Yoichiro Nambu toyed with a similar scheme, suggesting that there could be first two, then three different kinds of up-, down-, and strange-quarks. A young graduate student from Syracuse University in New York, Korean-born Moo-Young Han, wrote to him in 1965 elaborating this idea. Together they wrote a paper which was published later that year.
This was not a simple extension of Gell-Mann’s quark theory, however. Han and Nambu introduced a new type of ‘quark charge’ that was different from electric charge. The two up-quarks in the proton were now distinguished by their different quark charges, thereby avoiding conflict with Pauli’s exclusion principle. They reasoned that the force holding the quarks together inside the larger nucleons is based on a local SU(3) symmetry, not to be confused with the global SU(3) symmetry that lies behind the Eightfold Way.
They also decided to use this opportunity to rid the quark theory of its fractional electric charges, introducing instead overlapping SU(3) triplets with electric charges of +1, 0, and –1, alongside the quark charge.
Nobody took much notice. Han and Nambu had taken a big step towards the ultimate solution, but the world was not yet ready.
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Glashow finally returned to the problems of his SU(2)×U(1) electro-weak field theory in 1970, in the company of two Harvard postdoctoral associates, Greek physicist John Iliopoulos and Italian Luciano Maiani. Glashow had first met Iliopoulos at CERN and had been impressed with his efforts to find ways to renormalize a field theory of the weak force. Maiani arrived at Harvard with some curious ideas about the strength of weak-force interactions. All three realized that their interests converged.
At this stage none was aware of Weinberg’s 1967 paper applying spontaneous symmetry-breaking and the Higgs mechanism in an electro-weak theory of leptons.
Glashow, Iliopoulos, and Maiani now wrestled with the theory once again. Adding the masses of the W+, W−, and Z0 particles by hand produced unruly divergences in the equations that rendered the theory unrenormalizable. Then there was the problem of the weak neutral currents. For example, the theory predicted that a neutral kaon should decay by emission of a Z0 boson, changing the strangeness of the particle in the process and producing two muons – a weak neutral current. However, there was absolutely no experimental evidence for this decay mode. Rather than abandon the Z0 altogether, the physicists tried to work out why this particular mode might be suppressed.
The muon neutrino had been discovered in 1962, adding a fourth lepton alongside the electron, electron neutrino, and muon. The physicists started to tinker with the model of four leptons and three quarks, initially adding more leptons. But Glashow had actually published a paper in 1964 speculating on the possible existence of a fourth quark, which he had called the charm-quark. This seemed to make more sense. Nature would surely demand a balance between the numbers of leptons and the numbers of quarks. A model of four leptons and four quarks had a much more pleasing symmetry.
The theorists added a fourth quark to the mix, a heavy version of the up-quark with charge +. They realized that by doing this, they had switched off the weak neutral currents.
The weak neutral currents could arise through decays involving the Z0 and more complex decays involving emission of both W− and W+ particles. In both cases the end-result is the same – two oppositely charged muons, μ– and μ+. This latter decay path is depicted in Figure 15(a). Here, a neutral kaon (shown as a combination of down- and anti-strange-quarks) emits a virtual W− particle, and the down-quark (charge ) transforms into an up-quark (charge ). The virtual W− particle decays into a muon and muon anti-neutrino.
The resulting up-quark can then be thought to emit a virtual W+ particle, turning into a strange-quark in the process. The W+ particle decays into a positive muon and muon neutrino. This is referred to as a ‘one loop contribution’ to the net result, which involves decay of a neutral kaon into positive and negative muons.
FIGURE 15 (a) A neutral kaon decays into two muons through a complex mechanism involving emission of W− and W+ particles. There is no net change in charge and so this is a weak neutral current. (b) The decay path defined in (a) is cancelled out by this alternative decay path involving the charm-quark (denoted here by c).
There was, in principle, no reason why this example of a neutral current shouldn’t be observed. However, the common decay modes of neutral kaons produce pions, not muons. Somehow the decay path to muons was being suppressed. Glashow, Iliopoulos, and Maiani realized that an entirely analogous decay path involving the charm-quark would do the trick – Figure 15(b). A difference in signs relating to these two possible decay paths meant that they virtually cancel each other out. Caught like a rabbit in headlights, the neutral kaon can’t decide which way to jump, until it’s too late.
