Single pion contribution to the hyperfine splitting in muonic hydrogen

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 $π^0μ^+μ^-$, combining low energy chiral expansions together with experimental data on $π^0$ and $η$ decays into two leptons. A value of $Δ{E}^π_{HFS}= -(0.09 \pm 0.06)\ μ\rm{eV}$ is obtained for this contribution.

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