Measurement of the high-energy contribution to the Gerasimov-Drell-Hearn sum rule

We propose to measure the high-energy behavior of the integrand of the Gerasimov-Drell-Hearn (GDH) sum rule on the proton and the neutron up to 12 GeV. The convergence of the GDH integral will be investigated for the first time and to high precision. The validity of the GDH sum rule on the neutron will be accurately tested for the first time, while for the proton the uncertainty will be improved by $25\%$ relative. The data will allow precision testing of Regge phenomenology in the polarized domain. The $a_1$ and $f_1$ Regge trajectory intercepts will be obtained to an order of magnitude higher precision than the current best estimates. The data will also contribute to the determination of the real and imaginary parts of the spin-dependent Compton amplitude, the polarizability correction to hyperfine splitting in hydrogen, and to studying the transition between polarized DIS and diffractive regimes. The experiment will require a circularly polarized photon beam (produced from a longitudinally polarized electron beam) with a flux approximately 1/3 of the GlueX-II experiment E12-13-003. The experiment will run in two configurations which require two different CEBAF beam energies. A new longitudinal polarized proton and deuteron target will be needed in Hall D. The experiment will require 21 PAC days at the nominal CEBAF energy and another 12 PAC days at an energy 1/3 to 1/2 of the nominal.