We introduce a non-Abelian discrete $Δ_{27}$ family symmetry into the recently proposed classes of Exceptional Supersymmetric Standard Model ($E_6$SSM) based on a broken $E_6$ Grand Unified Theory (GUT) in order to solve the flavour problem in these models and in particular to account for tri-bimaximal neutrino mixing. We consider both the minimal version of the model (the ME$_6$SSM) with gauge coupling unification at the string scale and the E$_6$SSM broken via the Pati-Salam chain with gauge coupling unification at the conventional GUT scale. In both models there are low energy exotic colour triplets with couplings suppressed by the symmetries of the model, including the family symmetry. This leads to suppressed proton decay and long lived TeV mass colour triplet states with striking signatures at the LHC. We also present a dynamical solution to the $μ'$ problem (where $μ'$ is the mass of the additional pair of electroweak doublets in the E$_6$SSM).
We study electroweak baryogenesis in the E_6 inspired exceptional supersymmetric standard model ( E_6SSM ). The relaxation coefficients driven by singlinos and the new gaugino as well as the transport equation of the Higgs supermultiplet number density in the E_6SSM are calculated. Our numerical simulation shows that both CP-violating source terms from singlinos and the new gaugino can solely give rise to a correct baryon asymmetry of the Universe via the electroweak baryogenesis mechanism.
We discuss the spectrum of Higgs bosons in the framework of the exceptional supersymmetric standard model. The presence of a $Z'$ and exotic particles predicted by the exceptional SUSY model allows the lightest Higgs particle to be significantly heavier than in the MSSM and NMSSM. When the mass of the lightest Higgs boson is larger than $135-140 {GeV}$ the heaviest scalar, pseudoscalar and charged Higgs states lie beyond the ${TeV}$ range.
Supersymmetric unified models in which the Z' couples to the Higgs doublets, as in the E6 class of models, have large fine tuning dominated by the experimental mass limit on the Z'. To illustrate this we investigate the degree of fine tuning throughout the parameter space of the Constrained Exceptional Supersymmetric Standard Model (cE6SSM) that is consistent with a Higgs mass m_h ~ 125 GeV. Fixing tan beta = 10, and taking specific values of the mass of the Z' boson, with M_Z' ~ 2-4 TeV. We find that the minimum fine tuning is set predominantly from the mass of Z' and varies from ~ 200-400 as…
We consider the renormalisation group flow of gauge couplings within the so-called exceptional supersymmetric standard model (E$_6$SSM) based on the low energy matter content of 27 dimensional representations of the gauge group $E_6$, together with two additional non-Higgs doublets. The two--loop beta functions are computed, and the threshold corrections are studied in the E$_6$SSM. Our results show that gauge coupling unification in the E$_6$SSM can be achieved for phenomenologically acceptable values of $α_3(M_Z)$, consistent with the central measured low energy value, unlike in the minimal …
In this paper we explain the diphoton excess in the invariant mass M $\approx$ 750 GeV , claimed by the ATLAS and CMS collaborations at the run-2 LHC, as the signal of a scalar singlet in a string inspired exceptional supersymmetric standard model (ESSM). The scalar singlet might play a rule in the spontaneous breaking of the $U(1)^\prime$ gauge symmetry of the ESSM and couples to diphoton and/or gluon pair with the help of exotic quarks and Higgs-like supermultiplets, which are contained in the fundamental representation of the $E_6$ group. The model might give rise to a large enough producti…
We propose a theory of flavour based on abelian horizontal gauge symmetries and modular invariances. We construct explicit supergravity models where the scale of the horizontal $U(1)$ symmetry breaking is fixed by the Green-Schwarz mechanism for anomaly cancellation. The supersymmetric spectrum is obtained in terms of the $U(1)$ charges which are determined by the Yukawa matrices.
