Probing hidden sectors with a muon beam: Implication of spin-0 dark matter mediators for the muon (g-2) anomaly and the validity of the Weisz?cker-Williams approach

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 -mu- + N + S(P). Their possible subsequent invisible decay into a pair of Dirac DM particles, S(P) -chi chi over bar , 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 Weiszacker-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 NA64 mu, MUonE and M3; in neutrino experiments using powerful proton beams such as DUNE. In particular, we focus on the NA64 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 1011 and 1013 muons on target.