麻豆传媒

Editorial: 鈥�The Higgs is only half the problem鈥�

IN JULY, at a particle physics conference in Grenoble, France, Nobel laureate seemed to be channelling the spirit of Thomas Huxley. The scrappy 19th-century champion of Darwin鈥檚 theory of evolution by natural selection once spoke of 鈥渢he great tragedy of science 鈥� the slaying of a beautiful hypothesis by an ugly fact鈥�. Smoot, a cosmologist who made his name studying the afterglow of the big bang, thinks this is just the drama now playing out in particle physics.

Particle physics has a beautiful theory, known as supersymmetry. More than three decades in the making, its elegant mathematical structure was intended to replace the 鈥渟tandard model鈥�, the eminently serviceable but sometimes creaky and in parts aesthetically unpleasing theoretical construct that is currently our best description of matter鈥檚 fundamental workings.

Supersymmetry鈥檚 beauty is now meeting some ugly facts emerging from the Large Hadron Collider, the gargantuan particle accelerator situated at CERN near Geneva, Switzerland. Supersymmetry predicts a whole slew of new particles, and by most reckonings the LHC should have started producing some of them already. But it hasn鈥檛. That throws up some big questions. Is supersymmetry really the right answer? If not, what is?

Supersymmetry 鈥� SUSY to its legion of fans 鈥� has long been seen as a panacea for the standard model鈥檚 ills. Back in the early 1960s, one of the theories that went into making the standard model faced an embarrassment. It could not explain how elementary particles, things such as electrons and the quarks that make up protons and neutrons, get their mass. It predicted none of them had any mass at all.

Nonsense, clearly. A workaround, arrived at from several angles in 1964, was to postulate that an all-pervading field exists with which elementary particles interact differently, giving each a unique mass. This was the Higgs field, named after one of its progenitors, of the University of Edinburgh, UK.

The Higgs mechanism was neat, but created its own problem. Experimental clues indicated that the mass of the 鈥渜uantum鈥� of the Higgs field, the Higgs boson, was between about 114 and 180 gigaelectronvolts (GeV) 鈥� exactly the range in which the LHC is currently feverishly seeking the particle, with as yet only tantalising hints. The theory, though, made it something like a billion billion times bigger. This gigantic discrepancy came to be known as the hierarchy problem.

The only way to get rid of it was to jury-rig various crucial numbers that pop up within the standard model; numbers that fix, for example, the strengths of the electromagnetic and strong and weak nuclear forces that the theory describes. Set these numbers in the right way, and you can rein in the Higgs mass. Get it wrong, and the resulting theory has distressing consequences: particle masses, force strengths and the like all start going awry. 鈥淚t can completely destroy what we think of as the salient features of our universe,鈥� says theoretical physicist of the University of Maryland in College Park.

SUSY promised to clean up that mess. The price was a whole second set of particles, a heavier partner for each already known standard-model particle. Quarks have 鈥渟quark鈥� partners, the gluons that hold them together have partners called gluinos, and so on. The particle interactions that made the Higgs mass so outrageously large are neatly cancelled by opposing interactions between the Higgs field and these superpartners, elegantly disposing of the hierarchy problem.

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The simplest, most aesthetically pleasing forms of SUSY, 鈥渃onstrained minimal models鈥�, need just a few crucial numbers, or free parameters, to deliver testable predictions. One of these is that squarks have masses below 1000 GeV, or 1 teraelectronvolt (TeV), squarely in the LHC鈥檚 present-day energy range. Since the accelerator finally got going in March 2010 after a false start in September 2008, it has been operating at only half its design energy. Nevertheless, each head-on proton smash delivers 7 TeV of energy to be converted into new particles, so squarks should be produced in copious numbers. That led to a common presumption about supersymmetric particles among physicists working on the LHC: 鈥淚f SUSY exists, then when we turn on our detectors, they鈥檒l light up like Christmas trees,鈥� as of the 脡cole Normale Sup茅rieure in Paris, France, puts it.

鈥淚f supersymmetry exists, the particles should have lit up our detectors like Christmas trees鈥�

They didn鈥檛. No Christmas lights; not so much as a firefly flicker. What has gone wrong?

