IT WAS a true clash of the titans. In the blue corner: a multimillion-dollar particle accelerator. In the red: one of the world’s most powerful supercomputers. Both were battling to pin down the lifetime of an ephemeral subatomic particle known as the D-meson. Their deadline was 30 June.
Two days ahead of their target, the 20 or so theorists behind the supercomputer announced their answer. For 48 nail-biting hours, they waited for their rival’s result. They knew that if their numbers tallied, the supercomputer approach would have what it takes to revolutionise our understanding of the subatomic world. So when the 150-strong team at the accelerator finally announced that its answer matched, the theorists were over the moon.
It is a pretty impressive achievement, even by today’s standards in theoretical physics. For 30 years, researchers have been battling to make sense of the strong force – the glue that sticks protons and neutrons together in nuclei. Yet their best mathematical theory has been so complex that no one could turn the dense equations into useful predictions.
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Now all that is changing, thanks to the supercomputer’s calculations. And researchers are rubbing their hands at the bonanza of accurate computations set to follow. “We’ve got a whole universe of problems we were completely stymied by in the past,” says Peter Lepage of Cornell University in Ithaca, New York.
By assembling a working virtual replica of protons and other subatomic particles such as D-mesons, the work opens up a completely new way of finding physics beyond the “standard model”, physicists’ best theory so far about the particles and forces in nature. It is a tool that promises to help us understand why things weigh what they do and why the universe narrowly avoided disappearing in a flash of radiation shortly after the big bang.
This promising approach is based on a theory called quantum chromodynamics (QCD) and it goes by the name of lattice QCD. It has enjoyed a reversal of fortune in the past few months after many years when it was considered a poor relation of particle physics. While experiments churned out particles whose behaviour shed light on the internal workings of the strong force, lattice QCD theorists were left playing catch-up. And when they did finally produce a replica of a particle on their supercomputers, its properties fell laughably short of the real thing.
Dicing space-time
Lattice QCD theorists follow a simple strategy, much like meteorologists predicting the weather. Meteorologists rely on the mathematical equations that describe the motion of air masses. These equations are too complicated to solve exactly for the entire atmosphere. So to make the calculations possible, forecasters chop the atmosphere into more manageable cubes and use a computer to work out how these cubes interact with each other based on the equations. In theory, if the cubes are small enough, the computer simulation bears a close resemblance to reality.
Lattice QCD does the same. It attempts to find approximate solutions by taking space-time and dicing it into cubes. Theorists can then feed simplified versions of the QCD equations into the world’s most powerful supercomputers. After months of number crunching, out pops the answer and physicists finally get a better picture of the strange world inside atomic nuclei. Yet until now it hasn’t really worked.
So why has the strong force been such a hard nut to crack? The problem is that it is so much stronger than gravity, electromagnetism and the weak force, which is responsible for radioactive decay. Gravity might seem strong to us, but the strong force inside a nucleus is a staggering 1038 times as powerful.
It is this strength that locks protons inside atomic nuclei. Without it, the positively charged protons would repel each other and nuclei would fly apart. But the strong force also operates on even smaller scales. Inside protons and neutrons lurk still smaller particles – the quarks – and they too are glued together by the strong force.
That is why no one has ever seen a lonesome quark. If you try to pry one loose from a proton, the strong force is so rapacious that it rips a new quark and an antiquark out of empty space. The antiquark teams up with the ousted quark to form a new particle called a meson, made from a quark-antiquark pair, while the new quark takes the place of the one bumped from the nucleus. This is exactly the sort of thing that happens when physicists smash particles together in giant accelerators.
All this means that researchers cannot actually observe the particles they are most interested in – the quarks. Instead they have to infer quarks’ properties from the junk of mesons produced in a collision. It is an almighty headache for experimentalists, yet the strong force is even worse for theorists.
