The $Q^2$-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron, proton and neutron

TL;DR

This paper measures the $Q^2$-dependence of the generalized GDH integral for deuteron, proton, and neutron, revealing how resonance and deep inelastic scattering contributions vary with momentum transfer.

Contribution

It provides new measurements of the generalized GDH integral across a range of $Q^2$, including a re-analysis of proton data and derivation of the neutron GDH integral, confirming the Bjorken sum rule.

Findings

Resonance contribution decreases rapidly with increasing $Q^2$.

DIS contribution remains significant even at low $Q^2$.

The proton-neutron difference satisfies the Bjorken sum rule at $Q^2=5$ GeV$^2$.

Abstract

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. The data collected by HERMES with a deuterium target are presented together with a re-analysis of previous measurements on the proton. This provides a measurement of the generalised GDH integral covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. The contribution of the nucleon-resonance region is seen to decrease rapidly with increasing $Q^2$. The DIS contribution is sizeable over the full measured range, even down to the lowest measured $Q^2$. As expected, at higher $Q^2$ the data are found to be in agreement with previous measurements of the first moment of $g_1$. 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 $Q^2 = 5$ GeV$^2$.