Gauge-invariant description of Gauge-Higgs systems: from spectrum to phase structure

Gauge theories supplemented with Higgs fields are at the cornerstone of the Standard Model. The spontaneous symmetry breaking of a 'global gauge symmetry' is the only known way to provide masses for elementary vector bosons, such as the W-, Z-bosons, that is consistent with both controllable high energy properties (renormalizability) and a physical probabilistic interpretation (unitarity). At first sight, the Higgs-Brout-Englert-Hagen-Guralnik-Kibble mechanism seems to be well-understood perturbatively: although one has to break the local gauge invariance to quantize the theory in a continuum formulation (i.e., by gauge fixing), one can use the celebrated BRST symmetry to establish the Nielsen identities that guarantee gauge parameter independence of physical observables. Unfortunately, gauge parameter independence is less strong than strict gauge invariance, and the Nielsen identities can even suffer from infrared singularities making them invalid. Even more disturbing is the explicit gauge dependence of the elementary Källén spectral functions, thence no sensible physics can be extracted from the latter, in sharp contract with gauge-invariant spectral functions studied in e.g. lattice QCD.We will use local composite operators to not only access the spectrum but also the phase structure (confining-like vs. fundamental Higgs-like behaviour) in an explicitly gauge-invariant fashion, whilst adding non-perturbative effects via dealing with the Gribov gauge fixing ambiguity.

Keywords:Gauge-Higgs systems., Gauge-invariant local composite operator, Confinement.

Disciplines:Field theory and string theory, Theoretical particle physics, High energy physics