Nucleon-nucleon scattering from the dispersive N/D method: Next-to-leading order study

We consider nucleon-nucleon (NN) interactions from chiral effective field theory applying the N/D method. The dynamical input is given by the discontinuity of the NN partial-wave amplitudes across the left-hand cut (LHC) calculated in chiral perturbation theory by including one-pion exchange (OPE), once-iterated OPE, and leading irreducible two-pion exchange. We discuss both uncoupled and coupled partial waves. We show algebraically that the resulting integral equation has a unique solution when the input is taken only from OPE because it is of the Fredholm type with a squared integrable kernel and an inhomogeneous term. Phase shifts and mixing angles are typically rather well reproduced, and a clear improvement of the results obtained previously with only OPE is manifest. We also show that the contributions to the discontinuity across the LHC are amenable to a chiral expansion. Our method also establishes correlations between the S-wave effective ranges and scattering lengths based on unitarity, analyticity, and chiral symmetry.