In the theoretical study of proton-nucleus collisions, the colliding projectiles can be described as streams of color charges moving along their respective trajectories. These color charges couple to gluons, which then produce the particles that are observed in the final state (gluons, quarks, that eventually produce hadrons).
https://fr.wikipedia.org/wiki/Hadron
The traditional approach for carrying out these calculations has been to solve the equations that drive the gluon field (known as the Yang-Mills equations) in terms of the color sources. This solution is then used in order to calculate the probability of obtaining a given final state. A major complication with this approach comes from the fact that these are not unique: there are infinitely many of them, that nevertheless describe the same physical situation (there are related by gauge transformations). This complication implies that a lot of effort is spent in calculating terms that do not contribute to physical observables in the end.
In this work, François Gélis, physicist at IPhT, start from the observation that solutions of the Yang-Mills equations are in fact sums of tree Feynman graphs. Using this analogy, we were able to apply for this problem methods that were originally developed for scattering amplitudes.
He used an extension of a recursion discovered by Britto, Cachazo, Feng and Witten (this method enables to calculate recursively amplitudes without Feynman diagrams) in order to calculate directly the amplitude for producing a gluon in a proton-nucleus collision. This approach allowed him to obtain this result (that had been derived earlier using the traditional method) in a way that does not require fixing the gauge, and completely bypasses the calculation of Feynman diagrams.
Furthermore, this work opens the possibility to apply other methods developed in the field of high energy physics, such as generalized unitarity in order to obtain in a much simpler manner the next-to-leading correction to this process.