Gaussian effective potential for the standard modelSU(2)×U(1)electroweak theory

Abstract

The Gaussian Effective Potential (GEP) is derived for the non-Abelian SU(2)×U(1) gauge theory of electroweak interactions. First the problem of gauge invariance is addressed in the Abelian U(1) theory, where an optimized GEP is shown to be gauge invariant. The method is then extended to the full non-Abelian gauge theory where, at variance with naive derivations, the GEP is proven to be a genuine variational tool in any gauge. The role of ghosts is discussed and the unitarity gauge is shown to be the only choice which allows calculability without insertion of further approximations. The GEP for the standard model is derived and its predictions are compared to the known phenomenology, thus showing that the GEP provides an alternative non-perturbative description of the known experimental data. By a consistent renormalization of masses the full non-Abelian calculation confirms the existence of a light Higgs boson in the non-perturbative strong coupling regime of the Higgs sector.

Gluon propagator in Feynman gauge by the method of stationary variance

“…(20). In this paper we will limit to the special case of Feynman gauge and take t µν = η µν in the calculation.…”

“…Quite recently, the method of stationary variance [10,11] has been advocated as a powerful second order extension of the Gaaussian Effective Potential (GEP) [12][13][14][15]. The GEP is a genuine variational method and has been successfully applied to many physical problems in field theory, from scalar and electroweak theories [15][16][17][18][19][20][21][22] to superconductivity [23][24][25] and antiferromagnetism [26], but turns out to be useless for gauge interacting fermions [27]. Actually, since the GEP only contains first order terms, it is not suited for describing the minimal coupling of gauge theories that has no first-order effects.…”

Analytic structure of QCD propagators in Minkowski space

“…Thus, while we are not changing the content of the theory, the emerging perturbative approximation is going to depend on the masses and can be optimized by a choice of m and M that minimizes the effects of higher orders, yielding a variational tool disguised to look like a perturbative method [47]. The idea is not new and goes back to the works on the Gaussian effective potential [49,[59][60][61][62][63][64][65][66] where an unknown mass parameter was inserted in the zeroth order propagator and subtracted from the interaction, yielding a pure variational approximation with the mass that acts as a variational parameter. The shifts δS q , δS g have two effects on the resulting perturbative expansion: the free-particle propagators are replaced by massive propagators and new two-point vertices are added to the interaction, arising from the counterterms that read…”

Variational quantum electrodynamics

“…Actually, for the simple theory of a self-interacting scalar field, the total effective potential V (2) is unbounded and has no stationary points [20], while the stationary conditions Eq. (12) have been shown to have a solution [22], since the variance is always perfectly bounded.…”

“…Unfortunately, a simple variational method like the Gaussian Effective Potential (GEP) [4][5][6][7], which has been successfully applied to physical problems ranging from scalar theory and electroweak symmetry breaking [7][8][9][10][11][12][13][14] to superconductivity [15][16][17] and antiferromagnetism [18], fails to predict nontrivial results for gauge interacting fermions [19]. Actually, the GEP only contains first order terms, and the minimal coupling of gauge theories does not give any effect at first order.…”