Abstract
The Skyrme force parameters can be uniquely determined by coarse graining the Nucleon-Nucleon (NN) interactions at a characteristic momentum scale. We show how exact V lowk potentials to second order in momenta are saturated with physical NN scattering threshold parameters at Center of Mass (CM) cut-off scales of about Λ = 250 MeV for the S-waves and Λ = 100 MeV for the P-waves. The pattern of Wigner and Serber symmetries unveiled previously and suggested by Quantum Chromodynamics (QCD) large N c contracted symmetry emerges at these scales.
Highlights
The derivation of effective interactions from NN dynamics has been a major task in NuclearPhysics ever since the pioneering works of Moshinsky [1] and Skyrme [2]
We have provided a Wilsonian renormalization scale argument on how the much used effective interaction parameters of the venerable Skyrme interaction can be understood as coarse grained NN interactions over the suitable wavelengths
We have seen that, regarding the renormalization group, when running the parameters, there is scale saturation, i.e., above a certain scale, the effective interaction parameters do not depend strongly on the scale in a regime where most of the strength can be deduced from low energy NN scattering information regardless of the underlying forces
Summary
The derivation of effective interactions from NN dynamics has been a major task in Nuclear. Effective Field Theory (EFT) calculations (for a review see e.g., [23]), breaking rotational symmetry explicitly, provide a competitive scheme where coarse grained interactions allow ab initio calculations combining the insight of EFT and Monte-Carlo lattice experience, with lattice spacings as large as a = 2 fm These length scales match the typical inter-particle distance of nuclear matter d = 1/ρ 3 ∼ 2 fm. A particular implementation of the coarse graining idea [29] has facilitated benchmarking partial wave analyses of the NN interaction and has provided an alternative way to define the effective couplings as a function of the maximal fitting CM momentum p ≤ ΛFit [30], including different One. Pion Exchange (OPE) and Chiral Two Pion Exchange (χTPE) [31,32] and an evaluation of uncertainties of both statistical and systematic origin [33].
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