### A Nobel prizewinning physicist looks past the Higgs boson to dark matter, technicolour forces and WIMPs

by Steven Weinberg / November 16, 2011 / Leave a comment

*The moment of impact: protons collide within the Large Hadron Collider, creating over 100 charged particles*

Physicists working at the Large Hadron Collider at Cern are now engaged in a strenuous search for a particle of a new type, known as a Higgs boson. Much more is at stake in this search than the effort to add one more item to the quarks, electrons, and so on that make up the menu of known elementary particle types.

This is because the discovery of the Higgs boson would confirm a theory of how the symmetry between two of the fundamental forces of nature became broken, and how elementary particles get their masses. Not discovering it would be even more exciting, putting us back to work to understand all this. To explain what is at stake here, I first have to say something about what physicists mean by symmetries, and by symmetry breaking.

A symmetry of the laws of nature is a statement that the laws remain the same when we change our point of view in certain definite ways. A large part of the physics of the 20th century was devoted to the discovery of such symmetries. It started in 1905, when Einstein in his Special Theory of Relativity declared that all physical laws, including those that dictate the speed of light, remain the same when we change our point of view by viewing nature from a moving laboratory.

But the symmetries of the laws of nature are not limited to changes in the way we view space and time, as in Special Relativity. The laws of nature may also be unchanged when we replace various types of particles in our equations with other types of particles. For instance, there are two kinds of particles that make up atomic nuclei: protons and neutrons. In the 1930s it was discovered that the laws that govern the strong forces that hold these particles together in nuclei do not change their form if we replace protons with neutrons, or even replace protons (and neutrons) with a mixture, that might for example be 30 per cent proton (or neutron) and 70 per cent neutron (or proton).

It’s not that physicists in the 1930s knew the laws governing the strong nuclear force. The importance of symmetries is that we can learn about them from experiment, and use them to make new experimental predictions, even if we do not know the laws to which they apply.

For instance, even not knowing the nature of nuclear forces, physicists could infer from the proton-neutron symmetry that the energy of the lowest energy states of the nuclei of boron 12 and nitrogen 12 should be the same. It should also be the same as the energy of one of the excited states of carbon 12, because these three states can be converted into each other by changing protons and neutrons into *mixtures* of protons and neutrons. Symmetries are often invaluable clues to what is going on at a more fundamental level than we can otherwise approach.

In the early 1960s, theoretical physicists became excited by a new idea, that opened up the possibility that nature may obey a richer variety of symmetries than had previously been imagined. The idea was that the laws of nature, expressed as mathematical equations, might have symmetries that are not respected by physical phenomena, represented by solutions of these equations. In such cases, we say that the symmetries are broken—they may be exact properties of the laws of nature, but they are not immediately apparent in physical phenomena.

Broken symmetries do have physical consequences, just not easily-spotted consequences like those of the neutron-proton symmetry, which put physical particles or nuclear states in families of the same energy. In 1962 a theorem was proved by Jeffrey Goldstone, the late Abdus Salam, and myself, following earlier suggestions of Goldstone and Yoichiro Nambu, that deduced what seemed like a general consequence of broken symmetries. This theorem states that in any theory in which a symmetry like the proton-neutron symmetry is broken, there must exist particles with no mass or spin. Such new particles of zero mass were not known, and would not have escaped detection, because no minimum energy is required to create them, so this seemed to close off the possibility that nature actually obeys any broken symmetries.

The gloom lifted in 1964, when three groups of theorists independently pointed out an exception to our theorem. They were, in alphabetical order, Robert Brout and François Englert; Gerald Guralnik, Richard Hagen, and Thomas Kibble; and Peter Higgs (BEGHKH). They pointed out that the theorem of Goldstone and the others does not apply for a certain class of symmetries, known as local symmetries. For these symmetries, the transformations that leave the laws of nature unchanged can vary from point to point in space and time. To keep the equations unchanged under such transformations, theories with local symmetries must contain particles with zero mass and a certain definite amount of spin, equal to Planck’s constant.