We calculate flavour dependent lepton asymmetries within the $E_6$ inspired Supersymmetric Standard Model ($\rm E_6SSM$), which has an extra $U(1)_N$ symmetry. In this model, the right-handed neutrino doesn't participate in gauge interactions, allowing it to be used for both the see--saw mechanism and leptogenesis. Extra Higgs, leptons and leptoquarks predicted by the E$_6$SSM contribute to the ordinary lepton CP asymmetries induced by the decays of the lightest right--handed neutrino (and sneutrino) and give rise to a set of extra decay asymmetries. We find that the CP asymmetries can be rela…
We discuss two striking Large Hadron Collider (LHC) signatures of the constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m_0, soft trilinear coupling A_0 and soft gaugino mass M_{1/2}. The first signature we discuss is that of light exotic colour triplet charge 1/3 fermions, which we refer to as D-fermions. We calculate the LHC production cross section of D-fermions, and discuss their decay patterns. Secondly we discuss the E6 type U(1)_N spin-1 Z' gauge boson and show how it may decay into exotic states, increasing …
We discuss some phenomenological aspects of an $E_6$ inspired supersymmetric standard model with an extra $U(1)_{N}$ gauge symmetry under which right-handed neutrinos have zero charge, allowing a conventional see-saw mechanism. The $μ$ problem is solved in a similar way to the NMSSM, but without the accompanying problems of singlet tadpoles or domain walls. The above exceptional supersymmetric standard model (ESSM) involves the low energy matter content of three 27 representations of $E_6$, which is broken at the GUT scale, and allows gauge coupling unification due to an additional pair of Hig…
We discuss the predictions of a constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m_0, soft trilinear coupling A_0 and soft gaugino mass M_1/2. We predict a supersymmetry (SUSY) spectrum containing a light gluino, a light wino-like neutralino and chargino pair and a light bino-like neutralino, with other sparticle masses except the lighter stop being much heavier. In addition, the cE6SSM allows the possibility of light exotic colour triplet charge 1/3 fermions and scalars, leading to early exotic physics signals at …
Models that combine Abelian horizontal symmetries and spontaneous CP violation can (i) explain the smallness and hierarchy in quark parameters; (ii) satisfactorily suppress supersymmetric contributions to flavor changing neutral current processes; (iii) solve the $μ$-problem; and (iv) suppress supersymmetric contributions to CP violating observables to an acceptable level. The CKM phase is $Ø(1)$ and responsible, through Standard Model box diagrams, to $ε_K$. The supersymmetric CP violating phases are suppressed, $ϕ_A\simλ^6$ and $ϕ_B\simλ^{8}$ ($λ\sim0.2$), leading to an electric dipole momen…
We calculate threshold corrections to the running gauge and Yukawa couplings in the Exceptional Supersymmetric Standard Model (E6SSM) and analyse the more precise and reliable mass spectra in a constrained model (CE6SSM). Full expressions for the corrections are provided and the implementation into a spectrum generator is described. We find a dramatic reduction in the matching scale dependency of the masses of many states and observe a significant adjustment of the correlation of low-scale physical masses and high-scale parameters. Still, in substantial regions of parameter space the mass of t…
We discuss the $e^{+}e^{-}\to (h A)\to bbbb$ cross section in an Abelian extended SM. We work in that minimum of the scalar potential for which Higgs trilier coupling is greater than the soft mass parameters. We find that nex-to-lightest Higgs gives the essential contribution to the cross section in the small $Z-Z'$ mixing angle and leptophobic $Z'$ limit.
We propose and study a constrained version of the Exceptional Supersymmetric Standard Model (E6SSM), which we call the cE6SSM, based on a universal high energy scalar mass m_0, trilinear scalar coupling A_0 and gaugino mass M_{1/2}. We derive the Renormalisation Group (RG) Equations for the cE6SSM, including the extra U(1)_{N} gauge factor and the low energy matter content involving three 27 representations of E6. We perform a numerical RG analysis for the cE6SSM, imposing the usual low energy experimental constraints and successful Electro-Weak Symmetry Breaking (EWSB). Our analysis reveals t…
We present a supersymmetric SU(5) x U(1)_H model, free from gauge anomalies, where the Abelian factor U(1)_H, introduced to account for the hierarchy of fermion masses and mixings, is broken by the same adjoint representations of SU(5) that also break the GUT symmetry. The model predicts approximate, but never exact, bottom-tau Yukawa unification. The deviations are related to group theoretical coefficients and can naturally be at the level of 10%-20%.
We study the parameter space of the constrained exceptional supersymmetric standard model (cE6SSM) consistent with a Higgs signal near 125 GeV and the LHC searches for squarks, gluinos and Z'. The cE6SSM parameter space consistent with correct electroweak symmetry breaking, is represented by scans in the (m0, M1/2) plane for fixed Z' mass and tan beta, with squark, gluino and Higgs masses plotted as contours in this plane. We find that a 125 GeV Higgs mass only arises for a sufficiently large Z' mass, mostly above current limits, and for particular regions of squark and gluino masses correspon…
We analyze the Higgs production via the Higgs-strahlung process $e^{+}e^{-}\to h_{k}{\it{l}}^{+}{\it{l}}^{-}$ in an Abelian Extended Supersymmetric SM. We work in the large Higgs trilinear coupling driven minimum of the potential, and find that the next-to-lightest Higgs cannot be produced by this process. Other Higgs scalars, namely the lightest and the heaviest, have cross sections comparable to that in the pure SM. It is found that the present model has observable differences with the other popular model, NMSSM, in the same type of minimum.
