A simple supersymmetric SO(10) GUT in five dimensions is considered. The fifth dimension is compactified on the $S^1/(Z_2\times Z_2^\prime)$ orbifold possessing two inequivalent fixed points. In our setup, all matter and Higgs multiplets reside on one brane (PS brane) where the original SO(10) gauge group is broken down to the Pati-Salam (PS) gauge group, SU(4)$_c \timesSU(2)_L \times$ SU(2)$_R$, by the orbifold boundary condition, while only the SO(10) gauge multiplet resides in the bulk. The further breaking of the PS symmetry to the Standard Model gauge group is realized by Higgs multiplets on the PS brane as usual in four dimensional models. Proton decay is fully suppressed. In our simple setup, the gauge coupling unification is realized after incorporating threshold corrections of Kaluza-Klein modes. When supersymmetry is assumed to be broken on the other brane, supersymmetry breaking is transmitted to the PS brane through the gaugino mediation with the bulk gauge multiplet.
We propose a natural framework of SU(5) supersymmetric grand unified theory with the minimal particle contents, which does not contain dimension five proton decay operators. The suitable fermion mass hierarchy can be reproduced by higher dimensional operators of an adjoint Higgs field which breaks SU(5) gauge symmetry.
We review SO(10) grand unified theories (GUTs) in four and five dimensions (4D and 5D). The renormalizable minimal SO(10) SUSY GUT is the central theme of this review. It is very predictive and makes it possible to construct all mass matrices including those of the Dirac and heavy right-handed Majorana neutrinos. So it is not only able to reproduce all the low energy data, except for too larger $θ_{13}$ in the lepton mixing angles (which can be evaded without spoiling the basic ingredients), but also predicts almost all new physics beyond the standard model (SM) like neutrinoless double beta d…
We study colored Higgsino-mediated proton decay (dimension-five proton decay) in a model based on the flipped $SU(5)$ GUT. In the model, the GUT-breaking ${\bf10}$, ${\bf \overline{10}}$ fields have a GUT-scale mass term and gain VEVs through higher-dimensional operators, which induces an effective mass term between the color triplets in the ${\bf 5}$, ${\bf \bar{5}}$ Higgs fields that is not much smaller than the GUT scale. This model structure gives rise to observable dimension-five proton decay, and at the same time achieves moderate suppression on dimension-five proton decay that softens t…
The SUSY $SO(10)$ GUT is in severe tension with the experimental bounds on proton partial lifetimes because proton decay mediated by colored Higgsinos (dimension-five proton decay) is too rapid. In this paper, we pursue the possibility that a texture of the Yukawa coupling matrices in a renormalizable SUSY $SO(10)$ GUT model suppresses dimension-five proton decay. We focus on a general renormalizable SUSY $SO(10)$ GUT model which contains ${\bf 10}+{\bf 126}+{\bf \overline{126}}+{\bf 120}$ representation fields and where the Yukawa coupling matrices of the ${\bf 16}$ matter fields with the ${\…
The symmetry breaking of five-dimensional SU(6) GUT is realized by Scherk-Schwarz mechanisms through trivial and pseudo nontrivial orbifold S1/Z2 breakings to produce dimensional deconstruction 5D SU(6) \rightarrow4D SU(6). The latter also induces near-brane weakly-coupled SU(6) Baby Higgs to further break the symmetry into SU(3)C \otimes SU(3)H \otimes U(1)C. The model successfully provides a scenario of the origin of (Little) Higgs from GUT scale, produces the (intermediate and light) Higgs boson with the most preferred range and establishes coupling unification and compactification scale co…
Proton decay is one of the most important predictions of the grand unified theory (GUT). In the supersymmetric (SUSY) GUT, proton decays via the dimension-five operators need to be suppressed. In the $SO(10)$ model where ${\bf 10}+\overline{\bf 126}$ Higgs fields couple to fermions, neutrino oscillation parameters including the CP-violating Pontecorvo-Maki-Nakagawa-Sakata (PMNS) phase can be related to the Yukawa couplings to generate the dimension-five operators in the unified framework. We show how the suppressed proton decay depends on the PMNS phase, and stress the importance of the precis…
We consider the gravity induced dimension six terms in addition to the dimension five terms in the SUSY GUT Lagrangian and find that the prediction for $α_s$ may be washed out completely in supersymmetric grand unified theories unless the triplet higgs mass is smaller than $ 7\times 10^{16} $ GeV.
