Supersymmetric Unification Research Articles

Sculpting the Standard Model from low-scale gauge-Higgs-matter E8 grand unification in ten dimensions

The construction and general implications of a model with complete supersymmetric unification of the Standard Model matter content, interactions and families' replication into a single E8 gauge superfield in ten dimensions is presented. The gauge and extended Poincaré symmetries are broken through compactification of the T6/(Z3×Z3) orbifold with Wilson lines, which reduces the original symmetry and matter content into those of the Standard Model plus additional heavier states. Proton decay can be suppressed automatically while the compactification scale may be as low as 109GeV, so that the corresponding GUT-scale physics may be potentially accessible and testable by future collider measurements.

Minimal vectorlike model in supersymmetric unification

Compared to the minimal supersymmetric standard model, an extension by vectorlike fermions is able to explain the Higgs mass while retains the grand unification. We investigate the minimal vectorlike model by focusing on the vectorlike electroweak sector. We firstly derive the mass spectrum in the electroweak sector, then calculate the one-loop effects on the Higgs physics, and finally explore either vectorlike or neutralino dark matter. Collider constraints are briefly discussed.

750 GeV diphotons: implications for supersymmetric unification II

Perturbative supersymmetric gauge coupling unification is possible in six theories where complete SU(5) TeV-scale multiplets of vector matter account for the size of the reported $750~{\rm GeV}$ diphoton resonance, interpreted as a singlet multiplet $S = (s+ia)/\sqrt{2}$. One of these has a full generation of vector matter and a unified gauge coupling $\alpha_G \sim 1$. The diphoton signal rate is enhanced by loops of vector squarks and sleptons, especially when the trilinear $A$ couplings are large. If the $SH_u H_d$ coupling is absent, both $s$ and $a$ can contribute to the resonance, which may then have a large apparent width if the mass splitting from $s$ and $a$ arises from loops of vector matter. The width depends sensitively on $A$ parameters and phases of the vector squark and slepton masses. Vector quarks and/or squarks are expected to be in reach of the LHC. If the $SH_uH_d$ coupling is present, $a$ leads to a narrow diphoton resonance, while a second resonance with decays $s \rightarrow hh, W^+ W^-,ZZ$ is likely to be discovered at future LHC runs. In some of the theories a non-standard origin or running of the soft parameters is required, for example involving conformal hidden sector interactions.

750 GeV diphotons: implications for supersymmetric unification

A recent signal of 750 GeV diphotons at the LHC can be explained within the framework of supersymmetric unification by the introduction of vector quarks and leptons with Yukawa couplings to a singlet S that describes the 750 GeV resonance. We study the most general set of theories that allow successful gauge coupling unification, and find that these Yukawa couplings are severely constrained by renormalization group behavior: they are independent of ultraviolet physics and flow to values at the TeV scale that we calculate precisely. As a consequence the vector quarks and leptons must be light; typically in the region of 375 GeV to 700 GeV, and in certain cases up to 1 TeV. The 750 GeV resonance may have a width less than the experimental resolution; alternatively, with the mass splitting between scalar and pseudoscalar components of S arising from one-loop diagrams involving vector fermions, we compute an apparent width of 10s of GeV.

Visualizing gauge unification with high-scale thresholds

Tests of gauge coupling unification require knowledge of thresholds between the weak scale and the high scale of unification. If these scales are far separated, as is the case in most unification scenarios considered in the literature, the task can be factorized into IR and UV analyses. We advocate "$\Delta\lambda$ plots" as an efficient IR analysis projected to the high scale. The data from these plots gives an immediate qualitative guide to the size of threshold corrections needed at the high scale (e.g., the indices of high-scale representations) and provides precise quantitative data needed to test the viability of hypothesized high-scale unification theories. Such an approach shows more clearly the reasonable prospects of non-supersymmetric grand unification in large rank groups, and also shows the low summed values of high-scale threshold corrections required for supersymmetric unification. The latter may imply tuned cancellations of high-scale thresholds in theories based on weak-scale supersymmetry. For that reason we view non-supersymmetric unification to be just as viable as supersymmetric unification when confining ourselves only to the question of reasonable high-scale threshold corrections needed for exact unification. We illustrate these features for a non-supersymmetric $SO(10)$ graund unified theory and a supersymmetric $SU(5)$ theory.

Unification of SUSY breaking and GUT breaking

We build explicit supersymmetric unification models where grand unified gauge symmetry breaking and supersymmetry (SUSY) breaking are caused by the same sector. Besides, the SM-charged particles are also predicted by the symmetry breaking sector, and they give the soft SUSY breaking terms through the so-called gauge mediation. We investigate the mass spectrums in an explicit model with SU(5) and additional gauge groups, and discuss its phenomenological aspects. Especially, nonzero A-term and B-term are generated at one-loop level according to the mediation via the vector superfields, so that the electro-weak symmetry breaking and 125 GeV Higgs mass may be achieved by the large B-term and A-term even if the stop mass is around 1 TeV.

