Missing (up) Mass, Accidental Anomalous Symmetries, and the Strong CP Problem

TL;DR

This paper explores the possibility that a massless up quark, arising from an anomaly-free horizontal symmetry, can naturally solve the strong CP problem, challenging previous doubts about its phenomenological viability.

Contribution

It demonstrates that an anomaly-free horizontal symmetry can lead to a massless up quark and an accidental anomalous symmetry, providing a potential solution to the strong CP problem.

Findings

Massless up quark solution remains phenomenologically viable.

Horizontal symmetry can naturally produce a massless up quark.

Accidental anomalous symmetry plays a role in solving the strong CP problem.

Abstract

We reconsider the massless up quark solution of the strong CP problem. We show that an anomaly free horizontal symmetry can naturally lead to a massless up quark and to a corresponding accidental anomalous symmetry. Reviewing the controversy about the phenomenological viability of $m_u=0$ we conclude that this possiblity is still open and can solve the strong CP problem. To appear in the Proceedings of The Yukawa Couplings and the Origins of Mass Workshop.