Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves

Abstract

We consider nucleon-nucleon interactions from chiral effective field theory applying the N/D method. The case of coupled partial waves is now treated, extending Ref. [1] where the uncoupled case was studied. As a result three N/D elastic-like equations have to be solved for every set of three independent partial waves coupled. As in the previous reference the input for this method is the discontinuity along the left-hand cut of the nucleon-nucleon partial wave amplitudes. It can be calculated perturbatively in chiral perturbation theory because it involves only irreducible two-nucleon intermediate states. We apply here our method to the leading order result consisting of one-pion exchange as the source for the discontinuity along the left-hand cut. The linear integral equations for the N/D method must be solved in the presence of L - 1 constraints, with L the orbital angular momentum, in order to satisfy the proper threshold behavior for L>= 2. We dedicate special attention to satisfy the requirements of unitarity in coupled channels. We also focus on the specific issue of the deuteron pole position in the 3S1-3D1 scattering. Our final amplitudes are based on dispersion relations and chiral effective field theory, being independent of any explicit regulator. They are amenable to a systematic improvement order by order in the chiral expansion.

11 pages. Extends the work of uncoupled partial waves of M. Albaladejo and J. A. Oller, Phys. Rev. C 84, 054009 (2011) to the case of coupled partial waves. This version matches the published version. Discussion about the deuteron enlarged. Some references added

References in corpus (7)

• Improving the convergence of the chiral expansion for nuclear forces II: low phases and the deuteron
• On the size of the sigma meson and its nature
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Deconstructing triplet nucleon-nucleon scattering
• Deuteron form factors in chiral effective theory: regulator-independent results and the role of two-pion exchange
• Deconstructing 1S0 nucleon-nucleon scattering
• Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

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• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• The N/D method with non-perturbative left-hand-cut discontinuity and the ${}^1{S}_0$ $NN$ partial wave
• Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study
• $\rho \rho$ scattering revisited with coupled-channels of pseudoscalar mesons
• Rapidity Distributions of Hadrons in Proton-Nucleus Collisions