Proposal for an experiment to search for dark sector particles weakly coupled to muon at the SPS

The NA64 collaboration proposes to carry out further searches for dark sector and other rare processes in missing energy events from high energy muon interactions in a hermetic detector at the CERN SPS for the 2021 pilot run. A dark sector of particles predominantly weakly-coupled to the second and possibly third generations of the Standard Model is motivated by several theoretically interesting models. Additional to gravity this new very weak interaction between the visible and dark sector could be mediated either by a scalar ($S_\mu$) or $U'(1)$ gauge bosons ($Z_\mu$) interacting with ordinary muons. In a class of $L_\mu-L_\tau$ models the corresponding $Z_\mu$ could be light and have the coupling strength lying in the experimentally accessible region. If such $Z_\mu$ mediator exists it could also explain the muon $(g-2)_\mu$ anomaly - the discrepancy between the predicted and measured values of the muon anomalous magnetic moment. We propose an extension of the experiment called NA64$\mu$ to search for invisible decays of the $Z_\mu$ either to neutrinos or light Dark Matter particles. The primary goal of the experiment in the 2021 pilot run with the 100-160 GeV M2 beam is to commission the NA64$\mu$ detector and to probe for the first time the still unexplored area of the coupling strengths and masses $M_{Z_\mu} < 200$ MeV that could explain the muon $(g-2)_\mu$ anomaly. Moreover, the NA64$\mu$ has the capability of a sensitive search for $S_\mu$'s decaying invisibly to dark-sector particles, such as dark matter and millicharged particles and will cover a part of the parameter space complementary to what is intended to be probed by other searches.