Hierarchy of effective field theories of hot electroweak matter

A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over nonstatic modes leads to an effective theory containing a gauge field Aᵢᵃ an adjoint Higgs field A₀ᵃ and the fundamental Higgs field φₐ. We carry out the integration in the one-loop approximation, study renormalization effects, and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Second, because of the existence of well-separated thermal mass scales, A₀ᵃ can be integrated over, and finally also φₐ leaving an effective theory of the Aᵢᵃ. In the analysis of the subsequent models particular attention is paid to the screening of the magnetic fluctuations due to the integrated-out degrees of freedom.