Search for radiative leptonic decay <i>D</i> ⁺→<i>γe</i> ⁺ <i>ν_e </i> using deep learning*

Abstract Using 20.3 fb –1 of annihilation data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we report on an improved search for the radiative leptonic decay . An upper limit on its partial branching fraction for photon energies MeV was determined to be at a 90% confidence level; this excludes most current theoretical predictions. A sophisticated deep learning approach, which includes thorough validation and is based on the Transformer architecture, was implemented to efficiently distinguish the signal from massive backgrounds.