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

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 $Z^{\prime }$, 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 $min(m_{Z^{\prime }},m_S)$ 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.

Comments: 21 pages, 4 figures, 2 tables