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In April 2021, scientists active in muon physics met to discuss and work outthe physics case for the new High-Intensity Muon Beams (HIMB) project at PSIthat could deliver of order $10^{10}$\,s$^{-1}$ surface muons to experiments.Ideas and concrete proposals were further substantiated over the followingmonths and assembled in the present document. The high intensities will allowfor completely new experiments with considerable discovery potential and uniquesensitivities. The physics case is outstanding and extremely rich, ranging fromfundamental particle physics via chemistry to condensed matter research andapplications in energy research and elemental analysis. In all these fields,HIMB will ensure that the facilities S$\mu$S and CHRISP on PSI's High IntensityProton Accelerator complex HIPA remain world-leading, despite the competitionof muon facilities elsewhere.

Science Case for the new High-Intensity Muon Beams HIMB at PSI