A formula for calculating interactions between gluons, particles that carry the strong nuclear force, was first proposed by an artificial intelligence system, GPT-5.2 Pro, and subsequently proven by researchers, according to a pre-print study released February 12, 2026.
The finding, detailed in a paper posted to arXiv and verified by teams from the Institute for Advanced Study, OpenAI, Vanderbilt University, Cambridge University and Harvard University, challenges long-held assumptions about the behavior of gluons. Physicists had previously believed that certain gluon interactions, specifically those in a “single-minus” configuration, were impossible at the most basic level of calculation.
The study centers on “scattering amplitudes,” mathematical objects that determine the probability of particle collisions. Calculating these amplitudes becomes exponentially more complex as the number of particles involved increases. While physicists have successfully calculated amplitudes for a small number of gluons using Feynman diagrams, identifying a general formula applicable to any number has remained elusive. The challenge, according to commentary cited in a report by NewsDirectory3.com, isn’t a lack of understanding of the underlying physics, but the sheer computational burden of managing the expanding complexity of the equations.
Researchers found that under specific conditions – when the momenta, or directions and energies, of the particles are aligned in a particular way known as the half-collinear regime – the previously assumed impossibility dissolves. In this configuration, the single-minus amplitude does not vanish, but instead exists on a precisely defined slice of momentum space. The team then developed a recursive method, building on the Berends-Giele method, to determine these amplitudes for any number of gluons.
Initial calculations by hand produced complex expressions, even for a relatively small number of six particles. OpenAI reports that GPT-5.2 Pro was then used to simplify these expressions, identifying a pattern and conjecturing a general formula. An internal version of GPT-5.2 subsequently spent approximately 12 hours formally proving the formula’s validity, a result later verified by the human researchers.
“The physics of these highly degenerate scattering processes has been something I’ve been curious about since I first ran into them about fifteen years ago, so It’s exciting to see the strikingly simple expressions in this paper,” said Nima Arkani-Hamed, Professor of Physics at the Institute for Advanced Study, in a statement released by OpenAI. “It happens frequently in this part of physics that expressions for some physical observables, calculated using textbook methods, glance terribly complicated, but turn out to be very simple.”
The AI-assisted formula dramatically simplifies the calculation, replacing the superexponential growth of Feynman diagrams with a structured product applicable to any number of gluons. The formula was tested against established consistency rules in quantum field theory, including cyclic symmetry, reflection symmetry and Weinberg’s soft theorem, and passed all checks.
While the result applies specifically to tree-level amplitudes and the half-collinear regime, researchers suggest the approach could extend to calculations involving gravitons, the hypothetical carriers of gravity, and supersymmetric extensions. Nathaniel Craig, Professor of Physics at the University of California, Santa Barbara, described the perform as “a glimpse into the future of AI-assisted science,” adding that “coupling GPT‑5.2 with human domain experts…provides a template for validating LLM-driven insights and satisfies what we expect from rigorous scientific inquiry.”
The researchers have not yet announced plans for further investigation into loop corrections, which incorporate quantum fluctuations and remain significantly more complex. The study remains a pre-print, pending formal peer review.
