Proton Structure Corrections to Hydrogen Hyperfine Splitting

The largest uncertainty in calculations of hydrogen ground-state hyperfine splitting comes from corrections due to proton stucture. We review these corrections, with special mention of the inelastic, or polarizability, corrections which have been recently re-evaluated. Summing up the arguably best current values for the calculated corrections leaves us 1-2 ppm short of the experimental data. We speculate how one may explain this shortfall, and along the way broadly outline the derivations of the relevant formulas, attempting to explain how certain terms come to appear and commenting on the use of unsubtracted dispersion relations.