Limits on SUSY particle Spectra from Proton Stability and Dark Matter Constraints

It is shown that the combined constraints on the amount of cold dark matter and of proton stability produce a stringent upper limit on the gluino mass $m_{\tilde g}$ (and hence on the lightest neutralino mass $m_{\chi_1^0}\simeq m_{\tilde g}/7$) for a large class of gravity mediated supergravity unified models. One finds that for the minimal SU(5) model current data (Kamiokande) restricts $m_{\tilde g}\leq 400$ GeV for a scalar soft breaking mass $m_0\leq 1$ TeV. Expected future data from Super Kamionkande and ICARUS will be sensitive to the entire range of gluino mass for $m_0\leq 1$ TeV, and be able to exclude the region $m_{\tilde g}\geq 500$ GeV for $m_0\leq 5$ TeV. Effects of quark mass textures are studied and one finds that the bound $m_{\tilde g}\leq 500$ GeV holds when the experimental proton lifetime for the $p\to \bar \nu K^+$ mode becomes $\geq 5\times 10^{32}$ yr.Implications of these results for a test of these models at the Tevatron and at the LHC are discussed. The effects of non-universal soft breaking in the Higgs and the third generation squark sectors are also examined, and it is found that the proton lifetime is sensitive to these non-universal effects. The current data already eliminates some regions of non-universalities. The constraints of proton stability on the direct detection of dark matter are seen to reduce the maximum event rates by as much as a factor of $10^3$.Comment: 13 pages including 5 figure

Neutralino Proton Cross Sections In Supergravity Models

The neutralino-proton cross section is examined for supergravity models with R-parity invariance with universal and non-universal soft breaking. The region of parameter space that dark matter detectors are currently (or will be shortly) sensitive i.e. $(0.1-10)\times 10^{-6}$ pb, is examined. For universal soft breaking (mSUGRA), detectors with sensitivity $\sigma_{\tilde{\chi}_{1}^{0}-p} \geq 1 \times 10^{-6}$ pb will be able to sample parts of the parameter space for $\tan \beta \stackrel{>}{\sim} 25$. Current relic density bounds restrict $m_{\tilde{\chi}_{1}^{0}} \leq 120$ GeV for the maximum cross sections, which is below where astronomical uncertainties about the Milky Way are relevant. Nonuniversal soft breaking models can allow much larger cross sections and can sample the parameter space for $\tan \beta \stackrel{>}{\sim} 4$. In such models, $m_0$ can be quite large reducing the tension between proton decay bounds and dark matter analysis. We note the existance of two new domains where coannihilation effects can enter, i.e. for mSUGRA at large $\tan \beta$, and for nonuniversal models with small $\tan \beta$.Comment: 22 pages, latex, 18 figure

Dark Matter in SUSY Models

Direct detection experiments for neutralino dark matter in the Milky Way are examined within the framework of SUGRA models with R-parity invariance and grand unification at the GUT scale, M_G. Models of this type apply to a large number of phenomena, and all existing bounds on the SUSY parameter space due to current experimental constraints are included. For models with universal soft breaking at M_G (mSUGRA), the Higgs mass and b\to s\gamma constraints imply that the gaugino mass, m_{1/2}, obeys m_{1/2} >(300-400)GeV putting most of the parameter space in the co-annihilation domain where there is a relatively narrow band in the m_0 - m_{1/2} plane. For $\mu > 0$ we find that the neutralino -proton cross section >~ 10^{-10} pb for m_{1/2} < 1 TeV, making almost all of this parameter space accessible to future planned detectors. For \mu < 0, however, there will be large regions of parameter space with cross sections < 10^{-12} pb, and hence unaccessible experimentally. If, however, the muon magnetic moment anomaly is confirmed, then \mu >0 and m_{1/2}<~ 800 GeV. Models with non-universal soft breaking in the third generation and Higgs sector can allow for new effects arising from additional early universe annihilation through the Z-channel pole. Here cross sections that will be accessible in the near future to the next generation of detectors can arise, and can even rise to the large values implied by the DAMA data. Thus dark matter detectors have the possibility of studying the the post-GUT physics that control the patterns of soft breaking.Comment: 13 pages, latex, 10 figures, invited talk at NANP-01, Dubna, Russia, June 19--23, 200

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

Gravitational Forces on the Branes

We examine the gravitational forces in a brane-world scenario felt by point particles on two 3-branes bounding a 5-dimensional AdS space with $S^{1}/Z_2$ symmetry. The particles are treated as perturbations on the vacuum metric and coordinate conditions are chosen so that no brane bending effects occur. We make an ADM type decomposition of the metric tensor and solve Einstein's equations to linear order in the static limit. While no stabilization mechanism is assumed, all the 5D Einstein equations are solved and are seen to have a consistent solution. We find that Newton's law is reproduced on the Planck brane at the origin while particles on the TeV brane a distance $y_2$ from the origin experience an attractive force that has a growing exponential dependence on the brane position.Comment: Based on a talk given at PASCOS 2004/Pran Nath Fes

Supergravity Unified Models

The development of supergravity unified models and their implications for current and future experiments are discussed.Comment: Latex, 21 pages, to appear in book "Perspectives on Supergravity", World Scientific, Editor G. Kane; reference numbers and minor typos correcte