J.A. Casas

Model-independent properties and cosmological implications of the dilaton and moduli sectors of 4-D strings

Abstract We show that if there is a realistic 4D string, the dilaton and moduli supermultiplets will generically acquire a small mass ∼ O(m 3 2 ) , providing the only vacuum-independent evidence of low-energy physics in string theory beyond the supersymmetric standard model. The only assumptions behind this result are (i) softly broken supersymmetry at low energies with zero cosmological constant, (ii) these particles interact with gravitational strength and the scalar components have a flat potential in perturbation theory, which are well-known properties of string theories. (iii) They acquire a VEV of the order of the Planck scale (as required for the correct value of the gauge coupling constants and the expected compactification scale) after supersymmetry gets broken. We explore the cosmological implications of these particles. Similar to the gravitino, the fermionic states may overclose the Universe if they are stable or destroy nucleosynthesis if they decay unless their masses belong to a certain range or inflation dilutes them. For the scalar states it is known that the problem cannot be entirely solved by inflation, since oscillations around the minimum of the potential, rather than thermal production, are the main source for their energy and can lead to a huge entropy generation at late times. We discuss some possible ways to alleviate this entropy problem, that favour low-temperature baryogenesis, and also comment on the possible role of these particles as dark matter candidates or as sources of the baryon asymmetry through their decay.

The lightest Higgs boson mass in the Minimal Supersymmetric Standard Model

We compute the upper bound on the mass of the lightest Higgs boson in the Minimal Supersymmetric Standard Model in a model-independent way, including leading (one-loop) and next-to-leading order (two-loop) radiative corrections. We find that (contrary to some recent claims) the two-loop corrections are negative with respect to the one-loop result and relatively small (⪅ 3%). After defining physical (pole) top quark mass Mt, by including QCD self-energies, and physical Higgs mass MH, by including the electroweak self-energies ∏ (MH2) − ∏ (0), we obtain the upper limit on MH as a function of supersymmetric parameters. We include as supersymmetric parameters the scale of supersymmetry breaking Ms, the value of tan β and the mixing between stops Xt = At + μ cot β (which is responsible for the threshold correction on the Higgs quartic coupling). Our results do not depend on further details of the supersymmetric model. In particular, for Ms ⩽ 1 TeV, maximal threshold effect Xt2 = 6MS2 and any value of tan β, we find MH ⩽ 140 GeV for Mt ⩽ 190 GeV. In the particular scenario where the top is in its infrared fixed point we find MH ⩽ 86 GeV for Mt = 170 GeV.

One-loop analysis of the electroweak breaking in supersymmetric models and the fine-tuning problem

Abstract We examine the electroweak breaking mechanism in the minimal supersymmetric standard model (MSSM) using the complete one-loop effective potential V1. First, we study what is the region of the whole MSSM parameter space (i.e. M 1 2 , m0, μ, …) that leads to a successful SU(2) × U(1) breaking with an acceptable top-quark mass. In doing this it is observed that all the one-loop corrections to V1 (even the apparently small ones) must be taken into account in order to obtain reliable results. We find that the allowed region of parameters is considerably enhanced with respect to former “improved” tree-level results. Next, we study the fine-tuning problem associated with the high sensitivity of Mz to ht (the top Yukawa coupling). Again, we find that this fine-tuning, once the one-loop effects are considered, is appreciably smaller than in previous tree-level calculations. Finally, we explore the ambiguities and limitations of the ordinary criterion to estimate the degree of fine-tuning. As a result of all this, the upper bounds on the MSSM parameters, and hence on the supersymmetric masses, are substantially raised, thus increasing the consistency between supersymmetry and observation.

Supersymmetry breaking and determination of the unification gauge coupling constant in string theories

We study in a systematic and modular invariant way gaugino condensation in the hidden sector as a potential source of hierarchical supersymmetry breaking and a non-trivial potential for the dilaton S whose real part corresponds to the tree-level gauge coupling constant (Re S ∼ ggut−2). For the case of pure Yang-Mills condensation, we show that no realistic results (in particular no reasonable values for Re S) can emerge, even if the hidden gauge group is not simple. However, in the presence of hidden matter (i.e. the most frequent case) there arises a very interesting class of scenarios with two or more hidden condensing groups for which the dilaton dynamically acquires a reasonable value (Re S ∼ 2) and supersymmetry is broken at the correct scale (m32∼103 GeV with no need of fine-tuning. Actually, good values for Re S and m32 are correlated. We make an exhaustive classification of the working possibilities. Remarkably, the results are basically independent from the value of δGS (the contributions from the Green-Schwarz mechanism). The radius of the compactified space also acquires an expectation value, breaking duality spontaneously.

