Experimental limiting factors for the search of µ → Eγ at future facilities

The search for the Lepton Flavor Violating decay e exploits the most intense continuous muon beams, which can currently deliver approximate to 108 muons per second. In the next decade, accelerator upgrades are expected in various facilities, making it feasible to have continuous beams with an intensity of 109 or even 1010 muons per second. We investigate the experimental limiting factors that will define the ultimate performances, and hence the sensitivity, in the search for e with a continuous beam at these extremely high rates. We then consider some conceptual detector designs and evaluate the corresponding sensitivity as a function of the beam intensity.