Researchers collaborating across several universities and research centers have produced a preprint that challenges a standard textbook argument in gauge-theory scattering amplitudes. The paper, titled "Single-minus gluon tree amplitudes are nonzero," presents a condition under which tree-level amplitudes for a configuration with one negative-helicity gluon and the remaining gluons of positive helicity do not vanish.
The team lists contributors from Harvard University, the University of Cambridge, Vanderbilt University, the Institute for Advanced Study, and OpenAI. Their analysis identifies a particular alignment of gluon momenta, which they label the half-collinear regime. Under this special geometric condition for momenta, amplitudes that were previously argued to be zero can in fact take nonzero values.
The work combines traditional analytic work by human authors with substantial input from OpenAI’s GPT-5.2. According to the preprint, GPT-5.2 Pro formulated the conjectured closed-form expression after human collaborators derived and simplified complex expressions for limited, smaller instances. Building on these simplified cases, the AI recognized a pattern and proposed a formula intended to be valid in general.
In an internal development step, an internal version of GPT-5.2 is reported to have spent roughly 12 hours producing a formal proof of the conjectured formula. The proof was subsequently checked and validated using standard verification methods described by the authors.
Prominent theorists commenting on the work highlighted both the result and the role of AI in its production. Nima Arkani-Hamed, Professor of Physics at the Institute for Advanced Study, called the findings "exciting" and emphasized that the paper shows how modern AI tools can excel at pattern recognition in physics formulas. Nathaniel Craig, Professor of Physics at the University of California, Santa Barbara, described the effort as "journal-level research advancing the frontiers of theoretical physics" and as "a glimpse into the future of AI-assisted science."
The authors report that the same mix of human calculation and GPT-5.2 assistance has already been applied to extend the result from gluons to gravitons, and they note further generalizations are under development. The preprint documents the specific conditions and derivations relevant to the half-collinear regime but does not claim broader applicability beyond those stated constraints.
Key points
- The preprint "Single-minus gluon tree amplitudes are nonzero" provides conditions under which single-minus helicity gluon amplitudes are nonzero, identifying a half-collinear momentum alignment as the enabling regime.
- OpenAI's GPT-5.2 played a crucial role: GPT-5.2 Pro conjectured the general formula after humans worked smaller cases, and an internal version of GPT-5.2 generated a formal proof over about 12 hours that was later verified by standard methods.
- Sectors impacted include theoretical physics research and AI-driven computational tools used in advanced scientific problem solving.
Risks and uncertainties
- The result applies specifically to a half-collinear regime of momenta, indicating a limitation in scope rather than a universal overturning of prior textbook arguments; applicability outside this regime is not claimed.
- Reliance on AI to conjecture and generate proofs introduces the need for careful human verification and standard-method validation, which the authors performed in this case but which remains a necessary safeguard.
- Further generalizations are reported to be in development, and their outcomes and validity remain uncertain until documented and peer-reviewed.