Insider Brief
- An artificial intelligence system first identified a general formula for a class of gluon interactions long thought impossible at the simplest level of calculation, a result later rigorously proven by the researchers in a new preprint.
- The study shows that when the particles are arranged in a particular way, the interaction does not disappear and can be built step by step using a standard method in particle physics, turning what would normally be a sprawling set of diagrams into a compact mathematical expression.
- The AI-proposed formula was then tested against established consistency rules in quantum field theory, and the same approach is expected to extend to related calculations involving gravitons and other theoretical generalizations.
A long-dismissed class of particle interactions may exist after all — and human scientist say an artificial intelligence system served as a lab assistant to help them with the discovery. Or maybe rediscovery.
In a pre-print study posted to arXiv, the researchers report that a type of gluon interaction many physicists assumed could not occur at the simplest level of calculation can, under specific conditions, take on clean, compact mathematical forms. According to the study, the key closed-form expression was first conjectured by GPT-5.2 Pro before being formally proven and independently checked by humans.
The paper, published by researchers from Institute for Advanced Study, OpenAI, Vanderbilt University, Cambridge University and Harvard University, focuses on gluons, which are the particles that carry the strong nuclear force, which, as that sticky name suggests, binds quarks together inside protons and neutrons.
At the center of the work is a concept known as a scattering amplitude. In particle physics, a scattering amplitude is the mathematical object that encodes the probability that particles will collide and emerge in a particular configuration. These amplitudes are the bridge between abstract quantum field theory and real-world measurements. They are computed using Feynman diagrams, which depict every possible way particles can interact.
The problem is scale. As the number of particles increases, the number of diagrams grows faster than exponentially. What looks manageable at three or four particles becomes nearly intractable at six or seven. Yet physicists have repeatedly discovered that when all those diagrams are added together, the final answer often collapses into something surprisingly simple.
This tension — overwhelming intermediate complexity, unexpected final simplicity — has shaped modern theoretical physics for decades.
Vanishing? Maybe Not
The new study revisits a particular class of amplitudes involving gluons. Gluons, like photons, have a property called helicity, which can be thought of as the orientation of their spin relative to their direction of motion. At the risk of using an American football analogy so soon after the Super Bowl, helicity is like whether a football spirals clockwise or counterclockwise as it flies downfield.
For massless particles, helicity can take one of two values: positive or negative. In so-called “single-minus” configurations, one gluon has negative helicity while the remaining n−1 gluons have positive helicity.
Standard textbook arguments have long suggested that these amplitudes vanish — meaning the probability of that interaction is zero — at tree level, the baseline calculation that includes only the most direct interaction diagrams and leaves out the messier quantum loops that appear at higher orders.
According to the study, that conclusion rests on an assumption about the momenta — the directions and energies — of the particles. Those arguments hold when the momenta are generic, meaning they are not specially aligned.
The researchers show that when the momenta satisfy a particular alignment condition, known as the half-collinear regime, the reasoning breaks down. In this regime, certain spinor products — mathematical quantities used to represent particle momenta in a compact way — vanish in a coordinated fashion. The result is that the single-minus amplitude does not disappear.
Instead, it exists on a precisely defined slice of momentum space.
The researchers derive a recursion relation — a step-by-step construction rule based on the Berends-Giele method — that determines these amplitudes for any number of gluons. In other words, scientists can systematically build a complicated multi-particle interaction based on simpler ones.
When the team computed explicit examples for small numbers of gluons, the results were messy. Even at six particles, the expressions spanned dozens of terms, reflecting the superexponential growth of Feynman diagrams.
Enter AI.
According to the accompanying blog post from OpenAI, the human scientists first calculated the amplitudes for small values of n by hand, obtaining long expressions derived from Feynman diagrams. GPT-5.2 Pro was then used to simplify those expressions. From the simplified cases, the system identified a pattern and conjectured a general formula valid for all n.
An internal, scaffolded version of GPT-5.2 subsequently spent roughly 12 hours reasoning through the conjecture and produced a formal proof of its validity, according to the blog post. The researchers then verified the result analytically.
The formula was checked against the Berends-Giele recursion relation, ensuring that it reproduces the step-by-step construction of amplitudes. It was also tested against several standard consistency conditions in quantum field theory, including cyclic symmetry, reflection symmetry and Weinberg’s soft theorem — a rule that constrains how amplitudes behave when one particle’s energy becomes very small. According to the study, the result passed all of these checks.
