Precision calculation of the recoil--finite-size correction for the hyperfine splitting in muonic and electronic hydrogen

We present a high-precision calculation of the recoil–finite-size correction to the hyperfine splitting (HFS) in muonic and electronic hydrogen based on nucleon electromagnetic form factors obtained from dispersion theory. This will help guide the upcoming searches of the HFS transition in muonic hydrogen, and will allow a precise determination of the polarizability and Zemach radius contributions when this transition is found.