Tensor form factors of the $Δ^+$ baryon induced by isovector and isoscalar currents in QCD

TL;DR

This paper develops a fully symmetry-consistent tensor current description for the Δ^+ baryon by decomposing the Δ^+→Δ^+ matrix element into ten tensor form factors $F^T_{i,j}(Q^2)$, constrained by Lorentz covariance, Rarita–Schwinger conditions, Hermiticity, and PT invariance. Using a three-point QCD sum-rule framework, the authors compute both isoscalar and isovector QCD sides, perform a double Borel transform, and match to the hadronic side to extract the TFFs over $Q^2$ up to 10 GeV$^2$. The numerical analysis yields stable TFFs well described by a generalized $p$-pole fit and provides the quark tensor charges in the forward limit, highlighting distinct isoscalar and isovector flavor contributions. These results offer valuable inputs for spin-structure studies of spin-3/2 baryons, connections to transversity GPDs, and guidance for future experiments at facilities like JLab.

Abstract

The tensor form factors of the $Δ^+$ baryon are defined through the matrix element of the tensor current and describe its internal structure and spin distribution. We present the full Lorentz decomposition for the $Δ^+ \rightarrow Δ^+$ tensor current matrix element, including all independent structures consistent with Lorentz covariance, the Rarita-Schwinger constraints, and the discrete symmetries of Hermiticity, time-reversal, and parity invariance. By investigating the tensor form factors corresponding to both the isovector and isoscalar tensor currents, we observe differences that reflect the distinct contributions of up and down quark components in the $Δ^+$ baryon.

Figures (4)

• Figure 1: The $M^2$ dependence of the isoscalar TFFs of the $\Delta$ baryon at $Q^2 = 1.0~\text{GeV}^2$ for three values of the continuum threshold $s_0$.
• Figure 2: The $Q^2$ dependence of the isoscalar TFFs of the $\Delta$ baryon at $M^2 = 3.5~\text{GeV}^2$ for three values of the continuum threshold $s_0$.
• Figure 3: The $M^2$ dependence of the isovector TFFs of the $\Delta$ baryon at $Q^2 = 1.0~\text{GeV}^2$ for three values of the continuum threshold $s_0$.
• Figure 4: The $Q^2$ dependence of the isovector TFFs of the $\Delta$ baryon at $M^2 = 3.5~\text{GeV}^2$ for three values of the continuum threshold $s_0$.