The instability of protons is a crucial prediction of supersymmetric GUTs. We review the decay in minimal supersymmetric SU(5), which is dominated by dimension-five operators, and discuss the implications of the failure of Yukawa unification for the decay rate. In a consistent SU(5) model, where SU(5) relations among Yukawa couplings hold, the proton decay rate can be several orders of magnitude smaller than the present experimental bound. Finally, we discuss orbifold GUTs, where proton decay via dimension-five operators is absent. The branching ratios of dimension-six decay can significantly …
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.
Recent measurements of the values of gauge coupling constants as well as neutrino properties support the idea of a grand unified (GUT) description of particle physics at a large scale of $M_{GUT}\sim 10^{16}$ GeV. We discuss a strategy to incorporate this picture in the framework of superstring theory. In such a scheme successful predictions of GUTs can be realized while some of the more problematic aspects of grand unification might be avoided. The most promising models are expected in the framework of the heterotic $E_8\times E_8$ string theory.
We consider four-dimensional supersymmetric compactifications of the E8 x E8 heterotic string on Calabi-Yau manifolds endowed with vector bundles with structure group SU(N) x U(1) and five-branes. After evaluating the Green-Schwarz mechanism and deriving the generalized Donaldson-Uhlenbeck-Yau condition including the five-brane moduli, we show that this construction can give rise to GUT models containing U(1) factors like flipped SU(5) or directly the Standard Model even on simply connected Calabi-Yau manifolds. Concrete realizations of three-generation models on elliptically fibered Calabi-Ya…
This is the first paper of a series that will examine the options for embedding supersymmetric orbifold-GUTs into five-dimensional N=2 Yang-Mills-Einstein supergravity theories (YMESGTs). In particular, we focus on the allowed couplings of charged hypermultiplets in the lowest dimensional reps of the gauge groups SU(5), SO(10) and E(6). Our results are within the classification of homogeneous quaternionic scalar manifolds. In the minimal coupling of a generation of bulk matter hypermultiplets, supergravity requires the field content of an SO(10) scenario. In the minimal coupling of $n$ bulk ge…
In the minimal SUSY SU(5) GUT with $O(1)$ TeV SUSY particles and $O(1)$ or below self-coupling for the GUT-breaking Higgs field, the width of the dimension-6 proton decay is suppressed below the reach of Hyper-Kamiokande. In this paper, we point out that a SUSY SO(10) GUT which adopts only ${\bf 45}_{\rm H}+{\bf 16}_{\rm H}+{\bf \overline{16}}_{\rm H}$ GUT-breaking Higgs fields leads to an enhanced dimension-6 proton decay width detectable at Hyper-Kamiokande. The enhancement is because the SU(5)-breaking VEV of ${\bf 45}_{\rm H}$ arises due to Planck-suppressed terms, $W\propto ({\bf 45}_{\rm…
The symmetry breaking of 5-dimensional SU(6) GUT into 4-dimensional SU(3) x SU(3) x U(1) with orbifold S1/Z2 through Scherk-Schwarz mechanism is investigated. It is shown that the origin of Little Higgs can be generated to further break SU(3) x SU(3) x U(1) down to the electroweak scale through Higgs mechanism.
