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THE standard model of particle physics is like – a sprawling castle constructed by tacking on new rooms as needed, with no underlying grand design. It was built to house a particle-level explanation for the entire universe and it succeeds on many counts.

Some physicists are now looking to tack on annexes to accommodate the Higgs boson, dark matter and the graviton, if they can be found (see “Inside the standard model”). Others think the structure needs an overhaul, and they have worked up new blueprints for magnificent palaces based on ideas such as string theory. Trouble is, it’s almost impossible to tell whether these designs are realistic, or just fairy-tale constructions with clouds for foundations.

Even those who don’t want to tear the castle down wouldn’t mind testing its strength using some big artillery. That’s the main reason for building the Large Hadron Collider (LHC), the brawniest of all particle experiments at the CERN laboratory near Geneva, Switzerland.

Yet several smaller groups are successfully using a gentler approach, tapping at the castle walls, feeling for weak points. Among these, one experiment stands out for identifying what may be the first major crack in the edifice of the standard model.

“One experiment stands out for identifying the first major crack in the standard model”

For years the , based at in Upton, New York, studied particles called muons. These are unstable subatomic particles similar to electrons but about 200 times as heavy. The research was focused on a quantum property of the muon known as its magnetic moment, and it found the standard model wanting. According to the measurements, there is a mere 0.27 per cent probability that the standard model is correct.

The chances are good that the E821 team has discovered a crack in physics as we know it but, we need more precise measurements to be sure. A new collaboration called is planning an experiment that aims to hit the sort of precision required. Not only that, they hope their measurement of the magnetic moment will reveal new phenomena beyond the reach of even the mighty LHC.

The story of the muon’s magnetic moment dates back to 1928, when British physicist Paul Dirac devised equations describing how quantum particles behave near the speed of light. Muons and their lighter cousins, electrons, can be thought of as spinning balls of charge, which generate a tiny magnetic field – the magnetic moment.

Dirac calculated that a related quantity called the g-factor should be exactly 2 for electrons and muons. When researchers finally measured the electron’s magnetic moment, nearly 20 years later, they found it was slightly larger. By 1948, those laying the foundations of the standard model realised that the reason for the “anomalous” magnetic moment lies with the fleeting effects of virtual particles, entities that show up only to disappear again in an instant.

The g-factor

In fact, the magnetic moment is so sensitive it is affected by the presence of of particles unknown in Dirac’s day, including quarks, W and Z bosons and the Higgs boson. Indeed, quantum mechanics tells us that virtual versions of any kind of particle – including ones we haven’t discovered yet – can pop into existence by borrowing energy for a passing instant. This raises the possibility that even particles too heavy for us to make in the laboratory – even one as powerful as the LHC – could contribute too. “Basically, anything which is not strictly forbidden is mandatory,” says David Kawall at the University of Massachusetts at Amherst, echoing a quote from fantasy writer T. H. White’s book The Once and Future King.

The muon is affected much more than the electron because of its greater mass. That’s because they have more energy available for virtual particles to borrow. The magnetic moment of the electron is one of the most closely verified predictions of the standard model (91av, 12 September 2006, p 40). Not so for the muon. The first signs that all was not well came shortly after the E281 experiment got under way in the mid-1990s.

Once they appear, muons decay nearly 200,000 times faster than you can blink your eye, so a special trick is needed to measure their magnetic moment. It comes courtesy of relativity. Time slows down for muons if you accelerate them to close to the speed of light, ensuring they stay intact long enough for us to study them.

To make the muons, the E821 team slammed a proton beam into a series of nickel discs, creating a shower of other particles. Some of these decayed to muons, which were quickly stored by channelling them into a doughnut-shaped accelerator that used powerful electromagnets to zing them around the ring (see diagram).

A spinning muon behaves like a tiny magnet. Just as two fridge magnets a small distance apart exert a force on each other, the muon’s magnetic field interacts with the field of the accelerator’s electromagnet. This knocks the muon’s spin axis off course by an amount that depends on its magnetic moment. If its g-factor were exactly 2, the spin axis would always point in the same direction as the muon’s path. But the virtual particles popping in and out of existence around it make the muon’s g-factor slightly larger. This causes the muon’s spin axis to drift as it revolves around the ring.

To determine the magnetic moment, the E821 team waited until the muon decayed into an electron. A series of detectors placed around the ring measured the electron’s energy and path. From this information, the team was able to piece together how far the muon’s spin was knocked off course and calculate its g-factor.

When the E821 team completed the experiment, its members were shocked by what they found. The muon’s g-factor was nowhere near the value predicted by theory. In fact, the figure was so wildly out that it led them to calculate the 0.27 per cent probability of the standard model’s prediction matching reality. Either the standard model is correct and our understanding of the muon’s g-factor within the framework is incomplete, or the standard model is wrong.

E821 switched off in 2001, yet its result is still hotly debated today. The LHC is 600 times wider than E821’s 14-metre-diameter accelerator, and 900 times as powerful, yet E821 continues to punch above its weight. No other measurement is in such stark conflict with the standard model theory.

Knowing how heretical E821’s results still are, at the National Institute for Nuclear Physics in Padua, Italy, together with William Marciano at Brookhaven and Alberto Sirlin at New York University, examined the possibility that the standard model’s theoretical prediction of the muon’s magnetic moment had been miscalculated.

Of all the possible particles that can affect it, the least understood is the contribution of hadrons – particles composed of quarks. Passera and his colleagues wondered what would happen if they increased the effect of hadrons to bring the theoretical magnetic moment of the muon into agreement with E821’s experiment ().

