Electroweak Precision Data, Light Sleptons and Stability of the SUSY Scalar Potential

The light slepton-sneutrino scenario with non-universal scalar masses at the GUT scale is preferred by the electroweak precision data. Though a universal soft breaking mass at or below the Plank scale can produce the required non-universality at the GUT scale through running, such models are in conflict with the stability of the electroweak symmetry breaking vacuum. If the supergravity motivated idea of a common scalar mass at some high scale along with light sleptons is supported by future experiments that may indicate that we are living in a false vacuum. In contrast SO(10) D-terms, which may arise if this GUT group breaks down directly to the Standard Model, can lead to this spectrum with many striking phenomenological predictions, without jeopardizing vacuum stability.Comment: Plain Latex, 17 pages, 5 postscript figur

Are light sneutrinos buried in LEP data?

Supersymmetry may resolve the disagreement between the precision electroweak data and the direct limit on the higgs mass, if there are light sneutrinos in the mass range 55 GeV < m_{\snu} < 80 GeV. Such sneutrinos should decay invisibly with 100% branching ratio and contribute to the $\gamma$ + missing energy signal, investigated by all the LEP groups. It is shown that while the data accumulated by a single group may not be adequate to reveal such sneutrinos, a combined analysis of the data collected by all four groups will be sensitive to m_{\snu} in the above range. If no signal is found a lower bound on m_{\snu} stronger than that obtained from the $Z$-pole data may emerge.Comment: 12 pages, LaTeX, 1 postscript figure included, uses epsfig.sty Minor revisions in the discussion of future prospects, 1 ref adde

LHC Signature of the Minimal SUGRA Model with a Large Soft Scalar Mass

Thanks to the focus point phenomenon, it is quite {\it natural} for the minimal SUGRA model to have a large soft scalar mass m_0 > 1 TeV. A distinctive feature of this model is an inverted hierarchy, where the lighter stop has a significantly smaller mass than the other squarks and sleptons. Consequently, the gluino is predicted to decay dominantly via stop exchange into a channel containing 2b and 2W along with the LSP. We exploit this feature to construct a robust signature for this model at the LHC in leptonic channels with 3-4 b-tags and a large missing-E_T.Comment: Small clarifications added. Final version to appear in Phys. Lett.

Self-Repairing Codes for Distributed Storage - A Projective Geometric Construction

Self-Repairing Codes (SRC) are codes designed to suit the need of coding for distributed networked storage: they not only allow stored data to be recovered even in the presence of node failures, they also provide a repair mechanism where as little as two live nodes can be contacted to regenerate the data of a failed node. In this paper, we propose a new instance of self-repairing codes, based on constructions of spreads coming from projective geometry. We study some of their properties to demonstrate the suitability of these codes for distributed networked storage.Comment: 5 pages, 2 figure

Minimal Triangulations of Manifolds

In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a given pl manifold. (ii) Given positive integers $n$ and $d$, construction of $n$-vertex triangulations of different $d$-dimensional pl manifolds. (iii) Classifications of all the triangulations of a given pl manifold with same number of vertices. In Section 1, we have given all the definitions which are required for the remaining part of this article. In Section 2, we have presented a very brief history of triangulations of manifolds. In Section 3, we have presented examples of several vertex-minimal triangulations. In Section 4, we have presented some interesting results on triangulations of manifolds. In particular, we have stated the Lower Bound Theorem and the Upper Bound Theorem. In Section 5, we have stated several results on minimal triangulations without proofs. Proofs are available in the references mentioned there.Comment: Survey article, 29 page