Brout-Englert-Higgs physics: From foundations to phenomenology

The aim of this review is to describe the field-theoretical foundations of Brout-Englert-Higgs (BEH) physics, and to show how the usual phenomenology arises from it. This requires to give a precise and gauge-invariant meaning to the underlying physics. This is complicated by the fact that concepts like the Higgs vacuum expectation value or the separation between confinement and the BEH effect loose their meaning beyond perturbation theory. This is addressed by carefully constructing the corresponding theory space and the quantum phase diagram. The physical spectrum needs then to be also given in terms of gauge-invariant, i. e. composite, states. Using gauge-invariant perturbation theory, as developed by Froehlich, Morchio, and Strocchi, it is possible to rederive conventional perturbation theory. This derivation explicitly shows why the description of the standard model in terms of the unphysical, gauge-dependent, elementary states of the Higgs and W-bosons and Z-boson, but also of the elementary fermions, is adequate and successful. These are unavoidable consequences of the field theory underlying the standard model, from which the usual picture emerges. The validity of this emergence can only be tested non-perturbatively. Such tests, in particular using lattice gauge theory, will be reviewed as well. They fully confirm the underlying mechanisms. It will be seen that the structure of the standard model is very special, and qualitative changes occur beyond it. The extension beyond the standard model will therefore also be reviewed. Particular attention will be given to structural differences arising for phenomenology. Again, non-perturbative tests of these results will be reviewed. Finally, to make this review self-contained a brief discussion of issues like the triviality and hierarchy problem, and how they fit into a fundamental field-theoretical formulation, is included.

Comment: 116 pages, 19 figures, 1 table, v4: change of layout, added fully worked examples of gauge-invariant perturbation theory, other minor changes, version to appear in Prog. Part. Nucl. Phys. v3: added section on LSZ and asymptotic states, several minor changes, addition of references and further FAQs; v2: some added material and references, extended introduction, FAQ added, otherwise minor changes