Stuart Raby
I discuss an evolution of SUSY GUT model building, starting with the construction of 4d GUTs, to orbifold GUTs and finally to orbifold GUTs within the heterotic string. This evolution is an attempt to obtain realistic string models, perhaps relevant for the LHC. This review is in memory of the sudden loss of Julius Wess, a leader in the field, who will be sorely missed.
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Hadronic and leptonic EDMs in SUSY GUTs are reviewed in this article.
The gauge coupling unification is one of main motivations in the split-SUSY scenario, and the existence of the grand unified theories (GUTs) is assumed. We examine how to realize split-SUSY mass spectrum in the context of GUTs and find that the construction of split-SUSY GUTs is by no means straightforward. With R-symmetry breaking sources in the GUT sector, GUT particles play a role of the messengers in the gauge mediation scenario and their contributions to gaugino masses can be sizable. We find the upper bound on soft scalar masses of O(10^{10}) GeV from consistency for constructing the spl…
It is shown, that the presently accepted value for b-quark mass can be obtained from the requirement of the exact b-$τ$ unification in the both non-SUSY and SUSY non-chiral extended GUTs.
We discuss how to calculate Yukawa couplings in string-derived orbifold GUTs. As an application we investigate the quark mass hierarchies in these models. An interplay of different mechanisms derived from string theory leads to an interesting pattern. We discuss concrete examples in the context of heterotic orbifold compactifications.
Constraints from flavour changing neutral currents are discussed in the context of predictive Grand Unified Supersymmetric Theories. Uncertainties in the estimation of their amplitudes are minimized by using a successful mass matrix ansatz which predicts the arbitrary parameters of the Standard Model. Furthermore, Renormalization Group Equations are used in order to express the sparticle masses involved, in terms of the gaugino mass $m_{1/2}$, the universal scalar mass $m_0$ and the trilinear coupling $A$ at the GUT scale. Modifications in the low energy expressions for the squark masses due t…
After a short overview of the hypothesis of Yukawa unification within SUSY GUTs, I detail on the general conditions for its phenomenological viability, emphasizing the decisive role played by observables in the flavor sector.
We review the theoretical and experimental status of minimal grand unified theories (GUTS), contrasting the failure of minimal non-supersymmetric $SU(5)$ with the success of the minimal supersymmetric $SU(5)$ and minimal supersymmetric Flipped $SU(5)\times U(1)$ models. We show that a reasonable value for the universal soft supersymmetry-breaking gaugino mass, $45\GeV<m_{1/2}<1\TeV$, and a $1-σ$ range of the other inputs constrains the strong coupling, $\as>.114$. We define the supersymmetric standard model (SSM), the minimal supersymmetric extension of the standard model with gauge coupling u…
We propose a class of E6-based local orbifold Grand Unified Theories (GUTs) which yield an exceptional supersymmetric standard model as their low energy theory including leptoquark and unhiggs exotics and a Z' at the TeV scale. Unification is achieved in two steps through an intermediate scale symmetry breaking.
We point out that the null results of the hadronic electric dipole moment (EDM) searches constrain orbifold grand unified theories (GUTs), where the GUT symmetry and supersymmetry (SUSY) are both broken by boundary conditions in extra dimensions and it leads to rich fermion and sfermion flavor structures. A marginal chromoelectric dipole moment (CEDM) of the up quark is induced by the misalignment between the CP violating left- and right-handed up-type squark mixings, in contrast to the conventional four-dimensional SUSY GUTs. The up quark CEDM constraint is found to be as strong as those from…
In 5D SUSY GUTs, wave-function localization permits to reproduce flavour hierarchy. As this mechanism also acts on SUSY breaking parameters, it can potentially solve the SUSY flavour problem. We carry out an analysis of the Holographic Grand Unification framework, where we take properly into account effects of matrix anarchy. In this contribution, we focus on brane-localized SUSY breaking and its consequences.
The generalization of the "custodial symmetry" mechanism which leads to the natural (without fine tuning) explanation of the doublet-triplet hierarchy is suggested in the frames of extended $SU(N\geq 8)$ SUSY GUTs. It is shown also that such type of SUSY GUT can predict the value of strong gauge coupling constant $α_S(M_Z)$ consistent with present experimental data.
We discuss fermion masses and mixings in models derived from orbifold GUTs such that gauge coupling unification is achieved without low energy supersymmetry by utilizing a non-canonical U(1)_Y. A gauged U(1)_X flavor symmetry plays an essential role, and the Green-Schwarz mechanism is invoked in anomaly cancellations. Models containing vector-like particles with masses close to M_{GUT} are also discussed.
