Charanjit S. Aulakh

The neutrino as the supersymmetric partner of the majoron

Abstract We show that a supersymmetric extension of the standard SU (2) L ×U(1) model provides a natural framework for spontaneous breakdown of global lepton number symmetry leading to a “doublet” majoron with neutrino as its supersymmetric partner. A characteristic of this model is the appearance of a new contribution to neutrinoless double beta-decay (ββ)0ν mediated by the photino λγ which, however, is negligible for reasonable photino masses. We also predict the existence of a light mass (∼100 keV) scalar boson very weakly coupled to matter.

The minimal supersymmetric grand unified theory

Abstract We show that the minimal renormalizable supersymmetric SO(10) GUT with the usual three generations of spinors has a Higgs sector consisting only of a “light” 10 dimensional and “heavy” 126 , 126 and 210 supermultiplets. The theory has only two sets of Yukawa couplings with fifteen real parameters and ten real parameters in the Higgs superpotential. It accounts correctly for all the fermion masses and mixings, neutrinos included. The theory predicts at low energies the MSSM with exact R-parity. It is arguably the minimal consistent supersymmetric grand unified theory.

SO(10) theory of R-parity and neutrino mass

Abstract We study the Higgs sector of a SO(10) grand unified theory which predicts exact conservation of R-parity at all scales and incorporates the see-saw mechanism. We find possible intermediate scales and light states compatible with the constraints coming from the running of the gauge couplings. Such a pattern could lower the SO(10) breaking scale, allowing the d=6 proton decay operators to be comparable in magnitude to the d=5 ones.

Higher spin fields with mixed symmetry

Abstract Gauge invariant and gauge fixed BRS invariant actions are constructed in arbitrary dimensions for free massless integer spin fields carrying mixed representations of the Lorentz group described by Young tableaux (2, 1, 1, …, 1)n. The complete ghost spectrum is deduced by demanding nilpotency of the BRS transformations and leads to a correct count of the on-shell degrees of freedom. Dimensional reduction is used to study the corresponding gauge invariant massive theory. On-shell consistency is then ensured by the fact that the masses arise via a “telescopic Higgs effect”.

Minimal Supersymmetric Left-Right Model

We construct the truly minimal left-right symmetric model by utilizing only the fields dictated by supersymmetry and automatic R-parity conservation. Allowing for non-renormalizable operators in the superpotential, we show that parity can be spontaneously broken while preserving electromagnetic gauge invariance. The scale of parity breakdown is predicted in the intermediate region:

Reconciling High-Scale Left-Right Symmetry with Supersymmetry

M_R > 10^{10}- 10^{11} GeV

See-saw and supersymmetry or exact R-parity

, and R-parity remains exact. The theory contains a number of charged and doubly charged Higgs scalars with a low mass of order

MSGUT : From bloom to doom

M_R^2/M_{Planck}

Supersymmetry and large scale left-right symmetry

, accessible to experiment.

The New Minimal Supersymmetric GUT : Spectra, RG analysis and Fermion Fits

We construct the minimal supersymmetric left-right theory and show that at the renormalizable level it requires the existence of an intermediate