Single-minus gluon tree amplitudes are nonzero

TL;DR

This paper shows that single-minus tree-level n-gluon amplitudes, long thought to vanish, are nonzero in a restricted half-collinear regime accessible in Klein signature. Using a Berends–Giele recursion and a carefully organized set of two-dimensional preamplitudes, the authors derive a piecewise-constant, chamber-structured description of these amplitudes and prove a concise all-n formula in the region \\mathcal{R}_1: A_{1…n}|_{R1} = rac{1}{2^{n-2}} \,\prod_{m=2}^{n-1} ( \operatorname{sg}_{m,m+1} + \operatorname{sg}( [\tilde{λ}_1 \tilde{λ}_{2\cdots m}] ) ). They show vanishing of the vertex contribution V in this region, collapse the recursion to a single vertex, and then evaluate it to obtain the final product form, which passes consistency checks including Weinberg’s soft theorem. The results extend naturally to gravity and supersymmetric settings and have potential connections to broader structures such as celestial holography. Overall, the work reveals a surprisingly simple, all-n structure for an initially nontrivial class of amplitudes, shedding light on the underlying organization of Yang–Mills tree amplitudes in special kinematics.

Abstract

Single-minus tree-level $n$-gluon scattering amplitudes are reconsidered. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. We derive a piecewise-constant closed-form expression for the decay of a single minus-helicity gluon into $n-1$ plus-helicity gluons as a function of their momenta. This formula nontrivially satisfies multiple consistency conditions including Weinberg's soft theorem.