Theoretical framework to analyze searches for hidden light gauge bosons in electron scattering fixed target experiments

Motivated by anomalies in cosmic ray observations and by attempts to solve questions of the Standad Model of particle physics like the (g-2)_mu discrepancy, U(1) extensions of the Standard Model have been proposed in recent years. Such U(1) extensions allow for the interaction of Dark Matter by exchange of a photon-like massive force carrier \gamma' not included in the Standard Model. In order to search for \gamma' bosons various experimental programs have been started. One approach is the dedicated search at fixed-target experiments at modest energies as performed at MAMI or at the Jefferson Lab. In these experiments the process e(A,Z)->e(A,Z)l^+l^- is investigated and a search for a very narrow resonance in the invariant mass distribution of the l^+l^- pair is performed. In this work we analyze this process in terms of signal and background in order to describe existing data obtained by the A1 experiment at MAMI with the aim to give accurate predictions for exclusion limits in the \gamma' parameter space. We present a detailed theoretical analysis of the cross sections entering in the description of such processes.