Gravitational Wave Signatures of $\mathrm{U(1)_X}$ Breaking and Right-Handed Neutrino Dynamics

TL;DR

This paper explores a $U(1)_X$ extended Standard Model with right-handed neutrinos, analyzing its phase transition and gravitational wave signals, and its implications for neutrino masses, baryogenesis, and future experiments.

Contribution

It provides a comprehensive analysis linking $U(1)_X$ symmetry breaking, neutrino mass generation, and gravitational wave predictions within a minimal extension of the Standard Model.

Findings

Gravitational wave signals from phase transition are within reach of future detectors.

Model consistent with current neutrino oscillation data.

Right-handed neutrinos enable viable leptogenesis.

Abstract

The Standard Model (SM) leaves several fundamental questions unanswered, including the origin of neutrino masses, the baryon asymmetry of the Universe, and the nature of dark matter. Motivated by these gaps, we investigate an extension of the SM with an additional local $U(1)_X$ gauge symmetry and a complex scalar singlet that spontaneously breaks this symmetry via its vacuum expectation value. The extended framework naturally accommodates three right-handed neutrinos (RHNs) to ensure anomaly cancellation and implements a type-I seesaw mechanism for active neutrino masses. We perform a detailed numerical analysis demonstrating consistency with current neutrino oscillation data, including predictions for the effective Majorana mass parameter relevant to neutrinoless double beta decay. Furthermore, we estimate the key parameters of the first-order phase transition and compute the resulting stochastic gravitational wave spectrum, demonstrating that it can lie within the reach of forthcoming experiments such as LISA, DECIGO, BBO, and the Einstein Telescope. The right-handed neutrinos also open a viable path for thermal leptogenesis, providing a unified link between neutrino mass generation, baryogenesis, and gravitational wave signatures. Our results demonstrate that this minimal $U(1)_X$ scenario remains a promising probe for physics beyond the Standard Model, accessible through upcoming gravitational wave and neutrino experiments.