51动漫

Editorial: 鈥�In praise of the humble proton鈥�

We used to think we understood protons, but these bedrocks of the atomic nucleus could send our theories of particle physics tumbling

IN THE long life of a proton, 10 years is a mere trice. These peerlessly stable particles, the bedrock of the atomic nucleus, are not prone to the decadence and decay of some of their subatomic brethren. Measuring their lifetimes means watching very many of them do very little for a very long time. Our current best estimate is that they survive for upwards of 10²⁹ years 鈥� over a billion billion times the age of the universe.

Ten years, though, is what it took for and his colleagues to show that the proton is not all it seems. The results of their experiments at the Paul Scherrer Institute (PSI) in Villigen, Switzerland, were published in July last year. The proton hadn鈥檛 suddenly become less stable. But it was quite a bit smaller than theory or previous experiments allowed (51动漫, 10 July 2010, p 10).

In the hyperaccurate world of subatomic physics, this was dynamite. A firestorm of claim and counter-claim followed. But with simpler explanations for the discrepancy now running out, it seems the mysterious shrinking of the proton has opened up a fundamental hole in our understanding of what makes atoms tick. What gives?

The doings of protons, as of all charged particles, are dealt with by a theory called quantum electrodynamics, or QED. One facet of nature it describes is the electromagnetic force, for example how the to-ing and fro-ing of photons of light keeps negatively charged electrons orbiting positively charged protons and so makes atoms possible. Deeper in the atomic nucleus lies the realm of a companion theory, quantum chromodynamics or QCD, which describes how protons and the like are themselves assemblages of smaller particles 鈥� quarks 鈥� and gluons that bind these quarks together. Together, QED and QCD are the two pillars of particle physicists鈥� proudest accomplishment, their 鈥渟tandard model鈥�.

The inner life of protons is known to be murky and impenetrable (see 鈥淎ll in a spin鈥�). Outwardly, though, all seems sweetness and light. Take the proton鈥檚 radius, whose accepted value has been settled on using two different kinds of measurement. The first, direct approach is to shoot electrons in the general direction of protons, like firing rubber pellets at a fairground duck. By measuring at what point they start bouncing off, we can get an idea of where the electrons encounter the protons鈥� fuzzy ball of charge.

鈥淲e thought we had a good idea how far the proton鈥檚 fuzzy ball of charge extends鈥�

Muon mischief

The second approach involves measuring the orbital energy levels of the electron circling the central proton of a standard hydrogen atom. The energy levels can be fed into QED calculations to determine how far the proton鈥檚 ball of charge must extend to keep the electron in those orbits.

The results of these two approaches are in good agreement. Averaging them gives the proton a radius of 0.877 femtometres, or a fraction under a trillionth of a millimetre.

And so all was well, until Pohl and his colleagues set out in the late 1990s to determine the proton鈥檚 radius using a third, supposedly more accurate method. They created hydrogen-like atoms in which the electrons were replaced by muons. These particles have the same negative charge as electrons but are some 200 times weightier. That means they orbit 200 times closer in than electrons, giving them an up-close-and-personal feel for how big the proton is.

Measuring the muons鈥� orbital energy levels meant first guessing the gaps between the two levels of interest, so a laser could be tuned to the right frequency to bump a muon from one level to another. The team did this by reversing the QED equations and plugging in the accepted value for the proton鈥檚 radius to give an estimated starting point.

In the first couple of attempts to run the full experiment, in 2003 and 2007, that approach didn鈥檛 work: the muons did not respond. It was only in 2009, when the team had a new laser that could reach higher frequencies, that they found the muons鈥� sweet spot and persuaded them to dance. Feeding the experimentally determined energy levels back into the QED calculation produced the shocker. The error on the proton鈥檚 radius had shrunk by a factor of 10, as expected 鈥� but the radius had shrunk too. At 0.8418 femtometres, it was about 4 per cent lower than the previous average ().

Four per cent might not sound much, but in QED, where theory and experiment can agree to a part or two in a billion, it was a huge embarrassment. And there was no obvious flaw in the measurement. 鈥淲e had to take the discrepancy seriously,鈥� says Michael Distler of the University of Mainz, Germany.

Just a few weeks later, Distler and his colleagues thickened the plot still more. They published a measurement of the proton radius using the tried and tested electron-scattering method that not only doubled its accuracy, but brought its value perfectly into line with that from measuring energy level shifts in regular hydrogen (). The muon experiment, which should have been the most accurate, was the odd one out. But why?

One early proposal was that the proton is surrounded by a large and diffuse halo of positive charge, meaning the distantly orbiting electron and the closer muon 鈥渟ee鈥� protons of different sizes (51动漫, 25 Sept 2010, p 16). That model seems to have been discounted, though, as it made other predictions at odds with the improved electron-scattering experiments. Now attention has shifted to more fundamental possible flaws: that we might have overlooked subtleties in the workings of QED, or that QED itself is missing something.

