Elementary Particles

8. SYMMETRY BREAKING

The secret of nature is symmetry, but much of the texture of the world is due to mechanisms of symmetry breaking.

— David J. Gross, Proceedings of the National Academy of Sciences of the United States of America, 14256–14259

I have made the case why symmetry is so fundamental in physics, but breaking of symmetry is no less important and leads to very important results.

As an example, consider a spinning coin which is an illustration of a perfect symmetry. Although the coin has two states, head and tail, neither state is revealed while spinning, yet both states exist. Symmetry is broken when the coin hits the floor—it’s either a head or a tail—releasing energy in the process (in form of sound that the coin emits on hitting the ground).

Physicists traditionally believed that the laws of nature should be perfectly symmetrical: the laws of physics should behave in just the same way in a mirror world just as they do in the normal world. This is the concept of mirror symmetry. As we have seen earlier, a similar symmetry involving matter and antimatter, known as charge symmetry, proclaims that particles should behave exactly like their anti-particle twin.

But charge symmetry seems to have been broken in the early universe and is the source of one of the great mysteries in physics. Why is the universe made up almost exclusively of matter, when matter and antimatter were created in equal proportions in the Big Bang? Most of the anti-matter seems to have miraculously disappeared since the Big Bang. So what caused nature to “favor” particles over antiparticles?

8.1 CHARGE-MIRROR SYMMETRY BREAKING (OR CP VIOLATION)

In 1967 by Nobel Laureate Andrei Sakharov described three minimum properties of nature that are required for the dominance of matter over antimatter. By then the first evidence of a broken symmetry had been provided in 1956 by two physicists, T.D. Lee and C.N Yang, who proposed experiments that exhibited a violation of mirror symmetry (or parity in more technical terms) in weak interactions and subsequently demonstrated by an experiment by Madam Wu and her team of physicists. As a result Lee and Yang won the 1957 Nobel Prize in Physics.

While mirror symmetry and charge symmetry could be broken separately, perhaps the combination of the two would remain unbroken: in a mirror world made of antimatter, the laws of physics would perhaps remain the same. But in 1964 this last citadel of symmetry was also shattered: James Cronin and Val Fitch detected a violation of charge-mirror symmetry (or CP violation) in the radioactive decay of strange particles known as kaons. They received the 1980 Nobel Prize in Physics for their work.

The discovery of CP violation implied that there is a deep-rooted difference between particles and anti-particles.

Two Japanese physicists, Makoto Kobayashi and Toshihide Maskawa, were the first to work out the mathematical theory of the origin of the broken symmetry that predicted the existence of at least three families of quarks in nature. They realized that CP violation could be explained via a six-quark model (or via three families of quarks). We have already seen the three families of quarks in the Standard Model table, now we know why. Once the families were incorporated in the theory, the underlying mathematics agreeably worked out to predict symmetry breaking. The hypothetical particles arising from their theory, known as charm quarks, bottom quarks and top quarks, were later observed in experiments. Kobayashi and Maskawa also predicted symmetry violation in other particles called B-mesons, and this was verified by experiment in 2001.

Kobayashi and Maskawa were the 2008 Nobel Laureates in physics.

8.2 SPONTANEOUS SYMMETRY BREAKING

Spontaneous symmetry breaking is a ubiquitous concept in modern physics.

Steven Weinberg defines spontaneous symmetry breaking in the following way. When a physical system does not exhibit all the symmetries of the laws by which it is governed, we say that these symmetries are spontaneously broken.

CChig5_01_08
Figure 8-1: IMAGE CREDIT: TAKEN FROM THE ARTICLE “ FROM BCS TO THE LHC” IN CERN COURIER BY STEVEN WEINBERG

A simple and intuitive description of the phenomenon of spontaneous symmetry breaking is often provided through the example of a ball on the top of the “Mexican Hat” (imagine that the symmetry-breaking field has a “Mexican-Hat Potential”). The initial state of the system is clearly symmetric under rotations about the vertical axis. Yet, the system is unstable, and the ball will eventually would roll down and stop somewhere on the brim of the hat. Since gravity acts only in the vertical direction, there is no predetermined direction for the ball to fall. In its final configuration, the system is stable, but does not possess its previous rotational symmetry. We say that the rotational symmetry is “broken” or “hidden” — in the brim things look dramatically different in different directions. The symmetry is still there, but it’s “nonlinearly realized”. The actual position of the ball in the brim is chosen randomly, and cannot be predicted by the theory.

There are various examples of the breaking of spontaneous symmetry in physics: superfluidity, superconductors, ferromagnetism, phase transitions, and crystal formation, to name a few. In the early universe, spontaneous symmetry breaking played a pivotal role. According to Alan Guth’s inflation model, phase transitions are thought to occur in the very early universe, many times, as the universe expanded and the temperature steadily tumbled. These phase transitions are linked to spontaneous symmetry breaking. In the process, first gravity, and then the strong nuclear force became distinct from the weak nuclear force and electromagnetism.

Yoichiro Nambu of the University of Chicago was the first to develop a mathematical mechanism for spontaneous symmetry breaking in particle physics (1960). The idea was borrowed from condense matter physics—the breaking of (electromagnetic) gauge symmetry in superconductivity by J. Bardeen, L. N. Cooper and J. R. Schrieffer (1957). Nambu’s work had profound consequences and played a fundamental role in the improvement of the Standard Model of elementary particles.

A consequence of spontaneous breaking of continuous symmetries is the existence of massless scaler particles (spin 0 particles) called Nambu-Goldstone bosons. Thus, while Nambu’s models gave masses to fermions, they also predicted a new massless boson particle that was not observed experimentally. It looked like a predicament at the time but physicists were able to circumvent the appearance of the massless Nambu-Goldstone bosons using a mathematical trick, called the Higgs mechanism. We will discuss Higgs mechanism and the prediction of the Higgs boson in the next Section.

Nevertheless, Nambu’s work on broken symmetry led to the creation of mass for fundamental particles. Broken symmetry is also the reason that separates the electromagnetic and weak forces. In fact, Nambu’s work was an important precursor to the theory that unifies electromagnetic and weak forces; his ideas form the basis for a whole body of work in physics and astrophysics. Nambu’s mathematical description of spontaneous symmetry breaking in 1960 has subsequently become a cornerstone of the Standard Model and earned him the 2008 Nobel Prize in physics.

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