The no-show invites one of two conclusions. It could be that SUSY鈥檚 previously flawless countenance has some unexpected blemishes. That answer is favoured by many researchers, including CERN physicist , a member of the LHC鈥檚 collaboration. He points out that searches for supersymmetric particles at the LHC so far have concentrated on finding the 鈥渟top鈥�, the squark equivalent of the standard model鈥檚 top quark. Although the top quark is the heaviest one in the standard model, in most versions of SUSY, the stop is the lightest squark. Indeed, a stop mass of well below 1 TeV is in most cases a precondition for SUSY solving the hierarchy problem.

In 鈥減lain vanilla鈥� constrained minimal SUSY, the other squarks are not much heavier. All of them should be produced at the LHC, with the heavier ones decaying into the stop, resulting in a stop deluge that would be hard to overlook 鈥� exactly what hasn鈥檛 been seen.

That suggests a way forward to Padhi. 鈥淲e should try to get away from traditional constrained models,鈥� he says. SUSY doesn鈥檛 just come in vanilla but chocolate, pistachio, even chilli and garlic flavours: more complex, and perhaps less palatable variants that need more assumptions and free parameters to make them work. Some of these deliver higher values of squark and gluino masses in regions the LHC has not yet tested, while still giving a stop mass that is below 1 TeV. If these models are right, the LHC would have produced far fewer heavier squarks, or perhaps none at all. So, says Padhi, we just need to refine the stop search 鈥� looking, for example, for it being produced directly, rather than as a decay product of something heavier.

Radical colour

If only things were that simple, says , a theorist at Johannes Gutenberg University Mainz, in Germany. For a start, 鈥渨e will have to explain why the stop is much lighter than the other SUSY quarks, and that鈥檚 not so easy,鈥� he says. Suddenly, the talk is of fine-tuning a welter of free parameters in supersymmetric models to get the right results 鈥� just the fudge SUSY was designed to avoid. 鈥淚f you start making superpartners heavier, then SUSY starts looking more and more like the standard model,鈥� says Rychkov. 鈥淚t鈥檚 clear you are doing something that is anathema to the original motivation.鈥�

That invites a second, more radical conclusion. A makeover won鈥檛 do it: nothing can save SUSY. Already, some physicists are dusting off two old, largely discounted models that they think might just replace it.

The first is the brainchild of of the University of Texas, Austin, who won a share of a Nobel prize in 1979 for his work on the unification of the electromagnetic and weak nuclear forces, which was a crucial step towards the standard model. In the year of his award, working with of Stanford University, he suggested a radical way of getting round the hierarchy problem: you just get rid of the Higgs boson.

鈥淭here is a radical way of getting round the whole problem 鈥� just get rid of the Higgs boson鈥�

Weinberg and Susskind鈥檚 starting point was the humdrum proton. The proton is made of quarks bound together by gluons, which mediate the strong nuclear force, yet most of its mass comes not from the quarks but from the energy contained in the bonds between them. These 鈥渃olour interactions鈥� are the expression of the strong nuclear force at the low energies of today鈥檚 universe. If a similar mechanism had been at work at much higher energies in the early universe, Weinberg and Susskind reasoned, that could explain why elementary particles such as quarks themselves have mass, without ever mentioning the Higgs. It was a bright new prospect they dubbed 鈥渢echnicolor鈥�.

But it soon became clear that technicolor鈥檚 mathematics was so intractable as to make it extremely difficult to extract testable predictions from it. What鈥檚 more, the few it did make did not tally well with experimental results from the Large Electron-Positron Collider (LEP), CERN鈥檚 principal accelerator until 2001. Tweaks to the theory allayed some of those problems, but technicolor鈥檚 lustre soon faded. A different alternative was needed.

In the late 1990s Sundrum, together with of Harvard University, suggested one. The hierarchy problem has to do with the ballooning of the Higgs mass way beyond the masses of the other known particles, but it can be restated in another way: why is gravity, which is not covered by the standard model, so much weaker than the other forces? It is, for example, nearly 10³⁴ times punier than the electromagnetic force. If gravity were stronger, then particles that acquire their masses through the Higgs mechanism would be far weightier, and the hierarchy problem would melt away. Conversely, find a theory with an in-built explanation for why gravity is as weak as it is, and the problem dissolves.

Randall and Sundrum鈥檚 mathematics suggested a novel way to bring about the desired weakness: an unseen fifth dimension besides the four of our space and time. In this picture, we are rather like ants living on the two-dimensional surface of a piece of paper. They scuttle around unaware that their world also has an infinitesimally small third dimension, the paper鈥檚 thickness. Randall-Sundrum models suggested that the particles mediating gravity, gravitons, prefer to populate one side of a 5D universe 鈥� one side of a sheet of paper, if you will. Higgs bosons, meanwhile, hang out on 鈥渙ur鈥� side. This limits the interaction of gravitons with particles such as electrons and quarks that get their mass through the Higgs mechanism, and so gravity appears weak in our 4D approximation of space-time. In a full 5D view, meanwhile, it is just as strong as all the rest of the forces.