It was a neat solution. Kaons, the principal ground for experimental studies of weak-force interactions which should have exhibited weak neutral currents, almost never did so because of alternative decay modes involving the charm-quark.
Excited by their discovery, the physicists piled into a car and headed across to MIT and the office of American physicist Francis Low, who had also been working on the problem. Weinberg joined them and together they debated the merits of this new Glashow–Iliopoulos–Maiani (GIM) mechanism.
What followed was an extraordinary failure of communication.
Almost all the ingredients for a unified theory of the weak and electromagnetic forces were assembled in the minds of the theorists gathered in Low’s office. Weinberg had figured out how to apply spontaneous symmetry-breaking using the Higgs mechanism in an SU(2)×U(1) field theory of leptons, allowing the masses of the field particles to be calculated rather than input by hand. Glashow, Iliopoulos, and Maiani had found a potential solution to the problem of weak neutral currents in strange-particle decays and held out the promise that the SU(2)×U(1) theory could be extended to weak-force interactions involving the hadrons. But they were still inputting the masses of the field particles by hand and struggling with divergences.
Glashow, Iliopoulos, and Maiani knew nothing of Weinberg’s 1967 paper, and Weinberg said nothing about it. He later confessed to having a ‘psychological barrier’ against his earlier work, specifically in relation to the problem of demonstrating that the electro-weak theory could be renormalized.1 He also did not look kindly on the charm-quark proposal. What Glashow, Iliopoulos, and Maiani were invoking was not just one new particle, part of an extended family of particles of possibly dubious relevance, but an entirely new collection of ‘charmed’ baryons and mesons. If the charm-quark existed, then the Eightfold Way would simply be a subset of a much larger representation with many charmed members.
It was an awful lot to swallow just to explain the absence of weak neutral currents in strange-particle decays. ‘Of course, not everyone believed in the predicted existence of charmed hadrons,’ said Glashow.2
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There could be no further progress until someone was able to show that the Weinberg–Salam electro-weak theory could be renormalized.
Dutch theorist Martinus Veltman had studied mathematics and physics at the State University of Utrecht, becoming professor at the University in 1966. He began to work on the problems of renormalizing Yang–Mills field theories in 1968.
High-energy physics was not a popular subject for research in the Netherlands. This led to a certain sense of isolation. But this suited Veltman’s purposes, as it meant that he did not have to defend his choice of unfashionable research topics.
At the beginning of 1969 a young student, Gerard ’t Hooft, was assigned to him to complete a pre-doctoral thesis (known colloquially as a ‘scriptie’). Veltman shied away from getting his young student to work on Yang–Mills theories as he judged this subject too risky, and unlikely to lead to gainful employment. But after successfully completing his pre-doctoral thesis, ’t Hooft was offered a position at the University so that he could study for a PhD. ’t Hooft expressed a desire to continue working with Veltman.
Veltman still judged Yang–Mills field theories to be filled with dangers. He had made some considerable progress with renormalization, but the problem was extremely stubborn. But ’t Hooft felt strongly that this would prove to be fertile ground for his doctoral thesis. Veltman initially suggested an alternative topic, but ’t Hooft would not be diverted.
They were an unlikely pairing. Veltman’s was a larger-than-life, no-nonsense personality, proud of his achievements although indifferent to the physics community’s general lack of interest. ’t Hooft was slightly built and rather self-effacing, his modesty masking a mind of singular sharpness.
In his 1997 book In Search of the Ultimate Building Blocks, ‘t Hooft would introduce Veltman with an anecdote. One day Veltman entered an elevator that was already full. As the button was pressed, the elevator alarm warned that it was overloaded. All eyes turned to Veltman, relatively large of girth and one of the last to enter. But while others might have mumbled an embarrassed apology and stepped out, Veltman was having none of it. He understood Einstein’s equivalence principle, which underpins the general theory of relativity – if a person falls freely he will not feel his own weight. He knew what he needed to do.
‘When I say “yes”, then press!’ he exclaimed.3
He then proceeded to jump into the air. ‘Yes!’ he yelled.
