Proton structure corrections to electronic and muonic hydrogen hyperfine splitting

We present a precise determination of the polarizability and other proton structure-dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent data on proton spin-dependent structure functions from the EG1 collaboration experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part per million, and is about one standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and polarizability terms.