Unveiling atomic electron motion effects in $e^+e^-$ high energy collisions at NA64

Atomic electron motion is responsible for well-studied effects observed in low-energy (MeV-scale) processes. Recently, interest in this phenomenon has also emerged within the high-energy physics community, due to its potential to increase significantly the center-of-mass energy in fixed-target experiments. However, direct experimental evidence of this effect in high energy collisions has yet to be observed. We argue that a striking manifestation of atomic electron momenta could be revealed by the NA64 experiment at CERN during the proposed run with a 40 GeV positron beam. At this energy, $μ^+μ^-$ production via positron annihilation on electrons at rest is kinematically forbidden. The detection of $μ^+μ^-$ pairs from the annihilation channel would thus constitute direct evidence of an increase in the center-of-mass energy resulting from atomic electron motion. We also investigate the expected signatures for the proposed 60 GeV run, as well as for the data already collected at 70 GeV. Intriguingly, in both these cases, the predicted number of $μ^+μ^-$ pairs from positron annihilation is reduced compared to the electron-at-rest approximation.