The $U(1)_{L_\mu-L_\tau}$ breaking phase transition, muon $g-2$, dark matter, collider and gravitational wave

TL;DR

This paper explores a model extending the Standard Model with a new U(1) gauge symmetry to address dark matter and muon g-2 anomalies, analyzing phase transitions, gravitational waves, and collider signals.

Contribution

It introduces a comprehensive framework linking dark matter, muon g-2, phase transitions, gravitational waves, and collider constraints in a U(1) extension.

Findings

First order U(1) breaking phase transition can occur within the model.

Gravitational wave signals are detectable by U-DECIGO.

Collider searches impose strong bounds on particle masses.

Abstract

Combining the dark matter and muon $g-2$ anomaly, we study the $U(1)_{L_\mu-L_\tau}$ breaking phase transition, gravitational wave spectra, and the direct detection at the LHC in an extra $U(1)_{L_\mu-L_\tau}$ gauge symmetry extension of the standard model. The new fields includes vector-like leptons ($E_1,~ E_2,~ N$), $U(1)_{L_\mu-L_\tau}$ breaking scalar $S$ and gauge boson $Z'$, as well as the dark matter candidate $X_I$ and its heavy partner $X_R$. A joint explanation of the dark matter relic density and muon $g-2$ anomaly excludes the region where both $min(m_{E_1},m_{E_2},m_N,m_{X_R})$ and $min(m_{Z'},m_S)$ are much larger than $m_{X_I}$. In the parameter space accommodating the DM relic density and muon $g-2$ anomaly, the model can achieve a first order $U(1)_{L_\mu-L_\tau}$ breaking phase transition, whose strength is sensitive to the parameters of Higgs potential. The corresponding gravitational wave spectra can reach the sensitivity of U-DECIGO. In addition, the direct searches at the LHC impose stringent bound on the mass spectra of the vector-like leptons and dark matter.