Orbifold Grand Unified Theories Research Articles

Muon g−2 and proton lifetime in SUSY SU(5) GUTs with split superpartners

We consider the interplay of the muon g−2 anomaly and the proton decay in the supersymmetry (SUSY) SU(5) grand unified theories (GUTs) with generation-independent scalar soft masses. In these scenarios, we introduce a number of 5+5¯ messenger fields with doublet-triplet splitting in general gauge mediation to transmit SUSY breaking to the visible sector by gauge loops. As a result, squarks and sleptons receive generation-independent soft SUSY breaking masses, which are split already at the messenger scale. Taking into account the perturbative unification of gauge couplings as well as the bounds from electroweak precision and vacuum stability bounds, we showed the parameter space in general gauge mediation to explain the muon g−2 anomaly with smuon and sneutrino loops while evading the strong bounds on squarks and gluinos from the Large Hadron Collider. We also obtained the dominant Higgsino contributions to the proton decay mode, p→K+ν¯, with general generation-independent sparticle masses for squarks and sleptons. Even for split scalar soft masses in our model, however, we found that the bounds from the proton decay are satisfied only if the effective Yukawa couplings of the colored Higgsinos are suppressed further by a factor of order 10−4–10−3. We illustrated how such a suppression factor is realized in orbifold GUTs in the extra dimension where the colored Higgsinos in the bulk are not coupled to the matter fields localized at the orbifold fixed points at the leading order. Published by the American Physical Society 2024

E6 GUT and Baryon Asymmetry Generation in the E6CHM

Grand unified theories (GUTs) may result in the E6-inspired composite Higgs model (E6CHM) at low energies, almost stabilizing the electroweak scale. We consider an orbifold GUT in 6 dimensions in which the E6-gauge group is broken to the gauge symmetry of the standard model (SM) while different multiplets of the SM fermions come from different 27-plets. The strongly coupled sector of the E6CHM is confined on the brane where E6 is broken down to its SU(6) subgroup. Near the scale of f≳5TeV, this approximate SU(6) symmetry is expected to be further broken down to its SU(5) subgroup, which contains the SM-gauge group. Such a breakdown leads to a set of pseudo-Nambu–Goldstone bosons (pNGBs) that includes an SM-like Higgs doublet. The approximate gauge coupling unification in the E6CHM takes place at high energies when the right-handed top quark is a composite fermion. To ensure anomaly cancellation, the weakly coupled sector of this model contains extra exotic matter beyond the SM. We discuss the mechanism of the generation of matter–antimatter asymmetry within the variant of the E6CHM in which the baryon number and CP invariance are violated.

Seeing higher-dimensional grand unification in primordial non-gaussianities

The observed low-energy values of the SU(3) × SU(2) × U(1) gauge couplings, extrapolated via the minimal Standard Model Renormalization Group evolution, hint at the exciting possibility of a Grand Unified Theory (GUT) at MU ∼ 1014 GeV — a scale, however, too high to probe directly via collider searches. Fortunately, since the Hubble scale H can be as high as 5 × 1013GeV ∼ MU during the inflationary era, such GUT scale states can be cosmologically produced at that time and leave direct on-shell signatures such as their masses and spins, via primordial non-Gaussianity (NG). We explore this possibility in one of its simplest realizations given by the extra-dimensional framework of orbifold GUTs, in which proton decay can be straightforwardly suppressed to be within the stringent bounds. Here, along with the massive GUT states there must also be H-mass spin-2 Kaluza-Klein (KK) gravitons, collectively giving rise to striking NG signatures. In our set-up we localize the inflaton on one of the boundaries of an extra dimension. The inflationary vacuum energy can readily lead to formation of a horizon in the bulk, where the KK modes then form a continuum above a mass gap of ∼ mathcal{O} (H). We find that the optimal case for observable NG signals is when the extra dimension is stabilized close to the onset of this horizon, ensuring a discrete KK spectrum such that the lightest KK modes can be cosmologically produced without significant Boltzmann suppressions. Although we mostly focus on the case where there is no higher-dimensional cosmological constant, we also obtain considerable holographic insights from the AdS5/CFT4 correspondence when such a cosmological constant is included.

