The N/D method with non-perturbative left-hand-cut discontinuity and the 1S0 NN partial wave

In this letter we introduce an integral equation that allows to calculate the exact left-hand-cut discontinuity for an uncoupled S-wave partial-wave amplitude in potential scattering for a given finiterange potential. In particular this is applied here to the (1)S(0)nucleon-nucleon (NN) partial wave. The calculation of Lambda (A) is completely fixed by the potential because short-range physics (corresponding to integrated out degrees of freedom within the low-energy Effective Field Theory) does not contribute to Lambda (A). The results obtained from the N/Dmethod for a partial-wave amplitude are rigorous, since now the discontinuities along the left-hand cut and right-hand cut are exactly known. This solves in this case the open question with respect to the N/Dmethod and the effect on the final result of the nonperturbative iterative diagrams in the evaluation of Delta(A). The solution of this problem also implies the equivalence of the N/Dmethod and the Lippmann-Schwinger (LS) equation for the nonsingular one-pion exchange S-1(0) NN potential (Yukawa potential). The equivalence between the N/Dmethod with one extra subtraction and the LS equation renormalized with one counterterm or with subtractive renormalization also holds for the singular attractive S-1(0) NN potentials calculated by including higher orders in Chiral Perturbation Theory (ChPT). However, the N/Dmethod is more flexible and, rather straightforwardly, it allows to evaluate partial-wave amplitudes with a higher number of extra subtractions, that we fix in terms of shape parameters within the effective range expansion. We give results up to three extra subtractions in the N/Dmethod, which provide a rather accurate reproduction of the S-1(0) NN phase shifts when the NNLO ChPT potential is employed. Our new method then provides a general theory to renormalize non-perturbatively singular and regular potentials in scattering that can be extended to higher partial waves as well as to coupled channel scattering. (C) 2017 The Authors. Published by Elsevier B.V.