Electromagnetic corrections to the s-wave scattering lengths in pionic hydrogen

Abstract Motivated by the recently performed X-ray precision experiments on pionic hydrogen (preceding paper), we reconsider the problem of electromagnetic corrections to the π - N scattering lengths. Based on a relativistic two-channel approach, we find corrections to the π − p elastic and single-charge-exchange (SCE) scatering lengths due to the point-Coulomb interaction, the finite-size Coulomb interaction (including the pion size), the first-order vacuum polarization (Uehling potential) and the ( π − p ) - ( π 0 n ) mass difference (mass difference effect). We also estimate the contribution due to the ( γ , n ) decay channel. The total corrections to the elastic and the SCE scattering lengths are found to be δ e = −(2.1 ± 0.5) × 10 −2 and δ Γ = −(1.3 ± 0.5) × 10 −2 . Previously published values for the corrections are critically compared with our results.