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

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

ESTIMATING VARIANCE FUNCTIONS FOR WEIGHTED LINEAR REGRESSION

For linear models with heterogeneous error structure, four variance function models are examined for predicting the error structure in two loblolly pine data sets and one white oak data set. An index of fit and a simulation study were used to determine which models were best. The size of coefficients for linear and higher order terms varied drastically across different data sets, thus it is not desirable to recommend a general model containing both linear and higher order terms. The unspecified exponent model σ2vi = σ2(Di2 Hi)k 1 is recommended for all data sets considered. The k1 values ranged from 1.8 to 2.1. We recommend k1 = 2.0 for simplicity

Study of LHC Searches for a Lepton and Many Jets

Searches for new physics in high-multiplicity events with little or no missing energy are an important component of the LHC program, complementary to analyses that rely on missing energy. We consider the potential reach of searches for events with a lepton and six or more jets, and show they can provide increased sensitivity to many supersymmetric and exotic models that would not be detected through standard missing-energy analyses. Among these are supersymmetric models with gauge mediation, R-parity violation, and light hidden sectors. Moreover, ATLAS and CMS measurements suggest the primary background in this channel is from t-tbar, rather than W+jets or QCD, which reduces the complexity of background modeling necessary for such a search. We also comment on related searches where the lepton is replaced with another visible object, such as a Z boson.Comment: 23 pages, 12 figures, 1 tabl

Little Higgs Models and Precision Electroweak Data

We study the low energy limit of Little Higgs models. The method consists in eliminating the heavy fields using their classical equations of motion in the infinite mass limit. After the elimination of the heavy degrees of freedom we can directly read off deviations from the precision electroweak data. We also examine the effects on the low energy precision experiments.Comment: Misprint in eps3 for the custodial model corrected and additional discussion of the triplet higg

TeV Symmetry and the Little Hierarchy Problem

Constraints from precision electroweak measurements reveal no evidence for new physics up to 5 - 7 TeV, whereas naturalness requires new particles at around 1 TeV to address the stability of the electroweak scale. We show that this "little hierarchy problem" can be cured by introducing a symmetry for new particles at the TeV scale. As an example, we construct a little Higgs model with this new symmetry, dubbed T-parity, which naturally solves the little hierarchy problem and, at the same time, stabilize the electroweak scale up to 10 TeV. The model has many important phenomenological consequences, including consistency with the precision data without any fine-tuning, a stable weakly-interacting particle as the dark matter candidate, as well as collider signals completely different from existing little Higgs models, but rather similar to the supersymmetric theories with conserved R-parity.Comment: 15 pages, 1 figure; v.2: typos corrected and various minor modifications/expansions on the presentations. now 16 pages and 1 figure. version to appear on JHE

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

Little Technicolor

Inspired by the AdS/CFT correspondence, we show that any G/H symmetry breaking pattern can be described by a simple two-site moose diagram. This construction trivially reproduces the CCWZ prescription in the context of Hidden Local Symmetry. We interpret this moose in a novel way to show that many little Higgs theories can emerge from ordinary chiral symmetry breaking in scaled-up QCD. We apply this reasoning to the simple group little Higgs to see that the same low energy degrees of freedom can arise from a variety of UV complete theories. We also show how models of holographic composite Higgs bosons can turn into brane-localized little technicolor theories by "integrating in" the IR brane.Comment: 26 pages, 2 figures; v2: references added; v3: added section on vacuum alignment to match JHEP versio

Supersymmetry in Slow Motion

We construct new theories of electroweak symmetry breaking that employ a combination of supersymmetry and discrete symmetries to stabilize the weak scale up to and beyond the energies probed by the LHC. These models exhibit conventional supersymmetric spectra but the fermion-sfermion-gaugino vertices are absent. This closes many conventional decay channels, thereby allowing several superpartners to be stable on collider time scales. This opens the door to the possibility of directly observing R-hadrons and three flavors of sleptons inside the LHC detectors.Comment: A reference added. The discussion on the Higgs sector expanded. The version accepted for publication in JHE

Scalar Dark Matter From Theory Space

The scalar dark matter candidate in a prototypical theory space little Higgs model is investigated. We review all details of the model pertinent to dark matter. We perform a thermal relic density calculation including couplings to the gauge and Higgs sectors of the model. We find two regions of parameter space that give acceptable dark matter abundances. The first region has a dark matter candidate with a mass of order 100 GeV, the second region has a heavy candidate with a mass greater than about 500 GeV$. The dark matter candidate in either region is an admixture of an SU(2) triplet and an SU(2) singlet, thereby constituting a WIMP (weakly interacting massive particle).Comment: 18 pages, 2 figures, version to appear in PR