J. Pérez-Mercader

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.

Large-scale emergent properties of an autocatalytic reaction-diffusion model subject to noise

The nonequilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable fixed point at one-loop order, and the asymptotic scaling of the correlation functions is predicted for both spatial and temporally correlated noise sources. New effective three-body reaction terms, not present in the original GS model, are induced by the combined interplay of the fluctuations and nonlinearities.

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.

Schwinger's dynamical Casimir effect: Bulk energy contribution

Abstract Schwingers Dynamical Casimir Effect is one of several candidate explanations for sonoluminescence. Recently, several papers have claimed that Schwingers estimate of the Casimir energy involved is grossly inaccurate. In this letter, we show that these calculations omit the crucial volume term. When the missing term is correctly included one finds full agreement with Schwingers result for the Dynamical Casimir Effect. We have nothing new to say about sonoluminescence itself except to affirm that the Casimir effect is energetically adequate as a candidate explanation.

Proton stability in an asymptotically free SU(5) theory

Abstract In this note we point out a complication with the study of the mass-dependent low energy renormalization group equation for spontaneously broken gauge theories. We derive a new renormalization group theorem which avoids this complication. This theorem allows for a complete determination of an SU(5) grand unified theory that is asymptotically free. We report on the proton lifetime calculation including mass renormalization effects.

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.

Wormholes and scalar masses

Abstract We consider the effects of wormhole physics on the low energy masses of scalars. We take into account corrections to the effective action proportional to R3, where R is the Riemann-Christoffel tensor for the dominant topology in the effective action. We find that in S4, which is where a zero cosmological constant is most probable, the theory can readily support both zero mass and large mass scalars. We also find the existence of a regime where the scalar degrees of freedom shift from the zero mass domain to a massive domain.

The galaxy-galaxy correlation function as an indicator of critical phenomena in cosmology

Abstract We approximate the observable Universe by a collection of equal mass galaxies linked into a many body system by their mutual gravitational interaction. Under the assumptions of (i) nonrelativistic approximation and (ii) global quasi-equilibrium, the partition function of this system can be cast in terms of Ising model spin variables and maps exactly onto a three-dimensional scalar classical field theory. The full machinery of the renormalization group and critical phenomena is brought to bear on this field theory allowing one to calculate the galaxy-to-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, to be compared to the phenomenological/observational value of 1.6 to 1.8.

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.