Baggott J. The Quantum Story: A History in 40 Moments

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the quantum story

250

In frustration, they started to tinker with the model of four leptons

and three quarks, initially by adding more leptons. Eventually they hit

on the idea of adding a fourth quark. This was essentially a heavy version

of the up quark with spin-½ and charge +²⁄

. Glashow now recalled his

1964 paper with Bjorken, and proposed to call it the charm quark. Many

(though not all) of the unruly divergences disappeared.

They also realized that they had potentially solved another problem.

The introduction of a charm quark had switched off the weak neutral

currents. It turned out that the probability that a neutral kaon would

emit a Z

boson and transform into two oppositely charged muons was

almost equal to the probability that it would emit a Z

boson and become

a charmed particle, containing a charm quark. A difference in signs relat-

ing to these two possible decay paths meant that they virtually cancelled

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 romping ground for 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.

But then they realized that there were other ways that neutral kaons

could decay into two muons, mimicking neutral currents, that had noth-

ing to do with the Z

. The down quark in a K

kaon could be expected

to transform into an up quark with the emission of a W

−

boson. This

mirrors the process by which a neutron transforms into a proton in beta

radioactive decay. The up quark could then be expected to transform into

a strange quark with the emission of a W

particle. The two W bosons

would then combine through exchange of a muon neutrino to produce

two oppositely charged muons. The result looks just like a weak neutral

current.

Glashow, Iliopoulos, and Maiani now reasoned that the fact that this kind

of decay mechanism had not been seen in experiments was also evidence

for the charm quark. An equivalent mechanism involving a similar series of

transformations, from down to charm to strange, produced the same parti-

cles but cancelled the mechanism involving the intermediate up quark.

Excited by their discovery, the physicists piled into a car and headed across

to MIT and the ofﬁ ce of American physicist Francis Low, who had also been

of charm and weak neutral currents

251

working on the problem. Weinberg joined them and together they debated

the merits of the Glashow–Iliopoulos–Maiani (GIM) mechanism.

What followed was a spectacular breakdown in communication.

Almost all the ingredients for a uniﬁ ed theory of the weak and electro-

magnetic forces were assembled in the minds of the theorists gathered

in Low’s ofﬁ ce. Weinberg had ﬁ gured out how to apply spontaneous

symmetry-breaking using the Higgs mechanism in an SU(2) × U(1) ﬁ eld

theory of leptons, allowing the masses of the ﬁ eld particles to be deduced

rather than input by hand. Glashow, Iliopoulos, and Maiani had found a

potential solution to the problem of weak neutral currents in strange par-

ticle 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 ﬁ eld particles by hand and strug-

gling with divergences.

Glashow, Iliopoulos, and Maiani knew nothing of Weinberg’s 1967

paper, and Weinberg said nothing about it. He later confessed to a ‘psy-

chological barrier’ regarding the theory’s renormalisability. 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 collec-

tion of ‘charmed’ mesons and baryons. 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.

‘I do not care what and how,’ Dutch theorist Martinus Veltman told his

young graduate student Gerard ‘t Hooft early in 1971, as they walked

between buildings on the campus of the University of Utrecht, ‘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 ﬁ xed later by some model freak. In any

case, all possible models have been published already.’

‘I can do that,’ ‘t Hooft said.

Veltman, who had spent several years trying to ﬁ nd ways to renormal-

ize Yang–Mills ﬁ eld theories containing massive particles, almost walked

into a tree. ‘What do you say?’ he asked.

the quantum story

252

‘I can do that,’ ‘t Hooft replied.

‘Write it down and we will see,’ Veltman said.

In seeking a suitable topic for his doctoral thesis at Utrecht, ‘t Hooft

had identiﬁ ed Yang–Mills theories as fertile, if unfashionable, ground.

Veltman had picked up the challenge of renormalizing Yang–Mills the-

ories in 1968, and this was now a major preoccupation. ‘t Hooft had

worked quickly. He had learned about spontaneous symmetry-breaking

at a summer school in Cargèse, Corsica, in 1970 and by early 1971 had

shown that massless Yang–Mills ﬁ eld theories could be renormalized.

‘t Hooft’s conﬁ dence regarding the renormalizability of Yang–Mills

theories with massive particles was based on his understanding of what

spontaneous symmetry-breaking could do. Within a short time he had

indeed written it down.

Veltman was uneasy about the symmetry-breaking mechanism, a con-

cern he was later able to trace to its implications for cosmology.

They

argued back and forth. In the end, Veltman decided simply to accept

‘t Hooft’s results and ignore how he had arrived at them. He took the

results with him to CERN and checked them using a computer program

he had developed. He remained sceptical, but was soon calling ‘t Hooft

on the phone, declaring: ‘It nearly works. You just have some factors of

two wrong.’

