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

TL;DR

This paper derives total and differential cross-sections for vector boson production in muon bremsstrahlung, aiding fixed target experiments like NA64μ in probing hidden sectors and the muon g-2 anomaly.

Contribution

It provides exact and approximate calculations of cross-sections for vector boson production in muon bremsstrahlung, enhancing experimental sensitivity analysis.

Findings

Derived cross-sections using phase space and tree-level calculations.

Compared cross-sections and signal yields for NA64μ experiment.

Discussed implications for probing the (g-2)_μ anomaly.

Abstract

Vector bosons, such as Dark Photon $A'$ or $Z'$, can couple to muons and be produced in the bremsstrahlung reaction $\mu^- + N \rightarrow \mu^- + N + A'(Z')$. 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 $\psi_{\mu'}$. In this paper, we derive the total and the double differential cross-sections involved in this process using the phase space Weisz\"acker-Williams and improved Weisz\"acker-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$\mu$ experiment that uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We also discuss its impact on the NA64$\mu$ expected sensitivity to explore the $(g-2)_\mu$ anomaly favoured region with a $Z'$ boson considering $10^{12}$ muons accumulated on target.