In one special arrangement of the particles’ motion — known as region R1 — where a single negatively spinning gluon turns into many positively spinning ones, the math simplifies dramatically. What starts as a tangled web of interaction diagrams reduces to a short formula made of simple plus, minus, or zero values depending on how the particles are aligned.
According to the researchers, The simplification is dramatic. The direct Feynman-diagram expressions grow superexponentially in complexity as the number of particles increases. The AI-assisted formula replaces that growth with a structured product whose pattern holds for any number of gluons.
A Methodological Shift
The physics result itself occupies a narrow but conceptually important corner of Yang-Mills theory, the framework that describes gluons and underlies the Standard Model’s treatment of the strong force. Single-minus amplitudes were widely regarded as absent at tree level. Showing that they exist under well-defined conditions reopens questions about the internal structure of scattering amplitudes and the geometric principles that may organize them.
But the methodological aspect may draw even broader attention.
Here, the AI system did more than assist with algebraic manipulation. It inferred a general pattern from specific cases and proposed a closed-form formula. The human researchers then proved and validated that formula using established analytic methods.
In the blog post, the researchers write that this may serve as a template for AI-assisted theoretical research: conjecture generation by machine, verification by rigorous mathematics and cross-checking against known physical principles.
The study suggests that certain domains of theoretical physics — especially those involving hidden simplicity inside complex algebra — may be particularly well suited to this approach. Historically, recognizing such patterns required deep intuition built over years of experience. In this case, a large language model identified a structure that had not been written down in closed form.
Nima Arkani-Hamed, Professor of Physics, Institute for Advanced Study, said, in the post: “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 is exciting to see the strikingly simple expressions in this paper. It happens frequently in this part of physics that expressions for some physical observables, calculated using textbook methods, look terribly complicated, but turn out to be very simple. This is important because often simple formulas send us on a journey towards uncovering and understanding deep new structures, opening up new worlds of ideas where, amongst other things, the simplicity seen in the starting point is made obvious.”
Arkani-Hamed added: “To me, finding a simple formula’ has always been fiddly, and also something that I have long felt might be automatable by computers. It looks like across a number of domains we are beginning to see this happen; the example in this paper seems especially well-suited to exploit the power of modern AI tools. I am looking forward to seeing this trend continue towards a general purpose ‘simple formula pattern recognition’ tool in the near future.”
Limits, Next Steps
The results apply to tree-level amplitudes and to specific kinematic regimes. Loop corrections, which incorporate quantum fluctuations, remain far more complicated. The half-collinear configuration is mathematically consistent but not generic in ordinary Minkowski spacetime; it corresponds to a special alignment of momenta or to complexified momentum configurations.
According to the study, the construction generalizes from gluons to gravitons — the hypothetical quantum carriers of gravity — and supersymmetric extensions are also possible. The researchers note that the structural role of these amplitudes within the broader theory remains to be understood and that even simpler formulations may exist.
In general, the study suggests how AI might be integrated into probing some of the problems that continue to vex science, particularly quantum mechanics.
Nathaniel Craig, Professor of Physics at the University of California, Santa Barbara, said in the post: “I am already thinking about this preprint’s implications for aspects of my group’s research program. This is clearly journal-level research advancing the frontiers of theoretical physics, and its novelty will inspire future developments and subsequent publications. This preprint felt like a glimpse into the future of AI-assisted science, with physicists working hand-in-hand with AI to generate and validate new insights. There is no question that dialogue between physicists and LLMs can generate fundamentally new knowledge. By coupling GPT‑5.2 with human domain experts, the paper provides a template for validating LLM-driven insights and satisfies what we expect from rigorous scientific inquiry.”
The research team included Alfredo Guevara, of the Institute for Advanced Study; Alexandru Lupsasca of Vanderbilt University and OpenAI; David Skinner of the University of Cambridge, Andrew Strominger of Harvard University and Kevin Weil, of OpenAI
The paper is highly technical and for a deeper dive, it’s recommended the reader review the paper on arXiv.
Also, please note that arXiv is a pre-print server, which allows researchers to receive quick feedback on their work. However, it is not — nor is this article, itself — official peer-review publications. Peer-review is an important step in the scientific process to verify results.
