Single-Minus Gluon Amplitudes Are Nonzero
This presentation explores a groundbreaking discovery in Yang-Mills theory: single-minus gluon tree amplitudes, long assumed to vanish, are actually nonzero in special "half-collinear" kinematic regimes. The authors derive explicit piecewise-constant formulas through recursion and prove their consistency with fundamental symmetries. These results challenge conventional wisdom about helicity selection rules, provide new computational tools for scattering amplitudes, and offer fresh insights into self-dual Yang-Mills theory and celestial holography.Script
What if a fundamental assumption in particle physics—that certain gluon scattering amplitudes must vanish—turns out to be wrong? This paper reveals that single-minus gluon tree amplitudes are actually nonzero in a hidden kinematic regime, overturning decades of conventional wisdom.
Let's begin by understanding what was thought to be impossible.
Building on this challenge, traditional wisdom held that tree-level amplitudes with just one minus-helicity gluon must vanish everywhere. Helicity selection rules and power counting seemed ironclad, yet this left a puzzling gap in self-dual Yang-Mills, where classical solutions are rich but quantum amplitudes appeared trivial.
The breakthrough came from exploring an exotic kinematic regime.
This discovery hinges on the half-collinear regime, where all angle-bracket spinor products vanish but square brackets survive. In this exotic corner of complexified or signature (2,2) momentum space, the usual arguments for vanishing completely fail, and amplitudes spring to life.
Now let's see how the authors computed these amplitudes.
The authors built a recursion mirroring the classic Berends-Giele structure, revealing that amplitudes are piecewise-constant integers. Remarkably, a generative language model conjectured a compact product formula for certain kinematic regions, which was then rigorously proven by the research team.
This discovery fundamentally rewrites our understanding: what was thought impossible is now explicitly constructed. The contrast is stark—conventional wisdom ruled out these amplitudes entirely, while the new formulas provide explicit, recursively computable, integer-valued expressions in previously unexplored kinematic chambers.
Turning to validation, the formulas pass every consistency check: soft theorems, cyclicity, photon decoupling, and explicit numerical verification through six gluons. None of these properties are obvious from the formula itself, yet all emerge naturally, confirming the construction's deep correctness.
Beyond the immediate result, these amplitudes resolve a long-standing puzzle in self-dual Yang-Mills by providing quantum amplitude support for its rich classical structure. The framework extends naturally to gravity, supersymmetry, and celestial holography, suggesting a deeper algebraic architecture underlying scattering theory.
Single-minus amplitudes are no longer forbidden—they're piecewise-constant, recursively computable, and teeming with hidden symmetry. To dive deeper into this paradigm shift in amplitude theory, visit EmergentMind.com.
