Nucleon tensor form factors at large $N_c$

Abstract

We investigate nucleon tensor form factors in the large-$N_c$ limit. In this picture, the nucleon emerges as a state of the $N_c$ valence quarks, which were bound by pion mean fields that were created by the presence of the valence quarks self-consistently. We find that the tensor charge ($g_T^{u-d}=0.99$) and the anomalous tensor magnetic moment ($\hat{I}{º}_T^{u+d}=7.61$) are dominated by valence quarks, while the tensor quadrupole moment ($Q_T^{u-d}=-7.02$) shows significant sea quark effects. We examine how these quantities vary as the average size of the pion mean field is changed, showing interpolation between non-relativistic quark and Skyrme limits. We also observe that $g_T^{u-d}$ and $\hat{I}{º}_T^{u+d}$ depend weakly on the pion mass. In contrast, $Q_T^{u-d}$ exhibits strong enhancement near the chiral limit. The numerical results are in good agreement with available lattice QCD data and provide predictions for unmeasured quantities.

20 pages, 3 figures