Renormalization of chiral two pion exchange NN interactions with delta excitations: correlations in the partial wave expansion

Abstract

In this work we consider the renormalization of the chiral two-pion exchange potential with explicit delta-excitations for nucleon-nucleon scattering at next-to-leading (NLO) and next-to-next-to-leading order (N2LO). Due to the singular nature of the chiral potentials, correlations between different partial waves are generated. In particular we show that two-body scattering by a short distance power like singular attractive interaction can be renormalized in all partial waves with a single counterterm, provided the singularities are identical. A parallel statement holds in the presence of tensor interactions when the eigenpotentials in the coupled channel problem also coincide. While this construction reduces the total number of counterterms to eleven in the case of nucleon-nucleon scattering with chiral two-pion exchange interactions with delta degrees of freedom, the differences in the scattering phases as compared to the case with the uncorrelated partial wave renormalization become smaller as the angular momentum is increased in the elastic scattering region.

20 pages, 8 figures, a section has been added discussing cut-off dependence. Accepted for publication in PRC

References in corpus (16)

• Nuclear Force from Lattice QCD
• Theoretical Foundation of the Nuclear Force in QCD and its applications to Central and Tensor Forces in Quenched Lattice QCD Simulations
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Regularization, renormalization and "peratization" in effective field theory for two nucleons
• Improving the convergence of the chiral expansion for nuclear forces II: low phases and the deuteron
• Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Renormalization of Singular Potentials and Power Counting
• 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
• Renormalization Group Analysis of Boundary Conditions in Potential Scattering
• Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter
• Deuteron form factors in chiral effective theory: regulator-independent results and the role of two-pion exchange
• Nuclear forces from chiral EFT: The unfinished business
• Application of the operator product expansion to the short distance behavior of nuclear potentials
• A Two Potential Formula and its Application to Proton-Proton Scattering

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• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Delta isobars and nuclear saturation
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Short-range nuclear forces in singlet channels
• Heavy Baryon-Antibaryon Molecules in Effective Field Theory
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Full optimization and validation
• Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
• Perturbative chiral nucleon-nucleon potential for the ${}^3{P}_0$ partial wave
• Regulator constraints for the perturbative renormalizability of attractive triplets
• Residual cut-off dependence and power counting: the deuteron as a case study