Someone pressed the button, and the elevator began its ascent. By the time Veltman had returned to the floor, the elevator had picked up enough speed to continue its journey. ’t Hooft was in the elevator.
Sometime in the autumn or winter of 1970–71, Veltman and ’t Hooft were walking between buildings on the University campus.
‘I do not care what and how,’ Veltman told his student, ‘But what we must have is at least one renormalisable theory with massive charged vector bosons, and whether that looks like nature is of no concern, [those] are details that will be fixed later by some model freak. In any case, all possible models have been published already.’4
‘I can do that,’ ’t Hooft said, quietly.
Knowing full well the stubbornness of the problem, and that others – such as Richard Feynman – had tried, and failed, ’t Hooft’s declaration greatly surprised him. He almost walked into a tree.
‘What do you say?’ he asked.
‘I can do that,’ ’t Hooft repeated.
Veltman had been working on this problem for so long that he simply could not believe its solution was as easy as ’t Hooft was making out. He was understandably sceptical.
‘Write it down and we will see,’ he said.
But ’t Hooft had learned about spontaneous symmetry-breaking at a summer school in Cargèse, Corsica, in 1970. By late 1970 he had shown in his first paper that Yang–Mills field theories containing massless particles could be renormalized. ’t Hooft was confident that applying spontaneous symmetry-breaking would enable Yang–Mills theories with massive particles to be renormalized, too.
Within a short time he had indeed written it down.
Veltman was unhappy with ’t Hooft’s use of the Higgs mechanism. He was particularly concerned that the presence of a background Higgs field, pervading the entire universe, should reveal itself through gravitational effects.*
And so they argued back and forth. In the end, ’t Hooft decided to give his thesis advisor the results of his theoretical manipulations without showing explicitly where they had come from. Veltman knew well enough, but was content just to check the veracity of ’t Hooft’s results.
Some years earlier Veltman had developed a novel approach to performing complex algebraic manipulations using a computer program he called Schoonschip, ‘clean ship’ in Dutch.† This was one of the first computer algebra systems, able to manipulate mathematical equations in symbolic form. He now took ’t Hooft’s results with him to Geneva to check them on the CERN computer.
Veltman was excited but remained sceptical. Looking over the results as he set up his computer program, he decided to drop some factors of four that had appeared in ’t Hooft’s equations, factors that could be traced to the Higgs boson. He thought the factors of four were just crazy. He set up his program, and ran it without these factors.
He was soon calling ’t Hooft on the phone, declaring: ‘It nearly works. You just have some factors of two wrong.’5
’t Hooft wasn’t wrong. ‘So then he realized that even the factor of four was right,’ ’t Hooft explained, ‘and that everything canceled in a beautiful way. By that time he was as excited about it as I had been.’
’t Hooft had quite independently (and by sheer coincidence) re-created the broken SU(2)×U(1) field theory that Weinberg had developed in 1967, and had now shown how it could be renormalized. ’t Hooft had thought to apply the field theory to the strong force, but when Veltman asked a CERN colleague if he knew of any other applications of an SU(2)×U(1) theory, he was pointed in the direction of Weinberg’s paper. Veltman and ’t Hooft now realized that they had developed a fully renormalizable quantum field theory of electro-weak interactions.
It was a major breakthrough. ‘…the psychological effect of a complete proof of renormalizabiity has been immense,’ wrote Veltman some years later.6 In fact, what ’t Hooft had done was demonstrate that Yang–Mills gauge theories in general are renormalizable. Local gauge theories are actually the only class of field theories that can be renormalized.
’t Hooft was just 25 years old. Initially, Glashow didn’t understand the proof. Of ’t Hooft he said: ‘Either this guy’s a total idiot or he’s the biggest genius to hit physics in years.’7 Weinberg didn’t believe it, but when he saw that a fellow theorist was taking it seriously he decided to look more closely at ’t Hooft’s work. He was quickly convinced.
’t Hooft was appointed as an assistant professor at Utrecht.