The Exceptional Supersymmetric Standard Model (E$_6$SSM) provides a low energy alternative to the MSSM, with an extra gauged U(1)$_N$ symmetry, solving the $μ$-problem of the MSSM. Inspired by the possible embedding into an E$_6$ GUT, the matter content fills three generations of E$_6$ multiplets, thus predicting exciting exotic matter such as diquarks or leptoquarks. We present predictions from a constrained version of the model (cE$_6$SSM), with a universal scalar mass $m_0$, trilinear mass $A$ and gaugino mass $M_{1/2}$. We reveal a large volume of the cE$_6$SSM parameter space where the co…
A lepton flavor violating process $μ\to eγ$ is investigated in the supersymmetric extra U(1) models, which often appear as the low energy effective models of superstring and can potentially solve the $μ$-problem. The branching ratio of this process is calculated. It is numerically estimated and compared with that of the MSSM. In this study we take account of an abelian gaugino kinetic term mixing and discuss its influence on this process. The possibility to find the extra gauge structure through this process is discussed.
We propose a minimal supersymmetric Twin Higgs model that can accommodate tuning of the electroweak scale for heavy stops better than 10% with high mediation scales of supersymmetry breaking. A crucial ingredient of this model is a new SU(2)_X gauge symmetry which provides a D-term potential that generates a large SU(4) invariant coupling for the Higgs sector and only small set of particles charged under SU(2)_X, which allows the model to be perturbative around the Planck scale. The new gauge interaction drives the top yukawa coupling small at higher energy scales, which also reduces the tunin…
It is shown that using non-abelian horizontal gauge symmetry and anomalous U(1)_A symmetry in grand unified theories (GUTs), realistic quark and lepton mass matrices including large neutrino mixings can be obtained, while the differences among the scalar fermion masses are sufficiently small for suppression of various flavor changing neutral current (FCNC) processes, especially in E_6 GUT. Combining the Higgs sector, in which doublet-triplet splitting is realized, a complete E_6\times SU(3)_H GUT, in which three generations are unified into a single multiplet, Psi(27,3), is obtained.
The Exceptional Supersymmetric Standard Model (E$_6$SSM) is a low energy alternative to the MSSM with an extra $U(1)$ gauge symmetry and three generations of matter filling complete 27-plet representations of $E_6$. This provides both new D and F term contributions that raise the Higgs mass at tree level, and a compelling solution to the $μ$-problem of the MSSM by forbidding such a term with the extra $U(1)$ symmetry. Instead, an effective $μ$-term is generated from the VEV of an SM singlet which breaks the extra $U(1)$ symmetry at low energies, giving rise to a massive $Z^\prime$. We explore …
We make a comprehensive study of the theory and phenomenology of a low energy supersymmetric standard model originating from a string-inspired $E_6$ grand unified gauge group. The Exceptional Supersymmetric Standard Model (ESSM) considered here is based on the low energy SM gauge group together with an extra $Z'$ corresponding to an extra $U(1)_{N}$ gauge symmetry under which right--handed neutrinos have zero charge. The low energy matter content of the ESSM corresponds to three 27 representations of the $E_6$ symmetry group, to ensure anomaly cancellation, plus an additional pair of Higgs--li…
The 750-760 GeV diphoton resonance may be identified as one or two scalars and/or one or two pseudoscalars contained in the two singlet superfields S_{1,2} arising from the three 27-dimensional representations of E_6 . The three 27s also contain three copies of colour-triplet charge \mp 1/3 vector-like fermions D,\bar{D} and two copies of charged inert Higgsinos \tilde{H}^{+},\tilde{H}^{-} to which the singlets S_{1,2} may couple. We propose a variant of the E_6SSM where the third singlet S_3 breaks a gauged U(1)_N above the TeV scale, predicting Z'_N, D,\bar{D}, \tilde{H}^{+},\tilde{H}^{-} at…
We begin an investigation of supersymmetric theories based on exceptional groups. The flat directions are most easily parameterized using their correspondence with gauge invariant polynomials. Symmetries and holomorphy tightly constrain the superpotentials, but due to multiple gauge invariants other techniques are needed for their full determination. We give an explicit treatment of $G_2$ and find gaugino condensation for $N_f\leq 2$, and an instanton generated superpotential for $N_f=3$. The analogy with $SU(N_c)$ gauge theories continues with modified and unmodified quantum moduli spaces for…
Attention is called to potentially dangerous lepton-flavor violation (LFV) induced by the D-terms of additional U(1) flavor-dependent gauge symmetries in supersymmetric models. In such models, LFV persists despite an arbitrarily high scale for the U(1) breaking and despite arbitrarily small gauge couplings. In light of recent experimental observations of neutrino oscillations, these models are highly motivated experimentally and theoretically. Taking into account also the recent measurement of the muon anomalous magnetic moment, strong bounds are calculated for the magnitude of the D-term-indu…
For $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter it is demonstrated that there is a class of renormalization schemes, in which the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) formula for the renormalization group $β$-function, defined in terms of the renormalized coupling constant, is valid. These schemes are related with each other by finite renormalizations forming a one-parameter commutative subgroup of general renormalization group transformations. The analogy between the exact $β$-function in $\mathcal{N}=1$ supersymmetric Yang-Mills theory without matter an…
We demonstrate the existence of non-abelian non-topological solitons such as Q-balls in the spectrum of Wess-Zumino models with non-abelian global symmetries. We conveniently name them Q-superballs and identify them for short as Q-sballs. More specifically, we show that in contrast to the non-supersymmetric case, they arise in renormalizable potentials with cubic self-interactions of only one dimensionful parameter and for the entire parameter space of the model available. We solve the field equations and present the explicit form of the Q-sball solution. We compute its main physical propertie…
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 present a covariant, supersymmetric and kappa-symmetric action for non-Abelian multiwave system (nAmW) in D=3 AdS superspace. Its flat superspace limit provides a simplest counterpart of the recently proposed action for 11 dimensional system of N nearly coincident M-waves (multiple M0-branes), which is presently known for the case of flat target superspace only.
