Broken symmetries

Print edition : December 05, 2008

Yoichiro Nambu. He takes one half of the prize.-PETER THOMPSON/AFP

This years Physics Nobel goes to three physicists whose work sheds light on our understanding of the elementary particles of nature.

THREE physicists of Japanese origin share this years Nobel Prize in Physics: one half of the prize has gone to the 87-year-old Japanese-American Yoichiro Nambu of the University of Chicago for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics and the other half jointly to two Japanese physicists, 64-year-old Makoto Kobayashi of the High Energy Accelerator Research Organisation (KEK), Tsukuba, and 68-year-old Toshihide Maskawa of Kyoto Sangyo University, for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature.

What is broken symmetry and what does one mean by spontaneous broken symmetry?

Symmetries have an intrinsic beauty and aesthetic appeal about them we sense them in architecture, sculptures and shapes, for example. One might ask, well, why should it be so when most of the things around us are not symmetric? But, actually, many are almost symmetric, not perfectly though. Flowers, fruits, trees, animal forms, and so on do exhibit symmetry. There are reasons for this. Symmetry helps them grow. From the perspective of a blooming flower, for instance, all directions in space are identical. There is no reason for it to prefer one direction to another.

But a symmetric state need not always be the preferred state. A spinning top is in a perfectly symmetric state. There is perfect rotational symmetry. But it is an unstable state. The moment it stops, it falls down and points in an arbitrary direction in space, thus breaking the rotational symmetry. This phenomenon occurs in the description of physical systems at the microscopic level, too, though physicists have always looked for symmetries in their description of nature. Symmetry has an aesthetic value in physics as well. It simplifies notations and enables equations describing physical systems to be cast in elegant-looking compact forms that suggest unification of some kind. It also simplifies many awkward mathematical calculations and thus has a significant role in the mathematical description of the microscopic world.

More importantly, any underlying symmetry of a physical system implies the existence of a conservation law. For example, the fact that when two elementary particles collide and scatter (into two or more particles) the total initial energy is the same as the final energy is because of an underlying symmetry of invariance under time translation the physical process is the same whether it happens now or later of the equations of motion. Similarly, the conservation of electric charge is the consequence of a more subtle mathematical symmetry (called gauge symmetry) of Maxwells equations of electromagnetism.

While physicists did come across situations of broken symmetry in the early 20th century a crystal, for instance, is a state that breaks translational and rotational symmetry, or magnetised material one can say that the realisation that broken symmetries played a significant role in the description of the basic building blocks of matter and the interactions between them came some decades later. That was the period when attempts were afoot to evolve a unified theory of the fundamental particles and the forces of nature in one single mathematical structure.

Japanese scientists Makoto Kobayashi (right) and Toshihide Maskawa at a news conference in Tokyo on October 10. They share the other half of the prize.-DAVID GUTTENFELDER/AP

Initially, the only known particles were the proton, the neutron and the electron and the known forces of nature were the electromagnetic force and gravitation. Two additional forces became known, which also had to be incorporated: the weak nuclear force, which causes radioactivity and makes stars shine, and the strong nuclear force, which binds neutrons and protons inside the nuclei. But as experiments began to probe higher and higher energy domains, particle physics started becoming messy. Particles that physicists did not know how to fit into the known scheme of things proliferated.

The search for symmetries in this expanding zoo of particles led to the introduction of symmetries in abstract internal space unlike the more tangible symmetric operations in real space-time, such as rotations and translations. It also led to the consideration of more complex mathematical symmetries from global symmetries (symmetric operations that are same at every space-time point) to local symmetries (operations that vary from point to point). The latter are referred to as gauge symmetries. The simplest gauge symmetry is that associated with electromagnetism (called abelian gauge symmetry).

It also came to be realised soon that protons and neutrons were not elementary, that is, they were not the fundamental building blocks of matter, but that quarks (which, however, were not seen) were. Three quarks are needed to make up particles such as the neutron and the proton, which are called baryons, and a quark and an antiquark are needed to make up particles such as the pion, which are called mesons. It is also believed that the electron and its other cousins, collectively called the leptons, are not composite and are themselves elementary. Now, we also know why we do not see quarks. It is because of the more complex gauge symmetry (called non-abelian gauge symmetry) of the force of interaction between quarks, the manifestation of which is the strong nuclear force within nuclei.

But broken symmetries symmetries that are not exact were also part of this journey of discovery into the laws of sub-nuclear dynamics. In elementary particle theory, besides continuous symmetry operations such as rotations (in real space-time as well as in internal space), three symmetries that are discrete operations also play a very important role: mirror symmetry, or parity (P); charge symmetry (C); and time symmetry (T).