A symmetry breaking mechanism by parity assignment in the noncommutative Higgs model

We apply the orbifold grand unified theory (GUT) mechanism to the noncommutative Higgs model. An assignment of [Formula: see text] parity to the “constituent fields” induces parity assignments of both the gauge and Higgs bosons, because these bosons are treated as some kind of composite fields in this formalism.

Interpretation of the diphoton excess at CMS and ATLAS

We consider the diphoton resonance at the 13 TeV LHC in a consistent model with new scalars and vector-like fermions added to the Standard Model (SM), which can be constructed from orbifold grand unified theories and string models. The gauge coupling unification can be achieved, neutrino masses can be generated radiatively, and electroweak vacuum stability problem can be solved. To explain the diphoton resonance, we study a spin-0 particle, and discuss various associated final states.

E6inspired composite Higgs model

We consider a composite Higgs model embedded into a Grand Unified Theory(GUT) based on the E_6 gauge group. The phenomenological viability of this E_6 inspired composite Higgs model (E6CHM) implies that standard model (SM) elementary fermions with different baryon or lepton number should stem from different 27 representations of E_6. We present a six-dimensional orbifold GUT model in which the E_6 gauge symmetry is broken to the SM gauge group so that the appropriate splitting of the bulk 27-plets takes place. In this model the strongly coupled sector is localised on one of the branes and possesses an SU(6) global symmetry that contains the SU(3)_C\times SU(2)_W\times U(1)_Y subgroup. In this case the approximate gauge coupling unification can be attained if the right-handed top quark is a composite state and the elementary sector involves extra exotic matter beyond the SM which ensures anomaly cancellation. The breakdown of the approximate SU(6) symmetry at low energies in this model results in a set of the pseudo-Nambu-Goldstone states which include a Higgs doublet and scalar colour triplet. We discuss the generation of the masses of the SM fermions in the E6CHM. The presence of the TeV scale vector-like exotic quarks and scalar colour triplet may provide spectacular new physics signals that can be observed at the LHC.

A symmetry-breaking mechanism by parity assignment in the noncommutative Higgs model

We apply the orbifold grand unified theory (GUT) mechanism to the noncommutative Higgs model. An assignment of |$Z_{2}$| parity to the “constituent fields” induces parity assignments of both the gauge and Higgs bosons, because these bosons are treated as some kind of composite field in this formalism. As a result, some of the gauge bosons and the colored triplet Higgs boson receive heavy mass comparable to the GUT scale, and the gauge symmetry is broken. No particles appear other than the SM ones in the massless states.

General gauge and anomaly mediated supersymmetry breaking in grand unified theories with vector-like particles

In Grand Unified Theories (GUTs) from orbifold and various string constructions the generic vector-like particles do not need to form complete SU(5) or SO(10) representations. To realize them concretely, we present orbifold SU(5) models, orbifold SO(10) models where the gauge symmetry can be broken down to flipped SU(5) X U(1)_X or Pati-Salam SU(4)_C X SU(2)_L X SU(2)_R gauge symmetries, and F-theory SU(5) models. Interestingly, these vector-like particles can be at the TeV-scale so that the lightest CP-even Higgs boson mass can be lifted, or play the messenger fields in the Gauge Mediated Supersymmetry Breaking (GMSB). Considering GMSB, ultraviolet insensitive Anomaly Mediated Supersymmetry Breaking (AMSB), and the deflected AMSB, we study the general gaugino mass relations and their indices, which are valid from the GUT scale to the electroweak scale at one loop, in the SU(5) models, the flipped SU(5) X U(1)_X models, and the Pati-Salam SU(4)_C X SU(2)_L X SU(2)_R models. In the deflected AMSB, we also define the new indices for the gaugino mass relations, and calculate them as well. Using these gaugino mass relations and their indices, we may probe the messenger fields at intermediate scale in the GMSB and deflected AMSB, determine the supersymmetry breaking mediation mechanisms, and distinguish the four-dimensional GUTs, orbifold GUTs, and F-theory GUTs.

