Reggeization in Color

TL;DR

This paper develops a top-down effective field theory approach to sum large energy logarithms for Regge cut contributions in non-planar gauge theories, deriving matrix evolution equations for various color channels in QCD.

Contribution

It introduces a novel method using color projection and rapidity evolution to organize Regge cut contributions beyond the planar limit in gauge theories.

Findings

Derived a 6x6 matrix evolution equation for decupletons in QCD.

Established a 2x2 evolution equation for triantapentons.

Formulated a scalar evolution equation for tetrahexaconton.

Abstract

In the high energy limit, $s\gg -t$, amplitudes in planar gauge theories Reggeize, with power law behavior $\big( \frac{s}{-t} \big)^{\alpha(t)}$ governed by the Regge trajectory $\alpha(t)$. Beyond the planar limit this simplicity is violated by "Regge cuts", for which practical organizational principles are still being developed. We use a top-down effective field theory organization based on color projection in the $t$ channel and rapidity evolution equations for collinear impact factors, to sum large $s\gg -t$ logarithms for Regge cut contributions. The results are matrix equations which are closed within a given color channel. To illustrate the method we derive in QCD with $SU(N_c)$ for the first time a closed 6$\times$6 evolution equation for the "decupletons" in the $\text{10}\oplus\overline{\text{10}}$ Regge color channel, a 2$\times$2 evolution equation for the "triantapentons" in the $\text{35}\oplus\overline{\text{35}}$ color channel, and a scalar evolution equation for the "tetrahexaconton" in the 64 color channel. More broadly, our approach allows us to describe generic Reggeization phenomena in non-planar gauge theories, providing valuable data for the all loop structure of amplitudes beyond the planar limit.