Dawn of the quark ages


by Michael Brooks from NewScientist 3024, 6 june 2015

Ask them to name their heart’s truest desire, and many a science nut might say the answer to life, the universe and everything – or, failing that, a fully functioning lightsaber.
Odd, then, that one field of scientific enquiry that could conceivably provide both gets so little press. After all the hoopla of the past few years, you could be forgiven for believing that understanding matter’s fundamentals is all about the Higgs boson – the “God particle” that explains where mass comes from.
The Higgs is undoubtedly important. But it is actually pretty insignificant for real stuff like you and me, accounting for just 1 or 2 per cent of normal matter’s mass. And the huge energy needed to make a Higgs means we’re unlikely to see technology exploiting it any time soon.
Two more familiar, though less glamorous, particles might offer more. Get to grips with their complexities, and we can begin to explain how the material universe came to exist and persist, and explore mind-boggling technologies: not just lightsabers, but new sorts of lasers and materials to store energy, too. That’s easier said than done, granted – but with a lot of computing muscle, it is what we are starting to do.
Chances are you know about protons and neutrons. Collectively known as nucleons, these two particles make up the nucleus, the meaty heart of the atom. (In terms of mass, the weedy electrons that orbit the nucleus are insignificant contributors to the atom.)
The headline difference between protons and neutrons is that protons have a positive electrical charge, whereas neutrons are neutral. But they also differ ever so slightly in mass: in the units that particle physicists use, the neutron weighs in at 939.6 megaelectronvolts (MeV) and the proton at 938.3 MeV.
That’s a difference of just 0.14 per cent, but boy does it matter. The neutrons’ extra mass means they decay into protons, not the other way around. Protons team up with negatively charged electrons to form robust, structured, electrically neutral atoms, rather than the world being a featureless neutron gloop.
“The whole universe would be very different if the proton were heavier than the neutron,” says particle theorist Chris Sachrajda of the University of Southampton in the UK. “The proton is stable, so atoms are stable and we’re stable.” Our current best guess is that the proton’s half-life, a measure of its stability over time, is at least 1032 years. Given that the universe only has 1010 or so years behind it, that is a convoluted way of saying no one has ever seen a proton decay.
The exact amount of the neutron’s excess baggage matters, too. The simplest atom is hydrogen, which is a single proton plus an orbiting electron. Hydrogen was made in the big bang, before becoming fuel for nuclear fusion in the first stars, which forged most of the other chemical elements. Had the protonneutron mass difference been just a little bigger, adding more neutrons to make more complex elements would have encountered energy barriers that were “difficult or impossible” to overcome, says Frank Wilczek of the Massachusetts Institute of Technology. The universe would be stuck at hydrogen.
But had the mass difference been subtly less, hydrogen would have spontaneously changed to the more inert, innocuous helium before stars could form – and the cosmos would have been an equally limp disappointment. Narrow the gap further, and hydrogen atoms would have transformed via a process called inverse beta decay into neutrons and another sort of neutral particle, the neutrino. Bingo, no atoms whatsoever.
All of that leads to an unavoidable conclusion about the proton and neutron masses. “Without these numbers, people wouldn’t exist,” says Zoltán Fodor of the University of Wuppertal, Germany.
But where do they come from?
The question is fiendishly difficult to answer. We’ve known for half a century that protons and neutrons are not fundamental particles, but made of smaller constituents called quarks. There are six types of quark: up, down, strange, charm, bottom and top. The proton has a composition of up-up-down, while the neutron is up-down-down.

A full explanation of where stuff gets its mass from is buried deep in the atomic nucleus
A full explanation of where stuff gets its mass from is buried deep in the atomic nucleus

