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

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. The analysis is carried out in terms of partial wave sum rules for NN phase shifts, r-space potentials at long distances, and V 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 ππ 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.

Low Scale Saturation of Effective NN Interactions and Their Symmetries

“…It has been argued that counterterms are fingerprints of long distance symmetries [25][26][27]. This remarkable result holds regardless of the nature of the forces and applies, in particular, to both Wigner and Serber symmetries.…”

“…However, as discussed in [26], a more convenient representation is to separate off all polynomial dependence explicitly from the original potential:…”

“…A further objection to attempt the separation explicitly concerns the long distance pionic physics (see also [25][26][27][28]). Actually, we may separate the pionic contributions as follows:…”

“…If this d exists, one can replace the zero energy scattering problem by the truncated original potential, which, following [25][26][27], we denote as the V highr potential. The corresponding reduced potential, U highr (r) = MV highr (r), reads…”

“…However, there is no universal effective interaction definition. For definiteness, we will follow here the V lowk scheme to determine the effective parameters because, within this framework, some underlying old nuclear symmetries, namely those implied by Wigner and Serber forces, are vividly displayed [25][26][27][28].…”