Study of the discovery potential for hidden photon emission at future electron scattering fixed target experiments

Electron scattering fixed target experiments are a versatile tool to explore various physics phenomena. Recently these experiments came into focus to search for $U(1)$ extensions of the Standard Model of particle physics at low energies. These extensions are motivated from anomalies in astrophysical observations as well as from deviations from Standard Model predictions, such as the discrepancy between the experimental and theoretical determination of the anomalous magnetic moment of the muon. They also arise naturally when the Standard Model is embedded into a more general theory. In the considered $U(1)$ extensions a new, light messenger particle $\gamma^\prime$, the hidden photon, couples to the hidden sector as well as to the electromagnetic current of the Standard Model by kinetic mixing, which allows for a search for this particle e.g. in the invariant mass distribution of the process $e (A,\,Z)\rightarrow e (A,\,Z) l^+ l^-$. In this process the hidden photon is emitted by bremsstrahlung and decays into a pair of Standard Model leptons. In this work we study the applicability of the Weizs\"acker-Williams approximation to calculate the signal cross section of the process, which is widely used to design such experimental setups. Furthermore, based on a previous work, we investigate the discovery potential of future experimental setups at the Jefferson Lab. For that purpose we simulate the relevant cross sections for the signal and the QED background in the actual kinematical setups and obtain projected exclusion limits.