Two-nucleon scattering: merging chiral effective field theory with dispersion relations

Abstract

We consider two-nucleon scattering close to threshold. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes calculated in a relativistic formulation of chiral perturbation theory. The constraints set by unitarity are used in order to stabilize the extrapolation. Neutron-proton phase shifts are analyzed up to laboratory energies $T_{\mathrm{lab}}\simeq 250$ MeV based on the next-to-next-to-next-to-leading order expression for the subthreshold amplitudes. We find a reasonably accurate description of the empirical S- and P-waves and a good convergence of our approach. These results support the assumption that the subthreshold nucleon-nucleon scattering amplitude may be computed perturbatively by means of the chiral expansion. The intricate soft scales that govern the low-energy nucleon-nucleon scattering are generated dynamically via a controlled analytic continuation.

10 pages, 5 figures, version accepted for publication, a more detailed discussion of the results is added

References in corpus (8)

• Chiral effective field theory and nuclear forces
• Improving the convergence of the chiral expansion for nuclear forces II: low phases and the deuteron
• Roy-Steiner equations for pion-nucleon scattering
• Weinberg's approach to nucleon-nucleon scattering revisited
• Deconstructing triplet nucleon-nucleon scattering
• On causality, unitarity and perturbative expansions
• Deconstructing 1S0 nucleon-nucleon scattering
• Chiral potentials, perturbation theory, and the 1S0 channel of NN scattering

Cited by in corpus (23)

• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces
• Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering
• Low-energy theorems for nucleon-nucleon scattering at unphysical pion masses
• Theoretical analysis of the $\gamma \gamma \to {\pi }^0\eta$ process
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• The exact discontinuity of a partial wave along the left-hand cut and the exact $N/D$ method in non-relativistic scattering
• Dispersive analysis of the $\gamma \gamma \to D\bar{D}$ data and the confirmation of the $D\bar{D}$ bound state
• The N/D method with non-perturbative left-hand-cut discontinuity and the ${}^1{S}_0$ $NN$ partial wave
• Optical Potentials Derived from Nucleon-Nucleon Chiral Potentials at N4LO
• Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study
• Spectral representation for u- and t-channel exchange processes in a partial-wave decomposition
• Cutoff regulators in chiral nuclear effective field theory
• Coupled-channel dynamics with chiral long-range forces in the open-charm sector of QCD
• From pole parameters to line shapes and branching ratios
• Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
• A coupled-channel system with anomalous thresholds and unitarity
• On kinematical constraints in the hadrogenesis conjecture for the baryon resonance spectrum
• On coupled-channel dynamics in the presence of anomalous thresholds
• Analytical dispersive parameterization for elastic scattering of spinless particles
• Nucleon-nucleon potentials in phase-space representation