U(1) L μ -L τ breaking phase transition, muon g–2, dark matter, collider, and gravitational wave

Combining the dark matter and muon anomaly, we study the breaking phase transition, gravitational wave spectra, and direct detection at the LHC in an extra gauge symmetry extension of the standard model. The new fields include vector-like leptons ( ), the breaking scalar S , and the gauge boson , as well as the dark matter candidate and its heavy partner . A joint explanation of the dark matter relic density and muon anomaly excludes the region where both and are much larger than . In the parameter space accommodating the DM relic density and muon anomaly, the model can achieve a first-order breaking phase transition, whose strength is sensitive to the parameters of the Higgs potential. The corresponding gravitational wave spectra can reach the sensitivity of U-DECIGO. In addition, the direct searches at the LHC impose stringent bounds on the mass spectra of the vector-like leptons and dark matter.