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

The preprint studies a central concept in particle physics called a scattering amplitude. A scattering amplitude is the quantity physicists use to compute the probability that particles interact in a particular way. For gluons, the particles that carry the strong nuclear force, many amplitudes take unexpectedly simple forms “at tree level” (meaning calculations that keep only the simplest diagrams with no quantum loops). These simplifications have repeatedly revealed deeper structure in quantum field theory, the framework that provides a description of physics that unifies special relativity with quantum mechanics.

One case, however, has generally been treated as absent (having zero amplitude). When one gluon has negative helicity (meaning one of the two possible spin orientations a massless particle can have) and the remaining n−1 n-1 n−1 gluons have positive helicity, standard textbook arguments suggest that the corresponding tree-level amplitude must be zero. As a result, this configuration has largely been set aside.

The preprint shows that this conclusion is too strong. The standard argument assumes generic particle momenta, meaning the directions and energies are not in any special alignment. We identify a specific and precisely defined slice of momentum space where that reasoning no longer applies, known as the half-collinear regime. Half-collinear here means the gluon momenta obey a special alignment condition that is not typical, but is mathematically well-defined and consistent. On this slice, the amplitude does not vanish, and we compute it in a special kinematic regime. This result opens the door to many new questions that will be the subject of subsequent investigations. Important extensions include the computation of the analogous amplitudes for gravitons (the particles that mediate the gravitational force).