Polarization contribution to the hydrogen hyperfine structure and phenomenology of the electron-proton interaction

In order to understand the significance of the well-known discrepancy of 45 ppm in the hydrogen hyperfine structure we have calculated the polarization correction using an isobar model for the proton, and compared the sensitivity to electron-proton forces of the analysis of the hyperfine splitting with that of the Lamb shift and of electron-proton scattering. A methodological innovation of the calculation is the avoidance of the Rarita-Schwinger formalism for spin 3/2 by the construction of a covariant analytic amplitude from the familiar non-relativistic partial-wave amplitude. It is found that the 3-3 isobar, and by extension higher resonances, are more than an order of magnitude too small to be significant and that the discrepancy is genuine. We consider the introduction of a phenomenological electron-proton interaction term, representing unknown or neglected forces, to account for the discrepancy, and find that this would not necessarily lead to a contradiction with Lamb shift or electron-proton scattering data. We point out that, whatever the cause of the discrepancy, it is likely to be proportional, in percent, to the electron mass, so that it would be roughly 200 times greater in μ-mesic hydrogen (μ^--p) than in hydrogen. We strongly encourage a measurement of the hyperfine splitting of μ-mesic hydrogen, of sufficient accuracy to determine whether the discrepancy is common to both systems and proportional to the lepton mass.