Yukawa unification : MSSM at large tan(beta)
Talk given at PASCOS 2012, Merida, Mexico describing work in progress in collaboration with Archana Anandakrishnan, Christopher Plumberg and Akin Wingerter.
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arXiv subjects
Stuart Raby
Publications and source records attributed to Stuart Raby.
SU(6) GUT Breaking on a Projective Plane
We consider a 6-dimensional supersymmetric SU(6) gauge theory and compactify two extra-dimensions on a multiply-connected manifold with non-trivial topology. The SU(6) is broken down to the Standard Model gauge groups in two steps by an orbifold projection (or Wilson line), followed by a Wilson line. The Higgs doublets of the low energy electroweak theory come from a chiral adjoint of SU(6). We thus have gauge-Higgs unification. The three families of the Standard Model can either be located in the 6D bulk or at 4D N=1 supersymmetric fixed points. We calculate the Kaluza-Klein spectrum of states arising as a result of the orbifolding. We also calculate the threshold corrections to the coupling constants due to this tower of states at the lowest compactification scale. We study the regions of parameter space of this model where the threshold corrections are consistent with low energy physics. We find that the couplings receive only logarithmic corrections at all scales. This feature can be attributed to the large N=2 6D SUSY of the underlying model.
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A Global SU(5) F-theory model with Wilson line breaking
We engineer compact SU(5) Grand Unified Theories in F-theory in which GUT-breaking is achieved by a discrete Wilson line. Because the internal gauge field is flat, these models avoid the high scale threshold corrections associated with hypercharge flux. Along the way, we exemplify the `local-to-global' approach in F-theory model building and demonstrate how the Tate divisor formalism can be used to address several challenges of extending local models to global ones. These include in particular the construction of G-fluxes that extend non-inherited bundles and the engineering of U(1) symmetries. We go beyond chirality computations and determine the precise (charged) massless spectrum, finding exactly three families of quarks and leptons but excessive doublet and/or triplet pairs in the Higgs sector (depending on the example) and vector-like exotics descending from the adjoint of SU(5)_{GUT}. Understanding why vector-like pairs persist in the Higgs sector without an obvious symmetry to protect them may shed light on new solutions to the mu problem in F-theory GUTs.
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Problems with the MSSM : mu & proton decay
This paper describes a set of discrete R symmetries which can be used to define the minimal supersymmetric standard model or singlet extensions of it.
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Discrete R symmetries for the MSSM and its singlet extensions
We determine the anomaly free discrete R symmetries, consistent with the MSSM, that commute with SU(5) and suppress the $μ$ parameter and nucleon decay. We show that the order M of such $Z_M^R$ symmetries has to divide 24 and identify 5 viable symmetries. The simplest possibility is a $Z_4^R$ symmetry which commutes with SO(10). We present a string-derived model with this $Z_4^R$ symmetry and the exact MSSM spectrum below the GUT scale; in this model $Z_4^R$ originates from the Lorentz symmetry of compactified dimensions. We extend the discussion to include the singlet extensions of the MSSM and find $Z_4^R$ and $Z_8^R$ are the only possible symmetries capable of solving the $μ$ problem in the NMSSM. We also show that a singlet extension of the MSSM based on a $Z_{24}^R$ symmetry can provide a simultaneous solution to the $μ$ and strong CP problem with the axion coupling in the favoured window.
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Searching for the Standard Model in the String Landscape : SUSY GUTs
The goal of the present review article is to describe the ingredients necessary to find the Standard Model in the string landscape.
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Gauge Coupling Unification in Heterotic String Models with Gauge Mediated SUSY Breaking
We calculate the weak scale MSSM spectrum starting from a heterotic string theory compactified on an anisotropic orbifold. Supersymmetry breaking is mediated by vector-like exotics that arise naturally in heterotic string theories. The messengers that mediate SUSY breaking come in incomplete GUT multiplets and give rise to non-universal gaugino masses at the GUT scale. Models with non-universal gaugino masses at the GUT scale have the attractive feature of allowing for precision gauge coupling unification at the GUT scale with negligible contributions from threshold corrections near the unification scale. The unique features of the MSSM spectrum are light gluinos and also large mass differences between the lightest and the next-to-lightest neutralinos and charginos which could lead to interesting signatures at the colliders.