Simple supersymmetric SO(10) GUT in five dimensions is proposed, in which the fifth dimension is compactified on the $S^1/(Z_2\times Z_2^\prime)$ orbifold with two inequivalent branes at the orbifold fixed points. In this model, all matter and Higgs multiplets reside on one brane (PS brane) where the Pati-Salam (PS) symmetry is manifest, while only the SO(10) gauge multiplet resides on the bulk. The supersymmetry breaking on the other brane (SO(10) brane) is transmitted to the PS brane through the gaugino mediation with the bulk gauge multiplet. We examine sparticle mass spectrum in this setup…
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…
We investigate gauge coupling unification in higher dimensional GUT models with split supersymmetry. We focus on 5d and 6d orbifold GUTs, which permit a simple solution to several problems of 4D GUTs as well as control over GUT scale threshold corrections. In orbifold GUTs, calculable threshold corrections can raise or lower the prediction for $α_s(M_Z)$ in a way that depends on the location of Higgs fields. On the other hand, split supersymmetry lowers the prediction for $α_s(M_Z)$. Consequently, split supersymmetry changes the preferred location of the Higgs fields in orbifold GUTs. In the s…
In the GmSUGRA scenario with the high-dimensional operators containing the GUT Higgs fields, we systematically studied the supersymmetry breaking scalar masses, SM fermion Yukawa coupling terms, and trilinear soft terms in the E_6 SUSY GUT model where the gauge symmetry is broken down to the SO(10)\tm U(1) gauge symmetry, SU(3)_C\times SU(3)_L \times SU(3)_R gauge symmetry, SU(6)\times SU(2)_a (a={\rm L,R,X}) gauge symmetry, flipped SU(5) gauge symmetry etc. In addition, we considered the scalar and gaugino mass relations, which can be preserved from the GUT scale to the electroweak scale unde…
The infrared attractiveness of soft-supersymmetry breaking (SSB) parameters is investigated in extra dimensions. The SSB parameters are assumed to run from the Planck scale M_{PL} down to the GUT scale M_{GUT}. We find that, even for M_{PL}/M_{GUT}=100, the SSB parameters in six dimensions can align out of their anarchical disorder at M_{PL} in such a way that flavor-changing neutral currents as well as dangerous CP-violating phases are sufficiently suppressed at M_{GUT}. A concrete, realistic example based on SU(5) in six dimensions is presented.
Models of supersymmetric grand unified theories based on SU(5)_GUT \times U(N)_H gauge group (N = 2,3) have a symmetry that guarantees light Higgs doublets and absence of dimension-five proton decay operators. We analysed the proton decay induced by gauge-boson exchange in the models. Upper bounds of proton lifetime are obtained; τ(p\to π^0e^+) \lsim 6.0 \times 10^{33} yrs in the SU(5)_GUT \times U(2)_H model and τ(p\to π^0e^+) \lsim 5.3 \times 10^{35} yrs in the SU(5)_GUT \times U(3)_H model. Various uncertainties in the predictions are also discussed.
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the supersymmetric SO(10) grand unified theory in 6 dimensions compactified on a T^2/Z_2 orbifold. The gauge and Higgs fields propagate in 6 dimensions while ordinal chiral matter fields are localized in 4 dimensions. We introduce extra vector-like heavy fields in the extra dimensions. We show three models according to the configurations of vector-like fields in extra dimensions. The suitable fermion mass hierarchies and flavor mixings are generated by integrating out these vector-lik…
Using the freedom in SO(10) GUT's one can generalize the existing models without changing the mass spectrum of fermions to obtain a significant suppression of proton decay resulting from the baryon number violating operators of dimension 5. In some limiting cases, their contributions can be made negligible compared to the dimension 6 operators resulting from the heavy gauge bosons exchange.
