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Small x Phenomenology - summary of the 3rd Lund Small x Workshop in 2004

The Small x Collaboration, Jeppe R. Andersen Serguei Baranov, Jochen Bartels, Gergely G. Barnafoldi, Grigorios Chachamis, John Collins, Guenter Grindhammer, Goesta Gustafson, Magnus Hansson, Gunnar Ingelman, Hannes Jung, Leif Joensson, Albert Knutsson, Henri Kowalski, Krzysztof Kutak, Albrecht Kyrieleis, Peter Levai, Artem Lipatov, Leif Loennblad, Michael Lublinsky, Giuseppe Marchesini, Izabela Milcewicz, Christiane Risler, Agustin Sabio-Vera, Malin Sjoedahl, Anna Stasto, Jacek Turnau, Graeme Watt, Nikolai Zotov

TL;DR

This workshop synthesis addresses the challenges of QCD at small x, where conventional collinear factorization breaks down due to large logarithms and potential saturation effects. It surveys the k_t-factorization framework, unintegrated and doubly unintegrated parton densities, and advances in NLO BFKL and resummation to stabilize predictions, alongside practical implementations in Monte Carlo and global fits. Key contributions include formalism for DUPDFs, last-step UPDF construction, and NLL BFKL developments, coupled with phenomenological applications to heavy-quark production and electroweak boson p_T spectra. The work advances a cohesive approach to improving QCD predictions at HERA, Tevatron, and LHC energies and informs global fits and saturation studies.

Abstract

A third workshop on small-x physics, within the Small-x Collaboration, was held in Hamburg in May 2004 with the aim of overviewing recent theoretical progress in this area and summarizing the experimental status.

Small x Phenomenology - summary of the 3rd Lund Small x Workshop in 2004

TL;DR

This workshop synthesis addresses the challenges of QCD at small x, where conventional collinear factorization breaks down due to large logarithms and potential saturation effects. It surveys the k_t-factorization framework, unintegrated and doubly unintegrated parton densities, and advances in NLO BFKL and resummation to stabilize predictions, alongside practical implementations in Monte Carlo and global fits. Key contributions include formalism for DUPDFs, last-step UPDF construction, and NLL BFKL developments, coupled with phenomenological applications to heavy-quark production and electroweak boson p_T spectra. The work advances a cohesive approach to improving QCD predictions at HERA, Tevatron, and LHC energies and informs global fits and saturation studies.

Abstract

A third workshop on small-x physics, within the Small-x Collaboration, was held in Hamburg in May 2004 with the aim of overviewing recent theoretical progress in this area and summarizing the experimental status.

Paper Structure

This paper contains 14 sections, 27 equations, 14 figures.

Table of Contents

  1. Introduction
  2. The $k_\perp$-factorization formalism
  3. Future fits of uPDF parameterizations
  4. The need for doubly unintegrated parton density functions
  5. Doubly unintegrated PDFs
  6. Unintegrated PDFs from integrated ones
  7. Doubly-unintegrated PDFs
  8. NLO BFKL
  9. Resummation at small $x$
  10. The NLO ${\gamma^*}$ impact factor
  11. Applications of $k_\perp$-factorization
  12. Heavy quark production at the Tevatron
  13. Theoretical framework
  14. Numerical results

Figures (14)

  • Figure 1: Comparison of the CCFM uPDF obtained after changing the renormalization scale in the off-shell matrix element by a factor 2 up and down.
  • Figure 2: (a) and (b): Comparison between use of simple LO parton model approximation and of the use of $k_\perp$ densities for the $p_\perp$ of $c\bar{c}$ pairs in photoproduction, and for the $x_\gamma$. (c) and (d): Comparison of use of $k_\perp$ densities and full simulation.
  • Figure 3: Illustration of $(z,k_t)$-factorization for the doubly-unintegrated gluon distribution, $f_g(x,z,k_t^2,\mu^2)$, shown in the final diagram. In the first two diagrams the penultimate parton in the DGLAP evolution chain, with 4-momentum $k_{n-1}=(x/z)\,p$, splits into a gluon with 4-momentum $k_n\equiv k=x\,p-\beta\,q^\prime+k_\perp$.
  • Figure 4: Comparison with H1 inclusive jet production data Adloff:2002ew in three pseudorapidity ($\eta^\textsc{lab}$) bins. The predictions of the $(z,k_t)$-factorization approach based on DUPDFs Watt:2003mx (which is much simpler to implement) are in good agreement with the conventional QCD approach. In some bins the predictions of the latter approach are hidden beneath the bold lines of the $(z,k_t)$-factorization approach, at the respective order.
  • Figure 5: $p_T$ distribution of W bosons produced at the Tevatron calculated using $(z,k_t)$-factorization Watt:2003vf, compared to DØ data Abbott:2000xv.
  • ...and 9 more figures