Abstract
In this paper we encode the perturbative BFKL leading logarithmic resummation, relevant for the Regge limit behavior of QCD scattering amplitudes, in the IR-regulated effective action which satisfies exact functional renormalization group equations. This is obtained using a truncation with a specific infinite set of non local vertices describing the multi-Regge kinematics (MRK). The goal is to use this framework to study, in the high energy limit and at larger transverse distances the transition to a much simpler effective local reggeon field theory, whose critical properties were recently investigated in the same framework. We perform a numerical analysis of the spectrum of the BFKL Pomeron deformed by the introduction of a Wilsonian infrared regulator to understand the properties of the leading poles (states) contributing to the high energy scattering.
Highlights
Of large distances, for which still very little can be derived from a fundamental QCD description
Some time ago [1, 2] we have started a program which aims at finding an interpolation between the perturbative QCD Pomeron (BFKL Pomeron) and the nonperturbative soft Pomeron which describes elastic proton-proton scattering at high energies
We have studied the flow of the so called Reggeon Field Theory (RFT) for a single Pomeron field and for a Pomeron coupled to an Odderon field, in particular the critical universal properties of these two QFTs and some features of the flow associated to the scale change
Summary
We begin by recalling the massless color singlet BFKL equation [12,13,14,15] in the leading approximation (MRK). Let us start with the amputated BFKL Green’s function G(q , q − q ; q , q − q |ω) It is obtained as an infinite sum of ladder diagrams and satisfies the integral (Bethe-Salpeter like) equation: GBFKL(q , q − q ; q , q − q |ω) = KBFKL(q, q − q ; q , q − q ). The analytic expression of the LO BFKL kernel (the so called real part, induced by rapidity separated real gluon emissions) has the form: KBFKL(q , q − q ; q. This kernel is illustrated in figure 2a: The gluon trajectory function has the form:. The sum of the discrete set and the continuous part of eigenfunctions defines a complete set This Green’s function Gk satisfies the equation.
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