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 π0μ+μ-, combining low energy chiral expansions together with experimental data on π0 and η decays into two leptons. A value of ΔEHFSπ=-(0.09±0.06) μeV is obtained for this contribution.