In addition to vector ($V$) type new particles extensively discussed previously, both $CP$-even ($S$) and $CP$-odd ($P$) spin-0 dark matter (DM) mediators can couple to muons and be produced in the bremsstrahlung reaction ${\mu }^{-}+N\to {\mu }^{-}+N+S(P)$. Their possible subsequent invisible decay into a pair of Dirac DM particles, $S(P)\to \chi \overline{\chi }$, can be detected in fixed target experiments through missing energy signature. In this paper, we focus on the case of experiments using high-energy muon beams. For this reason, we derive the differential cross sections involved using the phase space Weiszäcker-Williams approximation and compare them to the exact-tree-level calculations. The formalism derived can be applied in various experiments that could observe muon-spin-0 DM interactions. This can happen in present and future proton beam-dump experiments such as NA62, SHIP, HIKE, and SHADOWS; in muon fixed target experiments as $\mathrm{NA}64\mu$, MUonE and M3; in neutrino experiments using powerful proton beams such as DUNE. In particular, we focus on the $\mathrm{NA}64\mu$ experiment case, which uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We compute the derived cross sections, the resulting signal yields and we discuss the experiment projected sensitivity to probe the relic DM parameter space and the $(g-2{)}_{\mu }$ anomaly favored region considering ${10}^{11}$ and ${10}^{13}$ muons on target.

• Received 24 May 2023
• Accepted 15 August 2023

DOI:https://doi.org/10.1103/PhysRevD.108.056018

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Published by the American Physical Society