The goal of the FAMU experiment at RIKEN RAL is the measure of the hyperfine splitting of the ground state of the muonic hydrogen, to allow a determination of the proton Zemach radius with a precision better than $5 times 10^{-3}$ . The comparison of this measurement with the ones done with ordinary hydrogen may help to solve the so-called proton radius puzzle, triggered by the $6 sigma$ discrepancy in the proton charge radius value as extracted from muonic Lamb shift and the value based on e-p scattering and ordinary hydrogen spectroscopy.
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