We demonstrate electric-magnetic duality in N=1 supersymmetric non-Abelian gauge theories in four dimensions by presenting two different gauge theories (different gauge groups and quark representations) leading to the same non-trivial long distance physics. The quarks and gluons of one theory can be interpreted as solitons (non-Abelian magnetic monopoles) of the elementary fields of the other theory. The weak coupling region of one theory is mapped to a strong coupling region of the other. When one of the theories is Higgsed by an expectation value of a squark, the other theory is confined. Ma…
In this paper we investigate the nature of the transition from Abelian to non-Abelian confinement (i.e. crossover vs. phase transition). To this end we consider the basic N=2 model where non-Abelian flux tubes (strings) were first found: supersymmetric QCD with the U(N) gauge group and N_f=N flavors of fundamental matter (quarks). The Fayet-Iliopoulos term ξtriggers the squark condensation and leads to the formation of non-Abelian strings. There are two adjustable parameters in this model: ξand the quark mass difference Δm. We obtain the phase diagram on the (ξ, Δm) plane. At large ξand small …
Local supersymmetry (SUSY) provides an attractive framework for the incorporation of gravity and unification of gauge interactions within Grand Unified Theories (GUTs). Its breakdown can lead to a variety of models with softly broken SUSY at low energies. In this review article we focus on the SUSY extension of the Standard Model (SM) with an extra U(1)_{N} gauge symmetry originating from a string-inspired E_6 grand unified gauge group. Only in this U(1) extension of the minimal supersymmetric standard model (MSSM) inspired by E_6 GUTs the right-handed neutrinos can be superheavy providing a m…
We present a supersymmetric extension of the Standard Model (USSM-A) with an anomalous U(1) and Stueckelberg axions for anomaly cancellation, generalizing similar non-supersymmetric constructions. The model, built by a bottom-up approach, is expected to capture the low-energy supersymmetric description of axionic symmetries in theories with gauged anomalous abelian interactions, previously explored in the non-supersymmetric case for scenarios with intersecting branes. The choice of a USSM-like superpotential, with one extra singlet superfield and an extra abelian symmetry, allows a physical ax…
We discuss perturbative four-dimensional compactifications of both the SO(32) heterotic and the Type I string on smooth Calabi-Yau manifolds endowed with general non-abelian and abelian bundles. We analyse the generalized Green-Schwarz mechanism for multiple anomalous U(1) factors and derive the generically non-universal one-loop threshold corrections to the gauge kinetic function as well as the one-loop corrected Fayet-Iliopoulos terms. The latter can be interpreted as a stringy one-loop correction to the Donaldson-Uhlenbeck-Yau condition. Applying S-duality, for the Type I string we obtain t…
The Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions are constructed in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite gauge coupling. The generic wall solutions require nontrivial configurations for either gauge fields or off-diagonal components of adjoint scalars depending on the gauge. Effective theories of moduli fields are constructed as world-volume gauge theories. Nambu-Goldstone and quasi…
The low energy structures of N=1 supersymmetric models with E_6, F_4 and E_7 gauge groups and fundamental irrep matter contents are studied herein. We identify sets of gauge invariant composites which label all flat directions in the confining/Higgs phases of these theories. The impossibility of mapping several of these primary operators rules out previously conjectured exceptional self duals reported in the literature.
Recently we discovered and discussed non-Abelian duality in the quark vacua of N=2 super-Yang-Mills theory with the U(N) gauge group and N_f flavors (N_f>N). Both theories from the dual pair support non-Abelian strings which confine monopoles. Now we introduce an N=2-breaking deformation, a mass term μ{\mathcal A}^2 for the adjoint fields. Starting from a small deformation we eventually make it large which enforces complete decoupling of the adjoint fields. We show that the above non-Abelian duality fully survives in the limit of N=1 SQCD, albeit some technicalities change. For instance, non-A…
