Elastic contribution to the Burkhardt-Cottingham and generalized Gerasimov-Drell-Hearn sum rules

The elastic contribution to the first moment of $g_2{(x,Q}^2)$ is analyzed using a Drell-Yan-West-type relation and is shown to be negative. For a qualitative estimate the one-loop contributions to the polarized DIS sum rules in QED are studied. The behavior of the generalized Gerasimov-Drell-Hearn (GDH) sum rule is sensitive to infrared regularization. With a lower threshold for the gluon virtuality the relation of the generalized GDH sum rule to the Burkhardt-Cottingham sum rule is studied. We conclude that the elastic part has to be included for long range interactions but can be consistently discarded for short-range interactions.