Serber symmetry, Large Nc and Yukawa-like One Boson Exchange Potentials

TL;DR

This paper explores Serber symmetry in nucleon-nucleon interactions, analyzing its fulfillment in different potentials, its interpretation within a large Nc framework, and the conditions for Yukawa potential approximation.

Contribution

It demonstrates how Serber symmetry can be understood as a long-distance symmetry in a large Nc context and clarifies the relation between resonance masses and Yukawa potentials.

Findings

Serber symmetry is well fulfilled for spin triplet states with odd angular momentum.

Serber symmetry is violated for odd singlet states in realistic potentials but not in chiral potentials.

Yukawa masses approximate resonance poles in the large Nc expansion.

Abstract

The Serber force has relative orbital parity symmetry and requires vanishing NN interactions in partial waves with odd angular momentum. We illustrate how this property is well fulfilled for spin triplet states with odd angular momentum and violated for odd singlet states for realistic potentials but fails for chiral potentials. We analyze how Serber symmetry can be accommodated within a large Nc perspective when interpreted as a long distance symmetry. A prerequisite for this is the numerical similarity of the scalar and vector meson resonance masses. The conditions under which the resonance exchange potential can be approximated by a Yukawa form are also discussed. While these masses arise as poles on the Second Riemann in pi-pi scattering, we find that within the large Nc expansion the corresponding Yukawa masses correspond instead to a well defined large Nc approximation to the pole which cannot be distinguished from their location as Breit-Wigner resonances.