Toward the measurement of the hyperfine splitting in the ground state of muonic hydrogen

Abstract

The recent Lamb shift experiment at PSI and the controversy about proton size revived the interest in measuring the hyperfine splitting in muonic hydrogen and extracting the proton Zemach radius. The efficiency of the experimental method depends on the energy dependence of the muon transfer rate to higher-Z gases in the near epithermal energy range. As long as the available experimental data only give the average transfer rate in the whole epithermal range, and the detailed theoretical calculations have not yet been verified, an experiment has been started for the measurement of the transfer rate in thermalized gas target at different temperatures and extracting from the data an estimate of the transfer rate for arbitrary energies. We outline the underlying mathematical method and estimate its accuracy.