Renormalization Group Analysis of Boundary Conditions in Potential Scattering

Abstract

We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting equation can be interpreted as a variable phase equation of a complementary boundary value problem. We discuss the corresponding infrared fixed points and the perturbative expansion around them generating a short distance modified effective range theory. We also discuss ultraviolet fixed points, limit cycles and attractors with a given fractality which take place for singular attractive potentials at the origin. The scaling behaviour of scattering observables can analytically be determined and is studied with some emphasis on the low energy nucleon-nucleon interaction via singular pion exchange potentials. The generalization to coupled channels is also studied.

31 pages, 8 figures

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Cited by in corpus (36)

• Chiral effective field theory and nuclear forces
• Nuclear effective field theory: status and perspectives
• Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering
• Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules
• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Short-range nuclear forces in singlet channels
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Renormalizing Chiral Nuclear Forces: A Case Study of 3P0
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
• ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ interactions in chiral effective field theory
• Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO
• Scale Invariance in Heavy Hadron Molecules
• Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter
• Nuclear forces from chiral EFT: The unfinished business
• Taking dibaryon fields seriously
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• The renormalisation group and nuclear forces
• Coarse graining Nuclear Interactions
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Renormalization of chiral two-pion exchange NN interactions with Delta-excitations: Central Phases and the Deuteron
• Nuclear Effective Field Theories: Reverberations of the early days
• Chiral potentials, perturbation theory, and the 1S0 channel of NN scattering
• Power counting for nuclear forces in chiral effective field theory
• Renormalization of chiral two pion exchange NN interactions with delta excitations: correlations in the partial wave expansion
• Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
• A Two Potential Formula and its Application to Proton-Proton Scattering
• Renormalization group procedure for potential $-g/r^2$
• Renormalization of the Off-shell chiral two-pion exchange NN interactions
• Reexamining the perturbative renormalizability of the coupled triplets
• Regulator constraints for the perturbative renormalizability of attractive triplets
• Renormalization of One-Pion Exchange in Chiral Effective Field Theory for Antinucleon-Nucleon Scattering
• Residual cut-off dependence and power counting: the deuteron as a case study
• Auxiliary counterterms and their role in effective field theory
• Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System