Quark QuirksDown quarks are slightly heavier than up quarks, but don’t expect that to explain the neutron’s sliver of extra mass: both quark masses are tiny. It’s hard to tell exactly how tiny, because quarks are never seen singly (see “Quark quirks“, right), but the up quark has a mass of something like 2 or 3 MeV, and the down quark maybe double that – just a tiny fraction of the total proton or neutron mass.
Like all fundamental particles, quarks acquire these masses through interactions with the sticky, all-pervasive Higgs field, the thing that makes the Higgs boson. But explaining the mass of matter made of multiple quarks clearly needs something else.
The answer comes by scaling the sheer cliff face that is quantum chromodynamics, or QCD. Just as particles have an electrical charge that determines their response to the electromagnetic force, quarks carry one of three “colour charges” that explain their interactions via another fundamental force, the strong nuclear force. QCD is the theory behind the strong force, and it is devilishly complex.
Electrically charged particles can bind together by exchanging massless photons. Similarly, colour-charged quarks bind together to form matter such as protons and neutrons by exchanging particles known as gluons. Although gluons have no mass, they do have energy. What’s more, thanks to Einstein’s famous E = mc2, that energy can be converted into a froth of quarks (and their antimatter equivalents) beyond the three normally said to reside in a proton or neutron. According to the uncertainty principle of quantum physics, these extra particles are constantly popping up and disappearing again (see diagram).
To try and make sense of this quantum froth, over the past four decades particle theorists have invented and refined a technique known as lattice QCD. In much the same way that meteorologists and climate scientists attempt to simulate the swirling complexities of Earth’s atmosphere by reducing it to a three-dimensional grid of points spaced kilometres apart, lattice QCD reduces a nucleon’s interior to a lattice of points in a simulated space-time tens of femtometres across. Quarks sit at the vertices of this lattice, while gluons propagate along the edges. By summing up the interactions along all these edges, and seeing how they evolve step-wise in time, you begin to build up a picture of how the nucleon works as a whole.
Trouble is, even with a modest number of lattice points – say 100 by 100 by 100 separated by one-tenth of a femtometre – that’s an awful lot of interactions, and lattice QCD simulations require a screaming amount of computing power. Complicating things still further, because quantum physics offers no certain outcomes, these simulations must be run thousands of times to arrive at an “average” answer. To work out where the proton and neutron masses come from, Fodor and his colleagues had to harness two IBM Blue Gene supercomputers and two suites of cluster-computing processors.
The breakthrough came in 2008, when they finally arrived at a mass for both nucleons of 936 MeV, give or take 25 MeV – pretty much on the nose (Science, vol 322, p 1224). This confirmed that the interaction energies of quarks and gluons make up the lion’s share of the mass of stuff as we know it. You might feel solid, but in fact you’re 99 per cent energy.
But the calculations were nowhere near precise enough to pin down that all-important difference between the proton and neutron masses, which was still 40 times smaller than the uncertainty in the result. What’s more, the calculation suffered from a glaring omission: the effects of electrical charge, which is another source of energy, and therefore mass. All the transient quarks and antiquarks inside the nucleon are electrically charged, giving them a “self-energy” that makes an additional contribution to their mass. Without taking into account this effect, all bets about quark masses are off. Talk about one compound particle being more massive than another because of a difference in quark masses is a “crude caricature”, says Wilczek, who won a share of a Nobel prize in 2004 for his part in developing QCD.
The subtle roots of the proton-neutron mass difference lie in solving not just the equations of QCD, but those of quantum electrodynamics (QED), which governs electromagnetic interactions. And that is a theorist’s worst nightmare. “It’s awfully difficult to have QED and QCD in the same framework,” says Fodor. The electromagnetic self-energy can’t even be calculated directly. In a limited lattice simulation, its interactions create an infinity – a mathematical effect rather like a never-ending reverberation inside a cathedral.
Fodor and his colleagues’ new workaround involves solving the QED equations for various combinations of quarks inside different subatomic particles. The resulting subtle differences are used to replace the results of calculations that would invoke infinities, and so grind out a value for the proton-neutron mass difference (Science, vol 347, p 1452).
The figure the team came up with is in agreement with the measured value, although the error on it is still about 20 per cent. It is nonetheless “a milestone”, says Sachrajda. Wilczek feels similarly. “I think it’s exciting,” he says. “It’s a demonstration of strength.”
You might be forgiven for wondering what we gain by calculating from first principles numbers we already knew. But quite apart from this particular number’s existential interest, for Wilczek the excitement lies in our ability now to calculate very basic things about how the universe ticks that we couldn’t before.
Take the processes inside huge stars that go supernova – the events that first seeded the universe with elements heavier than hydrogen and helium. Our inability to marry QED and QCD meant we couldn’t do much more than wave our hands at questions such as the timescale over which heavy elements first formed – and we couldn’t make a star to test our ideas. “Conditions are so extreme we can’t reproduce them in the laboratory,” says Wilczek. “Now we will be able to calculate them with confidence.”
The advance might help clear up some of the funk surrounding fundamental physics. The Large Hadron Collider’s discovery in 2012 of the Higgs boson, and nothing else so far, leaves many open questions. Why did matter win out over antimatter just after the big bang (New Scientist, 23 May, p 28)? Why do the proton and electron charges mirror each other so perfectly when they are such different particles? “We need new physics, and simulations like ours can help,” says Kálmán Szabó, one of Fodor’s Wuppertal collaborators. “We can compare experiment and our precise theory and look for processes that tell us what lies beyond standard physics.”

An open road

For Sachrajda, this kind of computational capability comes at just the right time, as the LHC fires up again to explore particle interactions at even higher energies. “We all hope it will give an unambiguous signal of something new,” he says. “But you’re still going to have to understand what the underlying theory is, and for that you will need this kind of precision.”
If that still sounds a little highfalutin, it’s also worth considering how modern technologies have sprung from an ever deeper understanding of matter’s workings. A century or so ago, we were just getting to grips with the atom – an understanding on which innovations such as computers and lasers were built. Then came insights into the atomic nucleus, with all the technological positives and negatives – power stations, cancer therapies, nuclear bombs – those have brought.
Digging down into protons and neutrons means taking things to the next level, and a potentially rich seam to mine. Gluons are far more excitable in their interactions with colour charge than are photons in electromagnetic interactions, so it could be that manipulating colour-charged particles yields vastly more energy than fiddling with things on the atomic scale. “I think the possibility of powerful X-ray or gamma-ray sources exploiting sophisticated nuclear physics is speculative, but not outrageously so,” says Wilczek.
Star Wars' lightsaberGluons, unlike photons, also interact with themselves, and this could conceivably see them confining each other into a writhing pillar of energy – hence Wilczek’s tongue-incheek suggestion they might make a Star Wars-style lightsaber. More immediate, perhaps, is the prospect of better ways to harness and store energy. “Nuclei can pack a lot of energy into a small space,” says Wilczek. “If we can do really accurate nuclear chemistry by calculation as opposed to having hit-andmiss experiments, it could very well lead to dense energy storage.”
For Fodor, that’s still a long way off – but with the accuracy that calculations are now reaching, the road is at last open. “These are mostly dreams today, but now we can accommodate the dreams, at least,” he says. “You’ve reached a level where these technological ideas might be feasible.”
Welcome, indeed, to the quark ages.

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