Gauge Symmetry Breakdown due to Dyanamical versus Elementary Higgs (original) (raw)

Gauge Symmetry Breakdown due to Dynamical Higgs Scalar

Assuming dynamical spontaneous breakdown of chiral symmetry for massless gauge theory without scalar fields, we present a method how to construct an effective action of the dynamical Nambu-Goldstone bosons and elemetary fermions by using auxiliary fields. Here dynamical particles are asssumed to be composed of elementary fermions. Various quantities including decay constants are calculated from this effective action. This technique is also applied to gauge symmetry breakdown, SU (5) → SU (4), to obtain massive gauge fields.

Gauge Symmetry Breakdown due to Dynamical Higgs Scalar a

2000

Assuming dynamical spontaneous breakdown of chiral symmetry for massless gauge theory without scalar fields, we present a method how to construct an effective action of the dynamical Nambu-Goldstone bosons and elemetary fermions by using auxiliary fields. Here dynamical particles are asssumed to be composed of elementary fermions. Various quantities including decay constants are calculated from this effective action. This technique is also applied to gauge symmetry breakdown, SU(5)→SU(4), to obtain massive gauge fields.

Gauge and Higgs boson masses revisited

In this work, the mass of the Higgs boson is calculated, its comparison with the W and Z boson masses established, and the μ 2 and λ parameters of the Higgs potential are fixed. This is done by looking at the ground states of three and four dimensional harmonic oscillators, and getting inferences from the strong black hole as well the MIT bag model formalisms. An "exact" relationship linking the masses of these bosons, advanced by DNA Forrester, is also taken in account. The Standard Model (SM) of Particle Physics is a theory describing the visible part of the stuff of the universe [1]. The SM Lagrangian contains fermionic fields, which excitations are quarks and leptons, and bosonic fields the mediators of the interactions and having as excitations the photon, W and Z bosons, and gluons. However, in order to give leptons and quarks (current) masses, and also to give masses to the W and Z bosons of the weak interactions, these fermionic and bosonic fields must interact (couple) with another spin-zero field:-the Higgs field. The quantum excitation of the Higgs field produces a Higgs boson (please see: "Higgs boson" in Wikipedia [2], and references cited therein). The Higgs mechanism, indeed also proposed by Robert Brout and François Englert; Gerald Guralnik, C. Richard Hagen, and Tom Kibble; besides Peter Higgs himself, gives particles their masses (current masses in the quark case).[3,4,5].The Higgs mechanism works through the process called spontaneous symmetry breaking [6]. As was pointed out by Wilczek [7], the mass of the Higgs particle itself is not explained in the theory, but appears as a free parameter. Here we are going to focus on the Higgs and Electroweak sectors of the SM.

Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions

Physical Review D, 2007

We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral SU (2)L × U (1)Y theory. Within this model we demonstrate: (1) Strong Yukawa interactions between massless fermion fields and a massive scalar field carrying the axial charge generate dynamically the fermion and boson proper self-energies, which are ultraviolet-finite and chirally noninvariant. (2) Solutions of the underlying Schwinger-Dyson equations found numerically exhibit a huge amplification of the fermion mass ratios as a response to mild changes of the ratios of the Yukawa couplings. (3) The 'would-be' Nambu-Goldstone boson is a composite of both the fermion and scalar fields, and it gives rise to the mass of the axialvector gauge boson. (4) Spontaneous breakdown of the gauge symmetry further manifests by mass splitting of the complex scalar and by new symmetry-breaking vertices, generated at one loop. In particular, we work out in detail the cubic vertex of the Abelian gauge boson.

The breaking of chiral gauge symmetry

Physics Letters B, 1989

We consider the possibility that the lack of a chiral gauge symmetry-preserving regulator is signaling a genuine quantum effect which breaks the chiral gauge symmetry and generates mass for the gauge bosons. A nonperturbative analysis of an SU(3)cxSU(2)L>(U(l)v model regularized on a lattice is presented. Although both SU(2)L and U(1)r symmetries in this model are broken in the regularized action, SU (3)c X U (1)o symmetry can be maintained throughout the calculations. Using a hopping parameter expansion, the effective action for the gauge bosons is derived. Mass terms for the gauge bosons are generated, and the mass ratio of the gauge bosons is discussed.

