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J. A. Casas

Publications and source records attributed to J. A. Casas.

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arXiv1995

New and Strong Constraints on the Parameter Space of the MSSM from Charge and Color Breaking Directions

Although the possible existence of dangerous charge and color breaking (CCB) directions in the MSSM has been known since the early 80's, only particular directions in the field-space have been considered, thus obtaining necessary but not sufficient conditions to avoid dangerous CCB minima. Furthermore, the radiative corrections to the potential were not normally included in a proper way, often leading to an overestimation of the restrictive power of the bounds. It turns out that when correctly evaluated, the ``traditional" CCB bounds are very weak. I give here a brief survey of recent results on this subject, which represent a complete analysis, showing that the new CCB bounds are very strong and, in fact, there are extensive regions in the parameter space that become forbidden. This produces important bounds, not only on the value of $A$, but also on the values of $B$ and $M_{1/2}$. The form of strongest one of the new bounds, the so called UFB-3 bound, is explicitely given.

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arXiv1995

Natural flavour mixing in the MSSM and $μ--> e, γ$

In the absence of any additional assumption it is natural to conjecture that sizeable flavour-mixing mass entries, $Δm^2$, may appear in the mass matrices of the scalars of the MSSM, i.e. $Δm^2\sim O(m^2)$. This flavour violation can still be reconciled with the experiment if the gaugino mass, $M_{1/2}$, is large enough to yield (through the renormalization group running) a sufficiently small $Δm^2 / m^2$ at low energy. This leads to a gaugino dominance framework (i.e. $M_{1/2}^2\gg m^2$), which permits a remarkably model--independent analysis. We study this possibility focussing our attention on the $μ\rightarrow e,γ$ decay. In this way we obtain very strong and general constraints, in particular $\frac{M_{1/2}^2}{Δm} \simgt 34\ {\rm TeV}$.

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arXiv1995

Supergravity and the $b\to s,γ$ decay

We evaluate the branching ratio BR($b\rightarrow s,γ$) in the minimal supersymmetric standard model (MSSM), determining the corresponding phenomenological restrictions on two attractive supergravity scenarios, namely minimal supergravity and a class of models with a natural solution to the $μ$ problem. We have included in the calculation some one--loop refinements that have a substantial impact on the results. It is stressed the fact that an eventual improvement of the experimental bounds of order $10^{-4}$ would strengthen the restrictions on the MSSM dramatically. This would be enough to discard these supergravity scenarios with $μ<0$ if no discrepancy is found with the standard model prediction, while for $μ>0$ there will remain low-energy windows.

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arXiv1995

Strong Constraints on the Parameter Space of the MSSM from Charge and Color Breaking Minima

A complete analysis of all the potentially dangerous directions in the field-space of the minimal supersymmetric standard model is carried out. They are of two types, the ones associated with the existence of charge and color breaking minima in the potential deeper than the realistic minimum and the directions in the field-space along which the potential becomes unbounded from below. The corresponding new constraints on the parameter space are given in an analytic form, representing a set of necessary and sufficient conditions to avoid dangerous directions. They are very strong and, in fact, there are extensive regions in the parameter space that become forbidden. This produces important bounds, not only on the value of $A$, but also on the values of $B$ and $M_{1/2}$. Finally, the crucial issue of the one-loop corrections to the scalar potential has been taken into account in a proper way.

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arXiv1995

Constraints on Supersymmetric Theories from $μ\to e,γ$

In the absence of any additional assumption it is natural to conjecture that sizeable flavour-mixing mass entries, $Δm^2$, may appear in the mass matrices of the scalars of the MSSM, i.e. $Δm^2\sim O(m^2)$. This flavour violation can still be reconciled with the experiment if the gaugino mass, $M_{1/2}$, is large enough, leading to a {\em gaugino dominance} framework (i.e. $M_{1/2}^2\gg m^2$), which permits a remarkably model--independent analysis. We study this possibility focussing our attention on the $μ\rightarrow e,γ$ decay. In this way we obtain very strong and general constraints, in particular $\frac{M_{1/2}^2}{Δm}\simgt 34\ {\rm TeV}$. On the other hand, we show that our analysis and results remain valid for values of $m^2$ much larger than $Δm^2$, namely for $\frac{Δm^2}{m^2}\simgt \frac{m^2} {10\ {\rm TeV^2}}$, thus extending enormously their scope of application. Finally, we discuss the implications for superstring scenarios.

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arXiv1995

Constraining Supergravity Scenarios through the $b\to s,γ$ Decay.

We evaluate the branching ratio BR($b\rightarrow s,γ$) in the minimal supersymmetric standard model (MSSM), determining the corresponding phenomenological restrictions on two attractive supergravity scenarios, namely minimal supergravity and a class of models with a natural solution to the $μ$ problem. We have included in the calculation some one--loop refinements that have a substantial impact on the results. The numerical results show some disagreements with part of the previous results in the literature, while they are in agreement with others. For minimal supergravity the CLEO upper and lower bounds put important restrictions on the scalar and gaugino masses in both cases $μ<0$ and $μ>0$. For the other supergravity scenarios the relevant CLEO bound is the upper one. It is stressed the fact that an eventual improvement of the experimental bounds of order $10^{-4}$ would strengthen the restrictions on the MSSM dramatically. This would be enough to discard these supergravity scenarios with $μ<0$ if no discrepancy is found with the standard model prediction, while for $μ>0$ there will remain low-energy windows.

