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

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

Rational Design of Pore Size and Functionality in a Series of Isoreticular Zwitterionic Metal-Organic Frameworks

The isoreticular expansion and functionalization of charged-polarized porosity has been systematically explored by the rational design of 11 isostructural zwitterionic metal-organic frameworks (ZW-MOFs). This extended series of general structural composition {[M3F(L1)3(L2)1.5]·guests}n was prepared by employing the solvothermal reaction of Co and Ni tetrafluoroborates with a binary ligand system composed of zwitterionic pyridinium derivatives and traditional functionalized ditopic carboxylate auxiliary ligands (HL1·Cl = 1-(4-carboxyphenyl)-4,4′-bipyridinium chloride, Hcpb·Cl; or 1-(4-carboxyphenyl-3-hydroxyphenyl)-4,4′-bipyridinium chloride, Hchpb·Cl; and H2L2 = benzene-1,4-dicarboxylic acid, H2bdc; 2-aminobenzene-1,4-dicarboxylic acid, H2abdc; 2,5-dihydroxy-1,4-benzenedicarboxylic acid, H2dhbdc; biphenyl-4,4′-dicarboxylic acid, H2bpdc; or stilbene-4,4′-dicarboxylic acid, H2sdc). Single-crystal structure analyses revealed cubic crystal symmetry (I-43m, a = 31-36 Å) with a 3D pore system of significant void space (73-81%). The pore system features three types of pores being systematically tunable in size ranging from 17.4 to 18.8 Å (pore I), 8.2 to 12.8 Å (pore II), and 4.8 to 10.4 Å (pore III) by the choice of auxiliary ligands. All members of this series have noninterpenetrating structures and exhibit robust architectures, as evidenced by their permanent porosity and high thermal stability (up to 300 °C). The structural integrity and specific surface areas could be systematically optimized using supercritical CO2 exchange methods for framework activation resulting in BET surface areas ranging from 1250 to 2250 m2/g. Most interestingly, as a structural landmark, we found the pore surfaces lined with charge gradients employed by the pyridinium ligands. This key feature results in significant adsorption of carbon dioxide and methane which is attributed to polarization effects. With this contribution we pioneer the reticulation of pyridinium building blocks into extended zwitterionic networks in which specific properties can be targeted

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

High scale perturbative gauge coupling in R-parity conserving SUSY SO(10) with longer proton lifetime

It is well known that in single step breaking of R-parity conserving SUSY SO(10) that needs the Higgs representations $126+\bar 126$ the GUT-gauge coupling violates the perturbative constraint at mass scales few times larger than the GUT scale. Therefore, if the SO(10) gauge coupling is to remain perturbative up the Planck scale(=2x10^{18} GeV), the scale $M_U$ of GUT symmetry breaking is to be bounded from below. The bound depends upon specific Higgs representations used for SO(10) symmetry breaking but, as we find, can not be lower than $1.5x10^{17}$ GeV. In order to obtain such high unification scale we propose a two-step SO(10) breaking through $SU(2)_LXSU(2)_RXU(1)_{B-L}XSU(3)_C(g_{2L} \neq g_{2R})$ intermediate gauge symmetry. We estimate potential threshold and gravitational corrections to the running of gauge couplings and show that they can make the picture of perturbative GUT- gauge coupling running consistent at least up to the Planck scale. We also show that when $SO(10) \to G_{2213}$ by $210 + 54$, gravitational corrections alone with negligible threshold effects may guarantee such perturbative gauge coupling. The lifetime of the proton is found to increase by nearly 6 orders over the current experimental limit for $p \to e^+\pi^0$. For the proton decay mediated by dim.5 operator a wide range of lifetimes is possible extending from the current experimental limit up to values 2-3 orders longer.Comment: 11 pages epjc LaTex as per specifications of European Physical Journal

Effects of R-parity violation on direct CP violation in B decays and extraction of γ\gamma

In the standard model, direct CP-violating asymmetries for $B^\pm \to \pi^\pm K$ are roughly 2% based on perturbative calculation. Rescattering effects might enhance it to at most (20-25)%. We show that lepton-number-violating couplings in supersymmetric models without R-parity are capable of inducing as large as 100% CP asymmetry in this channel. Such effects drastically modify the allowed range of the CKM parameter $\gamma$ arising from the combinations of the observed charged and neutral B decays in the $\pi K$ modes. With a multichannel analysis in B decays, one can either discover this exciting new physics, or significantly improve the existing constraints on it.Comment: Latex, 5 pages; minor changes, to appear in Phys Rev Let

Wilson Lines and a Canonical Basis of SU(4) Heterotic Standard Models

The spontaneous breaking of SU(4) heterotic standard models by Z_3 x Z_3 Wilson lines to the MSSM with three right-handed neutrino supermultiplets and gauge group SU(3)_C x SU(2)_L x U(1) x U(1) is explored. The two-dimensional subspace of the Spin(10) Lie algebra that commutes with su(3)_C + su(2)_L is analyzed. It is shown that there is a unique basis for which the initial soft supersymmetry breaking parameters are uncorrelated and for which the U(1) x U(1) field strengths have no kinetic mixing at any scale. If the Wilson lines "turn on" at different scales, there is an intermediate regime with either a left-right or a Pati-Salam type model. We compute their spectra directly from string theory, and adjust the associated mass parameter so that all gauge parameters exactly unify. A detailed analysis of the running gauge couplings and soft gaugino masses is presented.Comment: 59 pages, 9 figure

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

Higgs sector and R-parity breaking couplings in models with broken U(1)_B-L gauge symmetry

Four different supersymmetric models based on SU(2)_L X U(1)_R X U(1)_B-L and SU(2)_L X SU(2)_R X U(1)_B-L gauge symmetry groups are studied. U(1)_B-L symmetry is broken spontaneously by a vacuum expectation value (VEV) of a sneutrino field. The right-handed gauge bosons may obtain their mass solely by sneutrino VEV. The physical charged lepton and neutrino are mixtures of gauginos, higgsinos and lepton interaction eigenstates. Explicit formulae for masses and mixings in the physical lepton fields are found. The spontaneous symmetry breaking mechanism fixes the trilinear R-parity breaking couplings. Only some special R-parity breaking trilinear couplings are allowed. There is a potentially large trilinear lepton number breaking coupling - which is unique to left-right models - that is proportional to the SU(2)_R gauge coupling g_R. The couplings are parametrized by few mixing angles, making the spontaneous R-parity breaking a natural ``unification framework'' for R-parity breaking couplings in SUSYLR models.Comment: 19 pages, no figures, uses REVTeX. To be published in PR

Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,R), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown that any non-trivial co-cycle from the local BRST cohomology group H(s|d) can be taken to stop either at antighost number (k+1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H(gamma) and containing non-trivial elements from the (invariant) characteristic cohomology H^{inv}(delta|d).Comment: Latex, 50 pages, uses amssym