The Gdh Sum Rule for the Δ Isobar:. a Possible Anomaly?

The GDH sum rule is discussed for the Δ(1232) resonance. It is shown that apart from ordinary excitations to higher-energy states, the sum rule contains a large negative contribution due to de-excitation into the nucleon state. Therefore, a fulfillment of the sum rule assumes a strong coupling of Δ⁺ and Δ⁰ to resonances of {spin} >= (5)/(2). Calculations performed in quark models suggest that D₁₅(1675) may be such a resonance. However, its strength is found to be not sufficient for bringing the GDH sum rule to a theoretically expected positive magnitude.