Tree amplitudes of noncommutative U(N) Yang-Mills Theory

TL;DR

This paper develops a modified BCFW recursion relation to compute tree amplitudes in noncommutative U(N) Yang-Mills theory, clarifying their color structure and establishing key amplitude relations.

Contribution

It introduces a novel recursion relation for noncommutative Yang-Mills tree amplitudes and proves their analogs of known amplitude relations.

Findings

Derived a modified BCFW recursion relation for noncommutative amplitudes

Clarified the color structure of noncommutative tree amplitudes

Proved noncommutative analogs of key amplitude relations

Abstract

Following the spirit of S-matrix program, we proposed a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detail information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we wrote down the noncommutative analogies of U(1)-decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes, and proved them using the modified BCFW recursion relation.