Minimal Supersymmetric Grand Unified Theory Research Articles

SO(10) grand unified theories with dynamical Yukawa couplings

Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of "Yukawon" Higgs multiplets. For concrete illustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $\bf{210 \oplus {\overline{126}}\oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $\bf{{\overline{126}},10}$($\mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $\mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $\bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $\phi,S $, of which the latter's singlet part $S_s$ breaks supersymmetry and the traceless part $\hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.

The minimal and the new minimal supersymmetric Grand Unified Theories on noncommutative space-time

We construct noncommutative versions of both the minimal and the new minimal supersymmetric Grand Unified Theories (GUTs). The enveloping-algebra formalism is used to carry out such constructions. The beautiful formulation of the Higgs sector of these noncommutative theories is a consequence of the fact that, in the GUTs at hand, the ordinary Higgs fields can be realized as elements of the Clifford algebra . In the noncommutative supersymmetric GUTs we formulate, supersymmetry is linearly realized by the noncommutative fields; but it is not realized by the ordinary fields that define those noncommutative fields via the Seiberg–Witten map.

SUPERSYMMETRY AND UNIFICATION: HEAVY TOP WAS THE KEY

I review the history of the unification of gauge couplings of the Standard Model. I start by recalling the history of the most important prediction of low-energy supersymmetry: the correct prediction of the weak mixing angle tied to the prediction of a large top quark mass. I then turn to the discussion of the present day situation of the minimal supersymmetric Grand Unified Theories based on SU(5) and SO(10) groups. For the sake of completeness I also summarize the problems and possible solution of the minimal ordinary SU(5).

On unification and nucleon decay in supersymmetric grand unified theories based on

Abstract We investigate the unification constraints in the minimal supersymmetric grand unified theories based on SU ( 5 ) gauge symmetry. The most general constraints on the spectrum of minimal supersymmetric SU ( 5 ) and flipped SU ( 5 ) are shown. The upper bound on the mass of the colored Higgs mediating proton decay is discussed in detail in the context of the minimal supersymmetric SU ( 5 ) . In the case of the minimal SUSY SU ( 5 ) we show that if we stick to the strongest bound on the colored triplet mass coming from dimension five proton decay contributions there is no hope to test this model at future nucleon decay experiments through the dimension six operators. We find a lower bound on the partial proton decay lifetime for all relevant channels in the context of flipped SUSY SU ( 5 ) . We conclude that flipped SUSY SU ( 5 ) might be in trouble if proton decay is found at the next generation of experiments with a lifetime below 1037 years.

Consistency of the minimal supersymmetric GUT spectra

We show that with proper accounting of convention-dependent phases the mass spectra evaluated by us in an earlier paper satisfy the trace, $SU(5)$ reassembly and Goldstone counting consistency checks. Phase accounting shows that the transposition symmetry called Hermiticity will be manifest only if signs arising from the product of six phase factors are reinserted. This uncovers the errors in the claims of others (retracted in subsequent work) concerning the inconsistency of our results. The chiral multiplet spectra of the two calculations are equivalent. However our method also gives all gauge and gauge chiral spectra as well as a decomposition of all $SO(10)$ minimal supersymmetric grand unified theory couplings, for both tensors and spinors, which are unavailable, even in principle, using the methods of the above papers.

Minimal supersymmetric grand unified theory: Symmetry breaking and the particle spectrum

We discuss in detail the symmetry breaking and related issues in the minimal renormalizable supersymmetric grand unified theory. We find all the possible patterns of symmetry breaking, compute the associated particle spectrum and study its impact on the physical scales of the theory. In particular, the complete mass matrices of the $\mathrm{SU}(2)$ doublets and the color triplets are computed in connection with the doublet-triplet splitting and the $d=5$ proton decay. We explicitly construct the two light Higgs doublets as a function of the Higgs superpotential parameters. This provides a framework for the analysis of phenomenological implications of the theory, to be carried out in a second paper.

The minimal supersymmetric grand unified theory

We show that the minimal renormalizable supersymmetric SO(10) GUT with the usual three generations of spinors has a Higgs sector consisting only of a “light” 10 dimensional and “heavy” 126, 126 and 210 supermultiplets. The theory has only two sets of Yukawa couplings with fifteen real parameters and ten real parameters in the Higgs superpotential. It accounts correctly for all the fermion masses and mixings, neutrinos included. The theory predicts at low energies the MSSM with exact R-parity. It is arguably the minimal consistent supersymmetric grand unified theory.

Predictions of SUSY masses in the minimal supersymmetric grand unified theory

The MSSM distinguishes itself from other GUT's by a successful prediction of many unrelated phenomena with a minimum number of parameters. Among them: a) Unification of the couplings constants; b)Unification of the masses; c) Proton decay; d) Electroweak symmetry breaking. A combined fit of the free parameters in the MSSM to these low energy constraints shows that the MSSM model can satisfy these constraints simultaneously. From the fitted parameters the masses of the as yet unobserved superpartners of the SM particles are predicted. The 2nd order QCD coupling constant is required to be between 0.108 and 0.132. It is shown that a top mass of $174\pm16$ GeV, as suggested recently by the CDF Collaboration, constrains the mixing angle between the Higgs doublets in the MSSM to: $1.2<\tb<5.5$ at the 90% C.L.. The most probable value corresponds to $\tb = 1.56$, which leads to a stop mass below the top mass. In this case the stop production in $p\bar{p}$ collisions would contribute to the top signature. This could be an explanation for the large effective $t\bar{t}$ cross section observed by CDF.

Light scalar top squark in the minimal supersymmetric grand unified theory.

We point out that a light scalar top squark with mass as small as [ital m][sub [ital [tilde t]]][approx]20 GeV is still an allowed possibility within the standard, minimal supersymmetry grand unified theory, if the photino exists at mass slightly below the scalar top mass, so that coannihilation efficiently takes place for [tilde [gamma]][tilde [gamma]][r arrow][ital gg] in the early Universe. We show that this case, receiving a number of strong phenomenological constraints, leads to a restricted pattern of the mass spectrum of other supersymmetry particles.