Weinberg angle

The Weinberg angle ( according to Steven Weinberg ) or electroweak mixing angle is defined by the mass ratio of the W and Z bosons:

According to the theory of the electroweak interaction he describes the relationship between the coupling strengths - that is, the units of the electric charge ( elementary charge ) and the weak charge - as follows:

Next apply:

Herein, the electrical and the weak coupling constant ( also known as the fine structure constant ). is the Weinberg angle. Is the current value, that is

Approximation, we obtain thus that the weak coupling twice as large is roughly like the electric:

The weakness of the weak interaction thus can not be explained on the coupling constant but via the propagator, in which the high mass of the exchange bosons of the weak interaction quadratically in the denominator.

Origin

Experimental ( Wu- experiment ) is at disposal of the weak interaction a fixed parity violation, which is explained by the VA theory. That is, the charged exchange bosons of the weak interaction and couple only to left-handed fermions. Furthermore, it is found that neutrinos in nature only handed occur ( Goldhaber experiment). If we introduce now a weak isospin one, the left-handed electron and neutrino form a weak isospin doublet ( ±), the right-handed electron a weak isospin singlet ().

If we now consider a reaction of the type

And calls for conservation of weak isospin, so must the exchanged boson - here - also bear a isospin. As a consequence, a weak isospin triplet consisting of ( sometimes referred to as ), and with coupling strength as well as a singlet with coupling strength results.

In the context of the electroweak unification and the photon are now exposed as overlay or mixed states represented from the unobservable particles and:

The call here the wave functions of the individual particles, which are thus related by the Weinberg angle. In this respect, the vineyard angle finds its definition. This results in the context of the coupling strengths, and that ultimately lead to the above relationship as well.

By the way, and are represented as the complex superposition of the non-observable particles and also:

For details, see The W, Z and photon (WP s)

Consequences

As a consequence of the mixing state and the Weinberg angle arises inter alia, that the coupling strength of the Z bosons not with that of the W bosons is identical. The coupling strength of the W f to a fermion is given by

The coupling strength of f at a fermion is, however,

The charge of the fermion is in units of the elementary charge. denotes the weak isospin ( third component), for left-handed neutrinos applies, for example. Right-handed neutrinos have and are thus not subject to the interactions of the standard model. They are therefore (in the framework of the standard model ) is not observable and it is therefore often said they would do in nature before ( what, as long as we remain in the standard model, no difference is ). See also Article ' Weak load '.

Experimental determination

The Weinberg angle can be determined experimentally determine, for instance according to the above definition of the mass ratio of the W and Z bosons. Other possibilities are determining the neutrino -electron scattering and electroweak interference in electron-positron scattering, that is, the mixing of the exchange of virtual photons and virtual particles.