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Small x QCD effects in DIS with a forward jet or a forward pi0

J. Kwiecinski, A. D. Martin, J. J. Outhwaite

TL;DR

This work tests small-$x$ QCD dynamics in DIS by analyzing forward jet and forward $\pi^{0}$ production with an unintegrated BFKL gluon evolved from the virtual photon end. By incorporating a kinematic consistency constraint to capture dominant subleading effects, the authors obtain predictions for forward jets, forward $\pi^{0}$s, and forward dijets that are in good agreement with HERA data once hadronisation and fragmentation uncertainties are considered. The study demonstrates that subleading BFKL corrections are essential for stabilizing predictions while preserving the characteristic steep rise in $x$ and reproducing final-state observables. The results support a unified perturbative QCD description of forward-jet and forward-multiplicity channels at small $x$, with implications for future tests of high-energy QCD dynamics at lepton–hadron colliders.

Abstract

We compare predictions based on small x (QCD) dynamics with recent data for deep inelastic events containing forward jets or forward pi0 mesons. We quantify the effect of imposing the (higher order) consistency condition on the BFKL equation and study uncertainties inherent in the QCD predictions. We also estimate the cross-section for the forward production of two jets.

Small x QCD effects in DIS with a forward jet or a forward pi0

TL;DR

This work tests small- QCD dynamics in DIS by analyzing forward jet and forward production with an unintegrated BFKL gluon evolved from the virtual photon end. By incorporating a kinematic consistency constraint to capture dominant subleading effects, the authors obtain predictions for forward jets, forward s, and forward dijets that are in good agreement with HERA data once hadronisation and fragmentation uncertainties are considered. The study demonstrates that subleading BFKL corrections are essential for stabilizing predictions while preserving the characteristic steep rise in and reproducing final-state observables. The results support a unified perturbative QCD description of forward-jet and forward-multiplicity channels at small , with implications for future tests of high-energy QCD dynamics at lepton–hadron colliders.

Abstract

We compare predictions based on small x (QCD) dynamics with recent data for deep inelastic events containing forward jets or forward pi0 mesons. We quantify the effect of imposing the (higher order) consistency condition on the BFKL equation and study uncertainties inherent in the QCD predictions. We also estimate the cross-section for the forward production of two jets.

Paper Structure

This paper contains 11 sections, 41 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The unintegrated BFKL gluon from $\gamma^{*} g$ fusion
  3. Higher order corrections
  4. Forward jet production in DIS.
  5. QCD prediction for DIS + forward jet
  6. Comparison with HERA data
  7. DIS events containing a forward $\pi^{0}$
  8. Including forward jet $\rightarrow \pi^{0}$ fragmentation
  9. Comparison with forward $\pi^{0}$ data
  10. Forward dijet production
  11. Discussion

Figures (12)

  • Figure 1: Diagram showing the $\gamma^{*} g$ fusion, including the soft gluon radiation ladder.
  • Figure 2: Diagram to illustrate the radiation of soft gluons from the reggeized gluonic propagator in the t-channel.
  • Figure 3: Diagram showing forward jet production driven by $\gamma^{*} g$ fusion coupled to evolution through a BFKL-type ladder. The struck parton from the proton could in principle be either a gluon or a quark.
  • Figure 4: The DIS + forward jet differential cross-section versus Bjorken-$x$ as measured at the hadron level by the H1 h1 and ZEUS zeus collaborations. The kinematic cuts are given in Table \ref{['tab:cuts1']}. The curves are predictions at the parton level, based on the BFKL formalism including sub-leading corrections, corresponding to the three choices of scales and infrared cut-off given in (\ref{['eqn:scales']}) .
  • Figure 5: Schematic showing collinear fragmentation of a forward parton jet of momentum $k_{j}$ into a forward pion of momentum $z k_{\pi}$. The process is described by fragmentation functions, $D_{i}(z,\mu^{2})$
  • ...and 7 more figures