J. León

Renormalization group analysis for a general softly broken supersymmetric gauge theory

Abstract By using effective potential methods, we obtain the 1-loop renormalization group equations (RGEs) for an arbitrary softly broken supersymmetric gauge theory. Their solutions are explicitly exhibited. In particular for the parameters in the superpotential the evolution with the scale turns out to be given by finite multiplicative renormalizations. We analyze the possible sources and evolution of a cosmological constant term. Troubles with hierarchy stability in the presence of light singlet fields are displayed. As an application, the RGEs for the SU(5) theory are solved analytically with emphasis on cosmologically acceptable models (CAMs). We give absolute upper bounds on the top quark mass, based on both SU(5) and SU(3)×SU(2)×U(1) evolution of its Yukawa coupling. We also study how the initial conditions for the SU(3)×SU(2)×U(1) simple supergravity theory get modified due to SU(5) running. Finally we show the tendency of the CAM to be unstable in the adjoint Higgs sector.

A sensible finite SU(5) SUSY gut

Abstract We construct a one-loop finite grand unified SU(5) model with softly broken SUSY. Doublet-triplet splitting requires two fine-tunings and electroweak breaking goes through dimensional transmutation with a 40 GeV top quark. The superpartner spectrum is very tightly constrained and may be parametrized in terms of only one free parameter; it displays the properties that the gravitino mass is unobservable at low energy and the heavier squarks and the gluino are quasi-degenerate. For a slepton of 20 GeV, the photino has a mass of 15 GeV and there is a radiative Higgs with O(5 GeV) mass. We also find that in this type of scenario there is an absolute lower bound on the mass of the top quark of 32 GeV.

Local susy breaking induced by the GUT phase transition in the early universe

Abstract We show that the confining properties of the grand unification theory (GUT) may induce a transition to a ground state where both local SUSY and gauge symmetry are broken. The super-Higgs field belongs to the adjoint representation which breaks gauge symmetry taking a VEV of the order of the grand unification scale M X . A suitable class of superpotentials is proposed. We show that the critical temperature of the phase transition is 10 10 GeV. We get an approximate relation between M X and the gravitino mass: m 3 2 M ≅M X 2 exp (− 4π b SU(5) α GUT ).

Is spontaneous breaking of R-parity feasible in minimal low-energy supergravity?

Abstract Spontaneous violation of lepton number without breaking Lorentz invariance can, in principle, be incorporated in models with softly broken supersymmetry. We study the situation for minimal low-energy supergravity models coming from a GUT (hence not having hierarchy destabilizing light singlets) and where the SU(2) × U(1) breaking is radiative. It is found that for this type of model, R -parity breaking requires either too heavy a top quark for a realistic superpartner spectrum or too light a superpartner spectrum for a realistic top quark, making the spontaneous violation of lepton number in the third generation incompatible with present experimental data. We do not discard the possibility of having it in a fourth, heavier, generation.

Radiative residues of grand unification in the low energy phenomenology of simple supergravity

Abstract The radiative breaking of SU(2)L×U(1)Y in a cosmologically acceptable N = 1 supergravity model is reanalysed when the running of parameters, between the Planck and grand unification scales, is considered. The SU(5) running strongly constrains the conditions for stable radiative breaking, pointing towards very small tree level gaugino masses.

Supergravity induced radiative breaking of SU(5)

Abstract Using renormalization group techniques is spontaneously broken supergravity grand unified theories we show that quantum effects can produce the breaking of SU(5). We use a model in which the gauge group is unbroken at the level. The supergravity-induced soft-breaking terms are responsible for the radiative gravitino mass. For cosmologically acceptable models we find a remarkable with the low energy predictions for αGUT and MX. No fine tunings are required.

Towards a realistic supersymmetric SU8 model

Abstract Flavour superunification is accomplished via a SU 8 supersymmetric model, free of anomalies, asymptotically free, and with three families of light fermions, through a SU 8 → SU 5 → SU 3 × SU 2 × U 1 breaking. Possible patterns of supersymmetry breaking are described.

The Decoupling Theorem in Supersymmetric Theories

Abstract We introduce a superfield extension of Weisbergers method for decoupling calculations in multiscale field theories and generalize our previous method which does not require the computation of any Feynman diagram. We illustrate this for the two-scale Wess-Zumino model, showing explicitly how the decoupling takes place.

Spontaneously broken supersymmetric models free of fine-tuned parameters and ΔB, ΔL troubles (I). General survey

Abstract We propose a class of supersymmetric models based on canonical U( n ) gauge groups with the following properties: (i) absence of anomalies; (ii) no quadratic renormalizations for the D terms; (iii) absence of fine-tuned parameters; (iv) spontaneous SUSY breaking a la Fayet-Iliopoulos; (v) free of unobserved effective ΔB ≠ 0 and ΔL ≠ 0 interactions.

Patterns of local supersymmetry breaking in SUSY GUTS

Abstract The super-Higgs effect is analyzed in the framework of SUSY GUTS. We consider the cases where: (i) local SUSY is broken through a gauge singlet field, and (ii) local SUSY and the grand unification group are simultaneously broken when a non singlet field takes a non zero VEV. The second case is illustrated with the SU 5 SUSY GUT where the adjoint plays the role of the super-Higgs fields.