Isospin breaking in pion-nucleon scattering at threshold by radiative   processes
  We investigate the dispersive contribution by radiative processes such as (pi- proton to neutron gamma) and (pi- proton to Delta gamma) to the pion-nucleon 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 6.3(3)% to the 1s level shift of pionic hydrogen and give a chiral constant F_pi^2f_1=-25.8(8) MeV. 
T. E. O. Ericson (1), A. N. Ivanov (2 and 3) ((1) Cern, Geneva,   Switzerland (2) SMI and Technical University, Wien, Austri...