Borut Bajc

Localization of matter and cosmological constant on a brane in anti-de Sitter space

Abstract We study two issues, the localization of various spin fields, and the problem of the cosmological constant on a brane in five-dimensional anti de Sitter space. We find that spin-zero fields are localized on a positive-tension brane. In addition to the localized zero-mode there is a continuous tower of states with no mass gap. Spin one-half and three-half states can be localized on a brane with “negative tension”. Their localization can be achieved on the positive-tension brane as well, if additional interactions are introduced. The necessary ingredient of the scenario with localized gravity is the relation between the bulk cosmological constant and the brane tension. In the absence of supersymmetry this implies fine-tuning between the parameters of the theory. To deal with this issue we introduce a four-form gauge field. This gives an additional arbitrary contribution to the bulk cosmological constant. As a result, the model gives rise to a continuous family of brane Universe solutions for generic values of the bulk cosmological constant and the brane tension. Among these solutions there is one with a zero four-dimensional cosmological constant.

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.

Seesaw at LHC

We study the implementation of the type III seesaw in the ordinary nonsupersymmetric SU(5) grand unified theory. This allows for an alternative definition of the minimal SU(5) model, with the inclusion of the adjoint fermionic multiplet. The main prediction of the theory is the light fermionic SU(2) triplet with mass at the electroweak scale. Due to their gauge couplings, these triplets can be produced pair-wise via Drell-Yan, and due to the Majorana nature of the neutral component their decays leave a clear signature of same sign di-leptons and four jets. This allows for their possible discovery at LHC and provides an example of directly measurable seesaw parameters.

Proton decay in minimal supersymmetric SU(5)

We systematically study proton decay in the minimal supersymmetric SU(5) grand unified theory. We find that although the available parameter space of soft masses and mixings is quite constrained, the theory is still in accord with experiment.

Minimal supersymmetric grand unified theory: Symmetry breaking and the particle spectrum

We discuss in detail the symmetry breaking and related issues in the minimal renormalizable supersymmetric grand unified theory. We compute the particle spectrum and study its impact on the physical scales of the theory. This provides a framework for the analysis of phenomenological implications of the theory, to be carried out in part II.

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.

Probing the seesaw mechanism at CERN LHC

We have recently proposed a simple SU(5) theory with an adjoint fermionic multiplet on top of the usual minimal spectrum. This leads to the hybrid scenario of both type I and type III seesaw and it predicts the existence of the fermionic SU(2) triplet between 100 GeV and 1 TeV for a conventional GUT scale of about 1016 GeV, with main decays into W (Z) and leptons, correlated through Dirac Yukawa couplings, and lifetimes shorter than about 10−12 sec. These decays are lepton number violating and they offer an exciting signature of ∆L = 2 dilepton events together with 4 jets at future pp (pp̄) colliders. Increasing the triplet mass endangers the proton stability and so the seesaw mechanism could be directly testable at LHC.

Collider Signatures for Heavy Lepton Triplet in Type I+III Seesaw

The minimal SU(5) theory augmented by the fermionic adjoint representation restores the coupling constant unification and gives realistic neutrino masses and mixing through the hybrid Type I and Type III seesaw. The crucial prediction of the theory is an SU(2) lepton triplet with the mass below TeV. We study the signature of these heavy leptons at the hadron and lepton colliders. The smoking gun evidence of the theory, as in general seesaw mechanisms, is {Delta}L=2 lepton-number violation through events of a pair of like-sign leptons plus four jets without significant missing energy at hadron colliders. We find that via this unique channel the heavy lepton can be searched for up to a mass of 200 GeV at the Tevatron with 8 fb{sup -1}, and up to 450 (700) GeV at the LHC of 14 TeV C.M. energy with 10(100) fb{sup -1}. The 7 TeV LHC run of 1 fb{sup -1} is expected to probe a mass window of 110-200 GeV. We also comment on how to distinguish this theory from other models with similar heavy leptons. Finally, we compare the production rates and angular distributions of heavy leptons in e{sup +}e{sup -} collisions for various models.

Yukawa sector in nonsupersymmetric renormalizable SO(10)

We discuss the ordinary, nonsupersymmetric SO(10) as a theory of fermion masses and mixings. We construct two minimal versions of the Yukawa sector based on 126{sub H} and either 10{sub H} or 120{sub 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}{sub A}. It also relates the smallness of V{sub cb} with the largeness of {theta}{sub 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.

Fermion mass relations and the structure of the light Higgs in a supersymmetric SO(10) theory

Neutrino and charged fermion masses provide important constraints on grand unified theories. We illustrate this by focusing on a renormalizable, supersymmetric SO(10) theory proposed long ago, that recently attracted great interest in view of its minimality. We show how the nature of the light Higgs, which depends on the GUT scale fields, gets reflected on the precise predictions for fermion masses and mixings. We exemplify this on the case of dominant Type II see-saw, which gets severely constrained and is likely to fail.