Standard Model (mathematical formulation)

For a basic description, see the article on the Standard Model.

This is a detailed description of the standard model (SM) of particle physics. It describes how the leptons, quarks, gauge bosons and the Higgs particle fit together. It gives an outline of the main physics that the theory describes, and new directions in which it is moving.

It might be helpful to read this article along with the companion overview of the standard model.

A chiral gauge theory

The chirality projections of a Dirac field ψ are

:"Left" chirality:&nbsp;&nbsp;<math>psi_L = frac(1-gamma_5)psi</math>

:"Right" chirality:&nbsp;&nbsp;<math>psi_R = frac(1+gamma_5)psi</math>

where <math>gamma_5</math> is the fifth gamma matrix.

These are needed because the SM is a chiral gauge theory, i.e., the two helicities are treated differently.

This article uses the Dirac basis instead of the Weyl basis for describing spinors. The Weyl basis is more convenient because there is no natural correspondence between the left-handed and right-handed fermion fields other than that generated dynamically through the Yukawa couplings after the Higgs field has acquired a vacuum expectation value (VEV). In consulting common texts on the standard model one should expect to find the Weyl basis used.

Right handed singlets, left handed doublets

Under the weak isospin SU the left-handed and right-handed chiralities have different charges. The...
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