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

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.