Serber symmetry, largeNc, and Yukawa-like one-boson exchange potentials

Abstract

The Serber force has relative orbital parity symmetry and requires vanishing $\mathit{NN}$ 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. The analysis is carried out in terms of partial wave sum rules for $\mathit{NN}$ phase shifts, $r$-space potentials at long distances, and ${V}_{\mathrm{low} k}$ potentials. We analyze how Serber symmetry can be accommodated within a large-${N}_{c}$ 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. Although these masses arise as poles on the second Riemann in $\ensuremath{\pi}\ensuremath{\pi}$ scattering, we find that within the large-${N}_{c}$ expansion the corresponding Yukawa masses correspond instead to a well-defined large-${N}_{c}$ approximation to the pole that cannot be distinguished from their location as Breit-Wigner resonances.