Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism

Abstract

We apply the method proposed by Fröhlich, Morchio, and Strocchi to analyze the bound state spectrum of various gauge theories with a Brout-Englert-Higgs mechanism. These serve as building blocks for theories beyond the standard model but also stress the exceptional role of the standard model weak group. We will show how the Fröhlich-Morchio-Strocchi mechanism relates gaugeinvariant bound state operators to invariant objects of the remaining unbroken gauge group after gauge fixing. In particular, this provides a strict gauge-invariant formulation of the latter in terms of the original gauge symmetry without using the terminology of spontaneous gauge symmetry breaking. We also demonstrate that the Fröhlich-Morchio-Strocchi approach allows us to put new constraints on theories beyond the standard model by pure field-theoretical considerations. Particularly the conventional construction of grand unified theories has to be rethought. 3 We have chosen to decompose the Yang-Mills degrees of freedom at the level of the gauge potential A. This decomposition does generally not translate to the corresponding field strength tensors except for accidental cases. For instance, for the massive vector multiplet for the SO(N ) fundamental case, A f = Aφ 0 , and its field strength tensor F f , we obtain indeed F µν φ 0 ≡ F µν f

Testing the mechanism of lepton compositeness

“…That this is the case is a peculiarity of some theories like the standard model [15,29]. In generic theories, qualitative differences may already appear at leading order [10,11], as confirmed by lattice simulations [12][13][14].…”

“…The FMS mechanism manifests as a one-toone mapping between gauge multiplets and multiplets of an additional global SU (2) symmetry in the standard model. Qualitative differences occur in general non-Abelian gauge theories with a BEH mechanism already at tree-level in case global symmetries of the Higgs sector and the local gauge group are different [9][10][11]. Again, this has been quantitatively confirmed for the bosonic sector in lattice simulations [12][13][14], see Ref.…”

Gauge-invariant spectral description of the U (1) Higgs model from local composite operators

“…A standard way to cure this problem is to subtract from G(p 2 ) the first few (divergent) terms of its Taylor expansion at p = 0 [37], making the integral more and more convergent. These subtraction terms are directly related to the renormalization of the composite operators, and one can see that the modified Green's functions for the composite scalar field (38) and for the composite vector field (62) are in fact subtractions of the Taylor series to first and second order, respectively. In our theory we can make use of the subtracted equations at p = 0 because all fields are massive in the R ξ -gauge, so there are no divergences at zero momentum.…”

“…See also the recent work[38] for a discussion on higher dimensional gauge-invariant operators for different gauge groups and representations of the Higgs fields.…”

Spectral properties of local gauge invariant composite operators in the SU(2) Yang–Mills–Higgs model

“…denote the higher order loop corrections which will be the main subject of the present work. Equation 1shows in a very simple and intuitive way the relevance of the composite operators {Õ(x)} in order to provide a description of the gauge vector bosons and of the Higgs particle within a fully gauge invariant environment, see also the recent works [16][17][18][19] where, amongst other things, a lattice formulation has been proposed. Certain aspects of a gauge invariant version of the Higgs phenomenon were also covered in [20,21], albeit whilst assuming the "frozen" radial limit, ϕ † ϕ = fixed, corresponding to a Higgs coupling λ → ∞, a formal limit hampering explicit computations in the continuum.…”