Tensor-polarized parton density in the $N \to \Delta$ transition from the large-$N_c$ light-cone wave function

Abstract

The tensor-polarized parton density is defined by the forward matrix element of a partonic operator in the $N \to \Delta$ transition. In this work, we investigate it by employing the large-$N_c$ light-cone wave function derived from the mean-field approach. The mean-field picture is based on low-energy effective dynamics in the large-$N_c$ limit, where the baryon wave function is formulated in the rest frame. By exploiting the covariance of the mean-field solution, we derive the corresponding large-$N_c$ light-cone wave function$\unicode{x2013}$decomposed unambiguously into $3Q$, $5Q$, $7Q$, and higher Fock components$\unicode{x2013}$in the infinite momentum frame. Evaluating the overlap of these wave functions, we derive an overlap representation of the tensor-polarized parton density in the $N \to \Delta$ transition and find that the leading contribution arises from the $5Q$ Fock sector. This indicates that the tensor-polarized parton density directly probes the genuine $5Q$ component and is governed by chiral dynamics. Our numerical analysis shows that the $N \to \Delta$ tensor-polarized parton density is suppressed, consistent with standard large-$N_c$ expectations. Finally, we establish connections among the tensor-polarized parton density, the generalized parton distribution $H_X$, and the energy-momentum tensor form factor $F_4$.