If there is mirror symmetry, all events of the microworld should occur in the mirror-reflected world in exactly the same way as in the real world. Charge symmetry implies that a particle and its antiparticle (which is identical except for its opposite charge) behave and interact identically. Similarly, time symmetry requires that an event forwards in time should be identical to one backwards in time.

The mirror of physics was shattered in 1956. The two Chinese-American physicists T.D. Lee and C.N. Yang (Nobel Prize, 1957) suggested that P-symmetry might be broken by the weak force. They said that even though in the macroworld nature seemed to respect mirror symmetry, in the quantum world it might be broken.

And soon enough, the landmark experiments of C.S. Wu involving the beta decay of cobalt-60 revealed that there was a distinct up-down asymmetry in the decay products (see figure), thus proving that mirror symmetry was indeed broken in weak interactions.

Around the same time, there was a conundrum involving the decays of particles called the neutral kaon (a particle with the quantum attribute called strangeness), which could be resolved only by postulating that C-symmetry was broken in nuclear weak interactions. However, the Russian physicist Lev Landau suggested that all was not lost as the combined operation of C and P restored the symmetry of weak interactions. That is, if you went to a mirror-reflected world where all matter was replaced by antimatter, all physical phenomena (of the microworld) would be the same.

But this reconciliation did not last very long either. In 1964, James Cronin and Val Fitch (Nobel Prize, 1980) found that a very small fraction of kaon decays violated the CP symmetry as well. Now, in quantum physics it is known that the combined operation of all three discrete symmetries (CPT) has to be strictly exact. So if CP is violated to a small degree, it is tantamount to time symmetry being broken by that much. (If you were to meet an alien and did not know whether the being was from a matter world or an antimatter world, it would be a good idea to compare data on kaon decays in the two worlds before proceeding to shake hands. Otherwise, if the alien happened to be from the antiworld, shaking hands would be catastrophic and result in the annihilation of both of you because particle and antiparticle would combine to end up in a puff of energy.)

In 1967, the Russian physicist Andrei Sakharov proposed three conditions for the currently observed matter-antimatter asymmetry in the universe the universe is predominantly made of matter only and one of them was that the laws of physics should distinguish between matter and antimatter. What the breaking of CP symmetry achieves is precisely that. That is, we now at least have a qualitative understanding of why there is matter-antimatter asymmetry in the universe. But whether the degree of CP violation in the currently accepted theoretical models of particle physics is of the right amount to explain the surplus matter that was created along with the Big Bang remains to be demonstrated.

The currently accepted successful model that unifies particles and forces in one theoretical framework is called the Standard Model. According to it, the fundamental building blocks of matter comprise three families (or generations) of particles. The first and the lightest family includes the stable particles that make up the cosmos we observe the proton (made of three quarks up, up and down), the neutron (made of three quarks up, down and down) and the electron. The particles of the remaining heavier families are unstable and decay immediately to the lighter kinds.

The Standard Model also includes three of the four known forces along with their carrier particles: electromagnetism is mediated by the photon, which has zero mass; the weak force is mediated by the heavy carriers W and Z bosons; and the strong force between quarks is carried by eight particles called gluons. The most familiar of the forces, namely gravity, is yet to be incorporated because a quantum description of the force continues to defy physicists, who hope that a higher-level theory such as supersymmetry or string theory will enable gravity to be unified with the others.

One of the problems that confront physicists in the context of the Standard Model today is the so-called hierarchy problem: Why do the particles have such different masses? And why are the forces so different? At present, physicists believe that this arises because the underlying symmetry of the Standard Model, which is a gauge symmetry more complex than the simple one of electromagnetism, is spontaneously broken. This spontaneous symmetry breaking (SSB) is achieved through a hypothetical Higgs field that filled the space in the early universe. This destroyed the original underlying gauge symmetry and gave mass to particles and force carriers. The differences in masses arose because of the varying strengths of their interactions with the Higgs field.

In quantum theory, every particle is associated with a field and vice versa. But the Higgs particle (which also gets mass because of the spontaneous breaking of symmetry) has never been seen. It is believed that because of its high mass it could not have been produced in existing particle accelerators and hence has not been seen yet. However, physicists hope that if it exists, it should be produced at the Large Hadron Collider (LHC) at CERN (European Organisation for Nuclear Research), which was commissioned in September.

