TO MOST of us the mass of an eyelash seems like just about nothing. But to a Higgs boson – the particle believed to endow all others with their mass – it might as well weigh a tonne. The mass of the Higgs has a bearing on all the other particles that make up reality, and if it were as large as an eyelash the world would look very different. The electrons buzzing inside your computer’s circuits would be as weighty as the dust coating the top of it. If the dust bulked up on the same scale, each speck would have roughly the mass of a well-fed elephant.
A strange world indeed. Yet believe the standard model, our best theory of particle physics, and this is just the sort of situation we should expect to find ourselves in. According to this idea, the Higgs should be roughly the mass of an eyelash. This is so big that it would produce fundamental particles almost so massive and dense that they would create a microscopic black hole every time they collided.
Yet none of the fundamental particles – electrons, quarks, neutrinos and so on – are anywhere near the mass they ought to be. They’re all much smaller: 100 quadrillion times smaller.
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Why the clustering at the bottom? This “hierarchy problem” has haunted physicists for decades, and there’s never been an easy answer. The front runner, a theory known as supersymmetry, has fallen from grace now that the Large Hadron Collider (LHC), located near Geneva, Switzerland, has searched the most obvious avenues for evidence and failed to find it.
We’re desperate for a way to explain this puzzle. But perhaps the answer has been under our noses all along. According to a trio of physicists with a grand idea, a single particle known as the axion, a plaything of theorists since the 1970s, makes the problem disappear in a flash – and fixes a couple of other mysteries on the side.
“The axion could explain why everything is too light – plus two other mysteries on the side”
People had started to give up on the hierarchy problem as being solvable without resorting to far-fetched explanations, says at Johns Hopkins University in Baltimore, Maryland. “What’s shocking some is that the axion, a very old idea, is all of a sudden playing a role.”
Until recently, mass itself was an ill-defined concept. Everyone intuitively understands it as the thing that gravity acts on to bring objects down to Earth, and that makes it harder to accelerate a truck than a bicycle. Quite how mass does what it does, though, no one could say for sure.
That changed in 2012, when researchers at the LHC found what appeared to be the long-sought Higgs boson – thought to be the manifestation of an invisible Higgs field that permeates space. It is the gloopy, molasses-like quality of this field that provides the resistance to motion that is the hallmark of mass.
The discovery of the Higgs was a terrific victory for science, but it brought the hierarchy problem back into full view. If all the other particles are much, much lighter than we’d expect, then the Higgs must have something to do with it.
To grapple with that idea, we need to deal with a strange-sounding concept: the mass of the Higgs. How can the mass-giving particle have a mass of its own? It turns out that under the rules of quantum mechanics, it can temporarily shape-shift into all sorts of other particles, acquiring their masses in the process. Add up the effect of these quantum fluctuations and we get a value for the Higgs mass verging on the upper limit – that of the eyelash. Expressed in the normal units of particle physics, that’s about 1019 gigaelectronvolts (GeV).
A massive fudge
So when researchers at the LHC found the Higgs mass roughly where they thought it would be, at a paltry 125 GeV, it confirmed their worst fears: there’s something massive missing from our understanding of the Higgs.
A blunt resolution to this huge discrepancy is to assume that it has some sort of inherent mass, independent of all the quantum fluctuations, and that this is also very large. When physicists delved into the maths, they found a way to make the two masses just about cancel out, with whatever remains being the mass we actually measure.
In dark times a physicist might contemplate such a fudge. But what are the chances of two unrelated, multizillion figures cancelling almost perfectly? “In the case of the Higgs, something funny is going on,” says Kaplan.
Looked at this way, the hierarchy problem is a coincidence of cosmic proportions. It’s a bit like driving a golf ball towards the green, only to see it deflect off a tree into a bunker, bounce into a lake and then rebound to land within inches of the club you hit it with. And the improbability is not just limited to the boson. Because the masses of all the fundamental particles scale with the Higgs, the problem affects just about everything.
Theorists loved supersymmetry because it appeared to offer a path out of this mess. The theory posits that every known fundamental particle has a twin – a superparticle, or “sparticle” – that cancels out the contribution of its conventional partner when totting up all the Higgs’s quantum fluctuations. In this way, the mass due to quantum fluctuations drops almost to zero – the small remainder being the mass difference between particles and sparticles. That would leave everything neatly tied up.
There’s just one problem: sparticles should have been lurking just a bit further into unexplored territory than the Higgs, but none have shown up at the LHC. “The Higgs should have been the tip of the iceberg,” says Kaplan.
With supersymmetry looking shaky, many physicists are contemplating a last-ditch explanation. In a sprawling multiverse, runs the idea, the Higgs mass might take on any number of values and we just happen to be living in one of few regions in the universe where it is very small. The trouble with this idea is that it’s nigh on impossible to test.
“What we’re putting forward is a third way,” says Kaplan. It all started in 2014, when Kaplan’s colleagues, at the University of California, Berkeley, and at Stanford University, devised a new type of experiment to detect an axion.
They’re rather interesting things, axions. If they exist, they are light, electrically neutral particles that generate their own unique force. They were first proposed more than 40 years ago to explain a vexing issue known as the strong charge parity problem. They are also prime candidates for dark matter, so if they can add the hierarchy problem to their laundry list it would be an impressive feat for such a small – albeit hypothetical – object (see “Particle hat-trick“).
“Before this theory, people had almost given up trying to solve the hierachy problem”
But none of the axion detectors so far devised has seen anything. Rajendran and Graham had a up their sleeves and were about to apply for funding to build it when a team claimed to have detected long-sought evidence of a period of rapid inflation early in the universe, using the BICEP telescope near the South Pole. That looked to rule out the existence of axions.