It is shown that a realistic SUSY SU(6) GUT can dynamically generate the GUT scale and solve at the same time the doublet-triplet splitting problem. The cosmological implications of such a model are briefly reviewed.
Unification of GUT-scale t-b-τYukawa couplings is a significant feature of simple SO(10) SUSY GUTs. Here we present the results of a search that used the Markov Chain Monte Carlo technique to investigate regions of Yukawa unification and WMAP-compatible dark matter relic density in SO(10)-like MSSM parameter spaces. We mention the possible LHC signatures of Yukawa unified scenarios and discuss the consequences for dark matter.
The idea of GUT implies that the universe went through a series of phase transitions during which topological defects are expected to form. We investigate here the genericity of cosmic strings formation in realistic SUSY GUTs models. We conclude that all acceptable symmetry breaking schemes produce cosmic strings after the last inflationary phase. Generically, as they form at the end of inflation, they have a mass of order of the GUT scale. Since cosmological data coming from CMB measurements do not show evidence for such strings, they constrain GUT scale physics.
We look for a connection between string theories and Grand Unified Theories (GUTs), with the aim to look for new insights in the existing four dimensional string-GUT problems. We argue that the construction of consistent string-GUT models could require the use of non canonical affine levels. We list the most common level values related to realistic GUTs.
Grand Unified Theories (GUTs) are attractive candidates for more fundamental elementary particle theories. They can not only unify the Standard Model (SM) interactions but also different types of SM fermions, in particular quarks and leptons, in joint representations of the GUT gauge group. We discuss how comparing predictive supersymmetric GUT models with the experimental results for quark and charged lepton masses leads to constraints on the SUSY spectrum. We show an example from a recent analysis where the resulting superpartner masses where found just beyond the reach of LHC run 1, but ful…
We discuss the implications of large neutrino mixings for grand unified theories based on the seesaw mechanism. In SU(5) GUTs large mixings can be accomodated by means of $U(1)_F$ flavour symmetries. In these models the heavy Majorana neutrinos are essentially decoupled from low energy neutrino physics. On the contrary in SO(10) GUTs large neutrino mixings severely constrain the mass spectrum of the heavy Majorana neutrinos. This leads to predictions for a variety of observables in neutrino physics as well as for the cosmological baryon asymmetry.
We consider orbifold GUTs with N=1 supersymmetry in which the Standard Model (SM) gauge couplings are unified at M_GUT =~ 2 x 10^16 GeV with one of the third family (charged) Yukawa couplings. With split supersymmetry the SM Higgs mass is estimated to be 131 +/- 10 GeV for gauge-top quark Yukawa unification, which increases to 146 +/- 8 GeV for gauge-bottom quark (or gauge-tau lepton) Yukawa unification.
The scaling behavior and fixed points in the evolution of fermion Yukawa couplings and mixing angles are discussed. The relevance of fixed points in determining the top quark mass is described.
We introduce a new approach to the subject of grand unification which allows the GUT scale to be small, \lesssim 200 TeV, so that it is within the reach of {\em conceivable} laboratory accelerated colliding beam devices. Central to the approach is a novel abstraction of the heterotic string symmetry group physics ideas to render baryon number violating effects small enough to have escaped detection to date.
We consider a class of seven-dimensional N=1 supersymmetric orbifold GUTs in which the Standard Model (SM) gauge couplings and one of the Yukawa couplings (top quark, bottom quark or tau lepton) are unified, without low energy supersymmetry, at M_{GUT} \simeq 4 \times 10^{16} GeV. With gauge-top quark Yukawa coupling unification the SM Higgs boson mass is estimated to be 135 \pm 6 GeV, which increases to 144 \pm 4 GeV for gauge-bottom quark (or gauge-tau lepton) Yukawa coupling unification.
We study CP-conserving non-minimal flavour violation in $A_4 \times SU(5)$ inspired Supersymmetric Grand Unified Theories (GUTs), focussing on the regions of parameter space where dark matter is successfully accommodated due to a light right-handed smuon a few GeV heavier than the lightest neutralino. We find that it is necessary to scan over all NMFV parameters simultaneously in order to properly constrain the space of the model.
