Muon Tridents at FASER and NA64$\mu$: Motivation, Predictions, and Prospects for Precision Measurements
Abstract
The intense flux of high-energy muons produced in the far-forward region of $pp$ collisions at the LHC provides a unique opportunity to study rare electromagnetic interactions at TeV energies. In this work, we investigate the muon trident scattering in muon-nucleus interactions at the FASER experiment, which is expected to have recorded more than $10^5$ such events. The theoretical description of the process is reviewed and improved. Predictions for the total event rates and differential distributions expected during Run~3 of the LHC are presented, taking into account realistic detector acceptance and the main background contributions. The dependence of the predictions on the treatment of the nuclear form factors and the impact of higher-order QED effects such as Coulomb corrections are investigated. Our results indicate that the muon trident process can be measured for the first time at TeV energies using FASER's spectrometer, with a projected precision on the cross-section at the percent level. We also extended our analysis to the NA64$\mu$ experiment and showed that, together with FASER, these experiments can probe the energy dependence of the muon trident cross-section over a broad unexplored energy range.