Muon Beam Dump Experiments explicate five-dimensional nature of $U(1)_{L_μ-L_τ}$

Abstract

We have investigated the prospects of probing the five-dimensional $U(1)_{L_μ- L_τ}$ interactions in present and future muon dump experiments, namely, NA64$_μ$, 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 $U(1)_{L_μ- L_τ}$ 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.

Figures (9)

• Figure 1: The lowest-order $2 \to 3$ production process is given by: $\mu(p) + A(P_i) \rightarrow \mu(p') + A(P_f) + Z'(k)$, where $p$ and $P_i$ denote the initial four-momenta of the incoming muon and target nucleus, respectively, and $p'$ and $P_f$ are the final-state four-momenta of the outgoing muon and recoiling nucleus. The outgoing $Z'$ boson carries momentum $k$, while $q = P_i - P_f$ represents the momentum of the intermediate virtual photon exchanged in the process. Here, $A$, $\gamma$, $\mu$, and $Z'$ denote the target nucleus, photon, muon, and the new gauge boson, respectively.
• Figure 2: Feynman diagram illustrating a $2 \to 2$ scattering process mediated by the 4-D gauge boson $Z'$ associated with the $U(1)_{L_\mu - L_\tau}$ symmetry.
• Figure 3: Feynman diagram illustrating a $2 \to 2$ scattering process mediated by the extra-dimensional gauge boson $Z^{\prime(n)}_{\mu}$ associated with the $U(1)_{L_\mu - L_\tau}$ symmetry.
• Figure 4: Summary of current/future exclusion limits in the $(m_{\text{KK}},\, g')$ parameter space for the 5D $U(1)_{L_\mu - L_\tau}$ model under the benchmark choices $\epsilon_4 = 0$ and $\widetilde{y}_\text{SM} = 0$. They illustrate the sensitivity of various experiments for two KK mode truncations: $n_{\text{KKmax}} = 1$ (Left Panel) and $n_{\text{KKmax}} = 5$ (Right Panel). For the meaning of the vertical black dotted line in the right panel, refer to Footnote \ref{['foot:KK-treatments']}. For the definitions of each exclusion limit via the beam dump experiments, refer to Section \ref{['sec:Experiments']}.
• Figure 5: Comparison of MuSIC (Left) and future beam dump (Right) sensitivities for individual $n_{\text{KK}}$ modes for $\widetilde{y}_\text{SM} = 0$ and $\epsilon_4=0$.