There are two different types of perturbative unification in SUSY GUTs. Perturbative gauge unification is necessary for the extremely successful prediction of $\sin^2θ_w$. ``Perturbative validity'' requires that {\it all} couplings (not just the gauge couplings) remain small; this assumption is essential to the proof that any SUSY GUT must have a light Higgs with a mass below 140 GeV. It is pointed out here that if the latter bound is violated (so that there need be no light Higgs bosons), then it is plausible that the successful prediction of $\sin^2θ_w$ will {\it not} be significantly altere…
Gauge coupling unification in the Supersymmetric Standard Models strongly implies the Grand Unified Theories (GUTs). With the grand desert hypothesis, we show that the supersymmetric GUTs can be probed at the future proton-proton (pp) colliders and Hyper-Kamiokande experiment. For the GUTs with the GUT scale $M_{GUT} \le 1.0\times 10^{16}$ GeV, we can probe the dimension-six proton decay via heavy gauge boson exchange at the Hyper-Kamiokande experiment. Moreover, for the GUTs with $M_{GUT} \ge 1.0\times 10^{16}$ GeV, we for the first time study the upper bounds on the gaugino and sfermion mass…
We describe a class of supersymmetric unified models with the following properties: i) the full breaking of the gauge group is achieved by Higgs fields in the fundamental representation; ii) the correct unification of the strong and electroweak coupling constants is obtained without the need of any intermediate scale; iii) the problems of the doublet-triplet splitting and of the proton decay at dimension-5 level may receive a natural solution. The models, other than being interesting unified field theories per se, may constitute examples of string-derivable GUTs.
Certain supersymmetric grand unified models predict that the coefficients of the quadratic terms in the MSSM Higgs potential should be degenerate at the GUT scale. We discuss some examples for such models, and we analyse the implications of this peculiar condition of a GUT-scale degenerate Higgs mass matrix for low-scale MSSM phenomenology. To this end we explore the parameter space which is consistent with existing experimental constraints by means of a Markov Chain Monte Carlo analysis.
Extension of SUSY SU(5) GUTs with Nelson-Barr models
本文扩展了超对称 SU(5) 大统一理论，引入 Nelson-Barr 模型解决强 CP 问题，并成功重现 CKM 参数及解释下型夸克和轻子的质量比。
We discuss the fermion mass problem in SUSY GUTs, including such ideas as texture zeroes, and Georgi-Jarlskog textures. We focus on a specific supersymmetric model based on the gauge group $SU(4)\otimes SU(2)_L \otimes SU(2)_R$. In this model the gauge group is broken to that of the standard model at $10^{16}$ GeV, and supersymmetry is broken at low-energy. The model may be regarded as a ``surrogate SUSY GUT'', and has several advantages over the $SU(5)$ and $SO(10)$ SUSY GUTs, such as the absence of the doublet-triplet splitting problem, and a simpler Higgs sector which does not involve any l…
We show that gauge couplings unify more precisely in the region of SUSY parameter space already preferred by Yukawa unification. While proton decay due to dimension 5 operators is maximally suppressed in this region, the contribution from dimension 6 operators is enhanced as a consequence of lower unification scale.
We use our resummed quantum gravity approach to Einstein's general theory of relativity in the context of the Planck scale cosmology formulation of Bonanno and Reuter to estimate the value of the cosmological constant as ρ_Λ=(0.0024 eV)^4. We show that the closeness of this estimate to experiment constrains susy GUT models. We also address various consistency checks on the calculation.
We calculate the proton lifetime in an SO(10) supersymmetric grand unified theory [SUSY GUT] with U(2) family symmetry. This model fits the low energy data, including the recent data for neutrino oscillations. We discuss the predictions of this model for the proton lifetime in light of recent SuperKamiokande results which significantly constrain the SUSY parameter space of the model.
