Coupled-channel contributions to the GDH sum rule from the Jülich-Bonn approach

TL;DR

This work computes the GDH sum rule within the Jülich-Bonn dynamical coupled-channel framework, integrating a large data set of πN and γN processes to extract channel-resolved contributions to the GDH integral and to refine the light-baryon resonance spectrum. The model solves a Lippmann-Schwinger-type equation with pole and non-pole components, extended to photoproduction with phenomenological photon couplings, and fit to extensive experimental data, including new CLAS, LEPS2/BGOegg, and other measurements. The analysis yields updated resonance parameters and shows that the πN channels dominate the GDH integral, while higher-mass channels contribute modestly; the total saturates at about 170 ± 19 μb, leaving a missing piece likely from the ππN channel not yet included, which the authors plan to incorporate in future work. Overall, the study demonstrates how dynamical coupled-channel approaches can disentangle channel-specific contributions to fundamental sum rules and guide future experimental and theoretical efforts to complete the spin structure of the nucleon.

Abstract

We study the Gerasimov-Drell-Hearn (GDH) sum rule within a dynamical coupled-channel approach, the Jülich-Bonn model for light baryon resonances based on fits to an extensive data base of pion and photon induced data. Recently published photoproduction data for different observables with $πN$ and $ηN$ final states are analyzed simultaneously with older data for the reactions $πN\to πN$, $ηN$, $KΛ$, $KΣ$ and $γp\toπN$, $ηN$, $KΛ$, $KΣ$. The impact of the new data on the resonance spectrum is investigated and the contribution of the individual channels to the GDH integral is determined.

Figures (12)

• Figure 1: Current fit results (red) and 2022 fit Ronchen:2022hqk (blue) for comparison for the double spin polarization observable ${E}$ for the process $\gamma p\to \pi^0p$. Data from CLAS:2023ddn. The numbers in each plot denote the center of mass energy in MeV.
• Figure 2: Current fit results (red) and 2022 fit Ronchen:2022hqk (blue) for comparison for the double polarization observable ${G}$ for the process $\gamma p\to \pi^0p$. Data from CLAS:2021udy. The numbers in each plot denote the center of mass energy in MeV.
• Figure 3: Current fit results (red) and 2022 fit Ronchen:2022hqk (blue) for comparison for the double polarization observable ${G}$ for the process $\gamma p\to \pi^+n$. Data from CLAS:2021udy. The numbers in each plot denote the center of mass energy in MeV.
• Figure 4: Current fit results (red) and 2022 fit Ronchen:2022hqk (blue) for comparison for the differential cross section for the process $\gamma p\to \eta p$. Data from LEPS2BGOegg:2022dop. The numbers in each plot denote the center of mass energy in MeV.
• Figure 5: Current fit results (red) and 2022 fit Ronchen:2022hqk (blue) for comparison for the photon beam asymmetry $\Sigma$ for the process $\gamma p\to \eta p$. Data from LEPS2BGOegg:2022dop. The numbers in each plot denote the center of mass energy in MeV.