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Anatomy of the differential gluon structure function of the proton from the experimental data on F_2p

I. P. Ivanov, N. N. Nikolaev

TL;DR

This work provides the first phenomenological parameterization of the differential gluon structure function $\mathcal F(x,\kappa^2)$ at small $x$ by blending LO DGLAP gluon inputs with a nonperturbative soft component and a soft–hard diffusion scenario within the $\kappa$-factorization framework. It demonstrates how $F_2^p$ data and real photoabsorption constrain the unintegrated gluon density, revealing substantial soft contributions and a hard component with an intercept near $0.4$ that diffuses into the soft region. The study highlights significant differences between $G_D(x,Q^2)$ from $\kappa$-factorization and conventional DGLAP densities at small $x$, while showing that soft effects remain important across a wide range of $Q^2$. The results have direct implications for predictions of diffractive processes and vector-meson production, and they illustrate the utility and limitations of applying DGLAP at low $Q^2$ in small-$x$ QCD.

Abstract

The use of the differential gluon structure function of the proton ${\cal F}(x,Q^{2})$ introduced by Fadin, Kuraev and Lipatov in 1975 is called upon in many applications of small-x QCD. We report here the first determination of ${\cal F}(x,Q^{2})$ from the experimental data on the small-x proton structure function $F_{2p}(x,Q^{2})$. We give convenient parameterizations for ${\cal F}(x,Q^{2})$ based partly on the available DGLAP evolution fits (GRV, CTEQ & MRS) to parton distribution functions and on realistic extrapolations into soft region. We discuss an impact of soft gluons on various observables. The x-dependence of the so-determined ${\cal F}(x,Q^{2})$ varies strongly with Q^2 and does not exhibit simple Regge properties. None the less the hard-to-soft diffusion is found to give rise to a viable approximation of the proton structure function F_{2p}(x,Q^2) by the soft and hard Regge components with intercepts Δ_{soft}=0 and Δ_{hard}\sim 0.4.

Anatomy of the differential gluon structure function of the proton from the experimental data on F_2p

TL;DR

This work provides the first phenomenological parameterization of the differential gluon structure function at small by blending LO DGLAP gluon inputs with a nonperturbative soft component and a soft–hard diffusion scenario within the -factorization framework. It demonstrates how data and real photoabsorption constrain the unintegrated gluon density, revealing substantial soft contributions and a hard component with an intercept near that diffuses into the soft region. The study highlights significant differences between from -factorization and conventional DGLAP densities at small , while showing that soft effects remain important across a wide range of . The results have direct implications for predictions of diffractive processes and vector-meson production, and they illustrate the utility and limitations of applying DGLAP at low in small- QCD.

Abstract

The use of the differential gluon structure function of the proton introduced by Fadin, Kuraev and Lipatov in 1975 is called upon in many applications of small-x QCD. We report here the first determination of from the experimental data on the small-x proton structure function . We give convenient parameterizations for based partly on the available DGLAP evolution fits (GRV, CTEQ & MRS) to parton distribution functions and on realistic extrapolations into soft region. We discuss an impact of soft gluons on various observables. The x-dependence of the so-determined varies strongly with Q^2 and does not exhibit simple Regge properties. None the less the hard-to-soft diffusion is found to give rise to a viable approximation of the proton structure function F_{2p}(x,Q^2) by the soft and hard Regge components with intercepts Δ_{soft}=0 and Δ_{hard}\sim 0.4.

Paper Structure

This paper contains 19 sections, 58 equations, 25 figures.

Table of Contents

  1. Introduction: Why unintegrated gluon structure functions?
  2. Differential density of gauge bosons: the QED example
  3. The insight into the differential density of gluons
  4. Modeling virtual photoabsorption in QCD
  5. Where $\hbox{\boldmath $\kappa$}_{\perp}$-factorization meets DGLAP factorization
  6. The different evolution paths: soft-to-hard diffusion and vice versa
  7. The Ansatz for differential gluon structure function
  8. Determination of the differential gluon structure function of the proton
  9. The parameters of DGFS for different DGLAP inputs
  10. The description of the proton structure function $F_{2p}(x,Q^2)$
  11. Real photoabsorption cross section $\sigma^{\gamma p}$.
  12. Properties of differential gluon structure function in the momentum space
  13. Soft/hard decomposition of DGSF
  14. Soft/hard decomposition of the integrated gluon structure function
  15. Soft/hard decomposition of the proton structure function $F_{2}(x,Q^{2})$
  16. ...and 4 more sections

Figures (25)

  • Figure 1: The Fermi-Weizsäcker-Williams diagram for calculation of the flux of equivalent photons
  • Figure 2: The Fermi-Weizsäcker-Williams diagrams for calculation of the flux of equivalent photons in positronium.
  • Figure 3: The pQCD modeling of DIS in terms of multiproduction of parton final states.
  • Figure 4: The $\hbox{\boldmath $\kappa$}$-factorization representation for DIS at small $x$.
  • Figure 5: The Huygens principle for $Q^{2},x$ evolution of DIS structure functions with (a) DGLAP restricted transverse phase space and (b) for the BFKL $x$ evolution without restrictions on the transverse phase space and hard-to-soft & soft-to-hard diffusion.
  • ...and 20 more figures