Electroweak Spontaneous Symmetry Breaking

The concept of spontaneous symmetry breaking is one of the fundamental ingredients of the electroweak SM, giving rise to Goldstone excitations that can be associated to the mass terms of the gauge bosons. This procedure, commonly known as the Higgs Mechanism, is one of the possible procedures to describe short-range weak interactions using a gauge theory without destroying their invariance.

In the SM, symmetry breaking takes place linearly by means of a scalar field that acquires a non-zero expected value in a vacuum. As a result of the process, not only do vector bosons as well as fermions acquire mass, but also a new physical neutral scalar field appears: the Higgs particle.

Alternatively symmetry breaking could be generated dynamically by new strong forces on the 1 TeV scale. However, no such valid model has yet been formulated that provides a satisfactory description of the fermionic sector and reproduces the high precision of electroweak measurements.

There are two basic concepts on which the “Standard Model” has been built, the theory that partially unifies the forces of nature. Such principles are:

1. Principle gauge; associated with mathematical symmetries.
2. Spontaneous breakdown of symmetry.

Spontaneous Symmetry Breaking

A common example in physics is a pencil balanced on its tip. It is symmetrical in the sense that as long as you balance on your toe, any direction is as good as any other; however, it is unstable. When the pencil falls, something that must inevitably happen, it will fall randomly, in one direction or another, breaking the symmetry, although the symmetry is still there, in underlying laws.

Laws only describe the space of what can happen; the real world governed by those laws supposes the choice of one realization among many possibilities. We exchange the unstable freedom of possibilities for the stable experience of reality.

The four forces

This mechanism of spontaneous symmetry breaking can occur to the symmetries between the particles of nature. When it happens to the symmetries that, according to the gauge principle, make the forces of nature appear, it leads to differences in their properties. The forces become differentiated, they can have different scopes and intensities.

Before the symmetry is broken, the four fundamental interactions have an infinite range, just like electromagnetism, but after the break, the range of some of them is finite, like the two nuclear interactions (strong and weak).

Gauge unification and symmetries

Physicists F. Englert and R. Brout, in Belgium, and a few months later Peter Higgs, in Scotland, independently proposed combining spontaneous symmetry breaking with gauge theories. The three also demonstrated the existence of another particle that is a consequence of spontaneous symmetry breaking, and which we call the “Higgs boson”.

In the spontaneous breaking of symmetry there is a physical quantity whose value tells us that the symmetry has been broken and how this breaking has been produced. This quantity is usually a field, called the Higgs field.

Natural laws

The use of spontaneous symmetry breaking in a fundamental theory would have profound implications, not only for the laws of nature, but also for the broader question of what a law of nature consists of.

Before it was believed that the eternal laws of nature directly determined the properties of elementary particles, however, in a theory with spontaneous symmetry breaking a new element appears: the properties of elementary particles depend in part on of history and environment.

Symmetry can be broken in different ways, depending on conditions such as density and temperature. Putting it more generally, the properties of elementary particles do not depend only on the equations of the theory, but also on which of the solutions to these equations is applicable to our universe.