We present 'twin Higgs models', simple realizations of the Higgs as a pseudo-Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5 -10 TeV. In the ultra-violet these theories have a discrete symmetry which interchanges each Standard Model particle with a corresponding particle which transforms under a twin or mirror Standard Model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo-Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the Standard Model gauge groups.In the Standard Model (SM) the weak scale is unstable under quantum corrections. This suggests the existence of new physics at or close to a TeV that protects the Higgs mass parameter of the SM against radiative corrections. While the exact form that such new physics takes is unknown there are several interesting alternatives. One possibility, first proposed in [1,2] is that the Higgs is naturally light because it is the pseudo-Goldstone boson of an approximate global symmetry. This idea has recently experienced a revival in the form of little Higgs theories [3,4] (for a clear review and more references see [5]) that protect the Higgs mass from radiative corrections up to scales of order 5 -10 TeV.In this paper we propose a class of simple alternative realizations of the Higgs as a pseudo-Goldstone boson that also protect the weak scale from radiative corrections up to scales of order 5 -10

We present a new class of models that stabilize the weak scale against radiative corrections up to scales of order 5 TeV without large corrections to precision electroweak observables. In these 'folded supersymmetric' theories the one loop quadratic divergences of the Standard Model Higgs field are cancelled by opposite spin partners, but the gauge quantum numbers of these new particles are in general different from those of the conventional superpartners. This class of models is built around the correspondence that exists in the large N limit between the correlation functions of supersymmetric theories and those of their non-supersymmetric orbifold daughters. By identifying the mechanism which underlies the cancellation of one loop quadratic divergences in these theories, we are able to construct simple extensions of the Standard Model which are radiatively stable at one loop. Ultraviolet completions of these theories can be obtained by imposing suitable boundary conditions on an appropriate supersymmetric higher dimensional theory compactified down to four dimensions. We construct a specific model based on these ideas which stabilizes the weak scale up to about 20 TeV and where the states which cancel the top loop are scalars not charged under Standard Model color. Its collider signatures are distinct from conventional supersymmetric theories and include characteristic events with hard leptons and missing energy. * For an earlier approach to stabilizing the weak scale also based on the large N orbifold correspondence see [16].

We present twin Higgs models based on the extension of the Standard Model to left-right symmetry that protect the weak scale against radiative corrections up to scales of order 5 TeV. In the ultraviolet the Higgs sector of these theories respects an approximate global symmetry, in addition to the discrete parity symmetry characteristic of left-right symmetric models. The Standard Model Higgs field emerges as the pseudo-Goldstone boson associated with the breaking of the global symmetry. The parity symmetry tightly constrains the form of radiative corrections to the Higgs potential, allowing natural electroweak breaking. The minimal model predicts a rich spectrum of exotic particles that will be accessible to upcoming experiments, and which are necessary for the cancellation of one-loop quadratic divergences. These include right-handed gauge bosons with masses not to exceed a few TeV and a pair of vector-like quarks with masses of order several hundred GeV.

We discuss a minimal supersymmetric SO͑10͒ model where BϪL symmetry is broken by a 126 dimensional Higgs boson multiplet which also contributes to fermion masses in conjunction with a 10 dimensional superfield. This minimal Higgs boson choice provides a partial unification of neutrino flavor structure with that of quarks and has been shown to predict all three neutrino mixing angles and the solar mass splitting in agreement with observations, provided one uses the type II seesaw formula for neutrino masses. In this paper we generalize this analysis to include arbitrary CP phases in couplings and vacuum expectation values. We find that ͑i͒ the predictions for neutrino mixings are similar with U e3 Ӎ0.18 as before and other parameters in a somewhat bigger range and ͑ii͒ that to first order in the quark mixing parameter ͑the Cabibbo angle͒, the leptonic mixing matrix is CP conserving. We also find that in the absence of any higher dimensional contributions to fermion masses, the CKM phase is different from that of the standard model implying that there must be new contributions to quark CP violation from the supersymmetry breaking sector. Inclusion of higher dimensional terms however allows the standard model CKM phase to be maintained.

We show that the assumption of type II seesaw mechanism for small neutrino masses coupled with b − τ mass unification in a minimal SUSY SO(10) model leads not only to a natural understanding of large atmospheric mixing angle (θ 23 ) among neutrinos, as recently pointed out, but also to large solar angle (θ 12 ) and a small θ 13 ≡ U e3 as required to fit observations. This is therefore a minimal, completely realistic grand unified model for all low energy observations that naturally explains the diverse mixing patterns between the quark and leptons without any additional inputs such as extra global symmetries. The proposed long baseline neutrino experiments will provide a crucial test of this model since it predicts U e3 ≃ 0.16 for the allowed range of parameters.

We investigate the collider signals associated with scalar quirks ("squirks") in folded supersymmetric models. As opposed to regular superpartners in supersymmetric models these particles are uncolored, but are instead charged under a new confining group, leading to radically different collider signals. Due to the new strong dynamics, squirks that are pair produced do not hadronize separately, but rather form a highly excited bound state. The excited "squirkonium" loses energy to radiation before annihilating back into Standard Model particles. We calculate the branching fractions into various channels for this process, which is prompt on collider time-scales. The most promising annihilation channel for discovery is W+photon which dominates for squirkonium near its ground state. We demonstrate the feasibility of the LHC search, showing that the mass peak is visible above the SM continuum background and estimate the discovery reach.

A minimal SO(10) model with 126 Higgs field breaking B ÿ L symmetry has been shown recently to predict large solar and atmospheric mixings in agreement with observations if it is assumed that the neutrino mass follows from the triplet dominated type-II seesaw formula. No additional symmetries need to be assumed for this purpose. We discuss the conditions on the way SO(10) symmetry breaks down to the minimal supersymmetric standard model (MSSM) and the Higgs multiplets in the model, required for the triplet dominated type-II seesaw formula to hold. We find that (i) SO(10) must break to a nonminimal SU(5) before breaking to the standard model; (ii) B ÿ L symmetry must break at the time of SO(10) breaking and (iii) constraints of unification seem to require that the minimal model must have a 54 dimensional Higgs field together with a 210 and 126 to break the grand unified theory (GUT) symmetry.

We propose that the leptonic cosmic ray signals seen by PAMELA and ATIC result from the annihilation or decay of dark matter particles via states of a leptonic Higgs doublet to τ leptons, linking cosmic ray signals of dark matter to LHC signals of the Higgs sector. The states of the leptonic Higgs doublet are lighter than about 200 GeV, yielding largeτ τ and τ ττ τ event rates at the LHC. Simple models are given for the dark matter particle and its interactions with the leptonic Higgs, for cosmic ray signals arising from both annihilations and decays in the galactic halo. For the case of annihilations, cosmic photon and neutrino signals are on the verge of discovery.Recent observations of high-energy electron and positron cosmic ray spectra have generated tremendous interest, as they might provide the first non-gravitational evidence for Dark Matter (DM). The PAMELA [1] experiment reports an excess of positrons in the few GeV to 100 GeV range, providing further support to the earlier results of HEAT [2] and AMS [3]. In addition, results from the ATIC [4] and PPB-BETS [5] balloon experiments suggest an excess of electrons and positrons in the 300 GeV to 600 GeV range.While these observations have conventional astrophysical interpretations, they may result from annihilations or decays of DM particles in the galactic halo. Indeed, the PAMELA and ATIC data reinforce each other, since, for a certain range of DM masses, they have a unified interpretation. However, DM