Next-to-MHV Yang-Mills kinematic algebra

TL;DR

This paper advances the understanding of the kinematic algebra in Yang-Mills theory by explicitly constructing a comprehensive algebraic framework for all NMHV amplitudes, enabling systematic generation of BCJ numerators.

Contribution

It introduces a new algebraic approach to realize the kinematic algebra for all NMHV amplitudes and proposes a closed-form expression for master BCJ numerators.

Findings

Explicit realization of kinematic algebra for all NMHV amplitudes

Derivation of a closed-form expression for master BCJ numerators

A new method using permutation group algebra to resolve gauge freedom

Abstract

Kinematic numerators of Yang-Mills scattering amplitudes possess a rich Lie algebraic structure that suggest the existence of a hidden infinite-dimensional kinematic algebra. Explicitly realizing such a kinematic algebra is a longstanding open problem that only has had partial success for simple helicity sectors. In past work, we introduced a framework using tensor currents and fusion rules to generate BCJ numerators of a special subsector of NMHV amplitudes in Yang-Mills theory. Here we enlarge the scope and explicitly realize a kinematic algebra for all NMHV amplitudes. Master numerators are obtained directly from the algebraic rules and through commutators and kinematic Jacobi identities other numerators can be generated. Inspecting the output of the algebra, we conjecture a closed-form expression for the master BCJ numerator up to any multiplicity. We also introduce a new method, based on group algebra of the permutation group, to solve for the generalized gauge freedom of BCJ numerators. It uses the recently introduced binary BCJ relations to provide a complete set of NMHV kinematic numerators that consist of pure gauge.