Nucleon decay via dimension-6 operators in anomalousU(1)Asupersymmetric GUT

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 $\Lambda_u$ becomes smaller than the usual supersymmetric (SUSY) unification scale $\Lambda_G=2\times 10^{16}$ GeV in general. Since the predicted lifetime $\tau(p\rightarrow \pi^0+e^c)$ 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 $R_1\equiv\frac{\Gamma_{n \rightarrow \pi^0 + \nu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ and $R_2\equiv\frac{\Gamma_{p \rightarrow K^0 + \mu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ are important in identifying grand unification group and we show that three anomalous $U(1)_A$ SUSY GUT models with $SU(5)$, $SO(10)$ and $E_6$ grand unification group can be identified by measuring the two ratios. If $R_1$ is larger than $0.4$, the grand unification group is not $SU(5)$, and moreover if $R_2$ is larger than $0.3$, the grand unification group is implied to be $E_6$.

SUPERSYMMETRIC UNIFICATION AND R SYMMETRIES

We review the role of R symmetries in models of supersymmetric unification in four and more dimensions, and in string theory. We show that, if one demands anomaly freedom and fermion masses, only R symmetries can forbid the supersymmetric Higgs mass term μ. We then review the proof that R symmetries are not available in conventional grand unified theories (GUTs) and argue that this prevents natural solutions to the doublet–triplet splitting problem in four dimensions. On the other hand, higher-dimensional GUTs do not suffer from this problem. We briefly comment on an explicit string-derived model in which the μ and dimension-5 proton decay problems are solved simultaneously by an order four discrete R symmetry. We also comment on the higher-dimensional origin of this symmetry.

EFFECTS OF RRRR OPERATORS ON PROTON DECAY IN SUPERSYMMETRIC LEFT–RIGHT MODELS

Unlike all the previous studies on proton decay which worked only in the Minimal Supersymmetric Standard Model, we study the effects of the dimension-5 operators in the Supersymmetric Unification Models with left–right symmetry at low energy. The full chargino sector is used for the analysis. Dressing of the RRRR operators by the SU (2)R wino makes important or even dominant contributions to the proton decay modes into charged leptons.

Dual unified SU(5)

Despite the compelling simplicity of minimal supersymmetric unification, the proton does not decay as predicted. A possible explanation is that real unification takes place in a theory which is an electric dual of the MSSM GUT with messengers, which has Landau poles below the GUT scale. As was recently pointed out in ref. [1], unification predictions would be transmitted across such a duality, but proton decay would be negligible. In this paper we present electric Seiberg-duals for the minimal supersymmetric SU(5) GUT (plus messengers) that realise this idea, one particularly nice example being an asymptotically free SU(11) × Sp(1)3 model. We also discuss how gauge-mediated metastable supersymmetry breaking can be incorporated into an overall unified picture.

Anomalies, beta functions, and supersymmetric unification with multidimensional Higgs representations

In the framework of supersymmetric grand unified theories, the minimal Higgs sector is often extended by introducing multidimensional Higgs representations in order to obtain realistic models. However these constructions should remain anomaly-free, which significantly constrains their structure. We review the necessary conditions for the cancellation of anomalies in general and discuss in detail the different possibilities for supersymmetric SU(5) models. Alternative anomaly-free combinations of Higgs representations, beyond the usual vectorlike choice, are identified, and it is shown that their corresponding {beta} functions are not equivalent. Although the unification of gauge couplings is not affected, the introduction of multidimensional representations leads to different scenarios for the perturbative validity of the theory up to the Planck scale.

Astrophysical probes of unification

Traditional ideas for testing unification involve searching for the decay of the proton and its branching modes. We point out that several astrophysical experiments are now reaching sensitivities that allow them to explore supersymmetric unified theories. In these theories the electroweak-mass DM particle can decay, just like the proton, through dimension six operators with lifetime ~ 10^26 sec. Interestingly, this timescale is now being investigated in several experiments including ATIC, PAMELA, HESS, and Fermi. Positive evidence for such decays may be opening our first direct window to physics at the supersymmetric unification scale of M_GUT ~ 10^16 GeV, as well as the TeV scale. Moreover, in the same supersymmetric unified theories, dimension five operators can lead a weak-scale superparticle to decay with a lifetime of ~ 100 sec. Such decays are recorded by a change in the primordial light element abundances and may well explain the present discord between the measured Li abundances and standard big bang nucleosynthesis, opening another window to unification. These theories make concrete predictions for the spectrum and signatures at the LHC as well as Fermi.

