The Minimal Moose for a Little Higgs

Recently a new class of theories of electroweak symmetry breaking have been constructed. These models, based on deconstruction and the physics of theory space, provide the first alternative to weak-scale supersymmetry with naturally light Higgs fields and perturbative new physics at the TeV scale. The Higgs is light because it is a pseudo-Goldstone boson, and the quadratically divergent contributions to the Higgs mass are cancelled by new TeV scale ``partners'' of the {\em same} statistics. In this paper we present the minimal theory space model of electroweak symmetry breaking, with two sites and four link fields, and the minimal set of fermions. There are very few parameters and degrees of freedom beyond the Standard Model. Below a TeV, we have the Standard Model with two light Higgs doublets, and an additional complex scalar weak triplet and singlet. At the TeV scale, the new particles that cancel the 1-loop quadratic divergences in the Higgs mass are revealed. The entire Higgs potential needed for electroweak symmetry breaking--the quartic couplings as well as the familiar negative mass squared--can be generated by the top Yukawa coupling, providing a novel link between the physics of flavor and electroweak symmetry breaking.Comment: 15 pages. References added. Included clarifying comments on the origin of quartic couplings, and on power-counting. More elegant model for generating Higgs potential from top Yukawa coupling presente

Mooses, Topology and Higgs

New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking.Comment: 16 pages, 11 figure

Phenomenology of Electroweak Symmetry Breaking from Theory Space

Recently, a new class of realistic models for electroweak symmetry breaking have been constructed, without supersymmetry. These theories have naturally light Higgs bosons and perturbative new physics at the TeV scale. We describe these models in detail, and show that electroweak symmetry breaking can be triggered by a large top quark Yukawa coupling. A rich spectrum of particles is predicted, with a pair of light Higgs doublets accompanied by new light weak triplet and singlet scalars. The lightest of these new scalars is charged under a geometric discrete symmetry and is therefore stable, providing a new candidate for WIMP dark matter. At TeV energies, a plethora of new heavy scalars, gauge bosons and fermions are revealed, with distinctive quantum numbers and decay modes.Comment: 22 pages, latex, 6 figures. Numerical results corrected, clarifications added, conclusions unchange

Shape of Deconstruction

We construct a six-dimensional Maxwell theory using a latticized extra space, the continuum limit of which is a shifted torus recently discussed by Dienes. This toy model exhibits the correspondence between continuum theory and discrete theory, and give a geometrical insight to theory-space model building.Comment: 10 pages, 2 figures, RevTeX4. a citation adde

What Precision Electroweak Physics Says About the SU(6)/Sp(6) Little Higgs

We study precision electroweak constraints on the close cousin of the Littlest Higgs, the SU(6)/Sp(6) model. We identify a near-oblique limit in which the heavy W' and B' decouple from the light fermions, and then calculate oblique corrections, including one-loop contributions from the extended top sector and the two Higgs doublets. We find regions of parameter space that give acceptably small precision electroweak corrections and only mild fine tuning in the Higgs potential, and also find that the mass of the lightest Higgs boson is relatively unconstrained by precision electroweak data. The fermions from the extended top sector can be as light as 1 TeV, and the W' can be as light as 1.8 TeV. We include an independent breaking scale for the B', which can still have a mass as low as a few hundred GeV.Comment: 52 pages, 16 figure

A "Littlest Higgs" Model with Custodial SU(2) Symmetry

In this note, a ``littlest higgs'' model is presented which has an approximate custodial SU(2) symmetry. The model is based on the coset space $SO(9)/(SO(5)\times SO(4))$. The light pseudo-goldstone bosons of the theory include a {\it single} higgs doublet below a TeV and a set of three $SU(2)_W$ triplets and an electroweak singlet in the TeV range. All of these scalars obtain approximately custodial SU(2) preserving vacuum expectation values. This model addresses a defect in the earlier $SO(5)\times SU(2)\times U(1)$ moose model, with the only extra complication being an extended top sector. Some of the precision electroweak observables are computed and do not deviate appreciably from Standard Model predictions. In an S-T oblique analysis, the dominant non-Standard Model contributions are the extended top sector and higgs doublet contributions. In conclusion, a wide range of higgs masses is allowed in a large region of parameter space consistent with naturalness, where large higgs masses requires some mild custodial SU(2) violation from the extended top sector.Comment: 22 pages + 8 figures; JHEP style, added references and extra discussion on size of T contributions, as well as some other minor clarifications. Version to appear in JHE

