Hyperfine spectroscopy of muonic hydrogen and the PSI Lamb shift experiment

The recent Lamb shift experiment at PSI and the discussions about the incompatibility of the proton radii extracted using different methods have revived the interest in the measurement of the hyperfine splitting of the ground state in muonic hydrogen. We summarize the existing experimental ideas for this measurement and analyze quantitatively the main methodological difficulties, expected to be related to the required power of the IR laser source, the signal-to-noise ratio and other systematic factors. An elaborate model is developed to estimate the statistical uncertainty of the experimental value of the hyperfine splitting.