Flavored orbifold GUT — an SO(10) × S 4 model

Orbifold grand unified theories (GUTs) solve several problems in GUT model building. Therefore, it is intriguing to investigate similar constructions in the flavor context. In this paper, we propose that a flavor symmetry might emerge due to orbifold compactification of one orbifold and broken by boundary conditions of another orbifold. The combination of the orbifold parities in gauge and flavor space determines the zero modes. We demonstrate the construction in a supersymmetric (SUSY) SO(10) x S_4 orbifold GUT model, which predicts the tribimaximal mixing at leading order in the lepton sector as well as the Cabibbo angle in the quark sector.

An exceptional SSM from E 6 orbifold GUTs with intermediate LR symmetry

We propose a class of E 6-based local orbifold Grand Unified Theories (GUTs) which yield an exceptional supersymmetric standard model as their low energy theory including leptoquark and un-Higgs exotics and a Z’ at the TeV scale. Unification is achieved in two steps through an intermediate scale symmetry breaking at a unified coupling which is enhanced due to the contributions of leptoquarks to the QCD beta function.

Reconciling grand unification with strings by anisotropic compactifications

We analyze gauge coupling unification in the context of heterotic strings on anisotropic orbifolds. This construction is very much analogous to effective five-dimensional orbifold grand unified theory field theories. Our analysis assumes three fundamental scales: the string scale ${M}_{\mathrm{S}}$, a compactification scale ${M}_{\mathrm{C}}$, and a mass scale for some of the vectorlike exotics ${M}_{\mathrm{EX}}$; the other exotics are assumed to get mass at ${M}_{\mathrm{S}}$. In the particular models analyzed, we show that gauge coupling unification is not possible with ${M}_{\mathrm{EX}}={M}_{\mathrm{C}}$, and in fact we require ${M}_{\mathrm{EX}}\ensuremath{\ll}{M}_{\mathrm{C}}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{ }\text{ }\mathrm{GeV}$. We find that about 10% of the parameter space has a proton lifetime (from dimension six gauge exchange) ${10}^{33}\text{ }\text{ }\mathrm{yr}\ensuremath{\lesssim}\ensuremath{\tau}(p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{e}^{+})\ensuremath{\lesssim}{10}^{36}\text{ }\text{ }\mathrm{yr}$. The other 80% of the parameter space gives proton lifetimes below Super-Kamiokande bounds. The next generation of proton decay experiments should be sensitive to the remaining parameter space.

Realistic hybrid inflation in five-dimensional orbifoldSO(10) grand unified theory

We discuss the smooth hybrid inflation scenario in the context of a simple supersymmetricSO(10) grand unified theory (GUT) in a 5D orbifold. In this GUT model, theSO(10) gauge symmetry is broken down to the Pati–Salam (PS) gauge group,SU(4)c × SU(2)L × SU(2)R, by means of orbifold boundary conditions, and all matter and Higgs multiplets are placedonly on the brane (PS brane) where only the PS symmetry is manifest. Furtherbreaking of the Pati–Salam group to the standard model one is realized by meansof vacuum expectation values of the Higgs multiplets . The gauge coupling unification is successfully realized atMGUT = 4.6 × 1017 GeV after incorporating the threshold corrections of the Kaluza–Klein modes, with thecompactification scale (assumed to be the same as the PS symmetry breaking scale)Mc = vPS = 1.2 × 1016 GeV. We show that this orbifold GUT model can naturally lead us to smooth hybrid inflation, whichturns out to be consistent with the Wilkinson Microwave Anisotropy Probe five-year data, with theMGUT and vPS predicted within the model.

Fermion masses and mixings in grand unified theories with noncanonicalU(1)Y

We discuss fermion masses and mixings in models derived from orbifold grand unified theories such that gauge coupling unification is achieved without low-energy supersymmetry by utilizing a noncanonical 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 vectorlike particles with masses close to M(GUT) are also discussed.

CPviolation and flavor mixings in orbifold grand unified theories

We address the flavor problem by incorporating the hypothesis of universal strength of Yukawa couplings in the framework of a 5D GUT model compactified on an ${S}^{1}/({Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}^{\ensuremath{'}})$ 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 Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata matrices.

