Mechanism of Higgs

In Physique of the particles the mechanism of Higgs , introduced by Peter Higgs in 1964, described a process by which a local Symétrie of the theory can be broken spontaneously while making massive its Boson S of gauge when a scalar Champ, called Boson of Higgs acquires a nonnull median value in the Vide.

Example: the électrofaible crack

Within the framework of the standard Modèle it is the mechanism of Higgs which breaks the électrofaible Interaction based on the Groupe of gauge $SU (2) \ times U (1) \,$ by giving a nonnull mass to several of these Bosons of gauge and more precisely the bosons W and Z whereas the Photon remains to him of null mass. Consequently the weak Interaction which is transported by bosons W and Z (and whose group of gauge is $SU (2) \,$ ) with short is carried (about 10^-18m) whereas the eletromagnetic interaction which is transported by the photon (and whose group of gauge is $U (1) \,$ ) is known as of infinite range what is a synonym to say that it is visible macroscopically. In an indirect way the mechanism of Higgs is also the source of the nonnull mass of all the Fermion S which compose the matter.

Motivations

The standard model rests mainly on the concepts of symmetry and invariance, in particular the invariance of gauge which generates the interactions. This invariance relates to in particular Lagrangian model, and interdict to introduce terms of mass for bosons of gauges, vectors of the interaction. However it is known today that some of its bosons (W and Z of the weak interaction) have a mass. The challenge thus consists in generating its terms of mass in the Lagrangian one while avoiding calling into question all this beautiful theoretical building.

Principles

The idea then consists in introducing a scalar field $\ phi$ particular, characterized by its potential, which is selected of kind to have a state of the vacuum not no one.

This scalar field is a doublet of $SU (2)$ , and the most general potential which are invariant and renormalisable which corresponds to him are

$V (\ phi^ \ dagger \ phi) = \ mu^2 \ phi^ \ dagger \ phi+ \ lambda (\ phi^ \ dagger \ phi) ^2$ ,

built using the invariant quantity $\ phi^ \ dagger \ phi$ , with $\ lambda$ necessarily positive since one wishes to have a state of the lowest energy.

In order to have the crack of sought symmetry, it is necessary to consider $\ mu^2<0$ , thus the state of the vacuum is not more invariant by rotation in $SU (2)$ .

With low energy, it is convenient to develop calculations around these minimas of energy. It is this development which is at the origin of the crack of symmetry, one considering only certain terms of order low.

The terms of masses appear then naturally.

Here, the two Lagrangian ones, before and after crack, are quite equivalent, and physics remains the same one. If one could solve exactly the dynamic equations before crack, one would have a dynamics with bosons without mass, but of which the interaction with the field of Higgs led to a behavior equivalent to that of massive bosons. The development around the vacuum simply makes it possible to reveal explicietment terms which have the good properties to be an interpreter like masses.

See too

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