The FAMU experiment: Towards the measurement of the hyperfine splitting of the muonic hydrogen

The proton charge distribution radius is a nuclear physics related observable. QED calculations involve its value. It depends on the Lamb shift and hyperfine splitting which experimentally measured, are considered tests of QED, involving the Rydberg and the fine structure constant. The CREMA collaboration measured the proton radius by using muonic hydrogen spectroscopy. Muon, which is 200 times heavier than the electron, orbits close to the nucleus offering a unique probe for the proton structure. They obtained a precise measurement of the proton radius but 5% smaller than the one from hydrogen spectroscopy and electron-proton scattering. This discrepancy, called "the proton radius puzzle" and it is still an unanswered problem. There is another proton observable, related to both the charge and magnetic distribution, called the Zemach radius. This is dependent on QED and is strictly related to the hyperfine splitting. Different methods for measuring the Zemach radius are not in agreement and so far, a precise estimation of this observable for muonic hydrogen doesn't exist. In this context, FAMU, aims to measure the hyperfine splitting of the muonic hydrogen in the ground state which allows a level of uncertainty better than 1%. This will result in the first precise measurement of the Zemach radius with muonic hydrogen spectroscopy. Adding an independent precise measurement of the Zemach radius in the current panorama should give a hint to the proton radius puzzle solution. Moreover, it will influence the nuclear structure theories of simple atoms and act as a precise test of QED. The physical processes behind these measurements are related to muonic atomic physics. In particular, the ability of the muonic hydrogen to transfer its muon to nearby heavy atoms when in a gaseous mixture. The rate of this transfer process was found to be energy dependent for some elements.