Determination of the chiral coupling constants c₃ and c₄ in new pp and np partial-wave analyses

As a first result of two new partial-wave analyses, one of the pp and another one of the np scattering data below 500 MeV, we report a study of the long-range chiral two-pion exchange interaction which contains the chiral coupling constants c₁, c₃, and c₄. By using as input a theoretical value for c₁ we are able to determine in pp as well as in np scattering accurate values for c₃ and c₄. The values determined from the pp data and independently from the np data are in very good agreement, indicating the correctness of the chiral two-pion exchange interaction. The weighted averages are c₃=-4.78(10)/GeV and c₄=3.96(22)/GeV, where the errors are statistical. The value of c₃ is best determined from the pp data and that of c₄ from the np data.