MORE ABOUT SUPERPARTICLE SUM RULES IN GRAND UNIFIED THEORIES

Sum rules among superparticle masses are derived under the assumption that models beyond the MSSM are four-dimensional supersymmetric grand unified theories or five-dimensional supersymmetric orbifold grand unified theories. Sfermion sum rules are classified into four types and those sum rules can be useful probes of the MSSM and beyond.

Noncanonical MSSM, unification, and new particles at the CERN LHC

We consider noncanonical embeddings of the MSSM in high-dimensional orbifold grand unified theories (GUTs) based on the gauge symmetry SU(N), N=5, 6, 7, 8. The hypercharge normalization factor k(Y) can either have unique noncanonical values, such as 23/21 in a six-dimensional SU(7) model, or may lie in a (continuous) interval. Gauge coupling unification and gauge-Yukawa unification can be realized in these models by introducing new particles with masses in the TeV range which may be found at the LHC. In one such example there exist color singlet fractionally charged states.

Non-canonical gauge coupling unification in high-scale supersymmetry breaking

The string landscape suggests that the supersymmetry breaking scale can be high, and then the simplest low energy effective theory is the Standard Model (SM). Considering grand unification scale supersymmetry breaking, we show that gauge coupling unification can be achieved at about 10 16 – 17 GeV in the SM with suitable normalizations of the U ( 1 ) Y , and we predict that the Higgs mass range is 127 to 165 GeV, with the precise value strongly correlated with the top quark mass m t and SU ( 3 ) C gauge coupling. For example, if m t = 178 ± 1 GeV , the Higgs boson mass is predicted to be between 141 and 154 GeV. We also point out that gauge coupling unification in the Minimal Supersymmetric Standard Model (MSSM) does not imply the canonical U ( 1 ) Y normalization. In addition, we present 7-dimensional orbifold grand unified theories (GUTs) in which such normalizations for the U ( 1 ) Y and charge quantization can be realized. The supersymmetry can be broken at the grand unification scale by the Scherk–Schwarz mechanism. We briefly comment on a non-canonical U ( 1 ) Y normalization due to the brane localized gauge kinetic terms in orbifold GUTs.

Hadronic EDM constraints on orbifold GUTs

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 charged lepton flavor violation (LFV) searches. The interplay between future EDM and LFV experiments will probe the structures of the GUTs and the SUSY breaking mediation mechanism.

Gauge coupling unification in the Standard Model

The string landscape suggests that the supersymmetry breaking scale can be high, and then the simplest low energy effective theory is the Standard Model (SM). We show that gauge coupling unification can be achieved at about 1016–17 GeV in the SM with suitable normalizations of the U(1)Y. Assuming grand unification scale supersymmetry breaking, we predict that the Higgs mass range is 127 GeV to 165 GeV, with the precise value strongly correlated with the top quark mass and SU(3)C gauge coupling. We also present 7-dimensional orbifold grand unified theories in which such normalizations for the U(1)Y and charge quantization can be realized.

Gauge unification in highly anisotropic string compactifications

It is well known that heterotic string compactifications have, in spite of their conceptual simplicity and aesthetic appeal, a serious problem with precision gauge coupling unification in the perturbative regime of string theory. Using both a duality-based and a field-theoretic definition of the boundary of the perturbative regime, we reevaluate the situation in a quantitative manner. We conclude that the simplest and most promising situations are those where some of the compactification radii are exceptionally large, corresponding to highly anisotropic orbifold models. Thus, one is led to consider constructions which are known to the effective field-theorist as higher-dimensional or orbifold grand unified theories (orbifold GUTs). In particular, if the discrete symmetry used to break the GUT group acts freely, a non-local breaking in the larger compact dimensions can be realized, leading to a precise gauge coupling unification as expected on the basis of the MSSM particle spectrum. Furthermore, a somewhat more model dependent but nevertheless very promising scenario arises if the GUT breaking is restricted to certain singular points within the manifold spanned by the larger compactification radii.