Their handling of the strong force is modelled on the hugely successful approach to quantum calculations pioneered by the late Richard Feynman in the 1940s. Feynman’s speciality was quantum electrodynamics (QED), the theory of electrical interactions between charged particles. QED views the force between two electrons as arising from the exchange of photons between the two. Likewise, the theory of QCD explains the strong force in terms of particle exchange, with two quarks interacting by swapping particles called gluons. But that’s where the similarity ends.
When an electron moves through empty space it interacts with photons and electron-positron pairs that pop in and out of existence all the time. These interactions perturb the electron’s behaviour and have to be taken into account in theorists’ calculations – at least in principle. But because the electromagnetic force is relatively feeble, you can largely sweep these effects under the carpet. In QED, the more complicated the interactions, the less you have to worry about them.
But QCD is a different beast. The strong force is so mighty that theorists simply cannot ignore the plethora of gluons and quark-antiquark pairs dashing in and out of the vacuum. Each of these interactions has an enormous effect on a quark’s properties and every single one has to be included in calculations, no matter how complex they become. That’s what makes protons, mesons and other particles made of quarks such a nightmare to model. Inside a proton, three quarks buzz around amidst a constant ferment of gluons and quark-antiquark pairs.
One way to see through the ferment is to study particles produced in high-energy collisions. In 1973, Frank Wilczek, David Politzer and David Gross showed that the strong force actually gets weaker at high enough energies, an insight that won them the Nobel prize for physics last year. With this proviso, theorists can gleefully ignore many of the messy gluon interactions that spoil their calculations at low energies. Not only does this make their calculations easier, this simpler view of QCD bears a good resemblance to reality, and theorists can make meaningful predictions with it. But it only works at high energies. As Howard Trottier of Simon Fraser University in Burnaby, British Columbia, laments: “For 30 years, we’ve been able to do half of ϰ.”
Flitting quarks
Outside the mini fireball created when particles smash together, it is a different story. Here, lattice QCD is essential to take account of the gluon ferment. To model a proton, theorists cut up a proton-sized region of space-time into about 2 million chunks then plop the right configuration of quarks and gluons onto it. The supercomputer does the rest, solving the equations of QCD in one giant simulation of space-time.
Only it doesn’t work so easily. According to Lepage, accounting for the quark-antiquark pairs that flit in and out of the vacuum takes up 99.9 per cent of a supercomputer’s time. For years, even the best computers were too slow to do it. To get anywhere, lattice QCD theorists had to ignore the quark-antiquark pairs. They called it the “quenched approximation”, but it wasn’t really much of an approximation – it was just plain wrong. “We knew it was wrong, but we couldn’t afford to do it right,” Lepage says. Nobel prizewinner Kenneth Wilson, who founded lattice QCD in 1974, actually quit the field out of frustration in 1986.
Of course, today’s computers are much faster than those of two decades ago. But more importantly, physicists have figured out better ways to do the computations. Until recently, the main obstacle has been a technical issue to do with chopping up space-time. When theorists modelled continuous space-time with cubes, they were forced to rewrite the equation describing a quark’s motion. To their frustration, they discovered that this approximation led unavoidably to the appearance of 15 fictitious quarks for every real one – with no way to tell which is the authentic one. Keeping track of all 16 quarks greatly slowed down even the fastest supercomputers. And choosing the wrong quark as the real one gave incorrect results.
But thanks to a couple of mathematical tricks, theorists have been able to shake off that handicap. First they figured out a way of reducing the number of quarks from 16 to 4. To cut the number still further, they discovered a second trick that is still proving controversial because no one has proved it is mathematically correct. Roughly speaking, instead of figuring out which of the four quarks is genuine, theorists whizz them all together in a blender, pour out a quarter, and pretend that is the genuine quark.
Though purists howled – and are still howling – the technique works. In 2003, a team of 26 theorists including Lepage, Trottier and Christine Davies at the University of Glasgow, UK, re-computed nine physical constants where previous lattice QCD computations had missed the experimental values by 10 per cent or more. All nine values calculated with the new technique fell into line with the experiments, with errors of only 1 to 2 per cent.
