Parameterisation of [σ1/2−σ3/2] for Q2≥0 and non-resonance contribution to the GDH sum rule

Abstract

A description of the virtual photon absorption cross section difference σ 1/2 − σ 3/2 for the proton and neutron is obtained with a parameterisation based on a Regge type approach. The parametrisation is obtained from global fits to the cross section data derived from the spin asymmetries measured in deep inelastic scattering of longitudinally polarised leptons from polarised 1 H, 3 He and 2 H targets in the range 0.3 GeV 2 < Q 2 < 70 GeV 2 and 4 GeV 2 < W 2 < 300 GeV 2 . The fits give a reliable description of the data and provide predictions for the photo-production through a smooth Q 2 -transition. The contribution above the resonance region to the Gerasimov-Drell-Hearn sum rule for real and virtual photons has been evaluated. For the real photons this contribution accounts for a large fraction of the discrepancy between the sum rule expectations and the single pion photo-production analysis estimates.

Gerasimov-Drell-Hearn sum rule and related integrals

“…The still missing DIS contribution has been estimated by Bianchi et al [20] from an extrapolation of DIS to real photons. If we add those (26 ± 7) µb to our analysis in the resonance region, the total result for the proton is (−202 ± 10) µb.…”

$g_1$ at low x and low $Q^2$ with Polarized ep colliders

“…Phenomenological Regge based estimates [22,23] suggest that 25 ± 10µb (about 10%) of the sum-rule may come from √ s γp > 2.5GeV…”

The Q2-dependence of the generalised Gerasimov–Drell–Hearn integral for the proton

“…It has never been directly tested, due to the need for a circularly polarised beam with a longitudinally polarised target, and a wide range of photon energies that has to be covered. There are available several predictions for the contribution of nucleon-resonance excitation to the GDH integral [2], derived from multipole analyses of data for unpolarised single-pion photoproduction, and a prediction for the contribution of high-energy multihadron production [3], based on a multiple-reggeon exchange analysis of deep inelastic asymmetries. The estimate from multipole analysis was confirmed by preliminary results from the GDH experiment at Mainz [4], which covered the photonenergy range from 200 MeV up to 800 MeV.…”

“…The latter was calculated in each Q 2 -interval by adding to I meas GDH an estimate of the unmeasured contribution for W 2 > 45 GeV 2 . This was calculated using a multiplereggeon exchange parameterisation [3] for σ 1/2 (ν, Q 2 ) − σ 3/2 (ν, Q 2 ) at high energy, and amounted to about 3.5 µb for all Q 2 -bins. A parameterisation for g 1 [27] based on a NLO-QCD analysis provided within 5% the same results as the multiple-reggeon exchange analysis.…”