Higgsless Standard Model in Six Dimensions

2004

We present a Higgsless Standard Model in six dimensions, based on the Standard Model gauge group SU(2)L × U(1)Y, with two flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by (mixed) boundary

Physics Letters B, 2004

We present a six-dimensional Higgsless Standard Model with a realistic gauge sector. The model uses only the Standard Model gauge group SU(2) L × U(1) Y with the gauge bosons propagating in flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by boundary conditions, and the correct splitting between the W and Z gauge boson masses can be arranged by suitable choice of the compactification scales. The higher Kaluza-Klein excitations of the gauge bosons decouple from the effective low-energy theory due to dominant brane kinetic terms. The model has the following two key features compared to five-dimensional models. The dimensional couplings in the bulk Lagrangian, responsible for electroweak symmetry breaking using mixed boundary conditions, are of order the electroweak scale. Moreover, with respect to "oblique" corrections, the agreement with the precision electroweak parameters is improved compared to five-dimensional warped or flat space models. We also argue that the calculability of Higgsless models can be ameliorated in more than five dimensions. †

Nuclear Physics B, 2003

We construct realistic theories in which the Higgs fields arise from extra dimensional components of higher dimensional gauge fields. In particular, we present a minimal 5D SU (3) C ×SU (3) W model and a unified 5D SU (6) model. In both cases the theory is reduced to the minimal supersymmetric standard model below the compactification scale, with the two Higgs doublets arising from the 5D gauge multiplet. Quarks and Leptons are introduced in the bulk, giving Yukawa couplings without conflicting with higher dimensional gauge invariance. Despite the fact that they arise from higher dimensional gauge interactions, the sizes of these Yukawa couplings can be different from the 4D gauge couplings due to wave-function profiles of the matter zero modes determined by bulk mass parameters. All unwanted fields are made heavy by introducing appropriate matter and superpotentials on branes, which are also the source of intergenerational mixings in the low-energy Yukawa matrices. The theory can accommodate a realistic structure for the Yukawa couplings as well as small neutrino masses. Scenarios for supersymmetry breaking and the µ-term generation are also discussed.

Nuclear Physics B, 2006

We reconsider the idea of identifying the Higgs field as the internal component of a gauge field in the flat space R 4 × S 1 /Z 2 , by relaxing the constraint of having unbroken SO(4,1) Lorentz symmetry in the bulk. In this way, we show that the main common problems of previous models of this sort, namely the prediction of a too light Higgs and top mass, as well as of a too low compactification scale, are all solved. We mainly focus our attention on a previously constructed model. We show how, with few minor modifications and by relaxing the requirement of SO(4,1) symmetry, a potentially realistic model can be obtained with a moderate tuning in the parameter space of the theory. In this model, the Higgs potential is stabilized and the hierarchy of fermion masses explained.

Nuclear Physics B, 2002

The electroweak Higgs doublets are identified as components of a vector multiplet in a higher dimensional supersymmetric field theory. We construct a minimal model in 6D where the electroweak SU (2) ⊗ U (1) gauge group is extended to SU (3), and unified 6D models with the unified SU (5) gauge symmetry extended to SU (6). In these realistic theories the extended gauge group is broken by orbifold boundary conditions, leaving Higgs doublet zero modes which have Yukawa couplings to quarks and leptons on the orbifold fixed points. In one SU (6) model the weak mixing angle receives power law corrections, while in another the fixed point structure forbids such corrections. A 5D model is also constructed in which the Higgs doublet contains the fifth component of the gauge field. In this case Yukawa couplings are introduced as non-local operators involving the Wilson line of this gauge field.

Journal of High Energy Physics, 2015

We study the viability of five-dimensional gauge theories as candidates for the origin of the Higgs field and its mechanism for spontaneous symmetry breaking. Within the framework of lattice field theory, we consider the simplest model of an SU (2) gauge theory. We construct this theory on a five-dimensional orbifold which explicitly breaks the gauge symmetry to U (1) at the fixed points of the orbifold. Using anisotropic gauge couplings, we find that this theory exhibits three distinct phases which we label as confined, Higgs and hybrid. Within the Higgs phase, close to the Higgs-hybrid phase transition, we find that the ratio of the Higgs to gauge boson masses takes Standard Model-like values. Precisely in this region of the phase diagram, we find dimensional reduction via localisation.

Physical Review D, 2004

Recently, "Higgsless" models of electroweak symmetry breaking have been proposed. Based on compactified five-dimensional gauge theories, these models achieve unitarity of electroweak boson self-interactions through the exchange of a tower of massive vector bosons rather than the exchange of a scalar Higgs boson. In this paper, using deconstruction, we analyze the form of the corrections to the electroweak interactions in a large class of these models, allowing for arbitrary 5-D geometry, position-dependent gauge coupling, and brane kinetic energy terms. We show that many models considered in the literature, including those most likely to be phenomenologically viable, are in this class. By analyzing the asymptotic behavior of the correlation function of gauge currents at high momentum, we extract the exact form of the relevant correlation functions at tree-level and compute the corrections to precision electroweak observables in terms of the spectrum of heavy vector bosons. We determine when nonoblique corrections due to the interactions of fermions with the heavy vector bosons become important, and specify the form such interactions can take. In particular we find that in this class of models, so long as the theory remains unitary, S −4 cos 2 θ W T > O(1), where S and T are the usual oblique parameters. We concur with the result of Cacciapaglia et.al. that small or negative S is possible -though only at the expense of substantial negative T at tree-level. Although we stress our results as they apply to continuum 5-D models, they apply also to models of extended electroweak gauge symmetries motivated by models of hidden local symmetry.

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.

Nuclear Physics B, 2007

We perform a complete study of flavour and CP conserving electroweak observables in a slight refinement of a recently proposed five-dimensional model on R 4 × S 1 /Z 2 , where the Higgs is the internal component of a gauge field and the Lorentz symmetry is broken in the fifth dimension.

Physical Review Letters, 2004

We present a 5D gauge theory in warped space based on a bulk SU (2) L × SU (2) R × U (1) B−L gauge group where the gauge symmetry is broken by boundary conditions. The symmetry breaking pattern and the mass spectrum resembles that in the standard model (SM). To leading order in the warp factor the ρ parameter and the coupling of the Z (or equivalently the S-parameter) are as in the SM, while corrections are expected at the level of a percent. From the AdS/CFT point of view the model presented here can be viewed as the AdS dual of a (walking) technicolor-like theory, in the sense that it is the presence of the IR brane itself that breaks electroweak symmetry, and not a localized Higgs on the IR brane (which should be interpreted as a composite Higgs model). This model predicts the lightest W , Z and γ resonances to be at around 1.2 TeV, and no fundamental (or composite) Higgs particles. * Other interesting possibilities for EWSB using extra dimensions is to have the Higgs be the extra dimensional component of a gauge field, see for example , or to have a warped compactification where the would-be zero mode for the gauge field is not normalizable .