But ‘t Hooft wasn’t wrong. Veltman had ignored a factor of four in

‘t Hooft’s equations that could be traced back to the Higgs boson. ‘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 was.’

It was a major breakthrough. ‘. . . the psychological effect of a complete

proof of renormalisability has been immense,’ wrote Veltman some years

later. ‘t Hooft had independently re-created the broken SU(2) × U(1) ﬁ eld

theory that Weinberg had developed in 1967, and had shown how it could

be renormalized. In fact, what ‘t Hooft had done was demonstrate that

In particular, he realized three years later that the Higgs mechanism had implications

for the cosmological constant. See Martinus Veltman, Nobel Prize lecture, 8 December 1999,

p. 392.

of charm and weak neutral currents

253

‘t Hooft admitted that: ‘My own paper said in a footnote that the anomalies do not render

the theory nonrenormalisable. Of course, this should be interpreted as saying that renormalis-

ability 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.’ See Gerard ‘t Hooft in

Hoddeson, et al., p. 192.

Yang–Mills gauge theories in general are renormalizable. Local gauge theo-

ries are actually the only class of ﬁ eld 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.’ Weinberg didn’t believe it, but when he

saw that fellow theorist Benjamin Lee was taking it seriously he decided

to look more closely at ‘t Hooft’s work. He was quickly convinced.

Now all the ingredients were available. A renormalizable, spontaneously

broken SU(2) × U(1) ﬁ eld theory of the weak and electromagnetic forces

was now at hand. The masses of the W and Z

bosons emerged ‘naturally’

from the operation of the Higgs mechanism. Anomalies that remained

could be removed by adding another quark using the GIM mechanism.

Weinberg carefully reconstructed the electro-weak theory towards the

end of 1971. Weak neutral currents in the decays of neutral kaons were

now supposedly ruled out by the GIM mechanism, but neutral currents

should still be seen in the interactions between muon neutrinos and pro-

tons. In such collisions, exchange of a virtual W

−

boson turns the muon

neutrino into a negative muon and the proton into a neutron—a charged

current. Exchange of a virtual Z

boson leaves both the muon neutrino

and proton intact—a neutral current. Weinberg now estimated that the

ratio of neutral to charged currents should be of the order of 0.14–0.33,

the lower limit of which he believed should be observable in neutrino

scattering experiments. The challenge for the experimental particle phys-

icists was to search for events in the scattering of muon neutrinos from

protons which did not involve the production of muons.

This was not as easy as it sounds. A muon neutrino does not leave a track

in a bubble chamber detector, so the only signature of a ‘muonless’ event

of the kind Weinberg was seeking would be a spray of hadrons appear-

ing in the detector seemingly out of nowhere. However, stray neutrons

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254

It was named for the mother of the giant Gargantua, from French Renaissance author

François Rabelais’ sixteenth-century novels The Life of Gargantua and Pantagruel.

chipped from atoms in the walls of the detector by the muon neutrinos

could also produce sprays of hadrons that could be easily mistaken for

muonless events. Worse, if a muon produced in a charged current event

was scattered with a large recoil angle, it could easily be missed, leading

to the possibility of misinterpretation as a neutral current event.

It might, perhaps, be easier to identify weak neutral currents in the

collision of a muon neutrino with an electron. Again, an exchange of a

virtual Z

boson would leave the neutrino and the electron intact, but

the result would be the sudden appearance of an energetic electron, spi-

ralling in the detector’s magnetic ﬁ eld. Again, no charged muon would

be produced. This was an event that was not so fraught with potentially

misleading signals, but it was also expected to be about two thousand

times rarer than equivalent events from the scattering of muon neutrinos

from protons.

But Weinberg had thrown down the gauntlet at a propitious time. The

world’s largest bubble chamber, dubbed ‘Gargamelle’, had been built in

France and installed at CERN in 1970, alongside the proton synchrotron.

It had taken six years to construct, and was designed speciﬁ cally for stud-

ying collisions involving neutrinos.

The simple truth was that if weak neutral currents occurred as fre-

quently as Weinberg suggested, then perhaps the evidence for them

existed in Gargamelle photographs that had already been taken. The

CERN physicists had been in the habit of dismissing low-energy events

as the result of stray neutrons. But as there was no way of knowing how

much collision energy was carried away by the unchanged muon neu-

trino, it was quite possible that some of the events were the result of

neutral currents.

French physicist Paul Musset spent nearly a year examining photo-

graphs in the basement scanning room with a team of CERN colleagues.

