Constraining dark matter from strong phase transitions in a $U(1)_{L_{\mu}-L_{\tau}}$ model: Implications for neutrino masses and muon $g-2$

TL;DR

This paper explores a $U(1)_{L_{\mu}-L_{ au}}$ extension of the Standard Model, linking dark matter constraints, strong phase transitions, neutrino masses, and the muon g-2 anomaly, with implications for gravitational wave detection.

Contribution

It introduces a non-minimal $U(1)_{L_{\mu}-L_{ au}}$ model with new scalars and fermions, demonstrating its ability to explain dark matter, neutrino oscillations, and the muon g-2 anomaly, while analyzing phase transitions and gravitational wave signals.

Findings

Strong first-order phase transitions produce detectable gravitational waves.

Dark matter relic density is constrained by phase transition dynamics.

Model successfully explains neutrino oscillation parameters and muon g-2 anomaly.

Abstract

In this paper, we study a non-minimal gauged $U(1)_{L_{\mu}-L_{\tau}}$ model, where we add two complex singlet scalars, three right-handed Majorana neutrinos (RHN), and a vector-like dark fermion to the Standard Model (SM), all non-trivially charged under the extra gauge symmetry. The model offers an easy resolution to the muon $(g-2)$ anomaly, which fixes the scale of spontaneous symmetry breaking. Furthermore, the two-zero minor structure in the RHN mass matrix provides successful predictions for neutrino oscillation parameters, including the Dirac phase. The extended scalar sector can easily induce first-order phase transitions. We identify all possible phase transition patterns in the three-dimensional field space. We quantify the associated gravitational waves from the sound wave source and demonstrate that the signatures can be observed in future space-based experiments. We find that strong first-order phase transitions require large values of scalar quartic couplings which constrain the scalar dark matter (DM) relic density to a maximum of $10^{-2}$ and $10^{-5}$ when we consider the DM direct detection bound. Nonetheless, the model successfully explains the DM relic density via contribution from the vector-like dark fermion. We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study.