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arXiv1994

Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry

We re-examine the lower bound on the mass of the Higgs boson, $M_H$, from Standard Model vacuum stability including next-to-leading-log radiative corrections. This amounts to work with the full one-loop effective potential, $V(ϕ)$, improved by two-loop RGE, and allows to keep control of the scale invariance of $V$ in a wide range of the $ϕ$-field. Our results show that the bound is ${\cal O}\ (10\ GeV)$ less stringent than in previous estimates. In addition we perform a detailed comparison between the SM lower bounds on $M_H$ and the supersymmetric upper bounds on it. It turns out that depending on the actual value of the top mass, $M_t$, the eventually measured Higgs mass can discard the pure SM, the Minimal Supersymmetric Standard Model or both.

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arXiv1994

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 ($\simlt 3$\%). After defining physical (pole) top quark mass $M_t$, by including QCD self-energies, and physical Higgs mass $M_H$, by including the electroweak self-energies $Π\left(M_H^2\right)-Π(0)$, we obtain the upper limit on $M_H$ as a function of supersymmetric parameters. We include as supersymmetric parameters the scale of supersymmetry breaking $M_S$, the value of $\tan β$ and the mixing between stops $X_t= A_t + μ\cotβ$ (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 $M_S\leq 1$ TeV, maximal threshold effect $X_t^2=6M_S^2$ and any value of $\tanβ$, we find $M_H\leq 140$ GeV for $M_t\leq 190$ GeV. In the particular scenario where the top is in its infrared fixed point we find $M_H\leq 86$ GeV for $M_t = 170$ GeV.

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arXiv1993

The Fine-Tuning Problem of the Electroweak Symmetry Breaking Mechanism in Minimal SUSY Models

We calculate the region of the MSSM parameter space (i.e. $M_{1/2}$, $m_{0}$, $μ$, \ldots) compatible with a correct electroweak breaking and a realistic top-quark mass. To do so we have included {\em all} the one-loop corrections to the effective potential $V_{1}$ and checked their importance in order to obtain consistent results. We also consider the fine-tuning problem due to the enormous dependence of $M_{Z}$ on $h_{t}$ (the top Yukawa coupling), which is substantially reduced when the one-loop effects are taken into account. We also explore the reliability of the so-called "standard" criterion to estimate the degree of fine-tuning. As a consequence, we obtain a new set of upper bounds on the MSSM parameters or, equivalently, on the supersymmetric masses perfectly consistent with the present experimental bounds.

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arXiv1993

Model Independent Properties and Cosmological Implications of the Dilaton and Moduli Sectors of 4-d Strings

We show that if there is a realistic 4-d 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 can lead to a huge entropy generation at late times. We discus 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.

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arXiv1993

SUSY Soft Breaking Terms from String Scenarios

The general SUSY soft breaking terms for a large class of phenomenologically relevant string scenarios (symmetric orbifolds) are given. They show a certain lack of universality, but not dangerous for flavor changing neutral currents. To get more quantitative results a specific SUSY breaking mechanism has to be considered, namely gaugino condensation in the hidden sector. Then, it turns out that squark and slepton masses tend to be much larger than scalar masses ($m_ϕ > 10 M_a$), which probably is a quite general fact. Experimental bounds and the requirement of a successful electroweak breaking without fine tuning impose further restrictions on the soft breaking terms. As a consequence the gluino and chargino masses should be quite close to their present experimental limits, whereas squark and slepton masses should be much higher (> 1 TeV).

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arXiv1993

One-Loop Analysis of the Electroweak Breaking in Supersymmetric Models and the Fine-Tuning Problems

We examine the electroweak breaking mechanism in the minimal supersymmetric standard model (MSSM) using the {\em complete} one-loop effective potential $V_1$. First, we study what is the region of the whole MSSM parameter space (i.e. $M_{1/2},m_o,μ,...$) that leads to a succesful $SU(2)\times U(1)$ breaking with an acceptable top quark mass. In doing this it is observed that all the one-loop corrections to $V_1$ (even the apparently small ones) must be taken into account in order to get 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 $M_Z$ to $h_t$ (the top Yukawa coupling). Again, we find that this fine-tuning is appreciably smaller once the one-loop effects are considered 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.

