Studying the Perturbative Reggeon

TL;DR

This work develops a perturbative QCD description of the flavour non-singlet Reggeon as ladders of reggeized quarks and derives the associated Reggeon amplitude via a colour-singlet integral equation. To address the lack of conformal invariance when the coupling runs, the authors introduce a robust numerical method that reexpresses the problem in terms of a slowly evolving function, enabling inclusion of running coupling and nonperturbative masses for soft quarks and gluons. They show that a running coupling amplifies the low-$x$ rise of flavour non-singlet observables, while simultaneously suppressing the $Q^2$ dependence; conversely, introducing constituent masses for soft degrees of freedom dramatically dampens the low-$x$ growth, pushing the perturbative regime toward smaller kinematic windows. Overall, the study provides a controlled framework for assessing perturbative Reggeon dynamics in flavour non-singlet channels and highlights substantial challenges in isolating perturbative effects in experimental data.

Abstract

We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ``reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q^2 dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel.

Figures (16)

• Figure 2.1: The tree-level exchange of a soft quark
• Figure 2.2: One-loop leading $\ln s$ corrections to $q\ + \overline{q} \rightarrow\ g\ +\ g$. The 2-body cuts in the $s$-channel are shown, however (iii) and (iv) have similar cuts in the $u$-channel
• Figure 2.3: The effective quark-gluon vertex
• Figure 2.4: Examples of 2-loop ladders. Diagrams with a quark or antiquark rung have to be considered in addition to the gluon rungs with effective vertices
• Figure 2.5: The complete set of leading $\ln s$ two-loop, two particle cut diagrams