Prospects in the search for a new light Z0 boson with the NA64 mu experiment at the CERN SPS

A light Z0 vector boson coupled to the second and third lepton generations through the L mu - L tau current with mass below 200 MeV provides a very viable explanation in terms of new physics to the recently confirmed og - 2 thorn mu anomaly. This boson can be produced in the bremsstrahlung reaction mu N - mu NZ0 after a high energy muon beam collides with a target. NA64 mu is a fixed-target experiment using a 160 GeV muon beam from the CERN Super Proton Synchrotron accelerator looking for Z0 production and its subsequent decays, Z0 - invisible. In this paper, we present the study of the NA64 mu sensitivity to search for such a boson. This includes a realistic beam simulation, a detailed description of the detectors and a discussion about the main potential background sources. A pilot run is scheduled in order to validate the simulation results. If those are confirmed, NA64 mu will be able to explore all the remaining parameter space which could provide an explanation for the g - 2 muon anomaly in the L mu - L tau model.