Old nuclear symmetries and large N(c) as long distance symmetries in the two nucleon system

TL;DR

This paper explores how large Nc QCD and meson exchange forces underpin long-distance symmetries like Wigner and Serber in the two-nucleon system, revealing their approximate nature and limitations.

Contribution

It connects large Nc QCD insights with long-distance nuclear symmetries, deriving sum rules and analyzing symmetry breaking patterns in NN interactions.

Findings

Wigner SU(4) and Serber symmetries are not fully compatible everywhere.

Large Nc potentials are suitable for long-distance NN interactions.

Chiral expansion potentials do not exhibit these symmetries or scale properly with Nc.

Abstract

Wigner and Serber symmetries for the two-nucleon system provide unique examples of long distance symmetries in Nuclear Physics, i.e. symmetries of the meson exchange forces broken only at arbitrarily small distances. We analyze the large Nc picture as a key ingredient to understand these, so far accidental, symmetries from a more fundamental viewpoint. A set of sum rules for NN phase-shifts, NN potentials and coarse grained V_lowk NN potentials can be derived showing Wigner SU(4) and Serber symmetries not to be fully compatible everywhere. The symmetry breaking pattern found from the partial wave analysis data, high quality potentials in coordinate space at long distances and their V_lowk relatives is analyzed on the light of large N(c) contracted SU(4) symmetry. Our results suggest using large Nc potentials as long distance ones for the two-nucleon system where the meson exchange potential picture is justified and known to be consistent with large Nc counting rules. We also show that potentials based on chiral expansions do not embody the Wigner and Serber symmetries nor do they scale properly with Nc. We implement the One Boson Exchange potential realization saturated with their leading Nc contributions due to pi,sigma,rho and omega mesons. The short distance 1/r^3 singularities stemming from the tensor force can be handled by renormalization of the Schrodinger equation. A good description of deuteron properties and deuteron electromagnetic form factors in the impulse approximation for realistic values of the meson-nucleon couplings is achieved