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arXiv · 1305.5790

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

Zhi-Hui Guo·J. A. Oller·G. Rios
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Abstract

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 (ChPT) by including one-pion exchange (OPE), once-iterated OPE and leading irreducible two-pion exchange (TPE). 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.

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Zhi-Hui Guo, J. A. Oller, G. Rios. 2014-02-10. Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study. https://doi.org/10.1103/physrevc.89.014002

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