Abstract
We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction $x$ and the color coherence of gluon couplings at small $x$, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the $(1-x)$ power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire $x$ region. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.
Highlights
One of the outstanding problems in nuclear and particle physics is to understand the structure of hadrons in terms of quarks and gluons, the fundamental degrees of freedom in QCD
From Eqs. (9) and (11) it is seen that a calculation of Ioffe-time distributions (ITDs) of polarized gluon distributions in ω ∼ 15 region will give a reliable estimate for gluon helicity ΔG in the nucleon and several other higher moments which are currently unknown in theoretical calculations and not constrained by the experimental data
Using the fact that gluon parton distribution functions (PDFs) diverges much faster than the valence quark PDF in the limit x → 0, one can show that the asymptotic limit of the ITD corresponding to nucleon valence quark distribution will set in at earlier ω compared to the gluon ITDs, noted in [47]
Summary
One of the outstanding problems in nuclear and particle physics is to understand the structure of hadrons in terms of quarks and gluons, the fundamental degrees of freedom in QCD. One of the main physics goals of the upcoming Electron-Ion-Collider (EIC) [3] is to have precise measurements of the nucleon spin structure, the gluon and sea quark distributions. In light of the above discussions, we revisit the calculations in [20,21] which incorporated pQCD constraints at large x and coherent correlations of partons at low x to determine unpolarized and polarized gluon distributions These calculations [20,21] demonstrated that many properties of the exclusive reactions can be calculated by incorporating the knowledge of asymptotic freedom, power-law scaling, and helicity conservation rules of pQCD without explicit knowledge of the nonperturbative light-front wave function. The main goal of this article is to transcribe these insights from the small and large x physics and compare how adequate and compatible they are with the recent determinations of gluon distributions We emphasize this calculation does not aim to provide the precise determination of. We determine the asymptotic behavior of the unpolarized and polarized gluon ITDs which are not accessible within the current reach of LQCD calculations and can provide complementary information to reconstruct the full x-dependence of the unpolarized and polarized gluon distributions
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