# Limiting Majoron self-interactions from Gravitational waves experiments

## TL;DR

This paper explores how gravitational wave experiments can test Majoron models, especially those involving first order phase transitions that produce detectable gravitational waves, and discusses collider detection prospects.

## Contribution

It introduces the 'violent Majoron model' scenario where Majoron self-interactions cause phase transitions detectable via gravitational waves, with implications for low-scale B-L symmetry breaking.

## Key findings

- Sub-electroweak scale phase transition can produce observable gravitational waves.
- Next-generation detectors like eLISA, DECIGO, and BBO can detect these signals.
- Potential collider signatures at CEPC through Higgs portal interactions.

## Abstract

We show how Majoron models may be tested/limited in gravitational waves experiments. In particular, the Majoron self-interaction potential may induce a first order phase transition, producing gravitational waves from bubble collisions. We dubbed such a new scenario {\it violent Majoron model}, because it would be associated to a violent phase transition in the early Universe. Sphaleron constraints can be avoided if the global $U(1)_{B-L}$ is broken at scales lower than the electroweak scale, provided that the B-L spontaneously breaking scale is lower than $10\, {\rm TeV}$ in order to satisfy the cosmological mass density bound. The possibility of a sub-electroweak phase transition is practically unconstrained by cosmological bounds and it may be detected within the sensitivity of next generation of gravitational waves experiments: eLISA, DECIGO and BBO. We also comment on the possible detection in CEPC collider, where Majorons's production can be observed from Higgs' portals in missing transverse energy channels.