Developments in Supergravity Unified Models

A review is given of developments in supergravity unified models proposed in 1982 and their implications for current and future experiment are discussed.Comment: 24 pages, 1 figure. To appear in "Perspectives on Supersymmetry II"", edited by Gordon Kan

Very Large Intermediate Breaking Scale In The Gepner Three Generation Model

A detailed study of the intermediate symmetry breaking scale, via the renormalization group equations, for a three generation heterotic string model arising from the N=2 superconformal construction is reported. The numerical study shows that the model admits a very large intermediate breaking scale \op{>}{\sim}1.0\times10^{16} GeV. The role of the gauge singlets in this model is studied, and it is found that these fields play a crucial role in determining the directions and the scale of the intermediate symmetry breaking. The importance of the mixing in generation space is also studied. The generation mixing terms are found to have special effects in the intermediate symmetry breaking. Remarkably these terms can produce some {\it new} Yukawa couplings (not present at the Planck scale) through loops. These couplings are in general very small compared to the ones with non-vanishing tree level values and thus offer a {\it new} mechanism to solve the lepton/quark mass hierarchy problem.Comment: 19 pages, Plain Tex (Three Figures not included

Hyperbolicity and Constrained Evolution in Linearized Gravity

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them ({\it unconstrained} evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly "more correct" to introduce a scheme which actively maintains the constraints by solution ({\it constrained} evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations.Comment: 18 page

Sensitivity of dark matter dectectors to SUSY dark matter

ABSTRACT The sensitivity of dark matter detectors to the lightest neutralino ({\tilde {Z}_1}) is considered within the framework of supergravity grand unification with radiative breaking of SU(2)xU(1). The relic density of the {\tilde {Z}_1} is constrained to obey 0.10 \leq \Omega_{\tilde {Z}_1}h^2 \leq 0.35, consistent with COBE data and current measurements of the Hubble constant. Detectors can be divided into two classes: those most sensitive to spin dependent incoherent scattering of the {\tilde {Z}_1} (e.g. CaF_2) and those most sensitive to spin independent coherent scattering (high A nuclei e.g. Pb). The parameter space is studied over the range of 100GeV \leq m_0, m_{\tilde {g}} \leq 1~TeV; 2 \leq tan\beta \leq 20; and -2 \leq A_t/m_0 \leq 3 and it is found that the latter type detector is generally more sensitive than the former type. Thus at a sensitivity level of R \geq 0.1 events/kg da, a lead detector could scan roughtly 30\% of the ~parameter space studied, and an increase of ~this sensitivity by a factor of 10 ~would lead to coverage of about 70\% of the parameter space. Dark matter detectors are in general more sensitive to the high tan\beta, low m_{\tilde {g}} and low m_0 parts of the parameter space. The conditions of radiative breaking of SU(2)xU(1) enter importantly in analysing the efficiency of dark matter detectors

The Stau Neutralino Co-annihilation Region at an International Linear Collider

We probe the stau-neutralino co-annihilation domain of the parameter space allowed by the current experimental bounds on the light Higgs mass, the b-> s \gamma decay, and the amount of neutralino cold dark matter within the framework of minimal SUGRA models at a 500 GeV e+e- linear collider. The most favorable signals of SUSY are stau pair production and neutralino pair production where the small mass difference between the lighter stau and the lightest neutralino in the co-annihilation region is ~5-15 GeV and hence generates low-energy tau leptons in the final state. This small mass difference would be a striking signal of many SUGRA models. We find that a calorimeter covering down to 1^o from the beams is crucial to reduce the two-photon background and the mass difference could be measured at a level of 10% with 500 fb^-1 of data where an invariant mass of two-tau jets and missing energy is used as a discriminator.Comment: 17 pages, 7 figure