Early in 1972, the physicists believed they had found a single event: an

electron sent spinning out of a Freon molecule in the detector, dislodged

of charm and weak neutral currents

255

This was renamed the Fermi National Accelerator Laboratory (Fermilab) in 1974.

by an unseen muon neutrino. No charged muon was produced. This was

not an event that could be caused by a stray neutron, or a cosmic ray.

The CERN physicists were not alone. A team from universities in

Harvard, Pennsylvania, and Wisconsin were also on the trail of weak

neutral currents at the National Accelerator Laboratory (NAL)

in Chi-

cago, home of the world’s largest proton synchrotron, which achieved its

design energy of 200 GeV in March 1972. A team led by Italian physicist

Carlo Rubbia now sought evidence for weak neutral currents in colli-

sions of muon neutrinos with protons.

If it was a race, it was not without its moments of comedy. Rumours

bounced back-and-forth across the Atlantic. By August 1973 the CERN

group had identiﬁ ed muonless events in the collisions of muon neutri-

nos with protons and had estimated that the ratio of neutral to charged

current events is 0.21. For collisions involving muon anti-neutrinos, the

ratio was 0.45. The NAL group had found the combined ratio for both

neutrino and anti-neutrino collisions to be 0.29.

Rubbia’s visa expired in July 1973 and, despite holding a professorship at

Harvard, he was deported. The NAL physicists now began to back-track.

Concerned to prove that what they were observing were real neutral currents

and not experimental artefacts, the NAL physicists modiﬁ ed their detector.

The neutral currents promptly disappeared, with ratios of neutral to charged

current events falling as low at 0.05. When the CERN physicists heard about

this, they were greatly discomﬁ ted. Had they too been mistaken?

In fact, pions creeping in from other neutrino collisions had been misi-

dentiﬁ ed in the NAL detector as muons. When this was realized, the neutral

currents were restored. Some in the particle physics community began to

remark with amusement on the discovery of ‘alternating neutral currents’.

By April 1974, the confusion had cleared. Weak neutral currents were

an established experimental fact.

Now, the particle physicists wanted to know, why weren’t weak neutral

currents observed in strange particle decays? ‘I put them out of their mis-

ery and told them,’ said Glashow. ‘It was charm.’

Although the existence of quark–partons was implied by the phenomenon of scaling in

the deep inelastic scattering of electrons from nucleons, in the early 1970s the quark model

was still far from gaining wide acceptance. There were three obstacles.

The quarks were meant to be spin-½ fermions, and yet the model insisted that hadrons

should contain two or more quarks apparently in the same quantum state, in violation of

the Pauli exclusion principle. The proton, for example, was thought to consist of two up

quarks and a down quark. This was a bit like saying that an atomic electron orbit should

contain two spin-up electrons and one spin-down electron. It was just not possible. The

symmetry properties of the electron wavefunctions forbid it. There could be only two elec-

trons, one spin-up and one spin-down. There was no room for a third.

The phenomenon of scaling itself implied that the quarks inside protons and neutrons

acted like independent point-particles, almost as if they were free. How could this be? If,

as was reasonable to assume, the quarks were bound together by the strong, short-range

nuclear force, surely they must be held tightly together in the nucleon? It was difﬁ cult to

imagine a physical mechanism by which the quarks could be bound in the nucleon, yet free

to move around independently inside.

And ﬁ nally, irrespective of how free or tightly held the quarks were in the nucleon,

the deep inelastic scattering of electrons should surely have liberated them. Why weren’t

free quarks seen in the debris from such collisions? The complete absence of the expected

tell-tale tracks of fractionally charged particles was a major puzzle.

The Magic of Colour

Princeton/Harvard, April 1973

256

the magic of colour

257

The problem with the exclusion principle had been identiﬁ ed shortly after publica-

tion of Gell-Mann’s ﬁ rst quark paper. Whilst on leave from the University of Maryland,

physicist Oscar Greenberg had moved to the Institute for Advanced Study in Princeton.

He suggested in 1964 that quarks might be parafermions, which was tantamount to

saying that the quarks could be distinguished by other ‘degrees of freedom’ apart from the

one for which the quantum numbers were up, down, and strange. As a result there would

be different kinds of up quarks, for example. So long as they were of different kinds, two

up quarks could sit happily alongside each other in a proton without occupying the same

quantum state.

Yoichiro Nambu tried a similar scheme, suggesting that there should be three different

kinds of up quark (and three different kinds of down and strange quarks), each possessing

a new type of ‘charge’ that was different from electric charge. Confusingly, he called this

new type of charge charm. A young graduate student from Syracuse University in New

York, Korean-born Moo-Young Han, wrote to him in 1965 outlining much the same

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, as Nambu had thought to use

the opportunity to get rid of the fractional electric charges, introducing instead charges of

+1, 0 and −1 alongside the charm charge.

