Testing QED and BSM theories in purely leptonic atoms through advanced solutions of Dirac-Coulomb-Breit equation

The purpose of this work is to examine the possibilities of solving numerically the relativistic Dirac–Coulomb–Breit equation and provide predictions for some important properties of purely leptonic systems focusing on the Muonium (µ +e −) exotic leptonic atom. The investigation of bound-state energies and other properties of this exotic atom, is of fundamental interest in testing the Quantum Electrodynamics (QED) and in probing physics Beyond the Standard Model (BSM). In the next few years, high precision spectroscopy of Mu (Mu-MASS experiment) at PSI combined with ongoing hyper fine measurements of Mu (MUSEUM experiment) at J-PARC will provide one of the most sensitive tests of bound-state QED. These extremely sensitive experiments may probe new regions of the parameter space testing the existence of medium range spin-dependent and spin-independent dark forces between e − and µ + for testing BSM physics. On the other hand, improvement of the accuracy is required for QED calculations in the 1S → 2S transition of Mu by about one order of magnitude as well as for BSM predictions.