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The paper demonstrates that single-minus tree-level n-gluon scattering amplitudes, often assumed to be zero, are in fact non-zero for specific "half-collinear" configurations in Klein space or with complexified momenta. They derive a closed-form, piecewise-constant expression for the decay amplitude of a single minus-helicity gluon into n-1 plus-helicity gluons. This derived formula is shown to satisfy Weinberg's soft theorem and other consistency conditions.
Single-minus gluon tree amplitudes, long thought to vanish, actually exist in half-collinear configurations, unlocking new insights into gluon scattering.
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.
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