Savas Dimopoulos

THE HIERARCHY PROBLEM AND NEW DIMENSIONS AT A MILLIMETER

Abstract We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed weakness of gravity on distances ≳ 1 mm is due to the existence of n ≥2 new compact spatial dimensions large compared to the weak scale. The Planck scale M Pl ∼ G N −1/2 is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely propagate in the new dimensions, at sub-weak energies the Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale “thickness” in the extra dimensions. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of n =2 new dimensions, planned sub-millimeter measurements of gravity may observe the transition from 1/ r 2 →1/ r 4 Newtonian gravitation. For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum p T ≳ TeV. For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of ∼10 12 Hz or larger. As a concrete illustration, we construct a model with SM fields localized on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry SU (4)× SU (2)× SU (2) in the bulk.

New dimensions at a millimeter to a Fermi and superstrings at a TeV

Abstract Recently, a new framework for solving the hierarchy problem has been proposed which does not rely on low energy supersymmetry or technicolor. The gravitational and gauge interactions unite at the electroweak scale, and the observed weakness of gravity at long distances is due the existence of large new spatial dimensions. In this letter, we show that this framework can be embedded in string theory. These models have a perturbative description in the context of type I string theory. The gravitational sector consists of closed strings propagating in the higher-dimensional bulk, while ordinary matter consists of open strings living on D3-branes. This scenario raises the exciting possibility that the LHC and NLC will experimentally study ordinary aspects of string physics such as the production of narrow Regge-excitations of all standard model particles, as well more exotic phenomena involving strong gravity such as the production of black holes. The new dimensions can be probed by events with large missing energy carried off by gravitons escaping into the bulk. We finally discuss some important issues of model building, such as proton stability, gauge coupling unification and supersymmetry breaking.

Softly Broken Supersymmetry and SU(5)

We construct an explicit realistic SU(5) model in which softly broken supersymmetry is used to protect the Higgs doublets from quadratic mass renormalization. The model requires one natural but incredibly accurate adjustment of parameters. We argue that such an adjustment will be required in any supersymmetric GUT in which baryon number is not conserved.

Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC

The cosmological constant problem is a failure of naturalness and suggests that a fine-tuning mechanism is at work, which may also address the hierarchy problem. An example — supported by Weinbergs successful prediction of the cosmological constant — is the potentially vast landscape of vacua in string theory, where the existence of galaxies and atoms is promoted to a vacuum selection criterion. Then, low energy SUSY becomes unnecessary, and supersymmetry — if present in the fundamental theory — can be broken near the unification scale. All the scalars of the supersymmetric standard model become ultraheavy, except for a single finely tuned Higgs. Yet, the fermions of the supersymmetric standard model can remain light, protected by chiral symmetry, and account for the successful unification of gauge couplings. This framework removes all the difficulties of the SSM: the absence of a light Higgs and sparticles, dimension five proton decay, SUSY flavor and CP problems, and the cosmological gravitino and moduli problems. High-scale SUSY breaking raises the mass of the light Higgs to ~ 120−150 GeV. The gluino is strikingly long lived, and a measurement of its lifetime can determine the ultraheavy scalar mass scale. Measuring the four Yukawa couplings of the Higgs to the gauginos and higgsinos precisely tests for high-scale SUSY. These ideas, if confirmed, will demonstrate that supersymmetry is present but irrelevant for the hierarchy problem — just as it has been irrelevant for the cosmological constant problem — strongly suggesting the existence of a fine-tuning mechanism in nature.

Black holes at the Large Hadron Collider.

If the scale of quantum gravity is near a TeV, the LHC will be producing one black hole (BH) about every second. The BH decays into prompt, hard photons and charged leptons is a clean signature with low background. The absence of significant missing energy allows the reconstruction of the mass of the decaying BH. The correlation between the BH mass and its temperature, deduced from the energy spectrum of the decay products, can test experimentally the higher dimensional Hawking evaporation law. It can also determine the number of large new dimensions and the scale of quantum gravity.

Mass Without Scalars

Abstract We attempt to show that fundamental scalar fields can be eliminated from the theory of weak and electromagnetic interactions. We do this by constructing an explicit example in which the scalar field sectors are replaced by strongly interacting gauge systems. Unlike previous examples, our present work gives a natural explanation for fermion masses. The cost is a significant expansion of the size of the gauge group.

Aspects of Split Supersymmetry

We explore some fundamental differences in the phenomenology, cosmology and model building of Split Supersymmetry compared with traditional low-scale supersymmetry. We show how the mass spectrum of Split Supersymmetry naturally emerges from theories where the dominant source of supersymmetry breaking preserves an R symmetry, characterize the class of theories where the unavoidable R-breaking by gravity can be neglected, and point out a new possibility, where supersymmetry breaking is directly communicated at tree level to the visible sector via renormalizable interactions. Next, we discuss possible low-energy signals for Split Supersymmetry. The absence of new light scalars removes all the phenomenological difficulties of low-energy supersymmetry, associated with one-loop flavor and CP violating effects. However, the electric dipole moments of leptons and quarks do arise at two loops, and are automatically at the level of present limits with no need for small phases, making them accessible to several ongoing new-generation experiments. We also study proton decay in the context of Split Supersymmetry, and point out scenarios where the dimension-six induced decays may be observable. Finally, we show that the novel spectrum of Split Supersymmetry opens up new possibilities for the generation of dark matter, as the decays of ultraheavy gravitinos in the early universe typically increase the abundance of the lightest neutralino above its usual freeze-out value. This allows for lighter gauginos and Higgsinos, more accessible both to the LHC and to dark-matter detection experiments.

Naturalness constraints in supersymmetric theories with non-universal soft terms

Abstract In the absence of universality the naturalness upper limits on supersymmetric particle masses increase significantly. The superpartners of the two light generations can be much heavier than the weak scale without extreme fine-tunings; they can weigh up to about 900 GeV - or even up to 5 TeV, if SU(5) universality is invoked. This supresses sparticle-mediated rare processes and consequently ameliorates the problem of supersymmetric flavor violations. On the other hand, even without universality, the gluino and stop remain below about 400 GeV while the charginos and neutralinos are likely to be accessible at LEP2.

Composite Higgs Scalars

We construct models in which the Higgs doublet whose vacuum expectation breaks SU(2) × U(10 is a bound state of massive strongly interacting fermions. The couplings of the composite Higgs to ordinary fermions are induced by heavy gauge boson exchange in the manner of extended technicolor. Other heavy gauge bosons generate a negative mass term for the Higgs.

A Small cosmological constant from a large extra dimension

We propose a new approach to the Cosmological Constant Problem which makes essential use of an extra dimension. A model is presented in which the Standard Model vacuum energy “warps” the higher-dimensional spacetime while preserving 4D flatness. We argue that the strong curvature region of our solutions may effectively cut off the size of the extra dimension, thereby giving rise to macroscopic 4D gravity without a cosmological constant. In our model, the higher-dimensional gravity dynamics is treated classically with carefully chosen couplings. Our treatment of the Standard Model is however fully quantum field-theoretic, and the 4D flatness of our solutions is robust against Standard Model quantum loops and changes to Standard Model couplings.