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

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. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.