Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Quark-Antiquark Contribution to the Fully Exclusive BFKL Evolution at NLL Accuracy

Jeppe R. Andersen

TL;DR

In NLL BFKL, the standard real-emission kernel $K_r^{(2)}$ integrates over all invariant masses, which can violate energy-momentum conservation at the vertex; the paper recalculates the quark–antiquark contribution retaining full momentum dependence using the Lipatov effective action and a phase-space slicing framework. This leads to an exclusive, momentum-dependent expression for the quark–antiquark part of the real-emission kernel $K_r^{(2)}$ that is finite for nonzero momentum transfer and agrees with the known $1/N_c^2$-suppressed limit. The work provides a path to merging energy-momentum conservation with full NLL accuracy in BFKL evolution and clarifies the origin of the large NLL corrections observed in previous analyses.

Abstract

We calculate the quark-anti-quark contribution to the next-to-leading logarithmic corrections to the BFKL kernel, retaining the dependence on the momenta of the produced particles. This allows us to study the details of the NLL corrections. We demonstrate that the standard calculation of the NLL corrections to the scattering of two off-shell gluons includes contributions from energies far above that which is probed at LL. This explicitly violates energy and momentum conservation in the evolution and could be a source of the reported large NLL corrections. The presented calculation is a step towards combining energy and momentum conservation with full NLL accuracy in the evolution.

The Quark-Antiquark Contribution to the Fully Exclusive BFKL Evolution at NLL Accuracy

TL;DR

In NLL BFKL, the standard real-emission kernel integrates over all invariant masses, which can violate energy-momentum conservation at the vertex; the paper recalculates the quark–antiquark contribution retaining full momentum dependence using the Lipatov effective action and a phase-space slicing framework. This leads to an exclusive, momentum-dependent expression for the quark–antiquark part of the real-emission kernel that is finite for nonzero momentum transfer and agrees with the known -suppressed limit. The work provides a path to merging energy-momentum conservation with full NLL accuracy in BFKL evolution and clarifies the origin of the large NLL corrections observed in previous analyses.

Abstract

We calculate the quark-anti-quark contribution to the next-to-leading logarithmic corrections to the BFKL kernel, retaining the dependence on the momenta of the produced particles. This allows us to study the details of the NLL corrections. We demonstrate that the standard calculation of the NLL corrections to the scattering of two off-shell gluons includes contributions from energies far above that which is probed at LL. This explicitly violates energy and momentum conservation in the evolution and could be a source of the reported large NLL corrections. The presented calculation is a step towards combining energy and momentum conservation with full NLL accuracy in the evolution.

Paper Structure

This paper contains 3 sections, 20 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Exclusive States to Next-to-Leading Logarithmic Accuracy
  3. The Quark-antiquark Contribution to the NLL Corrections

Figures (2)

  • Figure 1: The quark--anti-quark production amplitude in Reggeon-Reggeon collisions (LHS) can be obtained as the sum of the contributing diagrams (RHS) according to the effective Feynman rules of Ref.Lipatov:1995pn. The zig-zag lines denote the Reggeons (off-shell gluons). The BFKL evolution consists of a string of such vertices (and their LL and NLL gluon emission counterparts) connected with Reggeised gluon propagators.
  • Figure :