Non-anomalous axions: lessons from the Majoron

TL;DR

This paper demonstrates that the Majoron, a Nambu-Goldstone boson, is associated with a non-anomalous symmetry, specifically B-L, which resolves the domain wall problem and impacts how axion-like particles are detected.

Contribution

It reveals that the Majoron arises from a non-anomalous B-L symmetry, challenging the common assumption that axion-like particles are necessarily linked to anomalous symmetries.

Findings

Majoron linked to non-anomalous B-L symmetry

Effective couplings do not confirm anomalous origin

Implications for detecting non-anomalous Nambu-Goldstone bosons

Abstract

We show that when an anomalous and a non-anomalous global symmetries are spontaneously and simultaneously broken, the resulting Nambu--Goldstone boson is associated with the non-anomalous one. Applied to the Majoron, this implies that its underlying symmetry is $B-L$ rather than $L$, naturally resolving the domain wall problem. This result further demonstrates that effective couplings of the form $a \, F \, \tilde{F}$ do not uniquely indicate an anomalous origin, allowing the detection of non-anomalous Nambu--Goldstone bosons, such as the Majoron, in searches for axion--gauge boson interactions, potentially serving as evidence for the existence of new charged fermions.