What holds the universe’s smallest building blocks together? It’s a question that has propelled particle physics for a century, and the answers keep getting stranger. The familiar picture of the proton as a neat package of quarks, glued together by gluons, is now giving way to something far more dynamic and weird, especially when those protons are smashed together at near-light speed.
A recent paper from Brookhaven National Laboratory takes a fresh look at what happens inside a proton when it’s hit hard — really hard — by another particle. Specifically, Yoshitaka Hatta and Jakob Schoenleber have revisited the “Feynman contribution” to the proton’s structure, a once-dismissed idea that’s making a roaring comeback.
The Unexpected Phoenix
For a long time, the dominant theory described hard collisions as direct interactions between the incoming projectile and the proton’s valence quarks – the primary quarks that define the proton’s identity. In this view, gluons acted as simple force carriers, and any other internal complexities were considered minor corrections. But experiments kept throwing curveballs, hinting that this tidy picture was missing something crucial.
That ‘something’ might just be the Feynman contribution. Originally proposed in the early days of particle physics, it suggests that when a proton is struck with sufficient force, the energy isn’t just absorbed by a single quark. Instead, it’s transferred to a complex network of virtual particles that briefly pop into existence, interact, and then vanish. Imagine a pool ball (the incoming particle) hitting a tightly packed cluster of marbles (the proton). The impact doesn’t just send one marble flying; it triggers a cascade of collisions throughout the entire cluster.
This older idea was largely discarded because perturbative QCD, the theory that describes interactions between quarks and gluons, seemed to suppress it. The math suggested the Feynman contribution should fade into insignificance at high energies. But, as Hatta and Schoenleber point out, real-world data stubbornly disagrees. The old calculations may be missing vital pieces of the puzzle, particularly in a specific kinematic regime where the momentum transfer is large, but not too large.
Sudakov’s Ghost and SCET to the Rescue
The key to this resurgence lies in something called Sudakov resummation, a technique for handling those troublesome logarithms that plague high-energy calculations. In essence, Sudakov resummation tames the wild behavior of radiative corrections, those endless loops and emissions of virtual particles that can make predictions blow up to infinity. The authors show that these Sudakov logarithms, previously identified in one-loop calculations, can be systematically resummed to all orders using Soft Collinear Effective Theory (SCET), a powerful tool for analyzing processes with multiple energy scales.
SCET allows physicists to break down a complex interaction into simpler, more manageable pieces. It separates the hard scattering (the initial impact) from the collinear radiation (particles emitted along the direction of motion) and the soft interactions (long-distance forces that bind the proton together). By carefully disentangling these scales, Hatta and Schoenleber demonstrate that the Feynman contribution doesn’t vanish as quickly as previously thought. It lingers, potentially dominating the proton’s behavior in a crucial energy range.
Gravitational Form Factors: A Bridge to the Cosmos?
One of the most intriguing aspects of this work is its connection to gravitational form factors (GFFs). These GFFs, buried within the proton’s structure, describe how mass and angular momentum are distributed inside. They are the proton’s equivalent of a blueprint for how gravity interacts with it. While we usually think of gravity as a force acting on massive objects, GFFs offer a glimpse into how gravity interacts with the fundamental constituents of matter at the quantum level.
Because the electromagnetic form factor can be expressed as the first moment of the generalized parton distribution (GPD), similar questions arise with regard to the large-t behavior of GPDs. This means that a better understanding of the GPDs and the Feynman contribution directly translates to a better understanding of GFFs. This connection is what makes the work by Hatta and Schoenleber so compelling; it suggests that high-energy collisions aren’t just about quarks and gluons. They’re also about gravity, albeit in a subtle and indirect way.
The authors show that the ratio of certain GFFs to the ordinary electromagnetic form factor becomes purely perturbative at large momentum transfer, meaning it can be calculated with increasing precision. This is a powerful result, suggesting that even complex properties like mass distribution can be extracted from high-energy experiments with a surprising degree of accuracy.
The Pre-Asymptotic Regime and a Lingering Mystery
It’s important to note that this work focuses on the “pre-asymptotic” regime, a region where the energy is high enough to probe the proton’s internal structure, but not so high that the familiar rules of perturbative QCD take over completely. This is precisely where the Feynman contribution is expected to be most significant, bridging the gap between low-energy, non-perturbative physics and the clean, predictable world of ultra-high-energy collisions.
One of the more puzzling implications of the authors’ calculations is that in order to accurately describe deeply virtual compton scattering (DVCS), a leading term of the GPD may be a delta function. The authors offer an alternative, “hybrid” formulation where they retain the convolution structure (4.13) and model hq as a function of y using light-cone wave functions.
The work by Hatta and Schoenleber, from Brookhaven National Laboratory, highlights the limitations of our current understanding and points towards a more nuanced picture of the proton, one where virtual particles and complex interactions play a starring role. It’s a reminder that even the most well-established theories can have hidden depths, and that the universe is often far stranger than we imagine.
