Reconstructing Transition GPDs for Delta(1232) from Helicity Amplitude A_1/2(Q^2) via Dipole Fits and Impact Parameter Analysis

TL;DR

This paper develops a modular, data-driven method to reconstruct the transverse spatial structure of the Delta(1232) resonance from helicity amplitude data, combining dipole fits and impact parameter analysis.

Contribution

It introduces a factorized GPD model for the Delta(1232) transition, linking amplitude data to spatial distributions with a reproducible, physically interpretable framework.

Findings

Successfully reconstructs transverse spatial distributions from helicity amplitudes.

Demonstrates how longitudinal shaping affects transverse localization.

Provides a versatile approach applicable to other transition channels.

Abstract

This work presents a modular reconstruction of the transition generalized parton distribution (GPD) H_T(x,t) for the Delta(1232) resonance, based on digitized helicity amplitude data and dipole fits to A_1/2(Q^2). From the fitted amplitude, we extract a Sachs-like form factor F(t) and define a separable GPD model H_T(x, t) = h(x)F(t), with h(x) modeled as a normalized Beta-like profile. This factorized ansatz satisfies the GPD sum rule and enables a direct two-dimensional Fourier transform to construct transverse spatial distributions q(x,b). We analyze how longitudinal shaping modulates transverse localization, and quantify spatial features using statistical diagnostics including mean radius, skewness, and kurtosis. The framework is reproducible, data-driven, and applicable to other transition channels, providing a physically interpretable map from amplitude behavior to spatial structure.