Polarizability Contribution to the Hydrogen Hyperfine Structure

At present there exists an apparent discrepancy of approximately 40±20 ppm (parts per million) between experiment and theory for the ground-state hyperfine splitting in hydrogen. The purpose of this paper is to examine critically the proton-structure corrections which go into the theoretical hfs value and to try to assess and improve the accuracy to which they are known. We review the theoretical expression for the hyperfine splitting (hfs) and the corrections to it. The origin of the proton-structure corrections is discussed along with the various physical effects: form factors, polarization, Bohr effect, etc., which have at various times been mentioned in regard to the hfs. We write down and solve the hfs for two nonrelativistic models of proton structure. The aim of these models is to provide insight into the less transparent and much less complete relativistic calculation of the structure correction. We also discuss their relation to the recent quark-model calculation of Fenster and Nambu. We discuss the relativistic calculation of the proton-structure correction, building on the recent work of Iddings. Calculation of the $\pi N$ and $\pi N^{*}$ intermediate states are presented. The problems of subtraction constants and contributions from high energy are taken up and our conclusions are presented.