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ELECTROWEAK PHASE TRANSITION

Under normal conditions, the electromagnetic force and the weak nuclear force have very different ranges. The electromagnetic force can be important over large distances, whereas the weak nuclear force is only effective on scales smaller than roughly 10-18 meters. This vast quantitative difference, between the two forces, which are fundamentally related, is due to electroweak symmetry breaking.

A standard physical example of symmetry breaking is a single magnetic domain of an isolated, idealized ferromagnet. The magnetic moments of the atoms in a ferromagnetic prefer to align with each other, producing a net magnetization of the domain. Nothing about the interactions between the magnetic moments prefers one direction of magnetization over another; yet, the atoms in a piece of ferromagnet randomly choose a direction in which to align. A person living inside the ferromagnet would think that one direction is different from the others; the alignment of the atoms has broken the symmetry between the directions. If you heat a ferromagnet, however, the magnetic moments of the hot atoms start to jiggle. The individual moments are no longer perfectly aligned, and so the net magnetization of the ferromagnet is less. As one increases the temperature, the disorder increases and the net magnetization drops further. There is a temperature (the Curie temperature) at which the individual moments jiggle so much that they become completely disordered and the net magnetization vanishes. The symmetry of directions is then restored—there is no longer a magnetization to pick out a direction. The cold, symmetry-broken (magnetized) behavior of the system, and the hot, symmetry-restored (unmagnetized) behavior of the system, are referred to as phases. The transition between them is an example of a phase transition.

Something analogous is predicted to occur in electroweak theory. If the temperature is high enough, the underlying symmetries relating the electromagnetic and weak forces are predicted to be restored. All the consequences of electroweak symmetry breaking, including the vast difference in ranges, disappear. The minimum temperature required for this restoration, and even whether there is a precise dividing temperature between the phases at all, depends on details of electroweak symmetry breaking (also known as the Higgs sector), not yet measured experimentally in 2002. However, the temperature is expected to be on the order 1015 K. Our universe was at that temperature approximately one billionth of a second after the beginning of the Big Bang.

One reason for interest in the electroweak phase transition is that it plays a pivotal role in one set of possible scenarios, known as electroweak baryogenesis, for explaining why there is vastly more matter than antimatter in the universe today (specifically, more baryons than antibaryons or, more fundamentally, more quarks than antiquarks). By theoretically tracing backward the history of the universe, one finds that, a millionth of a second after the Big Bang, there must have been almost as many antiquarks as quarks. But there was a slight imbalance: roughly, for every 30 million antiquarks, there were 30 million and one quarks. As the universe cooled, the quarks and antiquarks paired up and annihilated, leaving just that one part in 30 million excess of quarks to make up (with electrons) us, the Earth, and the stars. The goal for scenarios of baryogenesis is to find an explanation of the tiny early asymmetry between the numbers of quarks and antiquarks. Inspired by early investigations of the Soviet physicist Andrei Sakharov (1921–1989), three requirements have been distilled for any such explanation. First, it must be possible for the difference between the number of quarks and antiquarks to change with time, since otherwise the size of that difference is just an initial condition on the universe—an input into our theories of nature instead of an output. Such a change in the difference has never been observed experimentally, but is theoretically predicted to occur at temperatures above the electroweak phase transition. Second, the universe must be significantly out of equilibrium when the processes which effect such changes slow down and stop. (If allowed to change and equilibrate, the difference relaxes to zero.) Depending on the details of electroweak symmetry breaking, the electroweak phase transition may have been violent, providing this nonequilibrium. The hot symmetry-restored phase of electroweak theory might have experienced significant supercooling, ending with the formation of symmetry-broken-phase bubbles that violently expanded outward to fill the universe. Finally, there must be some difference between the behavior of matter and antimatter (known as violation of C and CP symmetry), since otherwise the rate for making a few extra quarks would equal the rate for making a few extra antiquarks, and no net asymmetry would develop. Electroweak interactions possess this difference, though whether strongly enough depends on details of electroweak symmetry breaking.

Bibliography

Cohen, A.; Kaplan, D.; and Nelson, A. "Progress in Electroweak Baryogenesis." Annual Reviews of Nuclear and Particle Science43 , 27–70 (1993).

Kolb, E. W., and Turner, M. S. The Early Universe (Addison-Wesley, Reading, MA, 1994).

Trodden, M. "Electroweak Baryogenesis." Reviews of Modern Physics71 , 1463–1500 (1999).

Peter Arnold