The first possibility stems from the fact that, according to QED, two charged particles orbiting each other will exchange photons. The stronger the bond between the particles, the more energy these photons will have. If the energy oversteps a certain mark, a photon can up the ante and briefly morph into a particle and its antiparticle 鈥� an electron and a positron, for example 鈥� before switching back to being a photon again.

Because a stronger bond is needed for a proton to rein in the more massive muon, there is more scope for this sort of thing in muonic hydrogen. The idea is that a thick cloud of ephemeral particles and antiparticles shields the orbiting muon from some of the attractive effect of the proton, reducing the proton鈥檚 effective radius (see diagram).

It sounds plausible, but there鈥檚 one problem: finding a particle-antiparticle pair that produces exactly the right amount of shielding. That would require the pair to have a combined mass of around 46 megaelectronvolts (MeV) 鈥� far more than an electron-positron pair, which weighs in at just over 1 MeV, but far below the more than 200 MeV needed for a muon-antimuon pair.

For , a physicist at the Missouri University of Science and Technology in Rolla, that makes things tricky. 鈥淭heory has a problem even inventing a particle that could explain the discrepancy without messing something else up,鈥� he says. He and others have been analysing the possibility that a new particle from a 鈥渉idden sector鈥� of the standard model might be rearing its head. So far, though, they have found nothing that would not also upset established experimental results in normal hydrogen (; ).

One proposal from the Mainz group is that the culprit is a fleet-footed pairing of a quark and an antiquark. That鈥檚 controversial. Quarks and their antiparticles are only known to bind together inside particles such as the proton, where they are weighed down with a lot of gluon baggage. The lightest known quark-antiquark pairing, the pion, tips the scales at 140 MeV. The researchers think that bound quark-antiquark pairs might appear and disappear so quickly that they never pick up the full gluon burden (). In that case, they could be lighter.

Not everyone is convinced. of the University of Warsaw in Poland agrees that QED might link up with the QCD of quarks and gluons to produce unforeseen or underestimated interactions 鈥� but points out that, again, we would expect to see the effects in other experiments.

That leaves the possibility that there is a blemish on QED itself. Few physicists think that likely, given the theory鈥檚 superlative accuracy in almost all its predictions. Even so, theorists have been combing the relevant equations for a sign of something missing. 鈥淯p to now, nothing large enough to explain a 4 per cent difference seems to show up,鈥� says , a theorist at the Kastler Brossel Laboratory in Paris, France, who was part of the PSI muonic hydrogen team.

Moustachioed Mona Lisa

Alexander Kholmetskii of the Belarusian State University in Minsk and his colleagues think they have something. The problem lies, they claim, with the equation 鈥� the Dirac equation 鈥� that was the foundation stone for QED and is used to describe the energy states of particles such as an orbiting electron or muon in an atom. There are two components to this equation, one describing how the particle ties up energy by binding itself to the nucleus with photons, and one describing how it can lose energy by radiating away photons.

In the lowest-energy orbital state, the researchers argue, this kind of radiative loss is not possible, and so they apply a small correction. Feeding this into the calculations of the proton radius leaves the value measured using muons virtually unchanged, while moving the electron result into almost perfect agreement with it () Exactly the same correction solves a similar energy-level problem in positronium, an 鈥渁tom鈥� in which an electron and a positron orbit each other.

It鈥檚 this explanation, though, that has raised the most hackles. The Dirac equation is . Bolting corrections onto it is, to many physicists, akin to scrawling a moustache on the Mona Lisa. 鈥淭here is no need to invoke whatever they do to explain radiative properties of atoms,鈥� says Indelicato. The fact that the lowest energy level can鈥檛 give up energy is already built into QED, he says.

All that leaves us at an impasse, with no explanation gaining universal approval. 鈥淭here are papers which claim to explain, but they are wrong,鈥� says Pachucki.

With theory at a deadlock, attention is now turning to another round of experiments. We have measured the proton鈥檚 radius by shooting electrons at it, and by measuring the energy levels of electrons and muons orbiting it. Might shooting muons at it bring some new insight? If these muon missiles see a differently sized proton, then there must be something fundamentally different in the way muons interact, such as the involvement of new particles or particle pairings we hadn鈥檛 thought of. And if they don鈥檛, says Jentschura, then we鈥檙e really stuck. 鈥淭hen the current discrepancy would seem all the more intriguing and strange,鈥� he says.

Meanwhile Pohl, Indelicato and their colleagues are starting to make measurements on muonic deuterium. This exotic atom鈥檚 nucleus, consisting of a proton and a neutron, can also be used to calculate the proton鈥檚 radius. Perhaps another decade might bring us a definitive answer.

鈥淚f there is a theory of everything, it will look a lot like the theory of the proton, but harder鈥