Charge Symmetry Breaking in Pion Production

Chiral effective field theory predicts a charge symmetry violating (CSB) amplitude for pion-nucleon scattering. This mechanism provides a very large contribution also to the CSB forward-backward asymmetry in the angular distribution of the reaction pn → dπ⁰. This contribution was so large that it had a potential to cause a large effect also in CSB elastic NN scattering and to disturb its present understanding. However, it can be seen that, contrary to pion production, in this case the ud-quark mass difference and electromagnetic contribution to the np-mass difference tend to cancel causing the total effect in the effective range parameters Δa = a_pp - a_nn and Δr₀ = r_0,pp - r_0,nn to be relatively small. In the lowest order and within the static approximation for the nucleons CSB pion-nucleon rescattering does not influence np scattering.