Nuclear Structure-Dependent Radiative Corrections to the Hydrogen Hyperfine Splitting

Radiative corrections to the Zemach contribution of the hydrogen hyperfine splitting are calculated. Their contributions amount to $-0.63(3)$ ppm to the HFS. The radiative recoil corrections are estimated to be $0.09(3)$ ppm and heavy particle vacuum polarization shifts the HFS by $0.10(2)$ ppm. The status of the nuclear-dependent contributions are considered. From the comparison of theory and experiment the proton polarizability contribution of $3.5(9)$ ppm is found. The nuclear structure-dependent corrections to the difference $\nu_{hfs}(1s) -n^3\nu_{hfs}(ns)$ are also obtained.