Contribution of single pion electroproduction to the generalized Gerasimov-Drell-Hearn sum rule for the deuteron

The generalized Gerasimov-Drell-Hearn sum rule is evaluated for the contribution of single pion production on the deuteron by explicit integration up to an energy of 1.5 GeV for both coherent and incoherent production. As elementary ${\gamma }^{\ast }N\to \pi N$ amplitude the MAID2003 model has been used. For incoherent production final state interaction is included in the final $NN$ and $\pi N$ subsystems. The resulting contribution to the generalized transverse GDH sum rule is considerably smaller than the negative contribution from the disintegration channel $d(e,e^{\mathrm{\prime }})np$ which dominates the sum rule at low $Q^2$.