We calculate the high and low scale threshold corrections to the D=6 proton decay mode in supersymmetric SU(5) grand unified theories with higher-dimensional representation Higgs multiplets. In particular, we focus on a missing-partner model in which the grand unified group is spontaneously broken by the 75-dimensional Higgs multiplet and the doublet-triplet splitting problem is solved. We find that in the missing-partner model the D=6 proton decay rate gets suppressed by about 60%, mainly due to the threshold effect at the GUT scale, while the SUSY-scale threshold corrections are found to be …
The Supersymmetric SO(10) theory ("NMSO(10)GUT") based on the\hfil\break ${\bf{210+126 +\oot}}$ Higgs system proposed in 1982 has evolved into a realistic theory capable of fitting the known low energy Particle Physics data besides providing a Dark matter candidate and embedding Inflationary Cosmology. It dynamically resolves longstanding issues such as fast dimension five operator mediated proton decay in Susy GUTs by allowing explicit and complete calculation of crucial threshold effects at $M_{Susy}$ and $M_{GUT}$ in terms of fundamental parameters. This shows that SO(10) Yukawas responsibl…
In this talk I discuss the problems and virtues of SUSY GUTs in four dimensions. I then show how to solve some of these problems, without foregoing the virtues, by considering an SO(10) SUSY GUT in five dimensions. I discuss gauge coupling unification and neutrino masses. In particular, it is shown that the 5D compactification scale and cutoff scale are determined by fitting the low energy values of the three standard model gauge couplings. Neutrino masses can be accommodated.
We consider a 5-dimensional SU(5) model wherein the symmetry is broken to the 4-dimensional Standard Model by compactification of the 5th dimension on an S^1/(Z_2 \times Z^\prime_2) orbifold. We identify the members of all SU(5) representations upto 75 which have zero modes. We examine how these light scalars affect gauge coupling unification assuming a single intermediate scale and present several acceptable solutions. The 5-D compactification scale coincides with the unification scale of gauge couplings and is determined via this renormalization group analysis. When SO(10) is considered as t…
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 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…
The fundamental chiral nature of the observed quarks and leptons and the emergence of the gauge group itself are most puzzling aspects of the standard model. Starting from general considerations of topological properties of gauge field configurations in higher space-time dimensions, it is shown that the existence of non-trivial structures in ten dimensions would determine a class of models corresponding to a grand unified GUT structure with complex fermion representations with respect to $ SU(3)_C \otimes SU(2)_L \otimes U(1)_Y$. The discussion is carried out within the framework of string the…
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…
Within supersymmetric SU(5) GUT we suggest mechanisms for suppression of baryon number violating dimension five and six operators. The mechanism is based on the idea of split multiplets (i.e. quarks and leptons are not coming from a single GUT state) which is realized by an extension with additional vector-like matter. The construction naturally avoids wrong asymptotic relation $\hat{M}_D=\hat{M}_E$. Thus, the long standing problems of the minimal SUSY SU(5) GUT can be resolved. In a particular example of flavor structure and with additional ${\cal U}(1)\tm {\cal Z}_{3N}$ symmetry we demonstra…
We propose a supersymmetric SU(5) orbifold GUT in 5 dimensions in which supersymmetry breaking at the boundaries give rise to split supersymmetry spectrum. The extra dimension is compactified on a $S^1/Z_2 \times Z_2^\prime$ orbifold having two fixed points. The standard model fermions are localized in the standard model brane, where supersymmetry is broken by the nonvanishing of the F-term of a superfield X at some intermediate scale. All scalar superpartners acquires mass at this stage. The standard model gauginos and higgsinos remain light, since their masses are protected by R-symmetry and…
We propose an $SO(10)$ supersymmetric grand unified theory (SUSY GUT), where the $SO(10)$ gauge symmetry breaks down to $SU(3)_c \times SU(2)_L \times U(1)_Y\times U(1)_{X}$ at the GUT scale and $U(1)_X$ is radiatively broken at the SUSY-braking scale. In order to achieve the observed Higgs mass around $126$ GeV and also to satisfy constraints on flavor- and/or CP-violating processes, we assume that the SUSY-breaking scale is $O(100)$ TeV, so that the $U(1)_X$ breaking scale is also $O(100)$ TeV. One big issue in the SO(10) GUTs is how to realize realistic Yukawa couplings. In our model, not o…
We show that in the framework of grand unified theory (GUT) with anomalous $U(1)_A$ gauge symmetry, the success of the gauge coupling unification in the minimal SU(5) GUT is naturally explained, even if the mass spectrum of superheavy fields does not respect SU(5) symmetry. Because the unification scale for most realizations of the theory becomes smaller than the usual GUT scale, it suggests that the present level of experiments is close to that sufficient to observe proton decay via dimension 6 operators, $p\to e+π$.
