The GDH sum rule for the Delta isobar: A possible anomaly?

The GDH sum rule is discussed for the Delta(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 Delta^+ and Delta^0 to resonances of spin 5/2 and higher. 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.