The reaction πN → ππN at threshold in chiral perturbation theory Original Research Article

In the framework of heavy baryon chiral perturbation theory, we give the chiral expansion for the πN → ππN threshold amplitudes D1 and D2 to quadratic order in the pion mass. The theoretical results agree within one standard deviation with the empirical values. We also derive a relation between the two threshold amplitudes of the reaction πN → ππN and the ππ S-wave scattering lengths, a00 and a20, respectively, to order (M2π). We show that there are uncertainties mostly related to resonance excitation which make an accurate determination of the ππ scattering length a00 from the ππN threshold amplitudes at present very difficult. The situation is different in the ππ isospin two final state. Here, the chiral series converges and one finds a20 = −0.031 ± 0.007 consistent with the one-loop chiral perturbation theory prediction.