In the previous paper, we have shown that $R_1\equiv\frac{Γ_{n \rightarrow π^0 + ν^c}}{Γ_{p \rightarrow π^0 + e^c}}$ and $R_2\equiv\frac{Γ_{p \rightarrow K^0 + μ^c}}{Γ_{p \rightarrow π^0 + e^c}}$ can identify the grand unification group $SU(5)$, $SO(10)$, or $E_6$ in typical anomalous $U(1)_A$ supersymmetric (SUSY) grand unified theory (GUT) in which nucleon decay via dimension-6 operators becomes dominant. When $R_1 > 0.4$ the grand unification group is not $SU(5)$, while when $R_1 > 1$ the grand unification group is $E_6$. Moreover, when $R_2 > 0.3$, $E_6$ is implied. Main ambiguities come f…
We construct a supersymmetric grand unified model in the framework of a latticized extra dimension. The SU(5) symmetries on the lattice are broken by the vacuum expectation values of the link fields connecting adjacent SU(5) sites, leaving just the MSSM at low energies. Below the SU(5) breaking scale, the theory gives rise to a similar spectrum as in orbifold breaking of SU(5) symmetry in 5 dimensions, and shares many features with the latter scenario. We discuss gauge coupling unification and proton decay emphasizing the differences with respect to the usual grand unified theories. Our model …
The semi-simple unification model based on SU(5)_GUT \times U(3)_H gauge group is an interesting extension of the minimal SU(5)_GUT grand unification theory (GUT), since it solves the two serious problems in the standard GUT: the triplet-doublet splitting problem and the presence of dangerous dimension five operators for proton decay. Here, the extra U(3)_H gauge interaction plays a crucial role on the GUT breaking. In this paper, we show that the full multiplet structure of the U(3)_H sector required for the desired GUT breaking is reproduced naturally on T^6/Z_12 orientifold in the type IIB …
In this talk, we introduce a new scenario of grand unified theory (GUT) with anomalous $U(1)_A$ gauge symmetry, which can explain doublet-triplet splitting, quark and lepton masses and mixing angles. In neutrino sector, the scenario realizes LMA solution for solar neutrino problem and large $U_{e3}=O(0.1)$. Moreover, the scenario predicts that the main decay mode of proton is from dimension 6 operators and the lifetime of proton must be near the present limit. The realization of gauge coupling unification requires that the cutoff scale of the scenario must be around the usual GUT scale $Λ_G\si…
We implement inflation in a supersymmetric SU(5) model with U(1) R-symmetry such that the cosmic microwave anisotropy $δT/T$ is proportional to $(M/M_{\rm Planck})^2$, where $M\sim M_{GUT}=2-3\times 10^{16}$ GeV, the SU(5) breaking scale, and $M_{\rm Planck}=2.4\times 10^{19}$ GeV. The presence of a global $U(1)_X$ symmetry, spontaneously broken also at scale $M_{GUT}$, provides an upper bound $M_{GUT}^2/M_{\rm Planck}\sim 10^{14}$ GeV on the masses of SU(5) singlet right handed neutrinos, which explains the mass scale associated with atmospheric neutrino oscillations. The SU(5) monopoles and …
We present a Grand Unified Theory (GUT) that has GUT fields with masses of the order of a TeV, but at the same time preserves (at the one-loop level) the success of gauge-coupling unification of the MSSM and the smallness of proton decay operators. This scenario is based on a five-dimensional theory with the extra dimension compactified as in the Randall-Sundrum model. The MSSM gauge sector and its GUT extension live in the 5D bulk, while the matter sector is localized on a 4D boundary.