Quite apart from the complication of an extra dimension, it soon became clear that Randall-Sundrum models also had other difficulties that made them hardly viable. Like supersymmetry, the models predict that known particles have heavier counterparts 鈥� 鈥渞esonances鈥� from the higher dimension 鈥� but these would be at lower masses already ruled out by earlier colliders such as the LEP.

And so for want of any strong rival, supersymmetry has reigned supreme. Now, though, it鈥檚 in trouble. Hence the latest suggestion for a replacement: technicolor and Randall-Sundrum models together.

How so? It all goes back to the 鈥�AdS/CFT correspondence鈥�, a mathematical trick derived from string theory by physicist of The Institute for Advanced Study in Princeton, New Jersey, in 1997. It showed how an intractable theory of strong interactions in a four-dimensional space-time such as our own can be made a lot more tractable by adding an extra dimension.

Randall and Sundrum saw that this could form a bridge between their theory and technicolor. 鈥淲e were first to sense that there might be some connection, but I don鈥檛 think we knew what we were talking about in the slightest detail,鈥� says Sundrum. Soon after, Maldacena himself suggested a connection between the two theories, and others began eagerly to work out the details.

By 2001, they had largely been established. The most promising technicolor-like theory that hasn鈥檛 yet been ruled out by the data does not get rid of the Higgs entirely, but says it is not an elementary particle. Instead, it is a composite of other, new elementary particles, a 鈥渂ound state鈥� rather as a proton is really a bound bunch of quarks and gluons.

This theory is still unwieldly in its conventional, four-dimensional form. Malcadena鈥檚 correspondence provides a Randall-Sundrum analogue that is easier to deal with, but invokes a fifth dimension. Neubert thinks the mathematical link makes this less of a problem. 鈥淲hen people talk about these Randall-Sundrum models and say, 鈥榙o you really believe there is a fifth dimension?鈥� you can get two different answers,鈥� he says. 鈥淵es, you can have a fifth dimension. But you can also say that it鈥檚 a mathematical tool to describe technicolor theories. It鈥檚 one and the same thing.鈥�

You can see the attraction. After a year of smashing protons, the LHC has created neither supersymmetric particles nor much of a sign of a conventional Higgs boson. A workable theory such as technicolor that does without either suddenly becomes alluring.

And whether you take its four or five-dimensional variant, it makes predictions that the LHC should be able to test. The composite Higgs particle predicted by some technicolor-like models is thought to have a mass of between 115 and 145 GeV, within the LHC鈥檚 reach. It should be just a case of skewing the search to look for their decay products, rather than those of the conventional Higgs. The extra-dimensional models themselves predict heavier resonances of known particles with masses greater than 1 TeV. Finding any of these particles would be a big boost for such ideas.

Not that anything is a foregone conclusion. Fine-tuning will still be necessary to make any theory fit the data. And as Padhi points out, SUSY could make a comeback if the LHC finds a stop squark with a mass of less than 1 TeV, produced directly and not as a decay product of heavier squarks. 鈥淔rom an experimental point of view, whatever happens to fine-tuning, who cares,鈥� says Padhi. 鈥淲e have to make sure that we don鈥檛 miss something, whether the theory agrees or not.鈥�

Smoot thinks so too: the lesson is that researchers at the LHC need to cast their nets wider. 鈥淲e are led by theorists who, when they have no data鈥� lock into a beautiful model because it鈥檚 beautiful,鈥� he said in Grenoble.

The hope and expectation is that in the next year or so, CERN鈥檚 behemoth should find something 鈥� anything 鈥� that points the way towards a newer and bigger theory of matter. Every irregularity, every incongruity is eagerly pored over. Discoveries such as that last month of an unexpectedly large imbalance in particle decay rates at one LHC experiment, , have theorists sharpening their pencils with rival interpretations (麻豆传媒, 26 November, p 6). Is it SUSY? Or something else? With SUSY losing its claim to beauty, few certainties exist, and Huxley鈥檚 words might never have rung truer. Sundrum for one shrugs his shoulders. Whatever the LHC finds, he says, 鈥淚 ask only let it be interesting鈥�.