Nucleon "tensor charges" and the Skyrme model.

Abstract

The lowest moment of the twist-two, chiral-odd parton distribution ${h}_{1}(x)$ of the nucleon can be related to the so-called "tensor charges" of the nucleon. We consider the tensor charges in the Skyrme model, and find that in the large-${N}_{c}$, SU(3)-symmetric limit, the model predicts that the octet isosinglet tensor charge ${g}_{T}^{8}$ is of order $\frac{1}{{N}_{c}}$ with respect to the octet isovector tensor charge ${g}_{T}^{3}$. The predicted $\frac{F}{D}$ ratio is then $\frac{1}{3}$, in the large-${N}_{c}$ limit. These predictions coincide with the Skyrme model predictions for the octet axial charges ${g}_{A}^{8}$ and ${g}_{A}^{3}$. (The prediction $\frac{F}{D}=\frac{1}{3}$ for the axial charges differs from the commonly quoted prediction of $\frac{5}{9}$, which is based on an inconsistent treatment of the large-${N}_{c}$ limit. A consistent treatment yields the result quoted above, and shows that the strange quark contribution to the nucleon spin is of order unity, and not of order ${N}_{c}$, as previously stated.) The model also predicts that the singlet tensor charge ${g}_{T}^{0}$ is of order $\frac{1}{{N}_{c}}$ with respect to ${g}_{T}^{3}$.