It was Yoichiro Nambu who introduced the concept of SSB in elementary particle physics, for which he has been chosen for this years Nobel award. In 1956, John Bardeen, Leon Cooper and Robert Schrieffer (BCS) found the long-sought theory to understand the puzzle of superconductivity (Nobel Prize, 1972), a mechanism by which electricity suddenly begins to conduct with zero resistance in certain materials under certain conditions. They showed that in the quantum domain lattice vibrations caused electrons to overcome the electrostatic repulsion between them and combine to form bound states, called Cooper pairs. Nambu tried to understand the BCS theory in terms of the breaking of the gauge symmetry of electromagnetism. It took two years for him to solve this problem. Through this formulation, he discovered SSB in the language of quantum field theory used in particle physics.

Nambu realised the crucial fact that for SSB to occur the properties of the vacuum, or the ground state of the theory, were important. He observed that in SSB, while the fundamental equations respected a symmetry, the ground state need not. In superconductivity, he showed that the vacuum was a charged state, with a charge of -2, formed by the condensation of Cooper pairs and was not an empty state with zero charge. This broke the gauge symmetry of electromagnetism. The really bold assumption that Nambu made in 1960 was to extend the idea that SSB could also exist in theories of elementary particles. (The term spontaneous symmetry breaking, says Nambu, is not a succinct one. But it has stuck for lack of a better one.) It is the mathematical tools that he developed in this context that have found applications in the Standard Model and in the Higgs mechanism.

In elementary particle theory, the vacuum was hitherto similarly assumed to be empty apart from quantum fluctuations. Nambu introduced the concept that there could be situations where the vacuum is not empty, with certain quantum fields having non-zero values analogous to the superconductivity case. In two landmark papers with Giovanni Jona-Lasinio, he established a solid theoretical framework to his ideas. He showed that when the symmetry was spontaneously broken, the particle spectrum of the theory must include a massless particle, which has come to be called the Nambu-Goldstone boson. Further, if the symmetry that was broken was a gauge symmetry, the Nambu-Goldstone boson became massive.

Now, in the light shed by Nambu, we can understand the Standard Model. The Higgs field breaks the gauge symmetry of the vacuum, and as a result we have a massive Higgs particle, which the particle physics community expects to detect with the new LHC. It is thought that at the time of the Big Bang, the universe (and the vacuum) was perfectly symmetrical. But the Higgs field, like the spinning top, was not in a stable configuration. So, as the universe cooled down, the Higgs field dropped to its lowest energy level, the stable state, which, however, broke the symmetry. The Higgs field became a kind of all-pervading moss, different amounts of which stuck to different particles to give them varying masses, as John Ellis of CERN explains the Higgs phenomenon in lay language.

There is, however, an important difference between the BCS theory of superconductivity and the Standard Model in particle physics. In the latter case, the symmetry-breaking Higgs field occurs as a hypothetical external input into the total energy of the system. In the former, on the other hand, the symmetry-breaking Cooper pairs arise as a consequence of the internal dynamics of the system. While the Higgs case is referred to as SSB, the BCS case is often called dynamical symmetry breaking (DSB). In Nambus view, however, both are the same. In my opinion, symmetry breaking is always a dynamical question, Nambu has said. Thus, a BCS theory and a Higgs theory can be equivalent.

According to Nambu, the Standard Model is only an intermediate theory, at the level of the phenomenological Ginzburg-Landau theory of superconductivity (formulated in 1950), which preceded the BCS theory. The BCS equivalent is yet to be found, he says. He has, however, postulated that, the Standard Model could be a phenomenological representation of BCS-like dynamics involving a condensate of a bound state of the top quark and its antiquark (analogous to the bound state of electrons, the Cooper pairs, in the BCS theory). The top quark (the heaviest of the quarks), according to Nambu, has the right order of high mass (about 175 giga electronvolt, or GeV) for the bound state to act like the Higgs that the Standard Model requires and be able to give the right masses to the various particles.

I too believe that the spontaneous symmetry breaking may not be because of the Higgs particle, says G. Rajasekaran of the Institute of Mathematical Sciences in Chennai. Nambus top quark condensate is one way [of realising SSB] and there are other ways, points out Rajasekaran, who himself suggested way back in 1971 another dynamical mechanism. However, the Higgs way is the simplest and most straightforward, and nature might have chosen it, he adds. Of course, seeing signatures of a Higgs-like particle at LHC energies will not tell us whether the Higgs particle is elementary or composite a la Nambu. This may, however, get resolved only at still higher energies. But for either picture of symmetry breaking, not finding a Higgs-like signal at all will definitely be a setback for the Standard Model.

