Some recoil corrections to the hydrogen hyperfine splitting

Abstract

We compute all of the recoil corrections to the ground-state hyperfine splitting in hydrogen, with the exception of the proton polarizability, that are required to achieve an accuracy of 1 ppm. Our approach includes a unified treatment of the corrections that would arise from a pointlike Dirac proton and the corrections that are due to the proton's non-QED structure. Our principal new results are a calculation of the relative order-${\ensuremath{\alpha}}^{2}$(${m}_{e}$/${m}_{p}$) contributions that arise from the proton's anomalous magnetic moment and a systematic treatment of the relative order-\ensuremath{\alpha}(${m}_{e}$/${m}_{p}$) contributions that arise from form-factor corrections. In the former calculation we introduce some new technical improvements and are able to evaluate all of the expressions analytically. In the latter calculation, which has been the subject of previous investigations by other authors, we express the form-factor corrections in terms of two-dimensional integrals that are convenient for numerical evaluation and present numerical results for the commonly used dipole parametrization of the form factors. Because we use a parametrization of the form factors that differs slightly from the ones used in previous work, our numerical results are shifted from older ones by a small amount.