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

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.