Searching for scalar boson decaying into light Z′ boson at collider experiments in U(1)${}_{L_{\pi }-L_{\tau }}$ model

We study a model with U(1)${}_{L_{\pi }-L_{\tau }}$ gauge symmetry and discuss collider searches for a scalar boson, which breaks U(1)${}_{L_{\pi }-L_{\tau }}$ symmetry spontaneously, decaying into light Z′ gauge boson. In this model, the new gauge boson, Z′, with a mass lighter than O(100) MeV, plays a role in explaining the anomalous magnetic moment of muon via one-loop contribution. For the gauge boson to have such a low mass, the scalar boson, ϕ with O(100) GeV mass appears associated with the symmetry breaking. We investigate experimental constraints on U(1)${}_{L_{\pi }-L_{\tau }}$ gauge coupling, kinetic mixing, and mixing between the SM Higgs and ϕ. Then collider search is discussed considering ϕ production followed by decay process ϕ→Z′Z′ at the large hadron collider and the international linear collider. We also estimate discovery significance at the linear collider taking into account relevant kinematical cut effects.