Probe of SUSY and Extra Dimensions by the Brookhaven g-2 Experiment

A brief review is given of $a_{\mu}=(g_{\mu}-2)/2$ as a probe of supersymmetry and of extra dimensions. It is known since the early to mid nineteen eightees that the supersymmetric electro-weak correction to $a_{\mu}$ can be as large or larger than the Standard Model electro-weak correction and thus any experiment that proposes to test the Standard Model electro-weak correction will also test the supersymmetric correction and constrain supersymmetric models. The new physics effect seen in the Brookhaven (BNL) experiment is consistent with these early expectations. Detailed analyses within the well motivated supergravity unified model show that the size of the observed difference ($a_{\mu}^{exp}-a_{\mu}^{SM}$) seen at Brookhaven implies upper limits on sparticle masses in a mass range accessible to the direct observation of these particles at the Large Hadron Collider. Further, analyses also show that the BNL data is favorable for the detection of supersymmeteric dark matter in direct dark matter searches. The effect of large extra dimensions on $a_{\mu}$ is also discussed. It is shown that with the current limits on the size of extra dimensions, which imply that the inverse size of such dimensions lies in the TeV region, their effects on $a_{\mu}$ relative to the supersymmetric contribution is small and thus extra dimensions do not produce a serious background to the supersymmetric contribution. It is concluded that the analysis of the additional data currently underway at Brookhaven as well as a reduction of the hadronic error will help pin down the scale of weak scale supersymmetry even more precisely.Comment: 11 pages,Latex.Invited talk at La Thuile,01 conference March 4-10,200

Dark Matter in SUGRA, Strings and Branes

A brief review is given of dark matter in SUGRA, strings and branes. For SUGRA models the implications of Yukawa coupling unification on dark matter are discussed in the light of $g-2$ and $b\to s\gamma$ constraints. A brief discussion is given of the dark matter in orbifold string compactifications under constraints of modular invariance and radiative breaking of the electroweak symmetry. Finally a new candidate for dark matter - an extra-weakly interacting massive particle or an XWIMP- is discussed. Such dark matter can arise in a wide class of models, including the Stueckelberg extensions of MSSM, in U(1) extensions of MSSM with off diagonal kinetic energy, and possibly in a wider class of models which may have a string/D-brane origin. Satisfaction of the relic density of XWIMPs consistent with WMAP is also discussed.Comment: Invited talk at the International Conference "Idenfication of Dark Matter-2006", September 11-16, 2006, Rhodes, Greece. 11 pages, 3 figure

Evidence for Inflation in an Axion Landscape

We discuss inflation models within supersymmetry and supergravity frameworks with a landscape of chiral superfields and one $U(1)$ shift symmetry which is broken by non-perturbative symmetry breaking terms in the superpotential. We label the pseudo scalar component of the chiral fields axions and their real parts saxions. Thus in the models only one combination of axions will be a pseudo-Nambu-Goldstone-boson which will act as the inflaton. The proposed models constitute consistent inflation for the following reasons: The inflation potential arises dynamically with stabilized saxions, the axion decay constant can lie in the sub-Planckian region, and consistency with the Planck data is achieved. The axion landscape consisting of $m$ axion pairs is assumed with the axions in each pair having opposite charges. A fast roll--slow roll splitting mechanism for the axion potential is proposed which is realized with a special choice of the axion basis. In this basis the $2m$ coupled equations split into $2m-1$ equations which enter in the fast roll and there is one unique linear combination of the $2m$ fields which controls the slow roll and thus the power spectrum of curvature and tensor perturbations. It is shown that a significant part of the parameter space exists where inflation is successful, i.e., $N_{\rm pivot} = {[50, 60]}$, the spectral index $n_s$ of curvature perturbations, and the ratio $r$ of the power spectrum of tensor perturbations and curvature perturbations, lie in the experimentally allowed regions given by the Planck experiment. Further, it is shown that the model allows for a significant region of the parameter space where the effective axion decay constant can lie in the sub-Planckian domain.Comment: 31 pages, 10 figures. Accepted for publication in JHE