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Towards a new global QCD analysis: low x DIS data from non-linear evolution

E. Gotsman, E. Levin, M. Lublinsky, U. Maor

TL;DR

The paper develops a new global QCD analysis for low-x DIS by combining the Balitsky-Kovchegov nonlinear evolution with a linear DGLAP-type correction to incorporate short-distance dynamics, enabling a unified description of the data with a single fitting parameter.This two-stage, QCD-based approach extrapolates parton distributions to very high energies (LHC) and to very low $Q^2$, producing accurate fits to the $F_2$ structure function and making concrete predictions for $F_L$ and high-energy observables.A notable finding is that the small-$x$ saturation effects yield a growth parameter $\lambda \approx 0.08$–$0.1$ at $Q^2 \ll 1~\mathrm{GeV}^2$, consistent with soft-pomeron intercepts without invoking nonperturbative soft physics, thanks to running coupling and unitarity constraints.The work also analyzes geometrical scaling and saturation scales, discusses the limitations of the current ansatz (notably the $b$-dependence and high-$x$ input), and outlines pathways for refinement and future phenomenological applications at THERA and LHC.

Abstract

A new approach to global QCD analysis is developed. The main ingredients are two QCD-based evolution equations. The first one is the Balitsky-Kovchegov nonlinear equation, which sums higher twists while preserving unitarity. The second equation is linear and it is responsible for the correct short distance behavior of the theory, namely it includes the DGLAP kernel. Our approach allows extrapolation of the parton distributions to very high energies available at the LHC as well as very low photon virtualities, $Q^2\ll 1 {\rm GeV^2}$. All existing low $x$ data on the $F_2$ structure function is reproduced using one fitting parameter. The resulting $χ^2/df=1$. Analyzing the parameter $λ\equiv \partial\ln F_2/\partial(\ln 1/x)$ at very low $x$ and $Q^2$ well below $1 {\rm GeV^2}$ we find $λ\simeq 0.08 - 0.1$. A result which agrees with the "soft pomeron" intercept without involving soft physics.

Towards a new global QCD analysis: low x DIS data from non-linear evolution

TL;DR

The paper develops a new global QCD analysis for low-x DIS by combining the Balitsky-Kovchegov nonlinear evolution with a linear DGLAP-type correction to incorporate short-distance dynamics, enabling a unified description of the data with a single fitting parameter.This two-stage, QCD-based approach extrapolates parton distributions to very high energies (LHC) and to very low $Q^2$, producing accurate fits to the $F_2$ structure function and making concrete predictions for $F_L$ and high-energy observables.A notable finding is that the small-$x$ saturation effects yield a growth parameter $\lambda \approx 0.08$–$0.1$ at $Q^2 \ll 1~\mathrm{GeV}^2$, consistent with soft-pomeron intercepts without invoking nonperturbative soft physics, thanks to running coupling and unitarity constraints.The work also analyzes geometrical scaling and saturation scales, discusses the limitations of the current ansatz (notably the $b$-dependence and high-$x$ input), and outlines pathways for refinement and future phenomenological applications at THERA and LHC.

Abstract

A new approach to global QCD analysis is developed. The main ingredients are two QCD-based evolution equations. The first one is the Balitsky-Kovchegov nonlinear equation, which sums higher twists while preserving unitarity. The second equation is linear and it is responsible for the correct short distance behavior of the theory, namely it includes the DGLAP kernel. Our approach allows extrapolation of the parton distributions to very high energies available at the LHC as well as very low photon virtualities, . All existing low data on the structure function is reproduced using one fitting parameter. The resulting . Analyzing the parameter at very low and well below we find . A result which agrees with the "soft pomeron" intercept without involving soft physics.

Paper Structure

This paper contains 19 sections, 24 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Reviewing a new approach to DIS
  3. DGLAP correction - analytical estimates
  4. Numerical solution of the equations
  5. Results
  6. Fitting strategy
  7. Fit to $F_2$ data
  8. $d F_2/d(\ln Q^2)$
  9. $d \ln F_2/d(\ln 1/x)$
  10. Prediction for $F_L$ at HERA
  11. Predictions for LHC and THERA
  12. Gluon density
  13. $F_2$
  14. Discussion
  15. The transverse hadron size $R^2$.
  16. ...and 4 more sections

Figures (12)

  • Figure 1: The kinematic map for the solutions.
  • Figure 2: The solution of Eq. (\ref{['EQ']}) (solid line) and Eq. (\ref{['DN']}) (dashed line) plotted versus $r_\perp$.
  • Figure 3: Fit to the $F_2$ structure function.
  • Figure 4: The logarithmic derivative $\partial F_2/\partial \ln Q^2$.
  • Figure 5: The logarithmic derivative $\lambda\,=\,\partial \ln F_2/\partial \ln 1/x$.
  • ...and 7 more figures