The exact tree-level calculation of the dark photon production in high-energy electron scattering at the CERN SPS

TL;DR

This paper presents exact tree-level calculations of dark photon production in high-energy electron scattering at CERN SPS, improving previous approximations and enabling precise experimental sensitivity studies for dark matter searches.

Contribution

It provides the first exact tree-level cross section calculations for dark photon production in electron scattering experiments, enhancing the accuracy of experimental simulations and analyses.

Findings

Exact calculations agree with other methods within uncertainties.

Significant corrections to previous approximations are identified.

Enhanced sensitivity estimates for future experiments are provided.

Abstract

Dark photon ($A'$) that couples to the standard model fermions via the kinetic mixing with photons and serves as a mediator of dark matter production could be observed in the high-energy electron scattering $e^- + Z ~\rightarrow e^- + Z + A'$ off nuclei followed by the $A' \to invisible $ decay. We have performed the exact, tree-level calculations of the $A'$ production cross sections and implemented them in the program for the full simulation of such events in the experiment NA64 at the CERN SPS. Using simulations results, we study the missing energy signature for the bremsstrahlung $A' \rightarrow $ invisible decay that permits the determination of the $\gamma-A'$ mixing strength in a wide, from sub-MeV to sub-GeV, $A'$ mass range. We refine and expand our earlier studies of this signature for discovering $A'$ by including corrections to the previously used calculations based on the improved Weizsaker-Williams approximation, which turn out to be significant. We compare our cross sections values with the results from other calculations and find a good agreement between them. The possibility of future measurements with high-energy electron beams and the sensitivity to $A'$ are briefly discussed.