Eur. Phys. J. C (2023) 83: 786
https://doi.org/10.1140/epjc/s10052-023-11955-4

Regular Article - Theoretical Physics

Multi muon/anti-muon signals via productions of gauge and scalar bosons in a $U{(1)}_{L_{\mu }-L_{\tau }}$ model at muonic colliders

¹ Institute for the Advancement of Higher Education, Hokkaido University, 060-0817, Sapporo, Japan
² Department of Physics, Hokkaido University, 060-0810, Sapporo, Japan
³ College of Physics, Sichuan University, 610065, Chengdu, China
⁴ Faculty of Education, University of Miyazaki, 1-1 Gakuen-Kibanadai-Nishi, 889-2192, Miyazaki, Japan
⁵ Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, 819-0395, Fukuoka, Japan

^b nomura@scu.edu.cn

Received: 1 April 2023
Accepted: 24 August 2023
Published online: 5 September 2023

Abstract

We discuss the discovery potential of a promising signals, $3\times {\mu }^{+}{\mu }^{-}$ at a ${\mu }^{+}{\mu }^{-}$ collider and ${\mu }^{+}{\mu }^{+}{\mu }^{+}{\mu }^{+}{\mu }^{-}{\mu }^{-}$ at a ${\mu }^{+}{\mu }^{+}$ collider, that are obtained via production of $Z^{\prime }$ and a new scalar boson $\varphi$ in a spontaneously broken local $U{(1)}_{L_{\mu }-L_{\tau }}$ model. We consider the $Z^{\prime }$ associated production from the process ${\mu }^{+}{\mu }^{-}\to \varphi Z^{\prime }$ in addition to a muonphilic $Z^{\prime }$ fusion process ${\mu }^{+}{\mu }^{\pm }\to \varphi {\mu }^{+}{\mu }^{\pm }$. The scalar boson is associated with $U{(1)}_{L_{\mu }-L_{\tau }}$ symmetry breaking and dominantly decays into $Z^{\prime }{Z}^{\prime }$ mode. We carry out numerical simulation analysis for signal and background processes to estimate a discovery significance for different benchmark points. It is shown that our signal can be observed with integrated luminosity less than $\mathcal{O}(100)$ fb${}^{-1}$ for both ${\mu }^{+}{\mu }^{-}$ and ${\mu }^{+}{\mu }^{+}$ colliders with more than 5-$\sigma$ significance.