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

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.Comment: 11 pages, 6 figures, revised version, improved cross-section integrator is used, comparison with bremsstrahlung spectrum is added, final conclusions remain unchange

Missing energy signature from invisible decays of dark photons at the CERN SPS

The dark photon ($A'$) production through the mixing with the bremsstrahlung photon from the electron scattering off nuclei can be accompanied by the dominant invisible $A'$ decay into dark-sector particles. In this work we discuss the missing energy signature of this process in the experiment NA64 aiming at the search for $A'\to invisible$ decays with a high-energy electron beam at the CERN SPS. We show the distinctive distributions of variables that can be used to distinguish the $A'\to invisible$ signal from background. The results of the detailed simulation of the detector response for the events with and without $A'$ emission are presented. The efficiency of the signal event selection is estimated. It is used to evaluate the sensitivity of the experiment and show that it allows to probe the still unexplored area of the mixing strength $10^{-6}\lesssim \epsilon \lesssim 10^{-2}$ and masses up to $M_{A'} \lesssim 1$ GeV. The results obtained are compared with the results from other calculations. In the case of the signal observation, a possibility of extraction of the parameters $M_{A'}$ and $\epsilon$ by using the missing energy spectrum shape is discussed. We consider as an example the $A'$ with the mass 16.7 MeV and mixing $\epsilon \lesssim 10^{-3}$, which can explain an excess of events recently observed in nuclear transitions of an excited state of $^8$Be. We show that if such $A'$ exists its invisible decay can be observed in NA64 within a month of running, while data accumulated during a few months would allow also to determine the $\epsilon$ and $M_{A'}$ parameters.Comment: 12 pages, 15 figures. Revised versio