Rajendran wasn’t so sure, and after some head-scratching, he figured out a way to square the BICEP result with the existence of axions. It required the axion to have had a large mass in the early universe, which then petered out. But this didn’t convince anyone to fund their detector. And to rub salt in the wound, a raft of reports soon appeared saying the BICEP claim wasn’t valid anyway.
But never mind: the episode had got Rajendran thinking about much broader issues than just axions. If that particle’s mass could decrease over time, he thought, could that apply to other particles such as the Higgs boson too?
Mass mystery
Rajendran and Graham got in touch with Kaplan, and together they began applying the diminishing-mass idea to the hierarchy problem. What if, they wondered, the masses of the axion and Higgs were somehow linked, like two wheels on an axle? That way both particles could start off in the early universe at the gigantic mass predicted by the standard model, and then slowly roll downhill.
On its own, the idea didn’t solve anything. Why would the Higgs mass grind to a halt at 125 GeV, rather than keep falling? Gradually, Graham, Kaplan and Rajendran arrived at the idea that the mass-giving nature of the Higgs itself may have switched on only when its mass dipped below a certain value. This could have locked everything in place, but it was tortuous to convert it into solid theory. “It took us six months to figure out something that actually works,” says Kaplan.
Understanding this mechanism requires a little detour into what makes the Higgs so special in the first place. The Higgs field is just like the electromagnetic field, through which we experience magnetism, light and solid objects – but with an important difference. Whereas electromagnetism is absent, or “off”, unless there is something nearby to generate it – a magnet or lamp, say – the Higgs field is on everywhere.
Physicists often explain this characteristic using headgear. If you were to turn a bowler hat upside down and drop in a marble, it would eventually come to rest at the centre – corresponding to a value of zero, or “off”. But now do the same with a Mexican hat, and keep it the right way up. Faced with that tall crown, the marble cannot remain at the hat’s central axis. Instead, it falls down to the brim, representing an “on” state (see “Playing with hats”).
Today the Higgs field is like a Mexican hat because mass is always on. Looking at their equations, however, Graham, Kaplan and Rajendran realised it needn’t always have been so. In its early supermassive state, the Higgs would have been an inverted bowler hat, its field turned off. By tweaking the link between the axion and the Higgs, they could design it so that the Mexican hat – and the mass-giving powers – only appeared when the Higgs’s own mass was close to zero.
Once the Higgs was in that state, it stayed that way thanks to a self-reinforcing loop. This kicked in because the fundamental particles gaining mass from the Higgs include quarks, which are glued together inside atoms by the strong force. And it turns out that axions interact with the strong field themselves, so the quarks’ sudden mass would have put a cap on the axion. It was just what the trio had been searching for. “Bingo! We solve the hierarchy problem,” says Rajendran.
Back in the 1970s, the axion was named after a then-popular detergent thanks to its ability to clean up the strong charge parity problem. But in their , published in April (), the team suggested tweaking the axion’s name to “relaxion”, given how it causes the mass of the Higgs to relax nicely down to its observed value.
“The relaxion idea is quite fascinating, and it has generated a lot of heated discussion,” says particle physicist at the Massachusetts Institute of Technology.
Cosmically relaxed
Some of this heat surrounds the mechanism governing the axion’s link to the Higgs – the fist that changes the shape of the hat, if you will. Graham, Kaplan and Rajendran admit they have invented this mechanism and jiggled its strength to suit their theory. It sounds slippery, but it could be a worthwhile tactic. At the very least, it may give physicists a thread to tug at, making the hierarchy problem easier to start tackling compared with the previous state of play, where there was no obvious starting place.
Not everyone sees it like that though. “It could be that this is easier, but it’s not guaranteed,” says theorist Jörg Jäckel at Heidelberg University in Germany.
The relaxion idea does have one advantage over other answers to the hierarchy problem. There are detectors out there hunting for axions now, such as the recently revamped at the University of Washington, Seattle.
But rather than waiting for the detectors to ping, Graham, Kaplan and Rajendran are working on an audacious new idea. Can relaxion theory solve a fourth big mystery?
The “cosmological constant” is the number physicists plug into equations to represent the energy pushing space apart, inflating the universe. But although the rules of quantum theory say this number must be gargantuan, an arbitrarily small number is famously needed for the expansion to tally with observations.
Sound familiar? The trio are wondering if maybe, just maybe, a similar sort of relaxation argument might unlock the problem. “It’s a rough one, but we’re having a go at it,” says Kaplan. “We’ve been buoyed by the fact that we’ve been able to hit the hierarchy problem so successfully, in such a dramatic way.”
(Image: Getty Images, Gjon Mili/Time and Life Pictures/Getty)
Particle hat-trick
If the hypothetical axion particle does exist, it has a shot at solving three of the biggest mysteries in physics at once.
After the hierarchy problem (see main story) there is the strong charge parity problem. Imagine an interaction between two particles, and then imagine what it would look like if you could view its mirror image, with the particles’ charges also swapped. By intuition, you would expect the result to be physically indistinguishable (known as charge parity symmety), but many processes we observe in nature aren’t like this. Those governed by the fundamental mechanism known as the strong force do however always appear to be, for reasons unknown. If the axion exists, its field would act like a strict drill sergeant and keep the symmetry violations in check.
Axions are also perfect candidates for dark matter, the invisible stuff that accounts for 80 per cent of the mass of the universe. They are uncharged and only interact very weakly with other matter, so they are very hard to observe directly. It’s worth trying though. These particles pay triple.
This article appeared in print under the headline “When axions strike”