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arXiv1993

A Natural Solution to the MU Problem

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 $H_1H_2$ is an allowed operator by all the symmetries of the theory, it is natural to promote the usual renormalizable superpotential $W_o$ to $W_o+λW_o H_1H_2$, yielding an effective $μ$ parameter whose size is directly related to the gravitino mass once supersymmetry is broken (this result is maintained if $H_1H_2$ couples with different strengths to the various terms present in $W_o$). On the other hand, the $μ$ term must be absent from $W_o$, otherwise the natural scale for $μ$ would be $M_P$. Remarkably enough, this is entirely justified in the supergravity theories coming from superstrings, where mass terms for light fields are forbidden in the superpotential. We also analyse the $SU(2)\times U(1)$ breaking, finding that it takes place satisfactorily. Finally, we give a realistic example in which supersymmetry is broken by gaugino condensation, where the mechanism proposed for solving the $μ$ problem can be gracefully implemented.

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arXiv1992

Soft SUSY Breaking Terms in Stringy Scenarios: Computation and Phenomenological Viability

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 $SU(2)\times U(1)_Y\rightarrow U(1)_{em}$ breaking process). This is certainly non--trivial and in fact imposes interesting constraints on measurable quantities. More precisely, we find that the gluino mass ($M_3$) and the chargino mass ($M_{χ^{\pm}}$) cannot be much higher than their present experimental lower bounds ($M_3\stackrel{<}{{}_\sim}285\ $GeV ; $M_{χ^\pm}\stackrel{<}{{}_\sim}80\ $GeV), while squark and slepton masses must be much larger ($\stackrel{>}{{}_\sim} 1\ $TeV). This can be considered as an observational signature of this kind of stringy scenarios. Besides, the top mass is constrained to be within a range ($80\ $GeV$\stackrel{<}{{}_\sim}m_t\stackrel{<}{{}_\sim}165\ $GeV)

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arXiv1992

Fitting the Quark and Lepton Masses in String Theories

The capability of string theories to reproduce at low energy the observed pattern of quark and lepton masses and mixing angles is examined, focusing the attention on orbifold constructions, where the magnitude of Yukawa couplings depends on the values of the deformation parameters which describe the size and shape of the compactified space. A systematic exploration shows that for $Z_3$, $Z_4$, $Z_6$--I and possibly $Z_7$ orbifolds a correct fit of the physical fermion masses is feasible. In this way the experimental masses, which are low--energy quantities, select a particular size and shape of the compactified space, which turns out to be very reasonable (in particular the modulus $T$ defining the former is $T=O(1)$). The rest of the $Z_N$ orbifolds are rather hopeless and should be discarded on the assumption of a minimal $SU(3)\times SU(2)\times U(1)_Y$ scenario. On the other hand, due to stringy selection rules, there is no possibility of fitting the Kobayashi--Maskawa parameters at the renormalizable level, although it is remarked that this job might well be done by non--renormalizable couplings.

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arXiv1992

Scalar--Tensor Theories of Gravity with \PHI Dependent Masses

We study new physical phenomena and constraints in generalized scalar--tensor theories of gravity with $Φ$--dependent masses. We investigate a scenario (which can arise in string theories) with two types of $Φ$--dependent masses which could correspond to visible and dark matter sectors. The parameters of this theory are constrained from post--Newtonian bounds, primordial nucleosynthesis and the age of the Universe. We present a perfect fluid formalism for the dark matter sector with variable masses and find an entropy increase effect during the matter era and, in principle, a measurable effect on the motion of the halo of spiral galaxies. For the case of string effective theories, the constancy of gauge couplings provide new bounds which are orders of magnitude stronger than the previous ones.

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arXiv1992

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 (${\rm Re}\ S\sim g_{gut}^{-2}$). For the case of pure Yang--Mills condensation, we show that no realistic results (in particular no reasonable values for ${\rm Re}\ S$) 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 (${\rm Re}\ S\sim 2$) and supersymmetry is broken at the correct scale ($m_{3/2}\sim 10^3\ GeV$) with no need of fine--tuning. Actually, good values for ${\rm Re}\ S$ and $m_{3/2}$ are correlated. We make an exhaustive classification of the working possibilities. Remarkably, the results are basically independent from the value of $δ^{GS}$ (the contributions from the Green--Schwarz mechanism). The radius of the compactified space also acquires an expectation value, breaking duality spontaneously.

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arXiv1991

Complete structure of Z_n Yukawa couplings

We give the complete twisted Yukawa couplings for all the Z_n orbifold constructions in the most general case, i.e. when orbifold deformations are considered. This includes a certain number of tasks. Namely, determination of the allowed couplings, calculation of the explicit dependence of the Yukawa couplings values on the moduli expectation values (i.e. the parameters determining the size and shape of the compactified space), etc. The final expressions are completely explicit, which allows a counting of the DIFFERENT Yukawa couplings for each orbifold (with and without deformations). This knowledge is crucial to determine the phenomenological viability of the different schemes, since it is directly related to the fermion mass hierarchy. Other facts concerning the phenomenological profile of Z_n orbifolds are also discussed, e.g. the existence of non--diagonal entries in the fermion mass matrices, which is related to a non--trivial structure of the Kobayashi--Maskawa matrix. Finally some theoretical results are given, e.g. the no--participation of (1,2) moduli in twisted Yukawa couplings. Likewise, (1,1) moduli associated with fixed tori which are involved in the Yukawa coupling, do not affect the value of the coupling.

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