Multipole structure of the nucleon tensor form factors

Abstract

We investigate the multipole structure of the nucleon tensor form factors within the chiral quark-soliton model based on the $1/N_c$ expansion. Extending the previous leading-order analysis~\cite{Ghim:2025gqo}, we include the rotational $1/N_c$ corrections. These corrections provide the leading nonvanishing contributions to the flavor components that are absent at leading order, thereby completing the flavor decomposition of the tensor multipole form factors at the present order. We numerically evaluate the isoscalar tensor charge, the isovector anomalous tensor magnetic moment, and the isoscalar tensor quadrupole moment, obtaining $g_T^{u+d}=0.81$, $\kappa_T^{u-d}=1.97$, and $E_T^{u+d}(0)=5.98$, respectively. The isoscalar tensor charge and quadrupole moment are mainly governed by the valence-quark contribution, whereas the isovector anomalous tensor magnetic moment receives a sizable Dirac-sea contribution. We also examine the momentum-transfer dependence of the corresponding form factors. They decrease monotonically with increasing $-t$. In particular, the isovector anomalous tensor magnetic form factor shows a pronounced falloff in the small-$|t|$ region, reflecting the importance of the Dirac sea in the tensor dipole structure.