Single-minus gluon tree amplitudes are nonzero

TL;DR

This paper demonstrates that single-minus gluon tree amplitudes, previously thought to vanish, are actually nonzero under specific conditions involving complex momenta or Klein space, providing a new explicit formula.

Contribution

It reveals nonvanishing single-minus gluon amplitudes and derives a closed-form expression for their decay, satisfying key physical consistency conditions.

Findings

Single-minus amplitudes are nonzero in certain complex or Klein space configurations.

Derived a piecewise-constant formula for gluon decay amplitudes.

The formula satisfies Weinberg's soft theorem and other consistency conditions.

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.