A natural solution to the μ problem

Abstract We propose a simple mechanism for solving the μ-problem in the context of minimal low-energy supergravity models. This is based on the appearance of non-renormalizable couplings in the superpotential. In particular, if H1H2 is an allowed operator by all the symmetries of the theory, it is natural to promote the usual renormalizable superpotential W0 to W0+λW0H1H2, yielding an effective μ parameter whose size is directly related to the gravitino mass once supersymmetry is broken (this result is maintained if H1H2 couples with different strengths to the various terms present in W0). On the other hand, the μ-term must be absent in W0, otherwise the natural scale for μ would be M>Pl. Remarkably enough, this is entirely justified in the SUGRA theories coming from superstrings, where mass terms for light fields are forbidden in the superpotential. We also analyze the SU(2)×U(1) breaking, finding that it takes place satisfactorily. Finally, we give a realistic example in which SUSY is broken by gaugino condensation where the mechanism proposed for solving the μ-problem can be gracefully implemented.

General RG equations for physical neutrino parameters and their phenomenological implications

Abstract The neutral leptonic sector of the Standard Model presumably consists of three neutrinos with non-zero Majorana masses with properties further determined by three mixing angles and three CP -violating phases. We derive the general renormalization group equations for these physical parameters and apply them to study the impact of radiative effects on neutrino physics. In particular, we examine the existing solutions to the solar and atmospheric neutrino problems, draw conclusions on their theoretical naturalness, and show how some of the measured neutrino parameters could be determined by purely radiative effects. For example, the mass splitting and mixing angle suggested by solar neutrino data could be entirely explained as a radiative effect if the small angle MSW solution is realized. On the other hand, the mass splitting required by atmospheric neutrino data is probably determined by unknown physics at a high energy scale. We also discuss the effect of non-zero CP -violating phases on radiative corrections.

Three generation SU(3)×SU(2)×U(1)Y models from orbifolds

Abstract Explicit SU(3) × SU(2) × U(1)Y four-dimensional string models are obtained from compactification of the heterotic string on the Z3 orbifold. The presence of a Fayet-Iliopoulos term, associated with an “anomalous” U(1), plays a crucial role in the symmetry breaking process. In the example presented here the spectrum of light particles is remarkably close to that of the standard model. It contains three generations of the standard particles, with the correct representations under SU(3) × SU(2) × U(1)Y, and all the extra colour triplets, which could mediate fast proton decay, become naturally massive. Finally, there is a true (not mixed) hidden sector. Despite these attractive facts the model still has some problems (related to renormalization group equations and fermion masses), which may be cured in other examples.

Nearly degenerate neutrinos, supersymmetry and radiative corrections

Abstract If neutrinos are to play a relevant cosmological role, they must be essentially degenerate with a mass matrix of the bimaximal mixing type. We study this scenario in the MSSM framework, finding that if neutrino masses are produced by a see-saw mechanism, the radiative corrections give rise to mass splittings and mixing angles that can accommodate the atmospheric and the (large angle MSW) solar neutrino oscillations. This provides a natural origin for the Δm 2 sol ≪ Δm 2 atm hierarchy. On the other hand, the vacuum oscillation solution to the solar neutrino problem is always excluded. We discuss also in the SUSY scenario other possible effects of radiative corrections involving the new neutrino Yukawa couplings, including implications for triviality limits on the Majorana mass, the infrared fixed point value of the top Yukawa coupling, and gauge coupling and bottom-tau unification.

Naturalness of nearly degenerate neutrinos

Abstract If neutrinos are to play a relevant cosmological role, they must be essentially degenerate. We study whether radiative corrections can or cannot be responsible for the small mass splittings, in agreement with all the available experimental data. We perform an exhaustive exploration of the bimaximal mixing scenario, finding that (i) the vacuum oscillations solution to the solar neutrino problem is always excluded; (ii) if the mass matrix is produced by a see-saw mechanism, there are large regions of the parameter space consistent with the large angle MSW solution, providing a natural origin for the Δm sol 2 ⪡ Δm atm 2 hierarchy; (iii) the bimaximal structure becomes then stable under radiative corrections. We also provide analytical expressions for the mass splittings and mixing angles and present a particularly simple see-saw ansatz consistent with all observations.

Soft SUSY breaking terms in stringy scenarios: computation and phenomenological viability

Abstract We calculate the soft SUSY breaking terms arising from a large class of string scenarios, namely symmetric orbifold constructions, and study its phenomenological viability. They exhibit a certain lack of universality, unlike the usual assumptions of the minimal supersymmetric standard model. Assuming gaugino condensation in the hidden sector as the source of SUSY breaking, it turns out that squark and slepton masses tend to be much larger than gaugino masses. Furthermore, we show that these soft breaking terms can be perfectly consistent with both experimental and naturalness constraints (the latter comes from the absence of fine tuning in the SU(2) × U(1) Y→ U(1)em breaking process). This is certainly non-trivial and in fact imposes interesting constraints on measurable quantities. More precisely, we find that the gluino mass (M3) and the chargino mass (Mχ±) cannot be much higher than their present experimental lower bounds (M3⪅285 GeV; Mχ± ⪅80 GeV), while squark and slepton masses must be much larger ( ⪆1 TeV ). This can be considered as an observational signature of this kind of stringy scenarius. Besides, the top mass is constrained to be within a range (80⪅mt⪅165 GeV) remarkably consistent with its present experimental bounds.