Nobody took much notice. However, in 1969 new experimental results on the decay of

neutral pions into two energetic photons were shown to be incompatible with the quark

model.

Speciﬁ cally, the decay rate predicted by the quark model was a factor of three too

small. Just as scaling promised to put quarks ﬁ rmly on the map, so anomalies in the decay

of neutral pions threatened to wipe them off again.

It was clear something had to be done. But Gell-Mann, recently returned from Stock-

holm where he had collected the 1969 Nobel Prize for physics, did not seem all that

concerned.

Harald Fritzsch was 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 ﬁ tted with an outboard

motor. They had travelled 200 miles down the Black Sea to Turkey.

Like the neutral kaon, the neutral pion evolves into a quantum superposition. It is formed

from the superposition of a state containing an up quark and an anti-up quark and a state con-

taining a down quark and an anti-down quark.

the quantum story

258

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. On his way

through America heading for SLAC in the summer of 1970 he encoun-

tered Gell-Mann at the Aspen Center for Physics in Aspen, Colorado.

Gell-Mann had retreated to Aspen with his family after, in typical style,

missing the deadline for submission of his Nobel Prize lecture for publi-

cation in the Swedish Academy’s Le Prix Nobel.

It was one among many

missed deadlines.

The Aspen Center was a peaceful place, where Gell-Mann would hike

in the nearby Rocky Mountains, relax, forget all about his work pressures,

and think only about physics. But Fritzsch was about to wake Gell-Mann

from his reverie. Fritzsch was a fervent believer in the quark model and

excited by what the SLAC results were beginning to reveal about scaling

and point-like quark–partons. He was surprised to ﬁ nd that Gell-Mann

was curiously ambiguous about his ‘mathematical’ creation.

It seemed that, even now, Gell-Mann had not grasped the full signiﬁ -

cance of his original proposal. As a student in East Germany, Fritzsch

had become convinced that quarks must lie at the heart of a quantum

ﬁ eld 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 ﬁ eld theory constructed from quarks.

When Fritzsch completed his graduate studies in early 1971, he trans-

ferred to Caltech. His arrival date, 9 February 1971, coincided with an

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.’

Results from SLAC on the ratio of neutron-to-proton deep inelastic

scattering events continued to point in the direction of quarks. The sci-

ence journalist Walter Sullivan wrote of the discovery in the New York

The Nobelprize.org website states ﬂ atly that: ‘Professor Gell-Mann has presented his Nobel

Lecture [on 11 December 1969], but did not submit a manuscript for inclusion in this volume.’

the magic of colour

259

Times in April 1971. He remarked: ‘Speciﬁ cally these ﬁ ndings suggest the

presence, in protons and neutrons, of points of electric charge that, in

several respects, resemble the elusive and long-sought quarks.’

Gell-Mann organized grants for himself and Fritzsch and in the

autumn of 1971 they both travelled to CERN. It was here that William

Bardeen, son of John Bardeen of the Bardeen–Cooper–Schrieffer theory

of superconductivity, told them about the anomalies in the decay of neu-

tral pions. Here was a direct experimental challenge to the original quark

model. The Han–Nambu model of integral-charged quarks actually did a

better job of predicting the decay rate.

Working together, Gell-Mann, Fritzsch, and Bardeen began to explore

the options. They wanted to see if it was possible to reconcile the results

on neutral pion decay with a model of fractionally charged quarks. They

tinkered with a parafermion model, before alighting on a variation of the

Han–Nambu idea.

They acknowledged that what they needed was a new quantum

number. Han and Nambu had used ‘charm’ but this was now associated

with Glashow’s hypothetical fourth quark. Instead, Gell-Mann decided to

call the new quantum number ‘colour’. This use of an abstract interpreta-

tion of colour was not a particularly new idea—Gell-Mann and Feynman

had in the past referred to different neutrinos as ‘red’ and ‘blue’, and other

physicists had used the term. In this new scheme, quarks would possess

three possible colour quantum numbers: blue, red, and green.

Baryons

are constituted from three quarks of different colour, such that their total

‘colour charge’ is zero and their product is ‘white’. For example, a proton

could be thought to consist of a blue up quark, a red up quark, and a

green down quark (u

). A neutron would consist of a blue up quark,

a red down quark, and a green down quark (u

). The mesons, such

as pions and kaons, could be thought to consist of coloured quarks and

their anti-quarks, such that the total colour charge is zero and the parti-

cles are also ‘white’.

In their original scheme Gell-Mann, Fritzsch, and Bardeen called them red, white, and blue

(inspired by the French national ﬂ ag). However, it soon became clear that the three primary

colours would work better as, when blended, they produce the colour white. To avoid confusion

I have adopted the currently accepted terminology from the outset.