Radiative corrections to hyperfine structure in hydrogen

Because of a reported discrepancy of (34±21) parts per million between measured and calculated values of the hyperfine separation of the ground state of atomic hydrogen, the next higher-order radiative corrections beyond the previously calculated order of α² S _h.f. were investigated. Besides the expected presence of corrections of order α³ ln αS _h.f., a larger correction of order α³ln² S _h.f. was found. The calculation of the level shift of both of these logarithmic orders has been completed yielding results which agree with those of Layzer. In the case of hydrogen the numerical contribution is - 9.28 ppm. When this is combined with previous results, the discrepancy between measured and calculated values is increased to (43±21) ppm. The uncertainty is due largely to the uncertainty in the value of α, which is obtained from finestructure measurements, and which appears in the theoretical formula for the hyperfine separation. Possible explanations of the discrepancy are either an inaccuracy in the accepted value of the fine-structure constant or an inadequate evaluation of the contribution from intermediate states in which mesons are excited.