Feynman rules for effective Regge action

TL;DR

The paper develops a gauge-invariant effective action for reggeized gluons in quasi-multi-Regge kinematics and derives a comprehensive set of explicit reggeon–particle vertices, including PPR, PRR, RRPP, PPPR, RRPPP, and RPPPP types. These vertices satisfy Bose symmetry and gauge invariance and are organized to facilitate practical calculations of high-energy amplitudes and next-to-leading corrections. By providing both the vertex expressions and the corresponding cross-section formulas for multi-jet production in QMRK, the work offers a practical toolkit for phenomenology and numerical implementation at collider energies. The framework aims to address unitarization issues in BFKL dynamics and enable precise predictions for multi-cluster processes relevant to RHIC and LHC.

Abstract

Starting from the gauge invariant effective action in the quasi-multi-Regge kinematics (QMRK), we obtain the effective reggeized gluon (R) -- particle (P) vertices of the following types: $RPP$, $RRP$, $RRPP$, $RPPP$, $RRPPP$, and $RPPPP$, where the on-mass-shell particles are gluons, or sets of gluons with small invariant masses. The explicit expressions satisfying the Bose-symmetry and gauge invariance conditions are obtained. As a comment to the Feynman rules for derivation of the amplitudes in terms of effective vertices we present a ``vocabulary'' for practitioners.

Figures (10)

• Figure 1: Quasi-multi-Regge kinematics: notations. Process of $n$-jet production $2 \to n_{jets}$ in the quasi-multi-Regge kinematics.
• Figure 2: Standard QCD Feynman rules: vertices (a-c), and the reggeized gluon propagator (d).
• Figure 3: List of the induced vertices.
• Figure 4: PPR (a-d) and RRP (e) effective vertices.
• Figure 5: Central $PPRR$ effective vertex.