A tale of two skyrmions: the nucleon's strange quark content in different large N_c limits

TL;DR

This paper investigates the strange quark content of nucleons within different large N_c limits using the Skyrme model, resolving a paradox about quark loop contributions by extending the model to include additional meson interactions.

Contribution

It demonstrates that including specific meson-meson interactions in the Skyrme model aligns its predictions with large N_c QCD expectations for strange quark content.

Findings

Skyrme model's initial form predicts vanishing strange content in both limits.

Adding meson-meson interactions reproduces the expected non-vanishing in OLNC limit.

The resolution clarifies the role of meson interactions in large N_c baryon models.

Abstract

The nucleon's strange quark content comes from closed quark loops, and hence should vanish at leading order in the traditional large $N_c$ (TLNC) limit. Quark loops are not suppressed in the recently proposed orientifold large $N_c$ (OLNC) limit, and thus the strange quark content should be non-vanishing at leading order. The Skyrme model is supposed to encode the large $N_c$ behavior of baryons, and can be formulated for both of these large $N_c$ limits. There is an apparent paradox associated with the large $N_c$ behavior of strange quark matrix elements in the Skyrme model. The model only distinguishes between the two large $N_c$ limits via the $N_c$ scaling of the couplings and the Witten-Wess-Zumino term, so that a vanishing leading order strange matrix element in the TLNC limit implies that it also vanishes at leading order in the OLNC limit, contrary to the expectations based on the suppression/non-suppression of quark loops. The resolution of this paradox is that the Skyrme model does not include the most general type of meson-meson interaction and, in fact, contains no meson-meson interactions which vanish for the TLNC limit but not the OLNC. The inclusion of such terms in the model yields the expected scaling for strange quark matrix elements.