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Small x Phenomenology: Summary and status 2002

The Small x Collaboration, J. Andersen, S. Baranov, J. Collins, Y. Dokshitzer, L. Goerlich, G. Grindhammer, G. Gustafson, L. Jonsson, H. Jung, J. Kwiecinski, E. Levin, A. Lipatov, L. Lonnblad, M. Lublinsky, M. Maul, I. Milcewicz, G. Miu, G. Nowak, T. Sjostrand, A. Stasto, N. Timneanu, J. Turnau, N. Zotov

TL;DR

The paper surveys two decades of small-$x$ QCD, detailing how $k_ot$-factorization and unintegrated parton densities (uPDFs) extend beyond traditional DGLAP evolution to incorporate BFKL/CCFM dynamics and saturation phenomena. It compares multiple parameterizations, provides semi-analytical insights into CCFM (including SLA and CC), and discusses nonlinear BK evolution and its success in describing HERA data, as well as the implications of energy-momentum conservation on BFKL predictions. The experimental status from HERA and the Tevatron shows both alignment with NLO DGLAP in many observables and notable deviations in forward-region measurements, underscoring the need for non-collinear approaches like CASCADE and LDC for a full description. The work argues that while there is no unambiguous smoking gun for new small-$x$ dynamics, forward jets, forward $0pi^0$ production, and polarization observables provide crucial tests and motivate future experiments (e.g., HERA 3) to unequivocally map high-energy QCD dynamics.

Abstract

A second workshop on small x physics, within the Small x Collaboration, was held in Lund in June 2002 with the aim of over-viewing recent theoretical progress in this area and summarizing the experimental status. This paper is dedicated to the memory of Jan Kwiecinski, who died unexpectedly on August 29, 2003.

Small x Phenomenology: Summary and status 2002

TL;DR

The paper surveys two decades of small- QCD, detailing how -factorization and unintegrated parton densities (uPDFs) extend beyond traditional DGLAP evolution to incorporate BFKL/CCFM dynamics and saturation phenomena. It compares multiple parameterizations, provides semi-analytical insights into CCFM (including SLA and CC), and discusses nonlinear BK evolution and its success in describing HERA data, as well as the implications of energy-momentum conservation on BFKL predictions. The experimental status from HERA and the Tevatron shows both alignment with NLO DGLAP in many observables and notable deviations in forward-region measurements, underscoring the need for non-collinear approaches like CASCADE and LDC for a full description. The work argues that while there is no unambiguous smoking gun for new small- dynamics, forward jets, forward production, and polarization observables provide crucial tests and motivate future experiments (e.g., HERA 3) to unequivocally map high-energy QCD dynamics.

Abstract

A second workshop on small x physics, within the Small x Collaboration, was held in Lund in June 2002 with the aim of over-viewing recent theoretical progress in this area and summarizing the experimental status. This paper is dedicated to the memory of Jan Kwiecinski, who died unexpectedly on August 29, 2003.

Paper Structure

This paper contains 26 sections, 32 equations, 32 figures, 3 tables.

Table of Contents

  1. Introduction
  2. $k_\perp$ - factorization formalism
  3. Unintegrated parton distributions
  4. Further questions on gauge invariance
  5. Theoretical applications
  6. Comparison of available parameterizations
  7. Semi analytical insight into the CCFM equation
  8. The single loop approximation
  9. CCFM equation with consistency constraint
  10. Effects of phase space constraints in BFKL
  11. The saturation scale
  12. Non-linear evolution versus HERA data
  13. Multiple Interactions in non-ordered cascades
  14. Spin dependent unintegrated parton distributions
  15. $J/\psi$-production and polarization effects
  16. ...and 11 more sections

Figures (32)

  • Figure 2: Comparison of the different sets of unintegrated gluon densities obtained from the CCFM evolution as described in the text. In $(a-c)$ the unintegrated gluon density is shown as a function of $x$ for different values of $k_\perp$ at a scale of $\bar{q}=10$ GeV. In $(d-f)$ the ratio $R=\frac{x{\@fontswitch\mathcal{A}}(x,k_\perp^2,\bar{q}^2)}{x{\@fontswitch\mathcal{A}}(x,k_\perp^2,\bar{q}^2)_{\bf JS}}$ as a function of $x$ for different values of $k_\perp$ is shown.
  • Figure 3: Comparison of the different sets of unintegrated gluon densities obtained within LDC at scale of $\bar{q}=10$ GeV. Standard refers to the full LDC including quarks in the evolution and the full gluon splitting function. For gluonic and leading only gluon evolution is considered with only singular terms in the splitting function for the latter. Also shown is the J2003 set 1 for comparison (divided by $\pi$).
  • Figure 4: Comparison of the unintegrated gluon densities obtained in the CCFM and single loop approximation, using the same input distributions of J2003 set 1.
  • Figure 5: The average center of mass energy in $gg\to gg$ scattering with (red/dashed) and without (green/dotted) BFKL evolution of the $t$ channel gluon, with $p_{\perp\mathrm{min}}=20$ GeV for the dijets and $\alpha_s=0.1635$. Also plotted is the hadronic center of mass energy squared for the Tevatron ($(1.8\mathrm{TeV})^2$) and the LHC($(14\mathrm{TeV})^2$).
  • Figure 6: The $0$--, $1$, $2$--, $3$-- and $4$--jet parton--level cross sections as a function of the cutoff $\mu_R$, for a rapidity span of $\Delta y = 5$ and $p_{\perp\mathrm{min}}=20$ GeV for the leading dijets. Also shown is the analytic $0$--jet prediction valid for small $\mu_R$.
  • ...and 27 more figures