Letter Of Intent for a future $\mu^+ \to \mathrm{e}^+ \gamma$ experiment at the High Intensity Muon Beam facility at PSI
Searches for charged lepton flavor violation in the muon sector stand out among the most sensitive and clean probes for physics beyond the Standard Model. Currently, $\mu^+ \to \mathrm{e}^+ \gamma$ experiments provide the best constraints in this field for a wide range of models while, in the coming years, new experiments investigating the processes of $\mu^+ \to \mathrm{e}^+ \mathrm{e}^+ \mathrm{e}^-$ and $\mu \to \mathrm{e}$ conversion in the nuclear field are anticipated to reach comparable or higher sensitivities. The High-Intensity Muon Beam (HIMB) facility at PSI, which is expected to deliver muon beam intensities up to two orders of magnitude higher than the existing beam lines, offers a unique opportunity to significantly enhance the sensitivity of $\mu^+ \to \mathrm{e}^+ \gamma$ searches. The discovery potential could be substantially boosted and a sensitivity comparable to that of all the other projects could be reestablished, which is essential for discriminating among competing new-physics scenarios should an observation occur in any of the channels. In this document, we express our interest in developing a $\mu^+ \to \mathrm{e}^+ \gamma$ experimental program at HIMB, with the goal of improving, within the next decade, the sensitivity of the $\mu^+ \to \mathrm{e}^+ \gamma$ search by more than one order of magnitude relative to the expected final result of the current leading experiment, MEG II. This effort would ensure that PSI retains its leadership in this field.