We consider supersymmetric grand unified theories with soft supersymmetry-breaking scalar masses $m_0$ specified above the GUT scale (super-GUTs) and patterns of Yukawa couplings motivated by upper limits on flavour-changing interactions beyond the Standard Model. If the scalar masses are smaller than the gaugino masses $m_{1/2}$, as is expected in no-scale models, the dominant effects of renormalization between the input scale and the GUT scale are generally expected to be those due to the gauge couplings, which are proportional to $m_{1/2}$ and generation-independent. In this case, the input…
In grand unified theories based on orbifold constructions in higher dimensions, Higgsino-mediated proton decay is absent. However, proton decay mediated by $X$ and $Y$ gauge bosons is typically enhanced to levels detectable by current and future experiments. We analyse the phenomenology of proton decay induced by the minimal coupling of $X,Y$ gauge bosons. In particular, we show that the novel realization of matter in orbifold GUTs can lead to unusual final state flavour structure, for example, the dominance of the $p\to K^0μ^+$ mode. Furthermore, we discuss proton decay induced by higher-deri…
SO(10) supersymmetric grand unified theories [SUSY GUTs] provide a beautiful framework for physics beyond the standard model. Experimental measurements of the three gauge couplings are consistent with unification at a scale $M_G \sim 3 \times 10^{16}$ GeV. In addition predictive models for fermion masses and mixing angles have been found which fit the low energy data, including the recent data for neutrino oscillations. SO(10) boundary conditions can be tested via the spectrum of superparticles. The simplest models also predict neutron and proton decay rates. In this paper we discuss nucleon d…
We construct SU(5) SUSY GUT in 5D compactified on S^1/Z_2 orbifold where the matter fields are living in the five dimensional bulk. SU(5) symmetry is broken down to the Standard Model gauge group by the orbifold projection which automatically ensures stability of proton in all orders of perturbation theory. The model predicts extra mirror quark-lepton families which along with the GUT particles and the excitations of extra dimensions could be observable at high energy colliders providing the unification scale is in the TeV range.
We study non-universal corrections to the gauge couplings due to higher dimensional operators in supersymmetric SU(5) grand unified theories. The corrections are, in general, parametrized by three components originating from {\bf 24}, {\bf 75} and {\bf 200} representations. We consider the prediction of $α_3(M_Z)$ along each {\bf 24}, {\bf 75} and {\bf 200} direction, and their linear combinations. The magnitude of GUT scale and its effects on proton decay are discussed. Non-SUSY case is also examined.
We propose a model in which $A_4$ Family Symmetry arises dynamically from a six dimensional orbifold SU(5) Supersymmetric Grand Unified Theory. The SU(5) is broken to the Standard Model gauge group by a particular orbifold compactification leading to $A_4$ Family Symmetry, low energy Supersymmetry and Higgs doublet-triplet splitting. The resulting four dimensional effective superpotential leads to a realistic description of quark and lepton masses and mixing angles including tri-bimaximal neutrino mixing and an inter-family mass hierarchy provided by a Froggatt-Nielsen mechanism. This model is…
Under the assumptions that 1) the quark/lepton mass matrices take Froggatt-Nielsen's factorized power form λ^{ψ_i+ψ_j} with anomalous U(1) charges ψ_i, and 2) the U(1) charges ψ_i respect the SU(5) GUT structure, we show that the quark mass data and the mass-squared difference ratio of solar and atmospheric neutrinos, as inputs, necessarily imply that both the 1-2 and 2-3 mixings in the MNS matrix U_{MNS} are large. This analysis also gives a prediction that U_{e3}\equiv (U_{MNS})_{13} is of order λ\sim (0.1 - 0.5). We also add an argument that E_6 GUT is favored.
A Supersymmetric Grand unified model is constructed based on SO(10)xSO(10) symmetry in which new types of Yukawa matrices couple standard and exotic fermions. Evolution of these couplings from the Grand Unified scale to the electroweak scale causes some of them to be driven to their fixed points. This solves the supersymmetric alignment problem and ensures that there are no observable flavor changing neutral currents mediated by supersymmetric particles. Fermion hierarchy and neutrino mixing constraints are automatically satisfied in this formalism.
We investigate the SU(N) supersymmetric Grand Unified Theories with ``custodial symmetry'' mechanism to explane the doublet-triplet hierarchy. We show that in such type of SU(7) SUSY theory intermediate scale appears naturally and the correct value for sin^2(θ)_W is predicted via vector-like matter superfields splitting. The unification appears to be closed to M_Pl for all the reasonable values of α_s and M_SUSY. Due to the large unification scale the baryon number violating d=5 operator is suppressed in comparison with that in minimal SU(5) theory.
We address the flavour problem by incorporating the hypothesis of universal strength of Yukawa couplings in the framework of a 5D GUT model compactified on an $S^1/(Z_2 \times Z_2^{\prime})$ orbifold. We show that a quantitatively successful picture of fermion masses and mixings emerges from the interplay between the bulk suppression factors of geometric origin and the phases of the Yukawa matrices. We give an explicit example, where we obtain a good fit for both the CKM and PMNS matrices.
