Design of a CsI(Tl) Calorimeter for Muonium-to-Antimuonium Conversion Experiment

The Muonium-to-Antimuonium Conversion Experiment (MACE) is proposed to search for charged lepton flavor violation and increase the sensitivity by three orders of magnitude compared to the PSI experiment in the 1990s. A clear signature of this conversion is the positron produced from antimuonium decay. This paper presents a near-$4\pi$-coverage calorimeter designed for MACE, which provides an energy resolution of 9% at 511 keV and 7.5% at 1.022 MeV. The signal efficiency for double $\gamma$ events is 67.5%. Detailed Monte-Carlo simulations using MACE offline software based on Geant4 are performed for geometry optimization, coincidence system design, background estimation, and benchmark detector validation.