Vacuum Stability in Split Susy and Little Higgs Models

We study the stability of the effective higgs potential in the split supersymmetry and Little Higgs models. In particular, we study the effects of higher dimensional operators in the effective potential on the higgs mass predictions. We find that the size and sign of the higher dimensional operators can significantly change the higgs mass required to maintain vacuum stability in Split Susy models. In the Little Higgs models the effects of higher dimensional operators can be large because of a relatively lower cut-off scale. Working with a specific model we find that a contribution from the higher dimensional operator with coefficient of O(1) can destabilize the vacuum.Comment: Latex 22 pages, 3 figures. Added discussion, published versio

Little Hierarchy, Little Higgses, and a Little Symmetry

Little Higgs theories are an attempt to address the little hierarchy problem, i.e., the tension between the naturalness of the electroweak scale and the precision measurements showing no evidence for new physics up to 5-10 TeV. In little Higgs theories, the Higgs mass-squareds are protected to the one-loop order from the quadratic divergence. This allows the cutoff to be raised up to \~10 TeV, beyond the scales probed by the precision data. However, strong constraints can still arise from the contributions of the new TeV scale particles and hence re-introduces the fine-tuning problem. In this paper we show that a new symmetry, denoted as T-parity, under which all heavy gauge bosons and scalar triplets are odd, can remove all the tree-level contributions to the electroweak observables and therefore makes the little Higgs theories completely natural. The T-parity can be manifestly implemented in a majority of little Higgs models by following the most general construction of the low energy effective theory a la Callan, Coleman, Wess and Zumino. In particular, we discuss in detail how to implement the T-parity in the littlest Higgs model based on SU(5)/SO(5). The symmetry breaking scale f can be even lower than 500 GeV if the contributions from the unknown UV physics at the cutoff are somewhat small. The existence of $T$-parity has drastic impacts on the phenomenology of the little Higgs theories. The T-odd particles need to be pair-produced and will cascade down to the lightest T-odd particle (LTP) which is stable. A neutral LTP gives rise to missing energy signals at the colliders which can mimic supersymmetry. It can also serve as a good dark matter candidate.Comment: 20 pages, 2 figures, RevTeX; v2: Yukawa sector in the SU(5)/SO(5) model slightly modified. Also added comments on the Dirac mass term for the fermionic doublet partner; v3: clarifying comments on the modified Yukawa sector. version to appear on JHE

Higher dimensional supersymmetry in 4D superspace

We present an explicit formulation of supersymmetric Yang-Mills theories from \D= 5 to 10 dimensions in the familiar \N=1,\D=4 superspace. This provides the rules for globally supersymmetric model building with extra dimensions and in particular allows us to simply write down $\N=1$ SUSY preserving interactions between bulk fields and fields localized on branes. We present a few applications of the formalism by way of illustration, including supersymmetric ``shining'' of bulk fields, orbifolds and localization of chiral fermions, anomaly inflow and super-Chern-Simons theories.Comment: Typos corrected. Added reference to early work by Marcus, Sagnotti and Siegel and a term to the non-Abelian Lagrangian for D>5 formally needed for gauge invariance. The results however remain unchange

Precision Electroweak Observables in the Minimal Moose Little Higgs Model

Little Higgs theories, in which the Higgs particle is realized as the pseudo-Goldstone boson of an approximate global chiral symmetry have generated much interest as possible alternatives to weak scale supersymmetry. In this paper we analyze precision electroweak observables in the Minimal Moose model and find that in order to be consistent with current experimental bounds, the gauge structure of this theory needs to be modified. We then look for viable regions of parameter space in the modified theory by calculating the various contributions to the S and T parameters.Comment: v2: 17 pages, 9 figures. Typeset in JHEP style. Added a references and two figures showing parameter space for each of two reference points. Corrected typo