On the role of vortex stretching in energy optimal growth of three dimensional perturbations on plane parallel shear flows

The three dimensional optimal energy growth mechanism, in plane parallel shear flows, is reexamined in terms of the role of vortex stretching and the interplay between the span-wise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille, and mixing layer shear profiles is robust and resembles localized plane-waves in regions where the background shear is large. The waves are tilted with the shear when the span-wise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification reflects on the optimal energy growth. This perspective provides an understanding of the three dimensional growth solely from the two dimensional dynamics on the shear plane

Color Superconductivity from Supersymmetry

A supersymmetric composite model of color superconductivity is proposed. Quarks and diquarks are dynamically generated as composite fields by a newly introduced strong gauge dynamics. It is shown that the condensation of the scalar component of the diquark supermultiplet occurs when the chemical potential becomes larger than some critical value. We believe that the model well captures aspects of the diquark condensate behavior and helps our understanding of the diquark dynamics in real QCD. The results obtained here might be useful when we consider a theory composed of quarks and diquarks.Comment: 4 pages, 2 figures, An error in Eq.(10) correcte

Anomaly Mediation, Fayet-Iliopoulos D-terms and the Renormalisation Group

We address renormalisation group evolution issues that arise in the Anomaly Mediated Supersymmetry Breaking scenario when the tachyonic slepton problem is resolved by Fayet-Iliopoulos term contributions. We present typical sparticle spectra both for the original formulation of this idea and an alternative using Fayet-Iliopoulos terms for a U(1) compatible with a straightforward GUT embedding.Comment: 20 pages, 2 figure

Purely Four-dimensional Viable Anomaly Mediation

Anomaly mediation of supersymmetry breaking solves the supersymmetric flavor problem thanks to its ultraviolet-insensitivity. However, it suffers from two problems: sleptons have negative masses-squared, and there are likely bulk moduli that spoil the framework. Here, we present the first fully ultraviolet-insensitive model of anomaly mediation with positive slepton masses-squared in a purely four-dimensional framework. Our model is based on the additional D-term contributions to the sparticle masses, and the conformal sequestering mechanism.Comment: 7 pages, Uses RevTex4 (included). References modifie

Abelian D-terms and the superpartner spectrum of anomaly-mediated supersymmetry breaking

We address the tachyonic slepton problem of anomaly mediated supersymmetry breaking using abelian D-terms. We demonstrate that the most general extra U(1) symmetry that does not disrupt gauge coupling unification has a large set of possible charges that solves the problem. It is shown that previous studies in this direction that added both an extra hypercharge D-term and another D-term induced by B-L symmetry (or similar) can be mapped into a single D-term of the general ancillary U(1)_a. The U(1)_a formalism enables identifying the sign of squark mass corrections which leads to an upper bound of the entire superpartner spectrum given knowledge of just one superpartner mass.Comment: 10 pages, 2 figures, [v2] reference added, [v3] Eq. (9) corrected, results unaffected, [v4] version to be published in Phys. Rev. D, expanded parameter space for figures to match tex

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

Minimal Gaugomaly Mediation

Mixed anomaly and gauge mediation ("gaugomaly'' mediation) gives a natural solution to the SUSY flavor problem with a conventional LSP dark matter candidate. We present a minimal version of gaugomaly mediation where the messenger masses arise directly from anomaly mediation, automatically generating a messenger scale of order 50 TeV. We also describe a simple relaxation mechanism that gives rise to realistic mu and B mu terms. B is naturally dominated by the anomaly-mediated contribution from top loops, so the mu/B mu sector only depends on a single new parameter. In the minimal version of this scenario the full SUSY spectrum is determined by two continuous parameters (the anomaly- and gauge-mediated SUSY breaking masses) and one discrete parameter (the number of messengers). We show that these simple models can give realistic spectra with viable dark matter.Comment: 18 pages, 4 figures; v2: corrected example generating non-holomorphic Kahler term

Folded Supersymmetry and the LEP Paradox

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.Comment: 18 pages, 5 figures, references correcte