Z Boson Radiative Decay $Z\to {\mu }^{+}{\mu }^{-}\gamma$ at the LHC

Abstract

We study the radiative decay of the $Z$ boson, $Z\to {\mu }^{+}{\mu }^{-}\gamma$, at the LHC, providing both Standard Model (SM) precision analysis and new physics projections. With detailed analysis of Run-2 and future HL-LHC performances, we demonstrate that this decay mode can be measured with a statistical precision at the sub-percentage level. From existing Run-1 data, we extract ${\text{Br}}^{\text{fid}}(Z\to \mu \mu \gamma )=(3.34\pm 0.016)\times 10^{-4}$. We further explore the sensitivity of this channel to axion-like particles (ALPs) and to an anomalous $U(1{)}_X$ gauge boson coupled to the muon. Both scenarios feature resonant structures in the dimuon invariant mass spectrum within the $Z\to a/X+\gamma \to {\mu }^{+}{\mu }^{-}\gamma$ final state. Our results show that the radiative $Z$ decay provides a clean and statistically powerful probe of such leptophilic new physics, extending the current collider reach for ALPs and anomalous gauge forces down to $g_X\sim \mathcal{O}(10^{-3})$. This study highlights the potential of rare electroweak gauge boson decays as precision tests of the SM and sensitive probes of new interactions at the LHC.

Comments: 16 pages, 8 figures, 2 tables