Gauge theory of Lorentz group as a source of the dynamical electroweak symmetry breaking

Journal of High Energy Physics, 2013

We consider the gauge theory of Lorentz group coupled in a nonminimal way to fermions. We suggest the hypothesis that the given theory may exist in the phase with broken chiral symmetry and without confinement. The lattice discretization of the model is described. This unusual strongly coupled theory may appear to be the source of the dynamical electroweak symmetry breaking. Namely, in this theory all existing fermions interact with the SO(3, 1) gauge field. In the absence of the other interactions the chiral condensate may appear and all fermionic excitations may acquire equal masses. Small corrections to the gap equations due to the other interactions may cause the appearance of the observed hierarchy of masses.

Spontaneous Breaking of Global Gauge Symmetries in the Higgs Mechanism

Spontaneous Breaking of Global Gauge Symmetries in the Higgs Mechanism, 2024

The Higgs mechanism is invoked to explain how gauge bosons can be massive while Yang-Mills theory describes only massless gauge fields. Central to it is the notion of spontaneous symmetry breaking (SSB), applied to the SU(2) × U(1) gauge symmetry of the electroweak theory. However, over the past two decades, philosophers of physics have challenged the standard narrative of the Higgs mechanism as an instance of gauge symmetry breaking. They have pointed out the apparent contradiction between the status of gauge symmetries as mathematical redundancies and the account of mass generation in the Higgs mechanism by means of gauge symmetry breaking. In addition, they have pointed to Elitzur's theorem, a result from lattice gauge theory forbidding local gauge symmetry breaking. This has led philosophers to the conclusion that there cannot be any SSB in the Higgs mechanism, an idea supported by the dressing field method of gauge symmetry reduction. In this thesis we mitigate this conclusion by showing that global gauge symmetries, i.e. transformations independent of spacetime, are not mere mathematical redundancies but carry direct empirical significance. This can be seen from constrained Hamiltonian analysis by the fact that the Gauss constraint in Yang-Mills theory only generates gauge transformations which asymptotically become the identity. The classical Higgs mechanism can indeed be reformulated as a breaking of only this global gauge symmetry. We subsequently extend this result to quantum field theory by considering SSB in algebraic quantum field theory (AQFT). The Abelian U(1) Higgs mechanism can be shown to be an instance of SSB in the algebraic sense and we discuss the extent to which this can be generalised to the non-Abelian case. Finally we discuss the implications of our results for the interpretation of the electroweak phase transition and the analogy between the Higgs mechanism and superconductivity.

Dynamical breaking of chiral symmetry: A new mechanism

Physical Review D, 2008

We consider a U(1) gauge theory, minimally coupled to a massless Dirac field, where a higher-derivative term is added to the pure gauge sector, as in the Lee-Wick models. We find that this term can trigger chiral symmetry breaking at low energy in the weak coupling regime. Then, the fermion field acquires a mass that turns out to be a function of both the energy scale associated to the higher-derivative term and the gauge coupling. The dependence of the fermion mass on the gauge coupling is nonperturbative. Extensions to SU(N ) gauge theories and fermion-scalar interactions are also analyzed, as well as to theories with massive gauge fields. A few implications of these results in the framework of quark-mass generation are discussed. * Anyhow, one should keep in mind that for a generic SU(N ) gauge theory the fundamental scale Λ SU(N ) is a free parameter.

Gauge Symmetry Breaking: Higgs-less Mass Generation and Radiation Phenomena

2004

Gauge symmetries generally appear as a constraint algebra, under which one expects all physical states to be singlets. However, quantum anomalies and boundary conditions introduce central charges and change this picture, thus causing gauge/diffeomorphism modes to become physical. We expose a cohomological (Higgs-less) generation of mass in U(N)-gauge invariant Yang-Mills theories through non-trivial representations of the gauge group. This situation is also present in black hole evaporation, where the Virasoro algebra turns out to be the relevant subalgebra of surface deformations of the horizon of an arbitrary black hole.