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

## TL;DR

This paper explores collider signatures of a scalar boson in a $U(1)_{L_m-tau}$ model, focusing on its decay into light $Z'$ bosons, with implications for muon magnetic moment anomalies and collider detection prospects.

## Contribution

It introduces a collider search strategy for a scalar boson decaying into light $Z'$ bosons within the $U(1)_{L_m-tau}$ framework, connecting theoretical model features with experimental detection.

## Key findings

- Constraints on gauge coupling and mixing parameters established.
- Potential for discovery at LHC and ILC analyzed.
- Significance estimates suggest feasible detection under certain conditions.

## Abstract

We study a model with $U(1)_{L_\mu - L_\tau}$ gauge symmetry and discuss collider searches for a scalar boson, which breaks $U(1)_{L_\mu - L_\tau}$ symmetry spontaneously, decaying into light $Z'$ gauge boson. In this model, the new gauge boson, $Z'$, with a mass lighter than $\mathcal{O}(100)$ 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, $\phi$ with $\mathcal{O}(100)$ GeV mass appears associated with the symmetry breaking. We investigate experimental constraints on $U(1)_{L_\mu - L_\tau}$ gauge coupling, kinetic mixing, and mixing between the SM Higgs and $\phi$. Then collider search is discussed considering $\phi$ production followed by decay process $\phi \to Z' Z'$ 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.