Inside a proton, gluons buzz around like bees in a hive, gluing quarks to each other and to themselves. The higher the collision energy, the more gluons emerge from the fog. Physicists have long sought a way to describe this swarm with a single simple function, but each time, they had to tweak the form to fit a specific experiment.
Now, a neural network is learning from physics itself. The equations of motion for gluons, known as Balitsky–Kovchegov dynamics, act as the “teacher”: they constrain possible solutions, much like rails guide a train. The “student”—the neural network — refines these solutions using real data from the HERA accelerator. This yields a model with no pre-set initial conditions.
The resulting picture of the gluon swarm predicted, with no adjustments whatsoever, the production of the J/ψ particle (a meson made of a charm quark and its antiquark) in photon–proton collisions. Both the absolute magnitude and the energy dependence matched. This is strong evidence that the gluon saturation scale is a universal quantity, not a fitting parameter.
A neural network that has absorbed physical laws opens the door to studying non-perturbative structures: those regions where gluons are so tightly intertwined that conventional calculations fail.
as written by the authors arXiv:2601.16391
The process-independence of the color dipole amplitude is a cornerstone of high-energy Quantum Chromodynamics (QCD). However, standard phenomenological approaches typically rely on rigid parametric ansatzes and often require ad-hoc geometric adjustments to reconcile inclusive and diffractive measurements. To resolve this tension, we introduce Physics-Informed Neural Networks (PINNs) employing a ``Teacher--Student'' strategy. The physics-based momentum-space Balitsky-Kovchegov evolution dynamics act as the ``Teacher,'' constraining the solution manifold, while the network ``Student'' is refined against inclusive HERA $$F_2$$ data. This approach extracts a model-independent dipole amplitude without assuming initial states. Strikingly, we demonstrate that this amplitude -- without parameter retuning or geometric rescaling -- successfully predicts the absolute normalization and kinematic dependence of exclusive $$J/\psi$$ photoproduction cross-sections. This parameter-free prediction of the saturation dynamics provides promising evidence for the process-independence of the gluon saturation scale and establishes PINNs as a transformative paradigm for uncovering non-perturbative QCD structures.
Gluons never exist alone: they can only be seen in a “swarm” inside a proton, and the harder you try to pull them apart, the more tightly they cling to each other.
In Liu Cixin's novel “The Three-Body Problem,” aliens unfold protons into multidimensional structures — much as physicists “unfold” the gluon swarm using neural networks.