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Investigation of the $Δ (1232)$ resonance substructure in the $p γ^{*} \to Δ (1232)$ process through helicity amplitudes

A. Kaewsnod ^1,*, K. Xu¹, T. Sangkhakrit ^1,2, Z. Zhao¹, W. Sreethawong¹, A. Limphirat ^1,†, K. Khosonthongkee ¹, and Y. Yan^1,‡

¹School of Physics and Center of Excellence in High Energy Physics and Astrophysics, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand
²KOSEN Institute, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

^*Contact author: a.kaewsnod@gmail.com
^†Contact author: ayut@g.sut.ac.th
^‡Contact author: yupeng@g.sut.ac.th

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Phys. Rev. D 113, 036010 – Published 10 February, 2026

DOI: https://doi.org/10.1103/ptgv-jx85

Abstract

The substructure of the $Δ (1232)$ resonance is studied in the $p γ^{*} \to Δ (1232)$ transition via helicity amplitudes within a quark-model framework that treats baryons as three-quark systems and includes both quark-core and meson-cloud contributions. In the calculation of the transition amplitudes, the proton wave function is Lorentz boosted from the proton rest frame to the $Δ (1232)$ resonance rest frame. The comparison of the calculated amplitudes $A_{1 / 2}$ , $A_{3 / 2}$ , and $S_{1 / 2}$ with experimental data indicates a non-negligible $L = 2$ admixture in the $Δ (1232)$ , about 80% of the $Δ (1232)$ wave function in the S wave and 20% in the D wave. In particular, the $S_{1 / 2}$ amplitude is found to be dominated by the $L = 2$ quark-core component rather than the $L = 0$ part. The results challenge the traditional understanding that the $Δ (1232)$ baryon is dominantly an $L = 0$ state.

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Phys. Rev. D 113, 036010– Published 10 February, 2026

Vol. 113, Iss. 3 — 1 February 2026

Received 28 May 2025
Accepted 21 January 2026

DOI: https://doi.org/10.1103/ptgv-jx85

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Investigation of the $Δ (1232)$ resonance substructure in the $p γ^{*} \to Δ (1232)$ process through helicity amplitudes

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Investigation of the Δ(1232) resonance substructure in the pγ*→Δ(1232) process through helicity amplitudes

Abstract

Physics Subject Headings (PhySH)

Article Text

References (35)

Investigation of the $Δ (1232)$ resonance substructure in the $p γ^{*} \to Δ (1232)$ process through helicity amplitudes