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String-derived MSSM vacua with residual R symmetries
Recently it was shown that there is a unique Z_4^R symmetry for the MSSM which allows the Yukawa couplings and dimension five neutrino mass operator, forbids the mu term and commutes with SO(10). This Z_4^R symmetry contains matter parity as a subgroup and forbids dimension four and five proton decay operators. We show how to construct string vacua with discrete R symmetries in general and this symmetry in particular, and present an explicit example which exhibits the exact MSSM spectrum, the Z_4^R symmetry as well as other desired features such as gauge-top unification. We introduce the Hilbert basis method for determining all D-flat configurations and efficient algorithms for identifying field configurations with a desired residual symmetry. These methods are used in an explicit example, in which we describe in detail how to construct a supersymmetric vacuum configuration with the phenomenologically attractive Z_4^R symmetry. At the perturbative level, this is a supersymmetric Minkowski vacuum in which almost all singlet fields (moduli) are fixed.
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A unique Z_4^R symmetry for the MSSM
We consider the possible anomaly free Abelian discrete symmetries of the MSSM that forbid the mu-term at perturbative order. Allowing for anomaly cancellation via the Green-Schwarz mechanism we identify discrete R-symmetries as the only possibility and prove that there is a unique Z_4^R symmetry that commutes with SO(10). We argue that non-perturbative effects will generate a mu-term of electroweak order thus solving the mu-problem. The non-perturbative effects break the Z_4^R symmetry leaving an exact Z_2 matter parity. As a result dimension four baryon- and lepton-number violating operators are absent while, at the non-perturbative level, dimension five baryon- and lepton-number violating operators get induced but are highly suppressed so that the nucleon decay rate is well within present bounds.
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Moduli stabilization and SUSY breaking in heterotic orbifold string models
In this paper we discuss the issues of supersymmetry breaking and moduli stabilization within the context of E_8 x E_8 heterotic orbifold constructions and, in particular, we focus on the class of "mini-landscape" models. In the supersymmetric limit, these models admit an effective low energy field theory with a spectrum of states and dimensionless gauge and Yukawa couplings very much like that of the MSSM. These theories contain a non-Abelian hidden gauge sector which generates a non-perturbative superpotential leading to supersymmetry breaking and moduli stabilization. We demonstrate this effect in a simple model which contains many of the features of the more general construction. In addition, we argue that once supersymmetry is broken in a restricted sector of the theory, then all moduli are stabilized by supergravity effects. Finally, we obtain the low energy superparticle spectrum resulting from this simple model.
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Precision gauge unification in the MSSM
We discuss the issue of precision gauge unification in the MSSM. We find that a comparably light gluino, as it emerges in certain patterns of soft supersymmetry breaking, can be a key ingredient for ensuring precision gauge unification without relying on the presence of extra particles around the scale of grand unification. In particular, the so-called mirage pattern for gaugino masses can naturally lead to precision gauge unification. There is also an interesting correlation with reduced fine-tuning, due to rather light gluinos.
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Stabilizing All Kahler Moduli in Type IIB Orientifolds
We describe a simple and robust mechanism that stabilizes all Kahler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G_2 compactifications of M-theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kahler moduli are worked out. We find that the stabilized volumes of all two- and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.
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String Model Building
In this talk I review some recent progress in heterotic and F theory model building. I then consider work in progress attempting to find the F theory dual to a class of heterotic orbifold models which come quite close to the MSSM.
