The paper, “Single-minus graviton tree amplitudes are nonzero,” is authored by Alfredo Guevara (Institute for Advanced Study), Alexandru Lupsasca (Vanderbilt University and OpenAI), David Skinner (University of Cambridge), Andrew Strominger (Harvard University), and Kevin Weil (OpenAI) on behalf of OpenAI.

Scattering amplitudes are mathematical quantities physicists use to calculate the probability that particles interact in particular ways. Rather than tracking every intermediate step of a collision through many diagrams, amplitudes encode the final observable outcomes in a compact form. Over the past several decades, researchers have found that amplitudes often display unexpected simplicity, revealing hidden mathematical structure not obvious from traditional calculations.

The new preprint studies gravitons, quantum particles associated with gravity in quantum field theory. In particular, the authors analyze a configuration known as a single-minus amplitude, meaning that one particle has negative helicity while the remaining particles have positive helicity. Helicity describes the orientation of a particle’s spin relative to its direction of motion and plays an important role in determining how interactions occur. Standard textbook arguments suggest that these amplitudes should vanish at the simplest level of approximation, called tree level, where only the most direct interaction diagrams are considered and quantum loop effects are ignored.

The preprint shows that this conclusion depends on assuming generic particle motion. When particle momenta satisfy a special alignment known as the half-collinear regime, the usual argument no longer applies. In this regime, the amplitudes do not vanish but instead exist as well-defined mathematical distributions supported on a restricted region of momentum space. The authors derive explicit formulas describing these interactions and show that they follow from symmetry principles and recursion relations that build complex interactions from simpler ones.