It has been recently argued that realistic models with warped extra dimensions can have KaluzaKlein particles accessible at the Large Hadron Collider if a custodial symmetry, SU (2) V × P LR , is used to protect the T parameter and the coupling of the left-handed bottom quark to the Z gauge boson. In this article we emphasize that such a symmetry implies that the loop corrections to both the T parameter and the Zb LbL coupling are calculable. In general, these corrections are correlated, can be sizable, and should be considered to determine the allowed parameter space region in models with warped extra dimensions and custodial symmetry, including Randall-Sundrum models with a fundamental Higgs, models of gauge-Higgs unification and Higgsless models. As an example, we derive the constraints that arise on a representative model of gauge-Higgs unification from a global fit to the precision electroweak observables. A scan over the parameter space typically leads to a lower bound on the Kaluza-Klein excitations of the gauge bosons of about 2 − 3 TeV, depending on the configuration. In the fermionic sector one can have Kaluza-Klein excitations with masses of a few hundred GeV. We present the constraints on these light fermions from recent Tevatron searches, and explore interesting discovery channels at the LHC. PACS numbers:1 FERMILAB-PUB-07-496-T

We consider supersymmetric theories where the standard-model quark and lepton fields are localized on a '3-brane' in extra dimensions, while the gauge and Higgs fields propagate in the bulk. If supersymmetry is broken on another 3-brane, supersymmetry breaking is communicated to gauge and Higgs fields by direct higher-dimension interactions, and to quark and lepton fields via standard-model loops. We show that this gives rise to a realistic and predictive model for supersymmetry breaking. The size of the extra dimensions is required to be of order 10-100 times larger than fundamental scale (e.g. the string scale). The spectrum is similar to (but distinguishable from) the predictions of 'no-scale' models. Flavor-changing neutral currents are naturally suppressed. The µ term can be generated by the Giudice-Masiero mechanism. The supersymmetric CP problem is naturally solved if CP violation occurs only on the observable sector 3-brane. These are the simplest models in the literature that solve all supersymmetric naturalness problems.

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We consider 'brane universe' scenarios with standard-model fields localized on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is rotationally symmetric about the brane, local quantities in the bulk are insensitive to the couplings on the brane. This potentially allows compactifications where the effective 4-dimensional cosmological constant is independent of the couplings on the 3-brane. We consider several possible singularity-free compactification mechanisms, and find that they do not maintain this property. We also find solutions with naked spacetime singularities, and we speculate that new short-distance physics can become important near the singularities and allow a compactification with the desired properties. The picture that emerges is that standard-model loop contributions to the effective 4-dimensional cosmological constant can be cut off at distances shorter than the compactification scale. At shorter distance scales, renormalization effects due to standard-model fields renormalize the 3-brane tension, which changes a deficit angle in the transverse space without affecting local quantities in the bulk. For a compactification scale of order 10 −2 mm, this gives a standard-model contribution to the cosmological constant in the range favored by cosmology. Revised

We show that Lorentz and gauge invariance explain the long proton lifetime within the standard model in six dimensions. The baryon-number violating operators have mass dimension 15 or higher. Upon TeV-scale compactification of the two universal extra dimensions on a square T 2 /Z2 orbifold, a discrete subgroup of the 6-dimensional Lorentz group continues to forbid dangerous operators.

We compute the one-loop Casimir energy of gravity and matter fields, obeying various boundary conditions, in 5-dimensional S 1 /Z 2 and 6-dimensional T 2 /Z k orbifolds. We discuss the role of the Casimir energy in possible radius stabilization mechanisms and show that the presence of massive as well as massless fields can lead to minima with zero cosmological constant. In the 5-d orbifold, we also consider the case where kinetic terms localized at the fixed points are not small. We take into account their contribution to the Casimir energy and show that localized kinetic terms can also provide a mechanism for radius stabilization. We apply our results to a recently proposed 5-dimensional supersymmetric model of electroweak symmetry breaking and show that the Casimir energy with the minimal matter content is repulsive. Stabilizing the radius with zero cosmological constant requires, in this context, adding positive bulk cosmological constant and negative brane-tension counterterms.

We consider theories with one or more compact dimensions with size r > 1/M, where M is the fundamental Planck scale, with the visible and hidden sectors localized on spatially separated '3-branes.' We show that a bulk U(1) gauge field spontaneously broken on the hidden-sector 3-brane is an attractive candidate for the messenger of supersymmetry breaking. In this scenario scalar mass-squared terms are proportional to U(1) charges, and therefore naturally conserve flavor. Arbitrary flavor violation at the Planck scale gives rise to exponentially suppressed flavor violation at low energies. Gaugino masses can be generated if the standard gauge fields propagate in the bulk; µ and Bµ terms can be generated by the Giudice-Masiero or by the VEV of a singlet in the visible sector. The latter case naturally solves the SUSY CP problem. Realistic phenomenology can be obtained either if all microscopic parameters are order one in units of M, or if the theory is strongly coupled at the scale M. In either case, the only unexplained hierarchy is the 'large' size of the extra dimensions in fundamental units, which need only be an order of magnitude. All soft masses are naturally within an order of magnitude of m 3/2 , and trilinear scalar couplings are negligible. Squark and slepton masses can naturally unify even in the absence of grand unification. *

Standard model gauge bosons propagating in two universal extra dimensions give rise to heavy spin-1 and spin-0 particles. The lightest of these, carrying Kaluza-Klein numbers (1,0), may be produced only in pairs at colliders, whereas the (1,1) modes, which are heavier by a factor of √ 2, may be singly produced. We show that the cascade decays of (1,1) particles generate a series of closely-spaced narrow resonances in the t ¯ t invariant mass distribution. At the Tevatron, s-channel production of (1,1) gluons and electroweak bosons will be sensitive to t ¯ t resonances up to masses in the 0.5-0.7 TeV range. Searches at the LHC for resonances originating from several higher-level modes will further test the existence of two universal extra dimensions.