KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry

TL;DR

This work extends KLT-type relations by exploiting color-factor symmetry to relate tree-level amplitudes across biadjoint, bicolor, QCD, and gravity. It introduces the bicolor scalar theory as a zeroth copy of QCD and develops KLT-type decompositions using the Melia/Johansson-Ochirov basis, together with the momentum-kernel S[σ|τ]_3 and an inverse matrix T to handle general quark content (k>2). The authors provide two derivations for the QCD KLT-type relations—via color-factor symmetry and via restricted generalized gauge invariance—and demonstrate that gravity amplitudes follow from a double-copy construction. Collectively, the results unify a broad class of tree-level amplitudes under a common KLT-like framework and extend double-copy ideas to theories with massive/multi-flavor matter content, including explicit $k\le 2$ expressions and conjectures for higher $k$.

Abstract

Color-factor symmetry is used to derive a KLT-type relation for tree-level QCD amplitudes containing gluons and an arbitrary number of massive or massless quark-antiquark pairs, generalizing the expression for Yang-Mills amplitudes originally postulated by Bern, De Freitas, and Wong. An explicit expression is given for all amplitudes with two or fewer quark-antiquark pairs in terms of the (modified) momentum kernel. We also introduce the bicolor scalar theory, the "zeroth copy" of QCD, containing massless biadjoint scalars and massive bifundamental scalars, generalizing the biadjoint scalar theory of Cachazo, He, and Yuan. We derive KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories using the color-factor symmetry possessed by these theories.

Figures (2)

• Figure 1: Cubic diagrams $i=1$ through 5 for ${\cal A} ^{\rm bicolor} _{5,2}$. Lines with arrows denote bifundamental scalars whereas curly lines denote biadjoint scalars.
• Figure 2: CHY prescription for computing the double-partial amplitude $m(2 3 \tau 1 | 1 3 \sigma 2)$.