Single pion contribution to the hyperfine splitting in muonic hydrogen

Abstract

A detailed discussion of the long-range one-pion exchange (Yukawa potential) contribution to the 2S hyperfine splitting in muonic hydrogen which had, until recently, been disregarded is presented. We evaluate the relevant vertex amplitudes, in particular $\ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{¼}^{-}$, combining low energy chiral expansions together with experimental data on $\ddot{I}{€}^0$ and $\hat{I}\cdot$ decays into two leptons. A value of $\hat{I}”E^{\ddot{I}}{€}_{HFS}=-(0.09\pm 0.06)\hat{I}¼\mathrm{eV}$ is obtained for this contribution.

v2: Expanded and completed version