Nucleon lifetimes for various decay modes via dimension 6 operators are calculated in the anomalous $U(1)_A$ GUT scenario, in which the unification scale $Λ_u$ becomes smaller than the usual supersymmetric (SUSY) unification scale $Λ_G=2\times 10^{16}$ GeV in general. Since the predicted lifetime $τ(p\rightarrow π^0+e^c)$ becomes around the experimental lower bound though it is strongly dependent on the explicit models, the discovery of the nucleon decay in near future can be expected. We explain why the two ratios $R_1\equiv\frac{Γ_{n \rightarrow π^0 + ν^c}}{Γ_{p \rightarrow π^0 + e^c}}$ and …
In this article, we review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with $S^2/Z_2$ topology in the extra spatial dimensions. On the extra $S^2/Z_2$ space, non-trivial boundary conditions are imposed. This review considers two scenarios for constructing a four-dimensional theory from the six-dimensional model. One scheme utilizes the SO(12) gauge symmetry with a special symmetry condition imposed on the gauge field, whereas the other employs the E$_6$ gauge symmetry without requiring the additional symmetry condition. Both models lead to a Stan…
We prove that it is impossible to construct a grand unified model, based on a simple gauge group, in four dimensions that leads to the exact MSSM, nor to a singlet extension, and possesses an unbroken R symmetry. This implies that no MSSM model with either a Z_{M>=3}^R or U(1)_R symmetry can be completed by a four-dimensional GUT in the ultraviolet. However, our no-go theorem does not apply to GUT models with extra dimensions. We also show that it is impossible to construct a 4D GUT that leads to the MSSM plus an additional anomaly-free symmetry that forbids the mu term.
There have been many theoretical models constructed which aim to explain the neutrino masses and mixing patterns. While many of the models will be eliminated once more accurate determinations of the mixing parameters, especially $\sin^2 2θ_{13}$, are obtained, charged lepton flavor violation (LFV) experiments are able to differentiate even further among the models. In this paper, we investigate various rare LFV processes, such as $\ell_{i} \to \ell_{j} + γ$ and $μ-e$ conversion, in five predictive supersymmetric (SUSY) SO(10) models and their allowed soft-SUSY breaking parameter space in the c…
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.
In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the generic gauge coupling relations at the GUT scale, and the general gaugino mass relations which are valid from the GUT scale to the electroweak scale at one loop. We define the index k for these relations, which can be calculated in GUTs and can be determined at the Large Hadron Collider and the future International Linear Collider. Thus, we give a concrete defin…
Dimension-5 corrections to the gauge kinetic term of Grand Unified Theories (GUTs) may capture effects of quantum gravity or string compactification. Such operators modify the usual gauge coupling unification prediction in a calculable manner. Here we examine SU(5), SO(10), and E(6) GUTs in the light of all such permitted operators and calculate the impact on the intermediate scales and the unification programme. We show that in many cases at least one intermediate scale can be lowered to even 1-10 TeV, where a neutral Z' and possibly other states are expected.
