Determination of the s-wave pion-nucleon threshold scattering parameters from the results of experiments on pionic hydrogen

We give the conversion equations which lead from experimental values of the 3 p → 1 s transition energy in pionic hydrogen and the total width of the 1s level to values of the s-wave threshold scattering parameters for the processes π^- p → π^- p and π^- p → π⁰ n respectively. Using a three-channel potential model, we then calculate the electromagnetic corrections to these quantities, which remove the effects of the Coulomb interaction, the external mass differences and the presence of the γn channel. We give the s-wave scattering parameters obtained from the present experimental data and these electromagnetic corrections. Finally we discuss the implications for isospin invariance.