The nucleon Drell-Hearn-Gerasimov sum rule within a relativistic constituent quark model

The Drell-Hearn-Gerasimov sum rule for the nucleon is investigated within a relativistic constituent quark model formulated on the light-front. The contribution of the N−Δ(1232) transition is explicitly evaluated using different forms for the baryon wave functions and adopting a one-body relativistic current for the constituent quarks. It is shown that the N−Δ(1232) contribution to the sum rule is sharply sensitive to the introduction of anomalous magnetic moments for the constituent quarks, at variance with the findings of non-relativistic and relativized quark models. The experimental value of the isovector-isovector part of the sum rule is almost totally reproduced by the N−Δ(1232) contribution, when the values of the quark anomalous magnetic moments are fixed by fitting the experimental nucleon magnetic moments. Our results are almost independent of the adopted form of the baryon wave functions and only slightly sensitive to the violation of the angular condition caused by the use of a one-body current. The calculated average slope of the generalized sum rule around the photon point results to be only slightly negative at variance with recent predictions of relativized quark models.