Supersymmetric Unification at the Millenium

We argue that the discovery of neutrino mass effects at Super-Kamiokande implies a clear logical chain leading from the Standard Model, through the MSSM and the recently developed Minimal Left Right Supersymmetric models with a renormalizable see-saw mechanism for neutrino mass, to Left Right symmetric SUSY GUTS : in particular, SO(10) and $SU(2)_L \times SU(2)_R\times SU(4)_c$. The progress in constructing such GUTS explicitly is reviewed and their testability/falsifiability by lepton flavour violation and proton decay measurements emphasized. Susy violations of the survival principle and the interplay between third generation Yukawa coupling unification and the structurally stable IR attractive features of the RG flow in SUSY GUTS are also discussed .Comment: Plenary Talk at WHEPP-6, Chennai, India, Jan. 3-15, 2000. ReVTeX. 9 pages. Two pairs of figures as separate postscript fil

Influence of plant residues on denitrification rates in conventional and zero tilled soils, The

Includes bibliographical references (page 794).A field study was conducted with treatments consisting of a factorial combination of N (0 or 100 kg N ha−1 as (NH4)2SO4, straw (0 or 3000 kg ha−1), and two tillage treatments. Ground straw was mixed with the plow layer of soil in the conventional till (CT) plots and chopped straw was spread over the surface of the zero till (ZT) plots. Wheat (Triticum aestivum L.) was grown as the test crop. Gaseous losses of N were measured using the acetylene inhibition-soil core technique and compared with loss estimates obtained from the imbalance in the N budget of 15N-treated microplots located within the larger yield plots. When adequate inorganic N was present, the incorporation of straw in CT soil or the application of straw on the surface of ZT soil approximately doubled the accumulative gaseous N losses. The straw apparently increased the supply of energy material available to denitrifying organisms, and also increased surface soil moisture content (particularly during the month of June). This further stimulated denitrification in ZT soil. Unaccounted 15N on the fertilizer N balance studies agreed closely with cumulative N losses using the acetylene inhibition technique

Gaseous nitrogen losses from cropped and summer-fallowed soils

Includes bibliographical references (pages 195-196).A study designed to assess gaseous losses of N as N2O and N2 from soils of conventional till fields seeded to wheat in the Chernozemic soil region of Saskatchewan, together with limited supporting laboratory investigations, has confirmed that for the May-November period losses were in the vicinity of 3 kg N∙ha−1 or less. In contrast, total losses from a summer-fallowed field were approximately 300% higher. Comparisons at one site were made of N losses from a conventionally tilled and zero-tilled Dark Brown Chernozemic soil seeded to wheat; the total losses of N were twice as high for the zero till as the conventional till treatments. The N2O fluxes were shown to be the result of both reductive (denitrification) and oxidative (nitrification) processes and generally, under the conditions of these field experiments, both occurred simultaneously. This experiment also confirmed that C2H2 inhibited nitrification in a manner very similar to N-serve, a well-known nitrification inhibitor

Spontaneous Parity Violation in a Supersymmetric Left-Right Symmetric Model

We propose a novel implementation of spontaneous parity breaking in supersymmetric left-right symmetric model, avoiding some of the problems encountered in previous studies. This implementation includes a bitriplet and a singlet, in addition to the bidoublets which extend the Higgs sector of the Minimal Supersymmetric Standard Model (MSSM). The supersymmetric vacua of this theory are shown to lead generically to spontaneous violation of parity, while preserving R parity. The model is shown to reproduce the see-saw relation for vacuum expectation values, $v_L v_R \approx m_{EW}^2$ relating the new mass scales $v_L$, $v_R$ to the electroweak scale $m_{EW}$, just as in the non-supersymmetric version. The scale $v_R$ determines the mass scale of heavy majorana neutrinos, which gets related to the obeserved neutrino masses through type II see-saw relation.Comment: 12 pages, revtex

