The Q-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron, proton and neutron
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The Gerasimov-Drell-Hearn (GDH) sum rule connects the anomalous contribution to the magnetic moment of the target nucleus with an energy-weighted integral of the difference of the helicity-dependent photoabsorption cross sections. Originally conceived for real photons, the GDH integral can be generalised to the case of photons with virtuality Q2. For spin-1/2 targets such as the nucleon, it then represents the non-perturbative limit of the first moment \(\Gamma_1\) of the spin structure function g 1 (x,Q 2 ) in deep inelastic scattering (DIS). The data collected by HERMES with a deuterium target are presented together with a re-analysis of previous measurements on the proton. This provides an unprecedented and complete measurement of the generalised GDH integral for photon-virtuality ranging over 1.2<Q 2 <12.0 GeV2 and for photon-nucleon invariant mass squared W2 ranging over 1<W 2 <45 GeV2, thus covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. These data allow the study of the Q2-dependence of the full GDH integral, which is sensitive to both the Q2-evolution of the resonance form factors and contributions of higher twist. The contribution of the nucleon-resonance region is seen to decrease rapidly with increasing Q2. The DIS contribution is sizeable over the full measured range, even down to the lowest measured Q2. As expected, at higher Q2 the data are found to be in agreement with previous measurements of the first moment of g1. From data on the deuteron and proton, the GDH integral for the neutron has been derived and the proton-neutron difference evaluated. This difference is found to satisfy the fundamental Bjorken sum rule at Q 2 = 5 GeV2.
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