Comments on the Hierarchy Problem in Effective Theories

We discuss aspects of the hierarchy problem in effective theories with light scalars and a large, physical ultraviolet (UV) cutoff. We make two main points: (1) The (naive) fine-tuning observed in an effective theory does not automatically imply that the UV completion is fine tuned. Instead, it gives a type of upper bound on the severity of the actual tuning in the UV completion; the actual tuning can be less severe than the naive tuning or even non-existent. (2) Within an effective theory, there appear to be two types of parameter relations that can alleviate the sensitivity of the scalar mass to the cutoff --- relationships among dimensionless couplings or relationships among dimensionful parameters. Supersymmetric models provide symmetry-motivated examples of the former, while scale-invariant models give symmetry-motivated examples of the latter.Comment: 13 page

Warping the Universal Extra Dimensions

We develop the necessary ingredients for the construction of realistic models with warped universal extra dimensions. Our investigations are based on the seven dimensional (7D) spacetime AdS_5 x T^2 and we derive the Kaluza-Klein (KK) spectra for gravitons, bulk vectors and the TeV brane localized Higgs boson. We show that, starting with a massive 7D fermion, one may obtain a single chiral massless mode whose profile is readily localized towards the Planck or TeV brane. This allows one to place the standard model fermions in the bulk and construct models of flavor as in Randall-Sundrum models. Our solution also admits the familiar KK parity of UED models so that the lightest odd KK state is stable and may be a dark matter (DM) candidate. As an additional feature the AdS_5 warping ensures that the excited modes on the torus, including the DM candidate, appear at TeV energies (as is usually assumed in UED models) even though the Planck scale sets the dimensions for the torus.Comment: 22 pages. V2 References added and minor changes mad

The Scale-Invariant Scotogenic Model

We investigate a minimal scale-invariant implementation of the scotogenic model and show that viable electroweak symmetry breaking can occur while simultaneously generating one-loop neutrino masses and the dark matter relic abundance. The model predicts the existence of a singlet scalar (dilaton) that plays the dual roles of triggering electroweak symmetry breaking and sourcing lepton number violation. Important constraints are studied, including those from lepton flavor violating effects and dark matter direct-detection experiments. The latter turn out to be somewhat severe, already excluding large regions of parameter space. None the less, viable regions of parameter space are found, corresponding to dark matter masses below (roughly) 10 GeV and above 200 GeV.Comment: 21 pages, 8 figures; v2 JHEP versio

A Radiative Model for the Weak Scale and Neutrino Mass via Dark Matter

We present a three-loop model of neutrino mass in which both the weak scale and neutrino mass arise as radiative effects. In this approach, the scales for electroweak symmetry breaking, dark matter, and the exotics responsible for neutrino mass, are related due to an underlying scale-invariance. This motivates the otherwise-independent O(TeV) exotic masses usually found in three-loop models of neutrino mass. We demonstrate the existence of viable parameter space and show that the model can be probed at colliders, precision experiments, and dark matter direct-detection experiments.Comment: 24 pages, 7 figures; v2 Published versio

Quartification On An Orbifold

We investigate quartification models in five dimensions, with the fifth dimension forming an $S^1/Z_2\times Z_2'$ orbifold. The orbifold construction is combined with a boundary Higgs sector to break the quartified gauge group directly to a group $H\subset SU(3)^4$ which is operative at the electroweak scale. We consider $H=G_{SM}\otimes SU(2)_\ell$ and $H=G_{SM}$, where $G_{SM}$ is the standard model gauge group, and find that unification occurs only when the remnant leptonic colour symmetry $SU(2)_\ell$ remains unbroken. Furthermore, the demands of a realistic low energy fermion spectrum specify a unique symmetry breaking route for the unifying case of $H=G_{SM}\otimes SU(2)_\ell$. We contrast this with four dimensional quartification models where unification may be achieved via a number of different symmetry breaking routes both with and without the remnant $SU(2)_\ell$ symmetry. The boundary Higgs sector of our model may be decoupled to achieve a Higgsless limit and we show that the electroweak Higgs doublet may be identified as the fifth component of a higher dimensional gauge field.Comment: 14 pages, misprint corrected, matches PRD versio