Nearly degenerate neutrinos, Supersymmetry and radiative corrections

If neutrinos are to play a relevant cosmological role, they must be essentially degenerate with a mass matrix of the bimaximal mixing type. We study this scenario in the MSSM framework, finding that if neutrino masses are produced by a see-saw mechanism, the radiative corrections give rise to mass splittings and mixing angles that can accommodate the atmospheric and the (large angle MSW) solar neutrino oscillations. This provides a natural origin for the $\Delta m^2_{sol} << \Delta m^2_{atm}$ hierarchy. On the other hand, the vacuum oscillation solution to the solar neutrino problem is always excluded. We discuss also in the SUSY scenario other possible effects of radiative corrections involving the new neutrino Yukawa couplings, including implications for triviality limits on the Majorana mass, the infrared fixed point value of the top Yukawa coupling, and gauge coupling and bottom-tau unification.Comment: 32 pages, 12 Postscript figures, uses psfig.st

Reconciling Supersymmetry and Left-Right Symmetry

We construct the minimal supersymmetric left-right theory and show that at the renormalizable level it requires the existence of an intermediate $B-L$ breaking scale. The subsequent symmetry breaking down to MSSM automatically preserves R-symmetry. Furthermore, unlike in the nonsupersymmetric version of the theory, the see-saw mechanism takes its canonical form. The theory predicts the existence of a triplet of Higgs scalars much lighter than the $B-L$ breaking scale.Comment: 4 pages, revtex, no figure

PeV scale Left-Right symmetry and baryon asymmetry of the Universe

We study the cosmology of two versions of supersymmetric Left-Right symmetric model. The scale of the $B-L$ symmetry breaking in these models is naturally low, $10^4 - 10^6$ GeV. Spontaneous breakdown of parity is accompanied by a first order phase transition. We simulate the domain walls of the phase transition and show that they provide requisite conditions, specifically, $CP$ violating phase needed for leptogenesis. Additionally soft resonant leptogenesis is conditionally viable in the two models considered. Some of the parameters in the soft supersymmetry breaking terms are shown to be constrained from these considerations. It is argued that the models may be testable in upcoming collider and cosmology experiments.Comment: 25 pages, 2 figures, revtex4, minor clarifications, references added, conclusion remains same, to appear in Nuclear Physics

Minimal SUSY SO(10) model and predictions for neutrino mixings and leptonic CP violation

We discuss a minimal Supersymmetric SO(10) model where B-L symmetry is broken by a {\bf 126} dimensional Higgs multiplet which also contributes to fermion masses in conjunction with a {\bf 10} dimensional superfield. This minimal Higgs choice provides a partial unification of neutrino flavor structure with that of quarks and has been shown to predict all three neutrino mixing angles and the solar mass splitting in agreement with observations, provided one uses the type II seesaw formula for neutrino masses. In this paper we generalize this analysis to include arbitrary CP phases in couplings and vevs. We find that (i) the predictions for neutrino mixings are similar with $U_{e3}\simeq 0.18$ as before and other parameters in a somewhat bigger range and (ii) that to first order in the quark mixing parameter $\lambda$ (the Cabibbo angle), the leptonic mixing matrix is CP conserving. We also find that in the absence of any higher dimensional contributions to fermion masses, the CKM phase is different from that of the standard model implying that there must be new contributions to quark CP violation from the supersymmetry breaking sector. Inclusion of higher dimensional terms however allows the standard model CKM phase to be maintained.Comment: 22 pages, 6 figure

R-parity violation in SU(5)

We show that judiciously chosen R-parity violating terms in the minimal renormalizable supersymmetric SU(5) are able to correct all the phenomenologically wrong mass relations between down quarks and charged leptons. The model can accommodate neutrino masses as well. One of the most striking consequences is a large mixing between the electron and the Higgsino. We show that this can still be in accord with data in some regions of the parameter space and possibly falsified in future experiments.Comment: 30 pages, 1 figure. Revised version. To appear in JHE