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

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.

58 pages, 26 figures, 2 tables. To match the published version. New mathematical developments are added. OPE is shown to have a unique solution. Necessary conditions for having solution are given

References in corpus (13)

• Chiral effective field theory and nuclear forces
• Improving the convergence of the chiral expansion for nuclear forces II: low phases and the deuteron
• Short-range nuclear forces in singlet channels
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Weinberg's approach to nucleon-nucleon scattering revisited
• Deconstructing triplet nucleon-nucleon scattering
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO
• Two-nucleon scattering: merging chiral effective field theory with dispersion relations
• Deconstructing 1S0 nucleon-nucleon scattering
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• A new EFT approach to NN scattering problem

Cited by in corpus (13)

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• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• ${\Sigma }_{c}N$ interaction in chiral perturbation theory
• The N/D method with non-perturbative left-hand-cut discontinuity and the ${}^1{S}_0$ $NN$ partial wave
• Cutoff regulators in chiral nuclear effective field theory
• $\rho \rho$ scattering revisited with coupled-channels of pseudoscalar mesons
• Transverse charge and current densities in the nucleon from dispersively improved chiral effective field theory
• Non-perturbative methods for NN singular interactions
• Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes
• Unitarization Technics in Hadron Physics with Historical Remarks
• Renormalization of NN Chiral EFT, my personal mixed feelings