The infra-red attractive force of the bulk gauge interactions is applied to soften the supersymmetric flavor problem in the orbifold SU(5) GUT of Kawamura. Then this force aligns in the infra-red regime the soft supersymmetry breaking terms out of their anarchical disorder at a fundamental scale, in such a way that flavor-changing neutral currents as well as dangerous CP-violating phases are suppressed at low energies. It is found that this dynamical alignment is sufficiently good compared with the current experimental bounds, as long as the diagonalization matrices of the Yukawa couplings are…
We consider 5 dimensional E_6 and E_7 supersymmetric grand unified theories (GUTs) on an orbifold S^1/Z_2, in which the Higgs fields arise from the 5th components of the 5D gauge fields. We introduce matter fields in 5 dimensions, then the Yukawa interactions are induced from the gauge interactions among the 5th component of gauge fields and the bulk hyper-multiplets. The adjoint and fundamental representations of bulk matter fields can induce all Yukawa interactions of the standard model in E_6 GUT. Furthermore, realistic fermion mass hierarchies and flavor mixings with the CP violating phase…
Gauge and Yukawa (for the third family) coupling unification seem to be the best predictions of the grand-unified theories (GUTs). In supersymmetric GUTs, one also expects that the sparticle masses unify at the GUT scale (for sparticles embedded in the same GUT multiplet). I show under what circumstances GUTs do not lead to sparticle mass unification. In particular, I give examples of SU(5) and SO(10) SUSY GUTs in which squarks and sleptons of a family have different tree-level masses at the unification scale. The models have interesting relations between Yukawa couplings. For example, I prese…
We consider neutralino dark matter within the framework of SUSY GUTs with non-universal gaugino masses. In particular we focus on the case of SU(5) with a SUSY breaking F-term in the 1, 24, 75 and 200 dimensional representations. We discuss the 24 case in some detail, and show that the bulk dark matter region cannot be accessed. We then go on to consider the admixture of the singlet SUSY breaking F-term with one of the 24, 75 or 200 dimensional F-terms, and show that in these cases it becomes possible to access the bulk regions corresponding to low fine-tuned dark matter. Our results are prese…
We discuss how the double missing partner mechanism solution to the doublet-triplet splitting problem in four-dimensional supersymmetric SU(5) Grand Unified Theories (GUTs) can be combined with predictive models for the quark-lepton Yukawa coupling ratios at the GUT scale. It is argued that towards this goal a second SU(5) breaking Higgs field in the adjoint representation is very useful and we discuss all possible renormalizable superpotentials with two adjoint Higgs fields and calculate the constraints on the GUT scale and effective triplet mass from a two-loop gauge coupling unification ana…
We construct an orbifold model in which all the standard model particles are unified in a gauge multiplet in higher dimensional supersymmetric gauge theory. We find that a flavor symmetry has to remain in four dimensions due to the discrete charge conservation for orbifold conditions if the colored Higgs components in the gauge multiplet are projected out. When the flavor symmetry originates from the E_8 bulk gauge symmetry, the successful unification model can be constructed. In the model, all the Dirac Yukawa couplings for quarks and leptons are generated by the higher dimensional gauge inte…
We use the amplitude-based resummation of Feynman`s formulation of Einstein`s theory to arrive at a UV finite approach to quantum gravity. We show that we recover the UV fixed point recently claimed by the exact field-space renormalization group approach. We use our approach in the context of the attendant Planck scale cosmology formulation of Bonanno and Reuter to estimate the value of the cosmological constant as ρ_Λ=(0.0024 eV)^4. We show that the closeness of this estimate to experiment constrains susy GUT models.
We consider the origin of new phases in supersymmetric grand unification model, and show how significant new contributions arise from the gluino mediated diagram. We then present a more general model independent analysis of various modes of B-decays suggested previously for measurement of the CKM phases and point out what they really measure. It is in principle possible to separate out all the phases.
We discuss the basic idea of the Gauge-Yukawa Unification that is based on the principle of the reduction of couplings. This method of unification relies on the search of successful renormalization group invariant relations among couplings, which do not originate from symmetry principles. The predictive power of Grand Unified Theories can be increased by this method, predicting for instance values of the top quark mass consistent with the recent experimental data. The hope is that this unification attempt might shed further light on the origin of the Yukawa sector of the standard model.
