Probing Hidden Sectors with a muon beam: Total and differential cross-sections for vector boson production in muon bremsstrahlung

Abstract

Vector bosons, such as Dark Photon $A'$ or $Z'$, can couple to muons and be produced in the bremsstrahlung reaction $μ^- + N \rightarrow μ^- + N + A'(Z')$. Their possible subsequent invisible decay can be detected in fixed target experiments through missing energy/momentum signature. In such experiments, not only is the energy transfer to $A'(Z')$ important, but also the recoil muon angle $ψ_{μ'}$. In this paper, we derive the total and the double differential cross-sections involved in this process using the phase space Weiszäcker-Williams and improved Weiszäcker-Williams approximations, as well as using exact-tree-level calculations. As an example, we compare the derived cross-sections and resulting signal yields in the NA64$μ$ experiment that uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We also discuss its impact on the NA64$μ$ expected sensitivity to explore the $(g-2)_μ$ anomaly favoured region with a $Z'$ boson considering $10^{12}$ muons accumulated on target.