Now all the ingredients were available. A renormalizable, spontaneously broken SU(2)×U(1) field theory of the weak and electromagnetic forces was now at hand. The masses of the W and Z0 bosons emerged ‘naturally’ from the application of the Higgs mechanism. Some anomalies remained, but ’t Hooft had pointed out in a footnote to his paper that these did not render the theory unrenormalizable. ‘Of course,’ he wrote years later, ‘this should be interpreted as saying that renormalizability can be restored by adding an appropriate amount of various kinds of fermions (quarks), but I admit that I also thought that perhaps this was not even necessary.’8
The anomalies that remained could be removed by adding more quarks to the model.
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What hopes now for a field theory of the strong force?
Gell-Mann collected the 1969 Nobel Prize for physics for his many contributions, most notably the discoveries of strangeness and the Eightfold Way. His achievements were listed in the ceremonial presentation speech, delivered by Ivar Waller, a member of the Nobel Committee for Physics. Waller also mentioned the quarks, explaining that, though eagerly sought, they had not been found. He graciously conceded that the quarks were nonetheless of great ‘heuristic’ value.
Gell-Mann had now to come to terms with the celebrity status bestowed upon Nobel Laureates. Inundated with requests to attend meetings and to submit papers, a writing process he had always found difficult now became impossible. He even missed the deadline for submission of his own Nobel Prize lecture for publication in the Swedish Academy’s Le Prix Nobel.* It was one among many missed deadlines.
In the summer of 1970 he retreated to Aspen, Colorado, with his family. But this was a retreat from commitments, not physics. They vacationed with the families of other physicists at the grounds of the Aspen Center for Physics.
The Center was tailor-made for Nobel Laureates seeking freedom from distraction. It had been established in 1962 by the Aspen Institute for Humanistic Studies following an approach from two physicists. Their idea was to create a facility that would offer a peaceful, relaxed, unstructured environment where physicists could escape the administrative demands of their day-to-day academic jobs and simply tal
k physics among themselves. The Institute set aside part of its Aspen Meadows campus, amidst a grove of aspen trees on the edge of the town.
It was in Aspen that Gell-Mann encountered Harald Fritzsch, a fervent believer in the quark model, astonished to discover that Gell-Mann was curiously ambivalent about his own ‘mathematical’ creation.
Fritzsch had been born in Zwickau, south of Leipzig in East Germany. Together with a colleague he had defected from Communist East Germany, escaping from the authorities in Bulgaria in a kayak fitted with an outboard motor. They had travelled 200 miles down the Black Sea to Turkey.
He had begun studying for a doctorate in theoretical physics at the Max Planck Institute for Physics and Astrophysics in Munich, West Germany, where one of his professors was Heisenberg. In the summer of 1970 he passed through Aspen on his way to California.
As a student in East Germany, Fritzsch had become convinced that quarks must lie at the heart of a quantum field theory of the strong nuclear force. These things were much more than mathematical devices. They were real.
Gell-Mann was impressed by the young German’s enthusiasm and agreed to have Fritzsch join him at Caltech, visiting about once a month. Together they began to work on a field theory constructed from quarks. When Fritzsch completed his graduate studies in West Germany in early 1971, he transferred to Caltech.
Fritzsch had triggered a small earthquake, shaking the foundations of Gell-Mann’s conservative attitude to the quarks. This was more than just a psychological earthquake: Fritzsch’s arrival at Caltech on 9 February 1971 coincided with a real earthquake that struck the San Fernando Valley early that morning near Sylmar, with a magnitude of 6.6 on the Richter scale. ‘In memory of that occasion,’ Gell-Mann later wrote, ‘I left the pictures on the wall askew, until they were further disturbed by the 1987 earthquake.’9
Gell-Mann organized grants for himself and for Fritzsch and in the autumn of 1971 they both travelled to CERN. It was here that William Bardeen, son of John Bardeen of the BCS theory of superconductivity, told them about some anomalies in the calculated decay rates of neutral pions. Bardeen had spent some time at Princeton working with Stephen Adler on this calculation. They had showed that the model of fractionally charged quarks predicted a decay rate which came out a factor of three too low compared with the measured value. Adler had gone on to show that the Han–Nambu model of integral-charged quarks actually did a better job of predicting the measured rate.
Higgs:The invention and discovery of the 'God Particle' Page 9