The trouble with – or beauty of, depending on your viewpoint – the standard model is that you cannot make changes to one part without affecting other parts. It is like remodelling a house: making one room bigger just makes the neighbouring room or hallway shrink. Similarly, increasing the hadrons’ influence on the muon’s magnetic moment causes the theoretical mass of the W boson to fall. Yet the W boson’s mass is constrained tightly by experiments, and so you need to change something else to explain the E821 result.

“You can’t make changes to one part of the standard model without affecting other parts”

That something else is the mass of the Higgs boson. Having never spotted a Higgs, we don’t know its mass. However previous experiments at CERN have ruled out values less than 114 gigaelectronvolts while the standard model suggests that it is less than 160 GeV.

Passera and his colleagues wondered what effect the various possible Higgs masses would have on the muon’s magnetic moment. To match the E821 result, their calculations suggest that the Higgs mass is far lower than 114 GeV, which has already been ruled out. Taken at face value, this raises the uncomfortable possibility that the standard model is wrong, as long as E821’s results are bona fide.

There is some wiggle room in Passera’s calculations, though. They show that the upper limit to the Higgs mass can be as large as 135 GeV. This makes for uncomfortable reading because it narrows the window of possibilities within the standard model and means it is more likely to be wrong.

But what is bad news for the standard model is good news for physicists trying to renovate it. The disagreement between the experimental and theoretical values of the muon’s g-factor suggests that as-yet-undiscovered particles may be contributing, muddying the experimental waters. Among the front runners are supersymmetric particles – theoretical heavyweight partners for every one of the standard model particles. “There are supersymmetric theories that would explain this discrepancy very well,” says Passera.

“Supersymmetric theories explain this discrepancy very well”

What’s your flavour

Nevertheless, physicists are curbing their excitement until more precise measurements confirm or debunk the disagreement between theory and experiment.

This is where Kawall, David Hertzog of the University of Illinois at Urbana-Champaign, and P989 come in. They have a plan to bring the next muon g-factor experiment to the Fermilab laboratory in Batavia, Illinois. The collider’s facilities should be able to provide six times as many muons for the number of protons used in E821’s set-up, and the storage ring would be filled four times as often. This means that in just a year, P989 could reap more than 20 times as much data as the entirety of E821’s experiment, slashing the uncertainties on the measurement. Several have determined that they could achieve the precision needed to finally knock a hole in the edifice of the standard model.

To deal with the higher data rates, the P989 team would need all-new detectors for the electrons, but other parts of the E821 experiment are worth recycling. Its 680-tonne electromagnet would travel from Upton to Batavia by a combination of air crane, barge and rail. “We could be ready at the end of 2014, depending on funding,” says Hertzog.

The g-factor experiments aren’t the only way researchers are trying to beat the LHC to the prize of new physics at much lower energies. A collaboration called is planning to build an experiment at Fermilab to look for something else forbidden within the walls of Gormenghast: a theoretical idea called “flavour violation”.

The standard model describes a well-established relationship between electrons and muons: when a muon decays, it produces an electron along with two neutrinos – the muon neutrino and the electron antineutrino. It also says that the decay process must conserve a property known as flavour. Imagine the muon is mint-flavoured. The decay process must be minty at the start and finish; it cannot end up tasting of lemon.

Muon neutrinos carry the same flavour as muons. Meanwhile, the flavour of the electron antineutrino cancels out the electron’s flavour. The net effect is that, thanks to the muon neutrino, the original muon’s flavour is conserved in the final decay products.

But several proposed revisions to the standard model call for muons to convert to electrons without the help of neutrinos. Such formulations call for new relationships between muons and electron.

According to these new theories, muons may instead interact with virtual supersymmetric particles, or maybe a new flavour-changing particle that we haven’t found yet. In such reactions, a mint-flavoured muon could decay into a lemon-flavoured electron, with no neutrinos required. This is what the Mu2e team will look for.

The plan is to crash protons into a gold target. Among the collision debris will be particles that decay into muons, and these in turn will fly off and become trapped inside some neighbouring aluminium foil. Because muons behave like heavy electrons, some of them will be attracted by aluminium atomic nuclei and will circle them, forming exotic atoms for a few moments until the muon decays.

The Mu2e team hope to catch about 10¹⁷ muons over the course of two years using this technique. They expect a muon to decay as the standard model describes, with an electron, muon neutrino and electron antineutrino carrying away its energy. Depending on how the decay products ping apart from each other, the team will see a spread of electron energies in its detector.

Should muon flavour violation occur, the decaying muon will give up almost all of its energy to the electron. So instead of seeing a spread of energies from three decay particles, these lone electrons are predicted to show up as a spike in energy at around 105 MeV.

To understand the experiment, high-energy physicists have had to join forces with nuclear physicists who know how aluminium nuclei interact with incoming particles. “It’s sort of like cousins you never see and you actually find out, once you start talking, that you have a lot in common,” says Bob Bernstein, a spokesman for Mu2e. This collaboration has figured out which other rare processes might kick out an electron at 105 MeV and therefore mimic the flavour changelings. They are confident they can tell them apart.

If they do see apparent flavour-violating muon decays, their next step will be to start swapping out the aluminium for other nuclei. “Each atomic nucleus will have a different muon-to-electron conversion rate, depending on the source of the new physics,” says Bernstein. This means the Mu2e team could identify the favourite successors of the standard model. With funding, they could get started in 2016.

Over the next few years, the edifice of the standard model will face an unprecedented barrage of new tests. For nearly 40 years it has stood firm. If it crumbles, even slightly, many physicists will jump at the chance to redesign the castle.