Transversity distributions in the nucleon in the large-N_c limit

Abstract

We compute the quark and antiquark transversity distributions in the nucleon at a low normalization point of 600 MeV in the large-$N_c$ limit, where the nucleon can be described as a soliton of an effective chiral theory (chiral quark-soliton model). The flavor-nonsinglet distributions, $\delta u(x)-\delta d(x)$ and $\delta \bar{u}(x)-\delta \bar{d}(x)$, appear in leading order of the $1/N_c$-expansion, while the flavor-singlet distributions, $\delta u(x)+\delta d(x)$ and $\delta \bar{u}(x)+\delta \bar{d}(x)$, are non-zero only in next-to-leading order. The transversity quark and antiquark distributions are found to be significantly different from the longitudinally polarized distributions $\Delta u(x)\pm \Delta d(x)$ and $\Delta \bar{u}(x)\pm \Delta \bar{d}(x)$, respectively, in contrast to the prediction of the naive non-relativistic quark model. We show that this affects the predictions for the spin asymmetries in Drell-Yan pair production in transversely polarized pp and ppbar collisions.

45 pages, 16 figures