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On the role of NLL corrections and Energy Conservation in the High Energy Evolution of QCD

Jeppe R. Andersen

TL;DR

This paper introduces a new, efficient method to solve the BFKL evolution at LL and NLL accuracy, tailored for multi-jet production in high-energy collisions. By reformulating the gluon Green's function evolution and presenting a direct Monte Carlo algorithm, it clarifies that energy-momentum conservation constraints are independent of the kernel's logarithmic accuracy and must be imposed at the level of final-state phase space. The authors demonstrate that incorporating these constraints, rather than relying solely on NLL kernel corrections, significantly impacts collider observables such as jet decorrelation. A public code implementing the method with energy-momentum conservation and LL evolution (with NLL running coupling) is made available, enabling practical phenomenology for Tevatron/LHC energies.

Abstract

We present a new method for solving the BFKL evolution applicable at both leading and next-to-leading logarithmic accuracy, and tailored to the study of QCD multi-jet events at colliders. We utilise this to discuss corrections to the standard analysis. There are known, large corrections from energy and momentum conservation. We show that, despite claims to the contrary in the literature, these are unrelated to the next-to-leading logarithmic corrections to the evolution kernel.

On the role of NLL corrections and Energy Conservation in the High Energy Evolution of QCD

TL;DR

This paper introduces a new, efficient method to solve the BFKL evolution at LL and NLL accuracy, tailored for multi-jet production in high-energy collisions. By reformulating the gluon Green's function evolution and presenting a direct Monte Carlo algorithm, it clarifies that energy-momentum conservation constraints are independent of the kernel's logarithmic accuracy and must be imposed at the level of final-state phase space. The authors demonstrate that incorporating these constraints, rather than relying solely on NLL kernel corrections, significantly impacts collider observables such as jet decorrelation. A public code implementing the method with energy-momentum conservation and LL evolution (with NLL running coupling) is made available, enabling practical phenomenology for Tevatron/LHC energies.

Abstract

We present a new method for solving the BFKL evolution applicable at both leading and next-to-leading logarithmic accuracy, and tailored to the study of QCD multi-jet events at colliders. We utilise this to discuss corrections to the standard analysis. There are known, large corrections from energy and momentum conservation. We show that, despite claims to the contrary in the literature, these are unrelated to the next-to-leading logarithmic corrections to the evolution kernel.

Paper Structure

This paper contains 5 sections, 5 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Iterative Solution of the BFKL Equation
  3. Direct Solution of the BFKL Evolution
  4. Phase space restrictions from energy and momentum conservation
  5. Conclusions

Figures (1)

  • Figure 1: The $2\!\to\!2\!+\!n$ gluon scattering process described using Regge factorisation, with the initial state at the bottom. The shaded blobs are the gluon-gluon--Reggeon impact factors $\Gamma_{a,b}$, and the hatched blobs are the (regularised) gluon-Reggeon-Reggeon vertices. The Reggeized gluon (Reggeon) propagators are marked with zigzag lines. Gluon emission is generated in the rapidity span between the impact factors by the evolution described by the BFKL equation of the Reggeized gluon. At NLL the vertices can emit one or two gluons, or a quark-anti-quark pair.