Mass of the Common Quark Finally Nailed Down

What a mess! A proton or a neutron is a nearly indecipherable tangle of quarks (purple), antiquarks (green), and gluons (squiggles).


It’s not every day that scientists reduce the uncertainty in a fundamental constant of nature from 30% to 1.5%, but a team of theoretical physicists claims to have done just that. Using supercomputers and mind-bogglingly complex simulations, the researchers have calculated the masses of particles called “up quarks” and “down quarks” that make up protons and neutrons with 20 times greater precision than the previous standard. The new numbers could be a boon to theorists trying to decipher particle collisions at atom smashers like Europe’s Large Hadron Collider (LHC) or trying to develop deeper theories of the structure of matter.

“It’s an audacious claim, and it will have to be looked at very carefully, but I think the result is robust,” says Paul Mackenzie, a theorist at Fermi National Accelerator Laboratory in Batavia, Illinois, who was not involved in the work.

Scientists have known since 1968 that protons and neutrons contain quarks bound together by the so-called strong force. Nonetheless, experimenters have never been able to measure the quarks’ masses directly, and theorists have not been able to calculate them with great precision. The reason for the impasse is simple: Quarks hold on to one another so tightly that it’s impossible to isolate one and study it by itself. “You can’t just put a quark on a scale and say, ‘This is what its mass is,’ ” says Christine Davies, a theorist at the University of Glasgow in the United Kingdom.

To make matters worse, particles made up of quarks are hideously complex. Nominally, a proton consists of two up quarks and a down quark that hold themselves together by exchanging gluons. (A neutron consists of two down quarks and an up quark.) In reality, the gluons themselves exchange gluons. And myriad quark-antiquark pairs flit in and out of existence. So the proton is actually a roiling infinity of quarks and gluons in which the three original “valence” quarks, which determine the proton’s identity, make up less than 2% of the mass. Quarks also come in four heavier types or “flavors”—strange, charm, bottom, and top—so theorists cannot analyze a particle like the proton in isolation. Instead, they must simultaneously explain the properties of a whole family of related particles, such as the Λ, which consists of an up quark, a down quark, and a strange quark.

Nevertheless, in recent years, physicists have made great progress in calculating the properties of particles made of quarks, which are known collectively as hadrons. A key approach is to simulate the particles using lattice quantum chromodynamics, or lattice QCD. In these simulations, researchers model the continuous space within a hadron as a grid of points called a lattice. They also imagine that time passes in discrete ticks, all of which makes the mathematics far easier. Researchers place the quarks and gluons on the lattice points and use supercomputers to simulate their interactions, using lattices with smaller and smaller spacing to approximate the real hadron. In November 2008, a different team of theorists used lattice QCD to calculate to high precision masses of the proton, neutron, and other three-quark particles.

Now, Davies and colleagues have essentially turned the process around and used lattice QCD to calculate the up-quark and down-quark masses. The individual quark masses usually serve as inputs that get tuned to the appropriate values during the calculation of the hadron’s properties. It might seem like physicists could simply write down those values and call the problem solved, but it gets tricky. The exact values of the quark masses depend on mathematical methods used in the simulation. Moreover, each quark mass comes out with a sizable uncertainty. Davies and colleagues found a way to get around such problems, however. Instead of trying to calculate the mass of each type of quark independently, they calculated ratios of those masses.

Specifically, they calculated the ratio of the charm-quark mass to the strange-quark mass. They combined this with calculations from another group of the ratios of strange-quark mass to up-quark mass and to the down-quark mass. Those ratios come out with much smaller uncertainties, explains G. Peter Lepage, a team member from Cornell University. And they can be combined with an already-known value of the charm-quark mass—which is easier to determine because it's about 500 times bigger—to finally nail down the masses of the lightest quarks, as the researchers report this week in Physical Review Letters. The team finds that an up quark weighs 2.01 +/- 0.14 megaelectron-volts, whereas a down quark weighs 4.79 +/- 0.16 MeV. That’s 0.214% and 0.510% of the mass of the proton, respectively.

Knowing the light-quark masses is “absolutely essential in a bunch of ways,” Mackenzie says. Those masses help predict what particle collisions at the LHC and elsewhere should look like according to theorists’ “standard model.” In turn, those calculations are key for spotting discrepancies that might point to new particles or phenomena, he says. What's more, whereas the standard model treats the quark masses as arbitrary, physicists hope to develop deeper theories that might explain, for example, why they have the values that they do. The quark masses would provide an important benchmark for such effort, Mackenzie says.

Still, Norman Christ, a theorist at Columbia University, says that Davies and colleagues make certain assumptions and approximations in their particular calculations that need to be tested. “You want to see it confirmed by an independent means, hopefully by a competing group that's trying to show this group is wrong and has to be dragged kicking and screaming to admit their results agree.”