Fermion number anomaly with the fluffy mirror fermion

TL;DR

This paper analyzes a lattice formulation of chiral gauge theories, revealing that the mirror fermion, or fluff, exhibits a fermion number anomaly similar to the physical fermion, with implications for the strong CP problem and dark matter.

Contribution

It demonstrates that the fluffy mirror fermion in the formulation suffers from a fermion number anomaly, offering potential solutions to the strong CP problem and dark matter scenarios.

Findings

Fluffy mirror fermion has a fermion number anomaly opposite in sign to the physical fermion.

Massless fluff quarks could provide a solution to the strong CP problem.

Interaction of fluff with gravity could realize asymmetric dark matter.

Abstract

Quite recently, Grabowska and Kaplan presented a 4-dimensional lattice formulation of chiral gauge theories based on the chiral overlap operator. We study this formulation from the perspective of the fermion number anomaly and possible associated phenomenology. A simple argument shows that the consistency of the formulation implies that the fermion with the opposite chirality to the physical one, the "fluffy mirror fermion" or "fluff", suffers from the fermion number anomaly in the same magnitude (with the opposite sign) as the physical fermion. This immediately shows that if at least one of the fluff quarks is massless, the formulation provides a simple viable solution to the strong CP problem. Also, if the fluff interacts with gravity essentially in the same way as the physical fermion, the formulation can realize the asymmetric dark matter scenario.