“The new physics will come in the second decimal place”
But theorists realised that they would have to do more to convince other physicists that lattice QCD was on the right track. “We knew that we had to get one or two predictions into the literature before the experimental results came out,” says Lepage. “I was eager for us to go out on a limb as theorists and expose ourselves.” Or as Ian Shipsey of Purdue University in Indiana, one of the leaders of the experimental team at Cornell, puts it: “Prediction is better than ‘postdiction’.”
Lepage knew a perfect limb for the theorists to crawl out onto. His colleagues working on a particle physics experiment called CLEO at Cornell were looking for a useful test to do with their ageing particle accelerator. They asked him if lattice QCD experts would be interested in measuring the “decay constant” of the D-meson. This parameter relates to the typical time it takes a D-meson to decay into an electron and a neutrino, or a muon and a neutrino. No one had measured this value before because there was no theory to compare it with. “I was stunned,” Lepage says. “I told them that this was precisely what we needed.” From that moment, the race was on.
At CLEO, the experimenters collided electrons and positrons in the hope of producing vast quantities of D-mesons. Meanwhile the theorists modelled a D-meson from a charm quark and a down antiquark on their supercomputer – “charm” and “down” being two of the six different “flavours” of quark.
For the experimenters, time was of the essence because CLEO is scheduled for mothballing in 2007, and they wanted to wring all the science they could from it. For the theorists, the critical thing was to get their calculation done before the experimenters announced their result. And both sides wanted to get their results in before a conference scheduled for 1 July in Uppsala, Sweden (see Graphic).
Although he was only watching from the sidelines, Lepage could feel the excitement. “For me, this was like a breath of fresh air,” he says. “I’ve been in and out of lattice QCD for 15 years, and this is the first time we’ve felt pressure from experimenters.”
Shipsey, who was on the CLEO team, also found the sense of urgency very appealing. “It was terribly exciting when Andreas Kronfeld, one of the theoretical team leaders, emailed his prediction to us.” And of course, we already know the exhilarating outcome.
Although the friendly competition has subsided for the moment, it isn’t over. Both sides are expecting to reduce their uncertainties by a factor of two or three over the next year. The CLEO team will do it simply by collecting more particle collisions, while Kronfeld’s team plans to make the supercomputer simulation more realistic by chopping space-time into finer chunks.
Ultimately lattice QCD theorists hope their improved simulations will point to new physics, possibly even before scientists switch on the most powerful particle accelerator ever built, the Large Hadron Collider near Geneva, in 2007. “There are two ways of discovering new physics,” says Lepage. One approach involves searching for new particles at the LHC, such as the hypothetical Higgs boson, thought to explain the origin of mass, or exotic particles from higher dimensions.
The other is to make extremely accurate measurements of particles at low energy and then compare them with theory. Any discrepancy might be down to a Higgs boson popping in and out of the vacuum and subtly altering the original particle’s mass, energy or lifetime. To spot such changes will demand pinpoint accuracy from both measurements and theory. “The new physics will come in the second decimal place,” Lepage points out.
The latest results show that theorists may be on their way to a breakthrough. They now know that they can calculate things like the decay constant of the D-meson with an uncertainty better than 10 per cent and that their results match experiments. Now they have to improve that accuracy and convince other physicists to trust their computations.
Two other recent triumphs could help to win them round. Besides the correct prediction of the D-meson decay constant, in May teams led by Kronfeld and Davies correctly forecast the mass of a particle called the charmed B-meson. It was confirmed five days later by an experiment at Fermilab in Batavia, Illinois.
And in March, lattice QCD researchers published the most accurate estimate yet of the strength of the strong force. It proves that lattice QCD calculations can produce answers with an error of just 1 per cent or better.
“We’ve finally mastered this technique for simulating the full theory on computers,” says Trottier. For Lepage, it is time for lattice theorists to hold their heads high. “At some point we should stop calling it lattice QCD,” he says. “Lattice QCD is ϰ.”
