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

TL;DR

This paper calculates the tensor form factors of the $^+$ baryon in QCD, revealing details about its internal structure and quark contributions through a comprehensive Lorentz decomposition.

Contribution

It provides the full Lorentz decomposition of the $^+$ tensor current matrix element, including all independent structures and symmetry constraints, for both isovector and isoscalar currents.

Findings

Differences in tensor form factors reflect up and down quark contributions.

Complete Lorentz decomposition including all symmetry constraints.

Insights into the internal spin structure of the $^+$ baryon.

Abstract

The tensor form factors of the $\Delta^+$ 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 $\Delta^+ \rightarrow \Delta^+$ 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 $\Delta^+$ baryon.