chapter  21
8 Pages

The Standard Model

The standard model describes the electromagnetic and weak interactions, unified in the so-called electro-weak theory of Glashow-Weinberg-Salam with the gauge group U(1)× SU(2) and the strong interactions, known as quantum chromodynamics (QCD) with gauge group SU(3). Theory and experiment, where tested, agree very well up to about 100 GeV, the energies reached by present-day accelerators. Now that the top quark has been found, at a mass of 174 GeV, only the Higgs particle remains to be detected. Its mass should be smaller than 1000 GeV (i.e., 1 TeV = Terra electronvolt) according to presentday theoretical insight. Gravitation has been left out so far. Its natural scale in energy where quantum effects would become important is the Planck energy, E pl =

√ h¯c5/G ≈ 1019 GeV. It is very well possible that a number of the funda-

mental parameters in the standard model will be determined, either directly or indirectly, by gravitational interactions. The standard model should then be considered as an effective field theory. The theory for which the standard model describes its effective low-energy behaviour is called a unified theory. An intermediate stage, which does not yet include gravity is the so-called grand unified theory (GUT). The simplest version unifies the electro-weak and strong interactions using a gauge group SU(5) [which has U(1)×SU(2)×SU(3) as a subgroup], thereby reducing the number of free parameters considerably. These GUTs predict proton decay, albeit at the tremendously low rate of one decay in every 1030−31years. Nevertheless, a swimming pool of (10 m)3

contains enough protons to verify that the proton decay is slower than can be comfortably accommodated by GUTs. Candidates that unify the standard model with gravity in the form of string theories and supergravity have been unable to provide predictions that either rule them out experimentally or provide evidence in favour of these theories. Much is therefore still to be discovered, in particular because theoretical insight of the last ten years has shown that a Higgs field is most likely not fundamental, although it is not yet ruled out that it will show its structure only at Planck energies. If that is the case, the mass of the Higgs should, however, not be much bigger than 100 GeV.