The proton is not a solid ball. Inside, it's a seething mix of quarks and gluons. Gluons are the particles that glue quarks together, much like wood glue binds pieces of wood. The question is: how much of the proton's "weight" comes from this glue? Physicists have calculated this on a computer by discretizing space and time into a fine grid.
The Standard Model describes how quarks and gluons interact. But calculating their contribution to the proton's momentum directly is nearly impossible — the equations are too complex. So they use the lattice method: space-time is replaced by a discrete grid, and then the grid spacing is taken to zero. The authors used configurations with two light quarks and one strange quark (in physics, this is called Nf = 2+1), with a pion mass of 358 MeV and a lattice spacing of 0.094 fm. It's like taking a photograph of the proton with an extremely short exposure, but for theory.
To extract the signal from the noise, they used two techniques. The variational method filters out excited states, leaving only the lowest level, like picking out a single pure note from a choir. The distillation method constructs a large set of operators to more accurately capture the gluon field. All fits were averaged using a Bayesian method — a way to honestly account for the uncertainty in model choice.
The result: gluons carry 48.2% of the proton's momentum (at an energy of 2 GeV). The rest comes from quarks. The uncertainty is currently only statistical, at 3.5%. This is close to values from other calculations and collider experiments. So, half of the "motion" inside the proton is gluon glue.
This calculation is not just an exercise. It tests our understanding of the strong interaction in the non-perturbative regime, where ordinary methods fail. If the number had been wildly different from expectations, we would have had to revise the theory. But everything adds up: the glue indeed holds half of the proton's momentum.
as written by the authors arXiv:2602.14260
We calculate the gluon momentum fraction of the nucleon using lattice quantum chromodynamics (QCD), with a nonperturbative renormalization technique based on the gradient flow. The gluon momentum fraction is determined on a single Wilson-clover ensemble using Nf = 2+1 flavors with pion mass 358 MeV and lattice spacing 0.094 fm. We employ the variational method to reduce excited-state contamination and apply the distillation framework to ensure a large operator basis. To reduce systematic uncertainties, we apply Bayesian model averaging to all fit procedures. We apply matching coefficients to the flow-time dependent lattice results to recover the gluon momentum fraction in the MS-scheme at 2 GeV. Our final result is
If gluons suddenly vanished, the proton would decay into quarks, and all matter in the universe would turn into a dilute gas.