Probing hidden sectors with a muon beam: Total and differential cross sections for vector boson production in muon bremsstrahlung
Dmitry V. Kirpichnikov, H. Sieber, L. Molina Bueno, P. Crivelli, M. Kirsanov · Physical review. D/Physical review. D. · 2021
Vector bosons, such as dark photon ${A}^{\ensuremath{'}}$ or ${Z}^{\ensuremath{'}}$, can couple to muons and be produced in the bremsstrahlung reaction ${\ensuremath{\mu}}^{\ensuremath{-}}+N\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+N+{A}^{\ensuremath{'}}({Z}^{\ensuremath{'}})$. 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 ${A}^{\ensuremath{'}}({Z}^{\ensuremath{'}})$ important but also the recoil muon angle ${\ensuremath{\psi}}_{{\ensuremath{\mu}}^{\ensuremath{'}}}$. In this paper, we derive the total and the double differential cross sections involved in this process using the phase space Weizs\"acker-Williams and improved Weizs\"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 $\mathrm{NA}64\ensuremath{\mu}$ experiment that uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We also discuss its impact on the $\mathrm{NA}64\ensuremath{\mu}$ expected sensitivity to explore the $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ anomaly favored region with a ${Z}^{\ensuremath{'}}$ boson considering ${10}^{12}$ muons accumulated on target.