Electroweak Interaction - Formulation

Formulation

Mathematically, the unification is accomplished under an SU(2) × U(1) gauge group. The corresponding gauge bosons are the three W bosons of weak isospin from SU(2) (W+, W0, and W−), and the B0 boson of weak hypercharge from U(1), respectively, all of which are massless.

In the Standard Model, the W± and Z0 bosons, and the photon, are produced by the spontaneous symmetry breaking of the electroweak symmetry from SU(2) × U(1)Y to U(1)em, caused by the Higgs mechanism (see also Higgs boson). U(1)Y and U(1)em are different copies of U(1); the generator of U(1)em is given by Q = Y/2 + I3, where Y is the generator of U(1)Y (called the weak hypercharge), and I3 is one of the SU(2) generators (a component of weak isospin).

The spontaneous symmetry breaking causes the W0 and B0 bosons to coalesce together into two different bosons – the Z0 boson, and the photon (γ) as follows:

\begin{pmatrix} \gamma \\ Z^0 \end{pmatrix} = \begin{pmatrix} \cos \theta_W & \sin \theta_W \\ -\sin \theta_W & \cos \theta_W \end{pmatrix} \begin{pmatrix} B^0 \\ W^0 \end{pmatrix}

Where θW is the weak mixing angle. The axes representing the particles have essentially just been rotated, in the (W0, B0) plane, by the angle θW. This also introduces a discrepancy between the mass of the Z0 and the mass of the W± particles (denoted as MZ and MW, respectively);

The distinction between electromagnetism and the weak force arises because there is a (nontrivial) linear combination of Y and I3 that vanishes for the Higgs boson (it is an eigenstate of both Y and I3, so the coefficients may be taken as −I3 and Y): U(1)em is defined to be the group generated by this linear combination, and is unbroken because it does not interact with the Higgs.

Read more about this topic:  Electroweak Interaction

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