Though the breaking of CP symmetry, required for our existence in the matter-dominated world as posited by Sakharov, and seen experimentally as well, should have also existed from the time soon after the birth of the universe, its origin would seem to be different from the SSB by the Higgs field at least given our present understanding within the context of the Standard Model. But an explanation of even that small degree of CP violation in kaon decays had to be somehow incorporated into the Standard Model. This is where the work of the other two Nobel laureates comes in.

In 1959, when large particle accelerators came into operation and a lot of data on weak particle decays were obtained, Nicola Cabibbo, an Italian physicist, made an important contribution to providing a consistent picture. In 1963, he proposed that in the internal abstract symmetry space, the weak interaction was tilted by an angle with respect to the strong interaction and to electromagnetic interactions. Of course, at that time quarks had not yet been postulated.

The first steps towards the Standard Model were then taken in 1970 in the form of the Glashow-Salam-Weinberg unified model, which had only three quarks as originally proposed by Murray Gell-Mann and George Zweig in 1964. However, this model predicted certain particle interactions that had not been seen. To solve this, S.L. Glashow, J. Iliopoulos and L. Maiani hypothesised the existence of another quark, called charm. With this additional quark, not only were two complete families of quarks obtained but also the unwanted reactions could be suppressed in a natural way by extending the Cabibbo tilt to two dimensions. This was achieved by applying the Cabibbo tilt as a two-dimensional rotation on all the four particles through a 2 2 matrix. The existence of charm was confirmed in 1974. This also tied up neatly with the two known families of leptons the electron and the muon families .

How does this double broken symmetry (of CP) occur? Each kaon is a combination of a quark and an antiquark. The weak force repeatedly flips a quark into an antiquark and vice versa, thus transforming a kaon into an antikaon time and again. In this way, the particle flips between itself and its antiself. But if there is CP violation, however minute, the symmetry between matter and antimatter will be broken at some point.

In 1972, Kobayashi and Maskawa (KM) investigated what kind of particle structure could accommodate the breakdown of CP symmetry. However, the above two-family structure, they found, could not accommodate the observed CP violation. They, therefore, extended the particle structure to three families and applied the Cabibbo rotation on all the six particles using a 3 3 matrix. It turned out that a minimum of three families (or six quarks) would be required to accommodate a CP-violating parameter in the rotation matrix. After the discovery of a third lepton in 1977, the Kobayashi-Maskawa idea was picked up as it could be naturally accommodated as the lepton of the third family. But, of course, the KM model predicted the existence of two more quarks. The bottom quark was discovered in 1977 and the top one in 1994.

Our work consists of two parts, pointed out Kobayashi in his post-award interview. One is [that] four quarks is [sic] not enough to explain the CP violation. And it is quite a logical consequence of the argument. But the second point is then that what kind of new particles can explain. And there are quite many possibilities logically. But six quarks came as one possibility. So, in that sense, we were confident about the first part. But the second part was quite uncertain at that time but gradually we came to believe that this is actually the case.

In 1964, under the assumption that CP violation was exclusive to kaons alone, Lincoln Wolfenstein proposed a mechanism. But if the Cabibbo-Kobayashi-Maskawa (CKM) mechanism is at work, then CP symmetry should be broken more strongly in bottom particles, the heavier cousins of kaons. This led to the setting up of the so-called B Factories, the BaBar detector at SLAC National Accelerator Laboratory at Standford and the Belle detector at KEK, capable of producing more than one million B mesons a day. In 2001, both the experiments confirmed the symmetry violation in B mesons in remarkable agreement with the CKM model that had predicted it 30 years earlier.

The Kobayashi-Maskawa explanation of the breaking of CP symmetry is, however, still only a parametrisation technique based on Cabibbos original idea. It is yet to be described in the more fundamental terms that someone like Nambu would approve of. The Kobayashi-Maskawa work nevertheless completes the major missing piece in the Standard Model. But, by ignoring Cabibbo, the Nobel award has left behind an unwarranted controversy. Indeed, the Italian National Institute for Nuclear Physics has expressed its bitterness about the omission.

The Nobel Committee has freed itself from this criticism by associating KMs work to the understanding of the origin of broken CP symmetry, which Cabibbos work had nothing to with, says Rajasekaran. However, the critics do have a point since Cabibbos contribution is of fundamental importance. The fact that it is called the CKM matrix shows how intricately connected the ideas of Cabibbo and KM are, he adds.

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