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

On the vacuum of the minimal nonsupersymmetric SO(10) unification

We study a class of nonsupersymmetric SO(10) grand unified scenarios where the first stage of the symmetry breaking is driven by the vacuum expectation values of the 45-dimensional adjoint representation. Three decade old results claim that such a Higgs setting may lead exclusively to the flipped SU(5) x U(1) intermediate stage. We show that this conclusion is actually an artifact of the tree level potential. The study of the accidental global symmetries emerging in various limits of the scalar potential offers a simple understanding of the tree level result and a rationale for the drastic impact of quantum corrections. We scrutinize in detail the simplest and paradigmatic case of the 45_{H} + 16_{H} Higgs sector triggering the breaking of SO(10) to the standard electroweak model. We show that the minimization of the one-loop effective potential allows for intermediate SU(4)_C x SU(2)_L x U(1)_R and SU(3)_c x SU(2)_L x SU(2)_R x U(1)_{B-L} symmetric stages as well. These are the options favoured by gauge unification. Our results, that apply whenever the SO(10) breaking is triggered by , open the path for hunting the simplest realistic scenario of nonsupersymmetric SO(10) grand unification.Comment: 22 pages, 1 figure. Refs added. To appear in Phys. Rev.

Yukawa sector in non-supersymmetric renormalizable SO(10)

We discuss the ordinary, non-supersymmetric SO(10) as a theory of fermion masses and mixings. We construct two minimal versions of the Yukawa sector based on $\bar{126}_H$ and either $10_H$ or $120_H$. The latter case is of particular interest since it connects the absolute neutrino mass scale with the size of the atmospheric mixing angle $\theta_A$. It also relates the smallness of $V_{cb}$ with the largeness of $\theta_A$. These results are based on the analytic study of the second and third generations. Furthermore, we discuss the structure of the light Higgs and the role of the Peccei-Quinn symmetry for dark matter and the predictivity of the theory.Comment: 8 pages. Reference added, one formula correcte

Supersymmetric Unification in the Light of Neutrino Mass

We argue that with the discovery of neutrino mass effects at Super-Kamiokande there is 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 proton decay measurements emphasized.Comment: 16 pages, REVTEX. Invited talk presented at XIII DAE Symposium on High Energy Physics, Chandigarh, December 199

A renormalizable SO(10) GUT scenario with spontaneous CP violation

We consider fermion masses and mixings in a renormalizable SUSY SO(10) GUT with Yukawa couplings of scalar fields in the representation 10 + 120 + 126 bar. We investigate a scenario defined by the following assumptions: i) A single large scale in the theory, the GUT scale. ii) Small neutrino masses generated by the type I seesaw mechanism with negligible type II contributions. iii) A suitable form of spontaneous CP breaking which induces hermitian mass matrices for all fermion mass terms of the Dirac type. Our assumptions define an 18-parameter scenario for the fermion mass matrices for 18 experimentally known observables. Performing a numerical analysis, we find excellent fits to all observables in the case of both the normal and inverted neutrino mass spectrum.Comment: 16 pages, two eps figure

Like Sign Dilepton Signature for R-Parity Violating SUSY Search at the Tevatron Collider

The like sign dileptons provide the most promising signature for superparticle search in a large category of $R$-parity violating SUSY models. We estimate the like sign dilepton signals at the Tevatron collider, predicted by these models, over a wide region of the MSSM parameter space. One expects an unambiguous signal upto a gluino mass of $200 - 300$ GeV ($\geq 500$ GeV) with the present (proposed) accumulated luminosity of $\sim 0.1~(1)~{\rm fb}^{-1}$.Comment: 12 page LaTeX file; 5 figures available upon request from the autho

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

Lepton Number Violating Radiative WW Decay in Models with R-parity Violation

Models with explicit R-parity violation can induce new rare radiative decay modes of the $W$ boson into single supersymmetric particles which also violate lepton number. We examine the rate and signature for one such decay, $W\rightarrow \tilde l\gamma$, and find that such a mode will be very difficult to observe, due its small branching fraction, even if the lepton number violating coupling in the superpotential is comparable in strength to electromagnetism. This parallels a similar result obtained earlier by Hewett in the case of radiative $Z$ decays.Comment: 10 pages, 2 figures(available on request), LaTex, ANL-HEP-PR-92-8

Baryogenesis with Scalar Bilinears

We show that if a baryon asymmetry of the universe is generated through the out-of-equilibrium decays of heavy scalar bilinears coupling to two fermions of the minimal standard model, it is necessarily an asymmetry conserving $(B-L)$ which cannot survive past the electroweak phase transition because of sphalerons. We then show that a surviving $(B-L)$ asymmetry may be generated if the heavy scalars decay into two fermions, \underline {and into two light scalars} (which may be detectable at hadron colliders). We list all possible such trilinear scalar interactions, and discuss how our new baryogenesis scenario may occur naturally in supersymmetric grand unified theories.Comment: LATEX, 14 pages, one figure include

Impact of R-Parity Violation on Supersymmetry Searches at the Tevatron

We evaluate cross sections for \eslt, 1$\ell$ and various dilepton and multilepton event topologies that result from the simultaneous production of all sparticles at the Tevatron collider, both within the minimal model framework as well as in two different $R$-parity violating scenarios. Our analysis assumes that these $R$-violating couplings are small, and that their sole effect is to cause the lightest supersymmetric particle to decay inside the detector. We reassess future strategies for sparticle searches at the Tevatron, and quantify by how much the various signals for supersymmetry could differ from their minimal model expectations, if $R$-parity is not conserved due to either baryon number or lepton number violating operators. We also evaluate the Tevatron reach in $m_{\tg}$ for the various models, and find that rate-limited multilepton signals ultimately provide the largest reach for both $R$-parity conserving and $R$-parity violating cases.Comment: preprint nos. FSU-HEP-941001, UR-1387, ER-40685-836 and UH-511-807-94, 13 pages (REVTEX) plus 3 uuencoded figures attache