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Energy Dependence of σ^{DD}/σ_{tot} in DIS and Shadowing Corrections

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

TL;DR

The paper scrutinizes the energy dependence of the diffractive-to-total DIS cross-section ratio $\sigma^{DD}/\sigma_{tot}$ by extending the Kovchegov-McLerran framework to include shadowing corrections via the Mueller-Glauber approach and AGK cutting rules, with both $q\bar{q}$ and $q\bar{q}G$ final states. It develops a detailed dipole-based, unitarity-consistent formalism (including nucleon excitations and multi-Pomeron exchanges) and performs numerical studies using GRV/DGLAP inputs, exploring mass-window cuts. The main finding is that, even with these perturbative shadowing mechanisms, the energy dependence remains too strong compared with the experimentally observed weak energy dependence, implying significant soft nonperturbative contributions are missing. The work thus highlights the limitations of a purely perturbative treatment for diffractive DIS and points to nonperturbative QCD effects as essential ingredients to reproduce HERA data.

Abstract

We gereralize the Kochegov-McLerran formula for the ratio $σ^{DD}/σ_{tot}$ in perturbative QCD, using Mueller-Glauber approach for shadowing corrections and AGK cutting rules. We investigate several phenomenological approaches with the goal of obtaining results consisent with experimental data. We fail to reproduce the observed weak energy dependence of the ratio, and conclude that the soft nonperturbative contribution present at short distances must also be included.

Energy Dependence of σ^{DD}/σ_{tot} in DIS and Shadowing Corrections

TL;DR

The paper scrutinizes the energy dependence of the diffractive-to-total DIS cross-section ratio by extending the Kovchegov-McLerran framework to include shadowing corrections via the Mueller-Glauber approach and AGK cutting rules, with both and final states. It develops a detailed dipole-based, unitarity-consistent formalism (including nucleon excitations and multi-Pomeron exchanges) and performs numerical studies using GRV/DGLAP inputs, exploring mass-window cuts. The main finding is that, even with these perturbative shadowing mechanisms, the energy dependence remains too strong compared with the experimentally observed weak energy dependence, implying significant soft nonperturbative contributions are missing. The work thus highlights the limitations of a purely perturbative treatment for diffractive DIS and points to nonperturbative QCD effects as essential ingredients to reproduce HERA data.

Abstract

We gereralize the Kochegov-McLerran formula for the ratio in perturbative QCD, using Mueller-Glauber approach for shadowing corrections and AGK cutting rules. We investigate several phenomenological approaches with the goal of obtaining results consisent with experimental data. We fail to reproduce the observed weak energy dependence of the ratio, and conclude that the soft nonperturbative contribution present at short distances must also be included.

Paper Structure

This paper contains 18 sections, 80 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Shadowing corrections in QCD
  3. Notations and definitions
  4. Shadowing corrections for penetration of $\mathbf{q \bar{q}}$ pair through the target.
  5. General approach
  6. Mueller-Glauber approach
  7. Diffractive production of nucleon excitations
  8. AGK cutting rules and diffractive production
  9. Cross section for $\mathbf{q \bar{q} G }$ diffractive production with SC
  10. First correction to the Mueller - Glauber formula for the total cross section
  11. Cross section for diffractive production
  12. Numerical calculation for $\mathbf{ \sigma^{DD}/\sigma_{tot}}$
  13. Ratio $\mathbf{ \sigma^{DD}/\sigma_{tot}}$ in the mass windows
  14. Summary and discussions
  15. Appendix
  16. ...and 3 more sections

Figures (17)

  • Figure 1: Experimantal data for the ratio $\sigma^{DD}/\sigma_{tot}$ taken from Ref. ZEUSDATA.
  • Figure 2: Diffractive dissociation of the virtual photon into quark - antiquark pair ( $q \bar{q}$ ) and quark - antiquark pair plus one extra gluon ( $q \bar{q} G$) in pQCD.
  • Figure 3: Diffractive production of a quark - antiquark pair.
  • Figure 4: Ratio $\sigma^{DD}/\sigma_{tot}$ calculated using Eq. (\ref{['AGLEST']}) in the Eikonal model for $q \bar{q}$ diffractive production.
  • Figure 5: $\kappa_{dipole}$ calculated in HERA kinematic region, using the GRV-94 parameterization GRV for the gluon distrubution. $lg x = log_{10}(x)$.
  • ...and 12 more figures