Dispersive e.m. corrections to πN scattering lengths

We investigate the dispersive contribution by radiative processes such as π−p→nγ and π−p→Δγ to the πN scattering lengths of charged pions in the heavy baryon limit. They give a large isospin violating contribution in the corresponding isoscalar scattering length, but only a small violation in the isovector one. These terms contribute 7.1(3)% to the 1s level shift of pionic hydrogen and give a chiral constant Fπ2f1=−28.0(8)MeV.