Renormalizing the Lippmann-Schwinger equation for the one pion exchange potential

Abstract

We address the question whether the cut-off dependence, which has to be introduced in order to properly define the Lippmann-Schwinger equation for the one pion exchange potential plus local (delta-function) potentials, can be removed (up to inverse powers of it) by a suitable tuning of the various (bare) coupling constants. We prove that this is indeed so both for the spin singlet and for the spin triplet channels. However, the latter requires such a strong cut-off dependence of the coupling constant associated to the non-local term which breaks orbital angular momentum conservation, that the renormalized amplitude lacks from partial wave mixing. We argue that this is an indication that this term must be treated perturbatively.

26 pages, 1 figure; extended version with references added

Cited by in corpus (31)

• Nuclear effective field theory: status and perspectives
• Renormalization of One-Pion Exchange and Power Counting
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions
• Subtractive renormalization of the chiral potentials up to next-to-next-to-leading order in higher NN partial waves
• Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions
• Renormalization Group Analysis of Boundary Conditions in Potential Scattering
• Chiral effective theory predictions for deuteron form factor ratios at low Q^2
• Consistency of the effective-field-theory approach to the nucleon-nucleon interaction problem revisited
• Taking dibaryon fields seriously
• The nucleon-nucleon potential beyond the static approximation
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• The exact discontinuity of a partial wave along the left-hand cut and the exact $N/D$ method in non-relativistic scattering
• Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves
• Nuclear Effective Field Theories: Reverberations of the early days
• Renormalization of $NN$ scattering: contact potential
• On the quark mass dependence of nucleon-nucleon S-wave scattering lengths
• Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study
• Deuteron Matrix Elements in Chiral Effective Theory at Leading Order
• Effective Field Theory with Dibaryon Fields: Nucleon-Nucleon amplitudes at NNLO
• What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish
• A nonperturbative parametrization and scenario for EFT renormalization
• The longitudinal response function of the deuteron in chiral effective field theory
• $NN$ scattering in ${}^3{S}_1{-}^3{D}_1$ channels of EFT ($/\pi$)
• A Padé-aided analysis of nonperturbative $NN$ scattering in ${}^1{S}_0$ channel
• Padé expansion and the renormalization of nucleon-nucleon scattering
• Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System
• Padé expansion and nucleon-nucleon scattering in coupled channels