The goal of the FAMU experiment at RIKEN RAL is to measure 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 $5×10^{-3}$. 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 6σ 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.