Grand unification in higher dimensions

Physical Review D, 1995

We reanalyse the problem of fermion masses in supersymmetric SO(10) grand unified models. In the minimal model, both low energy Higgs doublets belong to the same 10 representation of SO(10) implying the unification not only of the gauge but also of the third generation Yukawa couplings. These models predict large values of tan β ∼ 50. In this paper we study the effects of departing from the minimal conditions in order to see if we can find models with a reduced value of tan β. In order to maintain predictability, however, we try to do this with the addition of only one new parameter. We still assume that the fermion masses arise from interactions of the spinor representations with a single 10 representation, but this 10 now only contains a part of the two light Higgs doublets. This enables us to introduce one new parameter ω = λ b /λ t. For values of ω ≪ 1 we can in principle reduce the value of tan β. In fact, ω is an overall factor which multiplies the down quark and charged lepton Yukawa matrices. Thus the theory is still highly constrained. We show that the first generation quark masses and the CP-violation parameter ǫ K are sufficient to yield strong constraints on the phenomenologically allowed models. In the end, we find that large values of tan β are still preferred.

Journal of High Energy Physics, 2011

The idea of grand unification in a minimal supersymmetric SU(5) × SU(5) framework is revisited. It is shown that the unification of gauge couplings into a unique coupling constant can be achieved at a high-energy scale compatible with proton decay constraints. This requires the addition of a minimal particle content at intermediate energy scales. In particular, the introduction of the SU(2) L triplets belonging to the (15, 1) + (15, 1) representations, as well as of the scalar triplet Σ 3 and octet Σ 8 in the (24, 1) representation, turns out to be crucial for unification. The masses of these intermediate particles can vary over a wide range, and even lie in the TeV region. In contrast, the exotic vector-like fermions must be heavy enough and have masses above 10 10 GeV. We also show that, if the SU(5) × SU(5) theory is embedded into a heterotic string scenario, it is not possible to achieve gauge coupling unification with gravity at the perturbative string scale.

Nuclear Physics B, 1982

We consider the predictions for the weak mixing angle 0w and the scale M of unification in a supersymmetric extension of SU(5). with particular emphasis on the sensitivity to the number of Higgs multiplets. In the one-loop approximation, we also calculate the ratio nrJrn,.

Physical Review D, 2001

A complete 5-dimensional SU (5) unified theory is constructed which, on compactification on the orbifold with two different Z 2 's (Z 2 and Z ′ 2), yields the minimal supersymmetric standard model. The orbifold accomplishes SU (5) gauge symmetry breaking, doublet-triplet splitting, and a vanishing of proton decay from operators of dimension 5. Until 4d supersymmetry is broken, all proton decay from dimension 4 and dimension 5 operators is forced to vanish by an exact U (1) R symmetry. Quarks and leptons and their Yukawa interactions are located at the Z 2 orbifold fixed points, where SU (5) is unbroken. A new mechanism for introducing SU (5) breaking into the quark and lepton masses is introduced, which originates from the SU (5) violation in the zero-mode structure of bulk multiplets. Even though SU (5) is absent at the Z ′ 2 orbifold fixed point, the brane threshold corrections to gauge coupling unification are argued to be negligibly small, while the logarithmic corrections are small and in a direction which improves the agreement with the experimental measurements of the gauge couplings. Furthermore, the X gauge boson mass is lowered, so that p → e + π 0 is expected with a rate within about one order of magnitude of the current limit. Supersymmetry breaking occurs on the Z ′ 2 orbifold fixed point, and is felt directly by the gauge and Higgs sectors, while squarks and sleptons acquire mass via gaugino mediation, solving the supersymmetric flavor problem.

Journal of High Energy Physics, 2012

Naturalness in supersymmetry (SUSY) is under siege by increasingly stringent LHC constraints, but natural electroweak symmetry breaking still remains the most powerful motivation for superpartner masses within experimental reach. If naturalness is the wrong criterion then what determines the mass scale of the superpartners? We motivate supersymmetry by (1) gauge coupling unification, (2) dark matter, and (3) precision b − τ Yukawa unification. We show that for an LSP that is a bino-Higgsino admixture, these three requirements lead to an upper-bound on the stop and sbottom masses in the several TeV regime because the threshold correction to the bottom mass at the superpartner scale is required to have a particular size. For tan β ≈ 50, which is needed for t−b−τ unification, the stops must be lighter than 2.8 TeV when A t has the opposite sign of the gluino mass, as is favored by renormalization group scaling. For lower values of tan β, the top and bottom squarks must be even lighter. Yukawa unification plus dark matter implies that superpartners are likely in reach of the LHC, after the upgrade to 14 (or 13) TeV, independent of any considerations of naturalness. We present a model-independent, bottom-up analysis of the SUSY parameter space that is simultaneously consistent with Yukawa unification and the hint for m h = 125 GeV. We study the flavor and dark matter phenomenology that accompanies this Yukawa unification. A large portion of the parameter space predicts that the branching fraction for B s → µ + µ − will be observed to be significantly lower than the SM value.

