Muon Beam Dump Experiments probe five-dimensional nature of $U(1)_{L_{\mu}-L_{\tau}}$

Abstract

We have investigated the prospects of probing the five-dimensional $U(1)_{L_\mu - L_\tau}$ interactions in present and future muon dump experiments, namely, NA64$_\mu$, M$^3$, MuSIC, and a future muon beam dump experiment. These experiments are classified into two categories: the first two can probe processes where feebly interacting massive particles go into invisible channels, while the latter two can probe processes where these states decay into muon pairs. These two types of experiments are complementary in that they allow exploration of different parameter regions of a model. In our scenario, the presence of multiple massive gauge bosons as Kaluza-Klein (KK) particles leads to an enhancement in the signal events compared to the corresponding four-dimensional scenario. In particular, the decay process into muon pairs enables mass reconstruction of the parent particle, making it possible to directly demonstrate the existence of multiple KK particles in at least some parameter regions. This can provide clear evidence that the origin of the $U(1)_{L_\mu - L_\tau}$ interaction lies in five dimensions. Furthermore, the muon $(g-2)$ value, which is now consistent with the SM, can be used to exclude specific parameter regions for new particles interacting with muons. We also carefully discuss the non-trivial effects arising from nonzero kinetic mixing.