Higher-dimensional routes to the Standard Model bosons

Physical Review D, 2003

We consider the possibility that the standard model Higgs fields may originate from extra components of higher dimensional gauge fields. Theories of this type considered before have had problems accommodating the standard model fermion content and Yukawa couplings different from the gauge coupling. Considering orbifolds based on abelian discrete groups we are lead to a 6 dimensional G 2 gauge theory compactified on T 2 /Z 4 . This theory can naturally produce the SM Higgs fields with the right quantum numbers while predicting the value of the weak mixing angle sin 2 θ W = 0.25 at the tree-level, close to the experimentally observed one. The quartic scalar coupling for the Higgs is generated by the higher dimensional gauge interaction and predicts the existence of a light Higgs. We point out that one can write a quadratically divergent counter term for Higgs mass localized to the orbifold fixed point. However, we calculate these operators and show that higher dimensional gauge interactions do not generate them at least at one loop. Fermions are introduced at orbifold fixed points, making it easy to accommodate the standard model fermion content. Yukawa interactions are generated by Wilson lines. They may be generated by the exchange of massive bulk fermions, and the fermion mass hierarchy can be obtained. Around a TeV, the first KK modes would appear as well as additional fermion modes localized at the fixed point needed to cancel the quadratic divergences from the Yukawa interactions. The cutoff scale of the theory could be a few times 10 TeV. * The result concerns pure gauge theories in the bulk. Once matter is introduced, in a supersymmetric context for instance, some gauge invariant quadratic divergences can be generated at orbifold fixed points . * There is another possibility that the rank of the unbroken gauge group is higher than two, while the unwanted part of the group breaks itself because of the anomaly . In this case, one needs to rely on the Green-Schwarz mechanism for anomaly cancellation in the full theory.

We incorporate the parameters of the gauge group G into the gauge theory of interactions through a non-linear partial-trace σ-model Lagrangian on G/H . The minimal coupling of the new (Goldstone-like) scalar bosons provides mass terms to those intermediate vector bosons associated with the quotient G/H , without spoiling gauge invariance, remaining the H -vector potentials massless. The main virtue of a partial trace on G/H , rather than on the entire G, is that we can find an infinite-dimensional symmetry, with non-trivial Noether invariants, which ensures quantum integrability in a non-canonical quantization scheme. The present formalism is explicitly applied to the case G = S U (2) × U (1), as a Higgs-less alternative to the Standard Model of electroweak interactions, although it can also be used in low-energy phenomenological models for strong interactions.

1998

A new method of deriving the Higgs Lagrangian from vector-like gauge theories is explored. After performing a supersymmetric extension of gauge theories we identify the auxiliary field associated with the "meson" superfield, in the low energy effective theory, as the composite Higgs field. The auxiliary field, at tree level, has a "negative squared mass". By computing the one-loop effective action in the low energy effective theory, we show that a kinetic term for the auxiliary field emerges when an explicit non-perturbative mechanism for supersymmetry breaking is introduced. We find that, due to the naive choice of the Kähler potential, the Higgs potential remains unbounded from the below. A possible scenario for solving this problem is presented. It is also shown that once chiral symmetry is spontaneously broken via a non-zero vacuum expectation value of the Higgs field, the low energy composite fermion field acquires a mass and decouples, while in the supersymmetric limit it was kept massless by the 't Hooft anomaly matching conditions. 11.30.Pb, 11.30.Qc

Classical and Quantum Gravity, 2009

involves the spacetime metric g_{mu nu} as well as the induced metric \bar{g}_{mu nu} proportional to \eta_{a b} \partial_{mu} \phi^a \partial_{nu} \phi^b where \phi^{a} (a=0,...,3), as we call it, break all four diffeomorphisms spontaneously via the vacuum expectation values < \phi^a > proportional to x^a. In this framework, we construct and analyze the most general action density in terms of various invariants involving the curvature tensors, connexion coefficients, and the contractions and the determinants of the two metric fields. We show that this action admits a consistent expansion about the flat background such that the resulting Lagrangian possesses several novel features not found in the linearized Einstein-Hilbert Lagrangian with Fierz-Pauli mass term (LELHL-FP): (i) its kinetic part generalizes that of LELHL-FP by weighing the corresponding structures with certain coefficients generated by invariants, (ii) the entire Lagrangian is ghost-- and tachyon--free for mass terms not necessarily in the Fierz-Pauli form, and, (iii) a consistent mass term is generated with no apparent need to higher derivative couplings.

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.

Physical Review D, 2011

New Massive Gravity provides a non-linear extension of the Fierz-Pauli mass for gravitons in 2+1 dimensions. Here we construct a Weyl invariant version of this theory. When the Weyl symmetry is broken, the graviton gets a mass in analogy with the Higgs mechanism. In (anti)de Sitter backgrounds, the symmetry can be broken spontaneously, but in flat backgrounds radiative corrections, at the two loop level, break the Weyl symmetry à la Coleman-Weinberg mechanism. We also construct the Weyl invariant extensions of some other higher derivative models, such as the Gauss-Bonnet theory ( which yields an interesting result especially in three dimensions ) and the Born-Infeld type gravities.

The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortunately, it does not come from a coordinate change in the configuration space of the initial model and actually defines a new dynamical system. So, it is a questionable approach to the problem but it is shown here that the final result could still make sense as a Marsden-Weinstein reduced system. (This reduction can be seen as completely analogous to the procedure of obtaining the &quot;centrifugal&quot; potential in the classical Kepler problem.) It is shown that in the standard linearization approximation of the Coulomb gauged Higgs model geometrical constraint theory offers an explanation of the Higgs mechanism because solving of the Gauss law constraint leads to different physical submanifolds which are not preserved by the action of the (broken) global U(1) group.

1998

We explore a novel way of deriving the effective Higgs Lagrangian from strongly interacting vectorlike gauge theories. We consider the N = 1 supersymmetric extension of gauge theories and interpret the auxiliary field associated with the low energy effective "meson" superfield as the Higgs field. By introducing an explicit supersymmetry breaking term and computing the one-loop effective action at the effective theory level we show that the kinetic term for the Higgs field is generated, while the negative mass squared term is already present at the tree level. We further propose a scenario by which the complete Higgs potential can be generated and the fermion in the low energy effective theory acquires a mass. Spontaneous symmetry breaking as described by the Higgs Lagrangian (linear σ-model) has always been the least appealing ingredient of the standard model. It is a wide spread hope that some new and more fundamental gauge dynamics could explain it. However it is in general very hard to show how the Higgs Lagrangian actually appears as a low energy effective theory. This problem would indeed require to solve the full strong coupling dynamics for gauge theories. In this letter we explore a new method which shows how the effective Higgs Lagrangian can emerge from gauge theories.

Journal of Physics A, 2010

We consider a diffeomorphism invariant theory of a gauge field valued in a Lie algebra that breaks spontaneously to the direct sum of the spacetime Lorentz algebra, a Yang-Mills algebra, and their complement. Beginning with a fully gauge invariant action-an extension of the Plebanski action for general relativity-we recover the action for gravity, Yang-Mills, and Higgs fields. The low-energy coupling constants, obtained after symmetry breaking, are all functions of the single parameter present in the initial action and the vacuum expectation value of the Higgs.

2004

We present a Higgsless Standard Model in six dimensions, based on the Standard Model gauge group SU(2)xU(1), with two flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by boundary conditions and realistic gauge boson masses can be accomodated by proper choice of the compactification scales and brane kinetic terms. With respect to oblique corrections, the agreement with electroweak precision tests is somewhat improved compared to the simplest five-dimensional Higgsless models.