Advances in High Energy Physics, 2018

Nonsupersymmetric minimal SU(5) with Higgs representations 24 퐻 and 5 퐻 and standard fermions in 5 퐹 ⊕ 10 퐹 is well known for its failure in unification of gauge couplings and lack of predicting neutrino masses. Like standard model, it is also affected by the instability of the Higgs scalar potential. We note that extending the Higgs sector by 75 퐻 and 15 퐻 not only leads to the popular type-II seesaw ansatz for neutrino masses with a lower bound on the triplet mass Δ > 2 × 10 9 GeV, but also achieves precision unification of gauge couplings without proliferation of nonstandard light Higgs scalars or fermions near the TeV scale. Consistent with recent LUX-2016 lower bound, the model easily accommodates a singlet scalar WIMP dark matter near the TeV scale which resolves the vacuum stability issue even after inclusion of heavy triplet threshold effect. We estimate proton lifetime predictions for → + 0 including uncertainties due to input parameters and threshold effects due to superheavy Higgs scalars and superheavy ±4/3 , ±1/3 gauge bosons. The predicted lifetime is noted to be verifiable at Super Kamiokande and Hyper Kamiokande experiments.

Physical Review D, 2002

We consider the scenario where all the couplings in the theory are strong at the cutoff scale, in the context of higher dimensional grand unified field theories where the unified gauge symmetry is broken by an orbifold compactification. In this scenario, the noncalculable correction to gauge unification from unknown ultraviolet physics is naturally suppressed by the large volume of the extra dimension, and the threshold correction is dominated by calculable contribution from Kaluza-Klein towers that gives the values for sin 2 θ w and α s in good agreement with low-energy data. The threshold correction is reliably estimated despite that the theory is strongly coupled at the cutoff scale. A 5d SU (5) model is presented as an example, where rapid d = 6 proton decay is avoided by putting the first generation matters in the 5d bulk.

Physics Letters B, 1995

We derive a one-loop expression, including all thresholds, for the mass of the proton decay mediating color triplets, M D c , in minimal supersymmetric SU(5). The result for M D c does not depend on other heavy thresholds or extra representations with SU(5) invariant masses which might be added to the minimal model. We numerically correct our result to two-loop accuracy. Choosing inputs to maximize M D c and τ P , within experimental limits on the inputs and a 1 T eV naturalness bound, we derive a strict bound α 3 > 0.117. We discuss how this bound will change as experimental limits improve. Measurements of α 3 from deep inelastic scattering and the charmonium spectrum are below the bound α 3 > 0.117 by more than 3σ. We briefly review several ideas of how to resolve the discrepancy between these low values of α 3 and the determinations of α 3 from LEP event shapes.

2006

We investigate unification constraints in the simplest renormalizable non-supersymmetric SU (5) framework. We show that in the scenario where the Higgs sector is composed of the 5, 24, and 45 dimensional representations the proton could be practically stable. We accordingly demonstrate that of all the SU (5) scenarios only the non-renormalizable one with the 5, 24, and 15 dimensional Higgs multiplets can be verify if low-energy supersymmetry is not realized in Nature.

Advances in High Energy Physics, 2015

The present analysis addresses an interesting primary question on how do the gauge and Yukawa couplings unification scales vary with varying SUSY breaking scalesms, assuming a single scale for all supersymmetric particles. It is observed that the gauge coupling unification scale increases withmswhereas third-generation Yukawa couplings unification scale decreases withms. The rising of the unification scale and also the mass of the color triplet multiplets is necessary to increase the proton decay lifetime; the analysis is carried out with two-loop RGEs for the gauge and Yukawa couplings within the minimal supersymmetric SU(5) model, while ignoring for simplicity the threshold effects of the heavy particles, which could be as large as a few percentages.