Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen

While measurements of the hyperfine structure of hydrogen-like atoms are traditionally regarded as test of bound-state QED, we assume that theoretical QED predictions are accurate and discuss the information about the electromagnetic structure of protons that could be extracted from the experimental values of the ground state hyperfine splitting in hydrogen and muonic hydrogen. Using recent theoretical results on the proton polarizability effects and the experimental hydrogen hyperfine splitting we obtain for the Zemach radius of the proton the value 1.040(16) fm. We compare it to the various theoretical estimates the uncertainty of which is shown to be larger that 0.016 fm. This point of view gives quite convincing arguments in support of projects to measure the hyperfine splitting of muonic hydrogen.