A century of ideas: perspectives from leading scientists of the 20th century

Fifty Years of Cosmology Fred Hoyle. Science as an Adventure Hermann Bondi. The Early Universe William Fowler. The Long-Term Future of Particle Accelerators Simon van der Meer. Energy and Evolution George Porter. The Wonders of Pulsars Antony Hewish. Is the Future Given? Changes in our Description of Nature Ilya Prigogine. Bubbles, Foams and other Fragile Objects J.-P. De Gennes. Beyond the Standard Model: Will it be the Theory of Everything? Yuval Ne'eman. Living Joyfully with Complexity in Chemistry and Culture Roald Hoffmann. A Confrontation with Infnity Gerard 'tHooft. The Creative and Unpredictable Interaction of Science and Technology Charles Townes. The Link Between Neutrino Masses and Proton Decay in Supersymmetric Unification Jogesh Pati. The Nature of Discovery in Physics Douglas D. Osheroff. Symmetry in the Micro World - A Conversation with Nobel Laureate Eugene Wigner B.G. Sidharth

The internal dynamics of the exceptional Lie symmetry groups hierarchy and the coupling constants of unification

This short note focuses on the internal dynamics of exceptional Lie symmetry group hierarchies. Primitive invariants of harmonic two and three Stein compact and non-compact dual spaces are reconnected to the relevant Stein spaces of the first kind. We are able to deduce various fundamental inverse coupling constant for non-super symmetric and super symmetric unification of all fundamental interactions of high energy physics.

Effects of unparticles on running of gauge couplings

Unparticles charged under a gauge group can contribute to the running of the gauge coupling. We show that a scalar unparticle of scaling dimension d contributes to the β function a term that is (2-d) times that from a scalar particle in the same representation. This result has important implications for asymptotic freedom. An unparticle with d>2, in contrast to its matter counterpart, can speed up the approach to asymptotic freedom for a non-Abelian gauge theory and has the tendency to make an Abelian theory also asymptotically free. For not spoiling the excellent agreement of the standard model (SM) with precision tests, the infrared cut-off, m, of such an unparticle would be high but might still be reachable at colliders such as LHC and ILC. Furthermore, if the unparticle scale ΛU is high enough, unparticles could significantly modify the unification pattern of the SM gauge couplings. For instance, with three scalar unparticles of d∼2.5 in the adjoint representation of the strong gauge group but neutral under the electroweak one, the three gauge couplings would unify at a scale of ∼ 8×1012 GeV, which is several orders of magnitude below the supersymmetric unification scale.

On the phase transition to quarks confinement

In the present short note, we give three corresponding derivations of quarks confinement. The first derivation uses super-symmetric unification. The second uses non-super-symmetric grand unification. Finally, the third derivation is related to a phase transition from quarks to Planck particles. Remarkably all three derivations indicate complete quarks confinement. Thus by Witten’s T-duality we can never observe completely free quarks.

SU(5) completion of the dark scalar doublet model of radiative neutrino mass

Adding a second scalar doublet (η+,η0) and three neutral singlet fermions N1,2,3 to the Standard Model of particle interactions with a new Z2 symmetry, it has been shown that ηR0 or ηI0 is a good dark-matter candidate and seesaw neutrino masses are generated radiatively. A minimal extension of this new idea is proposed to allow for its SU(5) completion. Supersymmetric unification is then possible, and leptoquarks of a special kind are predicted at the TeV scale.

Asymptotic freedom and unification in a golden quantum field theory

By harmonizing the perturbation equations of renormalization, we find a set of exact and simple equations for determining the coupling constant of super symmetric unification. Using this exact equation, we demonstrate exact quarks confinement as energy tends toward the Planck energy. We conclude that confinement can be demonstrated without involving asymptotic freedom.

Conjectures regarding kissing spheres hierarchy and quantum gravity unification

Conjectures regarding connections between hyper-spheres kissing problems in one- to eight-dimensional spaces and the inverse coupling constant of quantum gravity are presented. In particular we demonstrate that in S (7) and S (8) the coupling constants of the non-super-symmetric and the super-symmetric unification are given by α ¯ g = K ( 128 ) 7 ≃ 42 and α ¯ gs = K ( 128 ) 8 ≃ 26 respectively where K(128) ≃ (2.18)(10) 11 is the sphere kissing number in D = 128 Euclidian space.

Top Compositeness and Precision Unification

The evolution of standard model gauge couplings is studied in a nonsupersymmetric scenario in which the hierarchy problem is resolved by Higgs compositeness above the weak scale. It is argued that massiveness of the top quark combined with precision tests of the bottom quark imply that the right-handed top must also be composite. If, further, the standard model gauge symmetry is embedded into a simple subgroup of the unbroken composite-sector flavor symmetry, then precision coupling unification is shown to occur at approximately 10(15) GeV, to a degree comparable to supersymmetric unification.