Hierarchy of effective field theories of hot electroweak matter

Abstract

A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over non-static modes leads to an effective theory containing a gauge field A a i , an adjoint Higgs field A a 0 and the fundamental Higgs field φ α . We carry out the integration in the 1-loop approximation, study renormalisation effects and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Secondly, because of the existence of well-separated thermal mass scales, A a 0 can be integrated over, and finally also φ α , leaving an effective theory of the A a i . 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.

Erratum to “Effective theories of MSSM at high temperature” [Nucl. Phys. B 481 (1996) 43–84]

“…Since there is also an arbitrary soft component in these terms [26] and since we assume the higgsinos to be so heavy that they have decoupled, the theory does in fact not depend at all on the true supersymmetric mass parameter µ. 12) where n F = 3 is the number of families and N s = 5 is the number of scalar doublets interacting with the SU(2) gauge fields. However, the couplings g 2 1 , g 2 2 , g 2 3 , g 2 4 = g 2 in the SU(2)-part of the scalar potential following from eq.…”

“…Perturbative studies exist up to 2-loop level [23,24,14,25]. Non-perturbative lattice studies rely on perturbative 2-loop dimensional reduction [12][13][14][15], and have been performed for a wide range of Higgs masses [18][19][20][21][22]. The Higgs mass bound in terms of the parameters of the 3d SU(2)+Higgs model was derived in [19].…”

“…The IR-problem calls for non-perturbative investigations of the problem. The method of choice for non-perturbative investigations is the framework of dimensional reduction [9][10][11][12][13][14][15][16][17]. Dimensional reduction means that one constructs an effective 3d theory producing the same Green's functions as the original theory for the light bosonic fields.…”

Gauge boson masses in the 3D, SU(2) gauge-Higgs model

“…The physics of the longest range fluctuations of the finite temperature electroweak theory is described by an effective 3-d theory which is matched to the complete model at the distance scale a ∼ (gT ) −1 [19,21,22,23]. Though this effective theory coincides formally with the superrenormalisable 3-d gauge-Higgs model, the optimal quantitative description of the original physics is expected to be obtained by choosing the lattice spacing according to Θ ≡ aT ∼ 1.…”

The electroweak phase transition at

“…The high-temperature limit of the 4-dimensional electroweak theory near the phase transition and for sufficiently large Higgs masses can be described by an effective 3-dimensional gauge-Higgs theory (for a discussion of high-temperature phase transitions see [1], for a general consideration of dimensional reduction see [2], for 3d EW theory see [3,4,5]). The effective theory is strongly coupled in the symmetric phase [6,7]; in particular, pure SU(2) gauge theory in 3d is confining.…”