Much of a proton’s mass comes from the energy of the particles inside it

A proton’s mass is more than just the sum of its parts. At last, scientists have figured out what accounts for this subatomic particle’s heft.

Protons are made up of even smaller particles known as quarks. It might seem reasonable that simply adding up the quarks’ masses would give you a proton’s mass. Yet it doesn’t. That sum is far too small to explain the proton’s bulk. New, detailed calculations show that only 9 percent of a proton’s heft comes from the mass of its quarks. The rest comes from complicated effects occurring inside the particle.

Quarks get their masses from a process connected to the Higgs boson. That’s an elementary particle first detected in 2012. But “the quark masses are tiny,” says theoretical physicist Keh-Fei Liu. A coauthor of the new study, he works at the University of Kentucky in Lexington. So for protons, he notes, the Higgs explanation falls short.

Instead, most of the proton’s 938 million electron volts of mass comes from something known as QCD. It’s short for quantum chromodynamics (KWON-tum Kroh-moh-dy-NAM-iks). QCD is a theory that accounts for the churning of particles within the proton. Scientists study the proton’s properties mathematically using the theory. But making calculations using QCD is quite hard. So they simplify things using a technique called lattice (LAT-iss) QCD. It breaks up time and space into a grid. Quarks can only exist on the points in the grid. It’s sort of like how a chess piece can only sit on a square, not somewhere in between.

Sound complicated? It is. Few people can comprehend it (so you’re in good company).

Researchers described their new finding in the November 23 Physical Review Letters.

Impressive feat

Physicists had used this technique to calculate the proton’s mass before. But until now, they hadn’t divvied up which parts of the proton provided how much of its mass, notes André Walker-Loud. He’s a theoretical physicist at Lawrence Berkeley National Laboratory in California. “It’s exciting,” he says, “because it’s a sign that … we’ve really hit this new era” in which lattice QCD can be used to better understand the cores of atoms.

In addition to mass that comes from quarks, another 32 percent comes from the energy of the quarks zipping around inside the proton, Liu and colleagues found. (That’s because energy and mass are two sides of the same coin. Albert Einstein described that in his famous equation, E=mc². E is energy, m is mass and c is the speed of light.) Massless particles called gluons, which help hold quarks together, contribute another 36 percent of a proton’s mass via their energy.

The remaining 23 percent arises from effects that occur when quarks and gluons interact in complicated ways. Those effects are the result of quantum mechanics. That’s the weird physics that describes very small things.

The results of the study aren’t surprising, says Andreas Kronfeld. He’s a theoretical physicist at Fermilab in Batavia, Ill. Scientists had long suspected that the proton’s mass was made up in this way. But, he adds, the new findings are reassuring. “This kind of calculation replaces a belief with scientific knowledge.”