Detailed study of quark-hadron duality in spin structure functions of the proton and neutron

Abstract

Background: The response of hadrons, the bound states of the strong force (QCD), to external probes can be described in two different, complementary frameworks: as direct interactions with their fundamental constituents, quarks and gluons, or alternatively as elastic or inelastic coherent scattering that leaves the hadrons in their ground state or in one of their excited (resonance) states. The former picture emerges most clearly in hard processes with high momentum transfer, where the hadron response can be described by the perturbative expansion of QCD, while at lower energy and momentum transfers, the resonant excitations of the hadrons dominate the cross section. The overlap region between these two pictures, where both yield similar predictions, is referred to as quark-hadron duality and has been extensively studied in reactions involving unpolarized hadrons. Some limited information on this phenomenon also exists for polarized protons, deuterons, and $^{3}\mathrm{He}$ nuclei, but not yet for neutrons.Purpose: In this paper, we present comprehensive and detailed results on the correspondence between the extrapolated deep inelastic structure function ${g}_{1}$ of both the proton and the neutron with the same quantity measured in the nucleon resonance region. Thanks to the fine binning and high precision of our data, and using a well-controlled perturbative QCD (pQCD) fit for the partonic prediction, we can make quantitative statements about the kinematic range of applicability of both local duality and global duality.Method: We use the most updated QCD global analysis results at high $x$ from the Jefferson Lab Angular Momentum Collaboration to extrapolate the spin structure function ${g}_{1}$ into the nucleon resonance region and then integrate over various intervals in the scaling variable $x$. We compare the results with the large data set collected in the quark-hadron transition region by the CLAS Collaboration, including, for the first time, deconvoluted neutron data, integrated over the same intervals. We present this comparison as a function of the momentum transfer ${Q}^{2}$.Results: We find that, depending on the integration interval and the minimum momentum transfer chosen, a clear transition to quark-hadron duality can be observed in both nucleon species. Furthermore, we show, for the first time, the approach to scaling behavior for ${g}_{1}$ measured in the resonance region at sufficiently high momentum transfer.Conclusions: Our results can be used to quantify the deviations from the applicability of pQCD for data taken at moderate energies and can help with extraction of quark distribution functions from such data.