Supersymmetric (SUSY) Grand Unified theories (GUTs) generally predict FCNC and CP violating processes to occur both in the leptonic and hadronic sectors. Assuming an underlying SU(5) group plus right-handed neutrinos (RN), we perform an extensive study of FCNC and CP violation, analyzing the correlations between leptonic and hadronic processes like mu-> e gamma and K-Kbar mixing, tau->mu gamma and b -> s transitions such as B_d -> phi K_s and Bs-Bsbar mixing. Moreover, we examine the impact of the considered scenario on the UT analyses, monitoring the low energy consequences implied by possibl…
We study proton decay in a supersymmetric {\sf SO(10)} gauge theory in six dimensions compactified on an orbifold. The dimension-5 proton decay operators are forbidden by R-symmetry, whereas the dimension-6 operators are enhanced due to the presence of KK towers. Three sequential quark-lepton families are localised at the three orbifold fixed points, where {\sf SO(10)} is broken to its three GUT subgroups. The physical quarks and leptons are mixtures of these brane states and additional bulk zero modes. This leads to a characteristic pattern of branching ratios in proton decay, in particular t…
A D-parity violated SUSY SU(4) x SU(2) _ L x SU(2)_R gauge model with the Higgs sector 2{(4,1,2)+(4-bar,1, 2)}+(1,2,2)+some(1,1,1)'s is shown to have the following advantages: (i) It is the simplest and almost unique solution that satisfies M_X = M_{string} ~0.6 x 10^{18} GeV and M_{INT} ~ 5 x10^{11} GeV in superstring derived SUSY SO(10) GUTs. (ii) The proton is stable enough by the automatic "doublet-triplet splitting" closely connected with the D-parity violation. (iii) The minimization of SUSY one-loop effective potential in a toy model suggests that the SO(10) gauge theory tends to break …
We investigate the possibility of a bosonic preheating in the simplest model of supersymmetric Hybridinflation (F-term inflation), which was considered first by Dvali et al. Here the inflationary superpotential is of the O'Raifertaigh-Witten type. The end of inflation is related to a non-thermal phase transition, which in the context of left-right symmetric models lowers the rank of the gauge group. Using the homogeneous classical field ansatz for the appearing condensates, our results indicate that the parametric creation of bosonic particles does not occure in the model under consideration.
A general analysis is made of the question whether the d=5 proton decay operators coming from exchange of colored Higgsinos can be completely eliminated in a natural way in supersymmetric grand unified models. It is shown that they can indeed be in SO(10) while at the same time naturally solving the doublet-triplet splitting problem, having only two light Higgs doublets, and using no more than a single adjoint Higgs field. Accomplishing all of this requires that the vacuum expectation value of the adjoint Higgs field be proportional to the generator I_{3R} rather than to B-L, as is usually ass…
A new procedure is developed which enables one to start from the quark and lepton mass and mixing data at the low scale and construct mass matrices which exhibit simple SO(10) structure at the SUSY GUT scale. This approach is applied to the present data involving quark and charged lepton masses, the CKM mixing matrix and the MSW solar neutrino and atmospheric neutrino depletion effects. In terms of just 12 model parameters suggested by the procedure for the 5 mass matrices, we can reproduce 15 masses and 8 mixing parameters remarkably consistent with the input starting values.
We present a global $χ^2$ analysis of electroweak data, including fermion masses and mixing angles, in SO(10) SUSY GUTs. Just as precision electroweak data is used to test the Standard Model, the well determined Standard Model parameters are the precision electroweak data for testing theories beyond the Standard Model. In this talk we use the latest experimentally measured values for these parameters. We study several models discussed in the literature. One of these models provides an excellent fit to the low energy data with $χ^2 \sim 1$ for 3 degrees of freedom. We present our predictions fo…
In this talk I discuss the qualitative features of an SO(10) SUSY GUT with an SU(2)x U(1)$^n$ family symmetry. I then describe the global fit of this theory to precision electroweak data [including charged fermion masses and mixing angles]. Finally, the predictions of the model for neutrino masses and mixing are discussed. The most predictive version of the model naturally fits atmospheric neutrino data with maximal $ν_μ\longrightarrow ν_τ$ oscillations and solar neutrino data with small mixing angle MSW $ν_e \longrightarrow ν_{sterile}$ oscillations.
I review proton decay in the SUSY SU(5) GUTs assuming the mini-split SUSY breaking model. In the mini-split SUSY breaking model, the squark and slepton masses are O(10^{(2-3)}) TeV while the gaugino masses are O(1) TeV. As the result, even the minimal SUSY SU(5) GUT is still viable in the model. We present the motivation of the mini-split SUSY model and discuss the future prospects of proton decay searches in the SUSY SU(5) GUTs.
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