We reanalyze the proton decay in the minimal SU(5) SUGRA GUT model. Unlike previous analyses, we take into account a Higgsino dressing diagram of dimension 5 operator with right-handed matter fields ($RRRR$ operator). It is shown that this diagram gives a dominant contribution for $p\to K^+\barν_τ$ over that from $LLLL$ operator, and decay rate of this mode can be comparable with that of $p\to K^+\barν_μ$ which is dominated by the $LLLL$ contribution. It is found that we cannot reduce both the decay rate of $p\to K^+\barν_τ$ and that of $p\to K^+\barν_μ$ simultaneously by adjusting relative ph…
We point out that in non supersymmetric GUTs, in which the SU(5) gauge symmetry is broken down to the Standard Model gauge group by a $\mathbf{24}$ Higgs multiplet the Appelquist-Carazzone decoupling is violated. This is because the $SU(2)_L$ Higgs triplet contained in the $\mathbf{24}$ acquires a dimensionfull coupling to the $SU(2)_L$ Higgs doublets which is proportional to the GUT breaking vacuum expectation value (VEV) $V$. As a result, at one loop heavy gauge and Higgs fields contribution to tadpoles generate a VEV of the triplet which is not suppressed for $V\to\infty$ and violates the c…
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 discuss the anomalous U(1) gauge symmetry as a mechanism of generating the grand-unification scale. We conclude that unification to a simple group cannot be realized unless some parameters are ``tuned'', and that models with product gauge groups are preferred. We consider the ``R-invariant natural unification'' model with gauge groups SU(5)_{GUT} \times U(3)_H. In this model the doublet-triplet splitting problem is solved and the unwanted GUT relation m_s = m_μis avoided maintaining m_b = m_τ. Moreover, R-invariance suppresses the dangerous proton decays induced by dimension four and five o…
We present a five-dimensional supersymmetric SU(5) theory in which the gauge symmetry is broken maximally (i.e. at the 5D Planck scale M_*) on the same 4D brane where chiral matter is localized. Masses of the lightest Kaluza-Klein modes for the colored Higgs and X and Y gauge fields are determined by the compactification scale of the fifth dimension, M_C ~ 10^{15} GeV, rather than by M_*. These fields' wave functions are repelled from the GUT-breaking brane, so that proton decay rates are suppressed below experimental limits. Above the compactification scale, the differences between the standa…
We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and gauge group is a direct product of two Lie groups. We list up candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space,we find fermion and scalar representations of $G_{\mathrm{GUT}} \times U(1)$ with $G_{\mathrm{GUT}}=SU(5), SO(10)$ and $E_6$ which accomodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with a different dim…
In the effective field theory framework, quantum gravity can induce effective dimension-5 operators, which have important impacts on grand unified theories. Interestingly, one of main effects is the modification of the usual gauge coupling unification condition. We investigate the gauge coupling unification in $E_{6}$ under modified gauge coupling unification condition at scales $M_X$ in the presence of one or more dimension-5 operators. It is shown that nonsupersymmetric models of $E_6$ unification can be obtained and can easily satisfy the constraints from the proton lifetime. For constructi…
Proton decay within 5-dimensional SU(6) GUT with orbifold S^1/Z_2 breaking is investigated using Scherk-Schwarz mechanism. It is shown that in the model neither leptoquark like heavy gauge bosons nor violation of baryon number conservation are allowed due to the orbifold breaking parity splitting. These results prevent too short proton lifetime within the model.
Boundary conditions on an extra-dimensional interval can be chosen to break bulk gauge symmetries and to reduce the rank of the gauge group. We consider this mechanism in models with gauge trinification. We determine the boundary conditions necessary to break the trinified gauge group directly down to that of the standard model. Working in an effective theory for the gauge symmetry-breaking parameters on a boundary, we examine the limit in which the GUT-breaking sector is Higgsless and show how one may obtain the low-energy particle content of the minimal supersymmetric standard model. We find…
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the 6 dimensional N=1 supersymmetric SO(10) grand unified theory compactified on a $T^2/(Z_2 \times Z_2')$ orbifold. We introduce 6D and 5D matter fields, which contains the 1st and 2nd generation matter fields as the zero modes, respectively. The 3rd generation matter fields are located on a 4D brane. The Yukawa couplings for bulk fields are suppressed by volume factors from extra dimensions. The suitable fermion mass hierarchies and flavor mixings are generated by the volume suppres…
We study a renormalizable SUSY $SO(10)$ GUT model where the Yukawa couplings of single ${\bf 10}$, single ${\bf \overline{126}}$ and single ${\bf 120}$ fields, $Y_{10},Y_{126},Y_{120}$, account for the quark and lepton Yukawa couplings and the neutrino mass. We pursue the possibility that $Y_{10},Y_{126},Y_{120}$ reproduce the correct quark and lepton masses, CKM and PMNS matrices and neutrino mass differences, and at the same time suppress dimension-5 proton decays (proton decays via colored Higgsino exchange) through their texture, so that the soft SUSY breaking scale can be reduced as much …
