a translational gauge field and a Lorentz gauge field are actually identified with the Einstein's gravitational field and a pair of ``Yang-Mills'' field and its partner, respectively.In this model we re-derive some special solutions and take up one of them. The solution represents a ``Yang-Mills'' field without its partner field and the Reissner-Nordstr\"om type spacetime, which are generated by a PGT-gauge charge and its mass.It is main purpose of this paper to investigate the interaction of massless Dirac fields with those fields. As a result, we find an interesting fact that the left-handed massless Dirac fields behave in the different manner from the right-handed ones. This can be explained as to be caused by the direct interaction of Dirac fields with the ``Yang-Mills'' field. Accordingly, the phenomenon can not happen in the behavior of the neutrino waves in ordinary Reissner-Nordstr\"om geometry. The difference between left- and right-handed effects is calculated quantitatively, considering the scattering problems of the massless Dirac fields by our Reissner-Nordstr\"om type black-hole.