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Viable and testable SUSY GUTs with Yukawa unification: the case of split trilinears
We explore general SUSY GUT models with exact third-generation Yukawa unification, but where the requirement of universal soft terms at the GUT scale is relaxed. We consider the scenario in which the breaking of universality inherits from the Yukawa couplings, i.e. is of minimal flavor violating (MFV) type. In particular, the MFV principle allows for a splitting between the up-type and the down-type soft trilinear couplings. We explore the viability of this trilinear splitting scenario by means of a fitting procedure to electroweak observables, quark masses as well as flavor-changing neutral current processes. Phenomenological viability singles out one main scenario. This scenario is characterized by a sizable splitting between the trilinear soft terms and a large mu term. Remarkably, this scenario does not invoke a partial decoupling of the sparticle spectrum, as in the case of universal soft terms, but instead it requires part of the spectrum, notably the lightest stop, the gluino and the lightest charginos and neutralinos to be very close to the current experimental limits. The above mechanism is mostly triggered by a non-trivial interplay between the requirements of negative, sizable SUSY threshold corrections to mb and an instead negligible modification of the B --> Xs gamma decay rate, in presence of various other constraints, most notably a successful EWSB and a not too large BR(Bs --> mu^+ mu^-). We present a model-building interpretation of our discussed scenario and emphasize the crucial role of SUSY spectrum determinations at the LHC for either falsifying Yukawa unification or else providing important hints on the mechanism of SUSY breaking at work.
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Modulino Dark Matter and the INTEGRAL 511 keV Line
In this paper we present a simple extension of the minimal supersymmetric standard model [MSSM] which "naturally" produces the INTEGRAL photon signal. The model can be embedded in an SU(5) grand unified theory [GUT] with gauge mediated SUSY breaking. The new ingredients are the addition of several MSSM singlets/moduli. While the masses of the singlets are at the weak scale, their mass splittings are suppressed by chiral symmetry breaking and naturally lie around an MeV. The decay of the heavier modulino to the lighter one with the associated production of electron - positron pairs explains the INTEGRAL signal. Finally, the detection of diffuse gamma rays from internal bremsstrahlung in the galactic halo would be a suggestive indication of dark matter decays associated with the 511 keV line, and is an unambiguous additional prediction of this model.
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On the string coupling in a class of stringy orbifold GUTs
In this short note, we examine the relationship between the string coupling constant, $\gstring{}$, and the grand unified gauge coupling constant, $\alphagut{}$, in a highly successful class of models based on anisotropic orbifold compactifications of the weakly coupled heterotic string. These models represent a stringy embedding of SU(6) gauge-Higgs unification in a five dimensional orbifold GUT. We find that the requirement that the theory be perturbative provides a non-trivial constraint on these models. Interestingly, there is a correlation between the proton decay rate (due to dimension six operators) and the string coupling constant. Finally, we make some comments concerning the extension of these models to the six (and higher) dimensional case.
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Addendum to Reconciling Grand Unification with Strings by Anisotropic Compactifications
In a recent paper, by working in the orbifold GUT limit of the Heterotic string, we showed how one could accommodate gauge coupling unification in the "mini-landscape" models of Lebedev et al. Furthermore, it was shown how one of the solutions was consistent with the decoupling of other exotics with F=0. In this short addendum, we show that this solution is also consistent with D=0.
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SUSY GUTs with Yukawa unification: a go/no-go study using FCNC processes
We address the viability of exact Yukawa unification in the context of general SUSY GUTs with universal soft-breaking sfermion and gaugino mass terms at the GUT scale. We find that this possibility is challenged, unless the squark spectrum is pushed well above the limits allowed by naturalness. This conclusion is assessed through a global fit using electroweak observables and quark flavour-changing neutral current (FCNC) processes. The problem is mostly the impossibility of accommodating simultaneously the bottom mass and the BR(B --> Xs gamma), after the stringent CDF upper bound on the decay Bs --> mu^+ mu^- is taken into account, and under the basic assumption that the b --> s gamma amplitude have like sign with respect to the Standard Model one, as indicated by the B --> Xs l^+ l^- data. With the same strategy, we also consider the possibility of relaxing Yukawa unification to b - tau Yukawa unification. We find that with small departures from the condition tan beta ~= 50, holding when Yukawa unification is exact, the mentioned tension is substantially relieved. We emphasize that in the region where fits are successful the lightest part of the SUSY spectrum is basically fixed by the requirements of b - tau unification and the applied FCNC constraints. As such, it is easily falsifiable once the LHC turns on.
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