The particle of light, the photon, is one such spinning massless particle. A large class of possible new local symmetries had been described a decade earlier by Chen-Ning Yang and Robert Mills, but these Yang-Mills theories had not yet found any application in realistic physical theories. What BEGHKH showed is that when a local symmetry is broken, the massless particles found by Goldstone et al are not realised as physical particles, but instead go to give mass to what would otherwise be the spinning massless particles of Yang and Mills.

None of the papers of BEGHKH proposed any specific realistic theory of particles and forces. In 1967 I was trying to work out a theory of the strong nuclear force, based on a broken local symmetry, without much success. At some point, I realised that I had been trying to apply good ideas in the wrong place. The right application was to the weak nuclear force, the force that allows a proton in a radioactive nucleus to turn into a neutron, or vice versa. The resulting theory turned out to be not just a theory of weak nuclear forces, but also of electromagnetism: the electroweak theory. That was of course very exciting. A little later pretty much the same theory was independently developed by Salam. Also, I found that Sheldon Glashow had explored this sort of theory, but without incorporating broken symmetry or Higgs bosons.

In the theory Salam and I developed, there is a local “electroweak” symmetry that if unbroken would require electrons, quarks, and the particles that carry the weak forces all to have zero mass. In the original version of this theory, there is also a quartet of fields, which would have zero values in empty space if the symmetry were unbroken. (Fields of this general type had already appeared in illustrative examples of local symmetry breaking presented by BEGHKH.) The electroweak symmetry is broken by the appearance of a non-zero empty-space value for one of these four fields. As a result, electrons, quarks, and the particles that carry the weak nuclear forces all acquire masses. Just one of the four spinless fields is manifested in this theory as a physical particle, an electrically neutral spinless particle, with interactions predicted by the theory but unfortunately with an unknown mass. This is the Higgs boson now being sought at Cern.

By now there is plenty of experimental evidence that nature really does have a broken local electroweak symmetry. New weak forces required by the theory were discovered at Cern in 1973. In 1984 the massive particles that carry the weak nuclear force were discovered, also at Cern, in both cases with just the properties predicted by the broken symmetry. What is not so clear is that the electroweak symmetry is broken in the way Salam and I described.

**Beyond the Higgs**

There are other possibilities. The symmetry may be broken by several quartets of spinless fields, in which case there would be several Higgs bosons, with complicated properties. A more radical possibility was suggested independently by Leonard Susskind and myself: the equations of the theory may involve no spinless fields at all. Instead, in addition to the known electroweak and strong nuclear forces, there would have to be even stronger “technicolour” forces, carried by particles that interact with the particles that carry the weak forces, and thereby break the electroweak symmetry. In this sort of theory there would be no Higgs bosons at all, but rather a whole zoo of new particles held together by the technicolour forces. One way or another, experiments at the Large Hadron Collider are going to settle the great outstanding question, of what breaks the electroweak symmetry and gives elementary particles their masses.

Important as that will be, even more exciting things may be discovered at the Large Hadron Collider. Astronomers have by now found several pieces of independent evidence showing that about five sixths of the mass of the universe consists of some sort of exotic “dark matter,” which is the dominant source of the gravitational fields of galaxies and clusters of galaxies, but otherwise interacts little if at all with ordinary matter. None of the particles in our present standard model of elementary particles (including the electroweak and strong nuclear forces) have the right properties to be the particles of dark matter. As one might have expected, various theorists have come up with various possible generalisations of the standard model, which contain candidates for the particles that make up dark matter.

Among the most promising of these candidates are WIMPs, or weakly interacting massive particles. These are particles that are individually stable, or at least can survive for billions of years, but that can annihilate each other in pairs, their energy turning into ordinary particles. The idea is that in the hot dense conditions of the early universe they would have been continually created and annihilated in pairs, until the expansion of the universe thinned them out so much that they could no longer find each other to annihilate.

We could calculate how many of these particles would survive to the present, if we knew their mass and how readily they annihilate each other. Or to put it another way, if we assume that these WIMPs make up the dark matter, and make a reasonable guess about how they annihilate each other, then we can calculate their mass. The so-called “WIMP miracle” is that their mass turns out to lie in the range of 10 to 100 times the mass of the proton, well within the range of masses that can be created at the Large Hadron Collider. So experiments at Cern may tell us what most of the universe is made of.