Recently, electron scattering fixed-target 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 determinations of the anomalous magnetic moment of the muon. In such $U(1)$ 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 $e(A,Z)\to e(A,Z)l^{+}{l}^{-}$. 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 Weizsäcker–Williams approximation to calculate the signal cross section of the process, which is widely used to design such experimental setups. Furthermore, we study the influence of the contribution from doubly virtual Compton scattering on experiments performed with proton targets. Based on a previous work, we investigate the discovery potential of future experimental setups at the Jefferson Lab and obtain a projected exclusion limit. We find that doubly virtual Compton scattering causes a 10% effect on the cross section for the kinematics of a planned experiment and therefore does not alter the obtained experimental reach significantly. In addition, we find that the Weizsäcker–Williams approximation can be applied to calculate the underlying cross sections in the kinematic range of most of the present and upcoming experiments, provided that the dependence on the energy and emission angle of the hidden photon is accounted for.

• Received 20 November 2013

DOI:https://doi.org/10.1103/PhysRevD.89.055006