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We consider nucleon-nucleon ($NN$) interactions from Chiral Effective FieldTheory applying the $N/D$ method. The dynamical input is given by thediscontinuity of the $NN$ partial-wave amplitudes across the left-hand cut(LHC) calculated in Chiral Perturbation Theory (ChPT) by including one-pionexchange (OPE), once-iterated OPE and leading irreducible two-pion exchange(TPE). We discuss both uncoupled and coupled partial-waves. We showalgebraically that the resulting integral equation has a unique solution whenthe input is taken only from OPE because it is of the Fredholm type with asquared integrable kernel and an inhomogeneous term. Phase shifts and mixingangles are typically rather well reproduced, and a clear improvement of theresults obtained previously with only OPE is manifest. We also show that thecontributions to the discontinuity across the LHC are amenable to a chiralexpansion. Our method also establishes correlations between the $S$-waveeffective ranges and scattering lengths based on unitarity, analyticity andchiral symmetry.

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