Nonlinear local supersymmetric SU(5)-model

We construct a realistic nonlinear supersymmetric SU(5) model without superpartner particles in curved space and investigate the Higgs sector in the limit of flat space. We need at least an adjoint-, a quintuplet- and an antiquintuplet-Higgs multiplet. In order to obtain a realistic breakdown of SU(5) to SU(3) × U(1) at tree level we have to modify the vacuum structure of the adjoint representation in comparison to other SU(5)-models. This model requires an “elegant” fine-tuning. We determine the mass spectrum of the electroweak Higgs sector.     

Proton decay in the minimal supersymmetric SU(5) GUT

I investigate the decay of proton and bound neutron in the minimal supersymmetric theory of Dimopoulos and Georgi and of Sakai based on SU(5). I give an outline of the employed formalisms and assumptions, which include current algebra, PCAC and vector meson dominance in order to get a reliable estimate of the decay rates and a Bethe-Salpeter model for the calculation of the matrix elements of the baryon and lepton number-violating interactions contained in the supersymmetric GUT. The resulting branching ratios are in agreement with general considerations and allow for an unambiguous discrimination between conventional and supersymmetric unified theories.     

Naturally massless Higgs doublets in supersymmetric SU(5)

We construct a supersymmetric SU(5) model characterized by: (a) naturally massless doublet Higgs superfields; (b) the natural appearance of “light” coloured triplet Higgses of mass of the order 10¹⁰ GeV, and study proton decay as well as the generation of cosmic baryon asymmetry. We find that an appropriate choice of Higgs sector renders dimension-five operators kinematically irrelevant for the stability of the proton. Proton decay proceeds through Higgs boson exchange in terms of dimension-six operators mainly to ${\overline{v}}_{\mu }{K}^{+},v^{+}{K}^0$.     

Implications of constraints on mass parameters in the Higgs sector of the nonlinear supersymmetric SU(5) model

By using the non-relativistic effective Lagrangian approach to bound states, a complete expression for the isospin-breaking corrections to the energy levels and the decay widths of kaonic hydrogen is obtained up-to-and-including in QCD. It is demonstrated that, although the leading-order corrections at emerging due to the unitarity cusp are huge, they can be expressed solely in terms of the KN S-wave scattering lengths. Consequently, at leading order, it is possible to derive parameter-free modified Deser-type relations, which can be used to extract the scattering lengths from the hadronic atom data.A. Rusetsky: On leave of absence from HEPI, Tbilisi State University, University st. 9, 380086 Tbilisi, Georgia     

Radiative pion decay and the SU(3) × SU(3) σ-model

We claim that there is a complete disagreement between the experimental values and those predicted by the SU(3) × SU(3) σ-model for the radiative pion decay.     

The O(5) nonlinear σ-model as a SU(2) gauge theory

We show how the O(5) nonlinear σ-model, coupled with “gravity” in a generally covariant way, can be translated into the quaternionic model HP¹, invariant under a local SU (2) gauge, and we discuss the classical solutions.     

Upper limit on the proton decay lifetime in SU(5) theory

Both diagrams which contribute to proton decays are calculated in the MIT bag model for all two-body decay modes. Their relative phases are model-determined. All results are presented in such a way that they can be easily deduced for any $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$. In minimal SU(5), with $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}\text{= 160}\text{MeV}$, a theoretical upper limit seems to be 10³⁰ y.     

Symmetry breaking of supersymmetric SU(5)

Numerous inequivalent ground states are shown to exist in the supersymmetric SU(5) model. We derive necessary conditions for an explicit breaking of supersymmetry to yield a potential bounded from below and to select the phenomenologically desired vacuum. These requirements are fulfilled in an example.     

Enhancement factors for supersymmetric proton decay in SU(5) and SO(10) with superfield techniques

The anomalous dimensions of the proton decay operators of dimension six are calculated in supersymmetric SU(5) and SO(10) with superfield techniques. The corresponding enhancement factors are remarkably similar in both cases and practically identical to the non-supersymmetric case. Also results are given for the enhancement factors of the dimension-five operators for both unification groups.     

The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model

Calculations of the ultraviolet counterterms of the bosonic and supersymmetric nonlinear σ-models in two space-time dimensions are undertaken in order to verify conclusions of a recent argument based on differential geometry in the supersymmetric case. The background field method and the normal coordinate expansion are discussed in detail, and the generalized renormalization group pole equations applicable to the nonlinear σ-model are derived. Both component and superfield calculations of the counterterms are presented.     

The weak mixing angle and unification mass in supersymmetric SU(5)

We consider the predictions for the weak mixing angle θ_W 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 m_b/m_τ. We discuss generally the effects of an intermediate threshold between the weak interaction scale and M and estimate the sensitivity of θ_W and M to the scale of supersymmetry breaking.The evolution of the coupling constants of the supersymmetric SU(3) ? SU(2) ? U(1) effective gauge theory is described and the two-loop corrections to θ_{W and M} are calculated.     

The Higgs sector of the minimal supersymmetric standard model including radiative corrections

We discuss the Higgs sector of the minimal supersymmetric standard model including effects of radiative corrections. The formalism is explained in detail for computing radiative corrections to the masses and the coupling constants of the Higgs bosons. The radiative corrections to the masses are studied in the on-shell renormalization scheme. The radiative corrections to the mixing angles between the two CP-even Higgs bosons and the Higgs self-coupling constants are investigated in a simple procedure. The explicit analytic expressions are given for the radiative corrections due to the loops containing the top and bottom quarks and their superpartners. Simple approximate formulae are derived from the analytic expressions obtained in the on-shell renormalization scheme. We numerically study the effects of radiative corrections on the mass of the lighter Higgs boson and the mixing angles between the two CP-even Higgs bosons.     

SU(5) effective potential including Higgs loop contribution and bounds for the Higgs masses

We refine the calculation of the SU(5) effective potential including Higgs and radiative contributions in the one-loop level. We give the mass spectrum and from this and the stability of the symmetry breaking pattern we derive bounds for the Higgs masses and inequalities between the Higgs couplings and the gauge coupling.     

mixing phase and lepton flavor violation in supersymmetric SU(5)

We inspect consequences of the latest B_s mixing phase measurements on lepton flavor violation in a supersymmetric SU(5) theory. The phase, preferring a non-vanishing squark mixing, generically implies τ→(e+μ)γ and μ→eγ. Depending on the gaugino and the scalar mass parameters as well as tanβ, the rates turn out to be detectable or even already excessive, if the RR mass insertion of down-type squarks is nonzero. We find that it becomes easy to reconcile B_s mixing phase with lepton flavor violation given: gaugino to scalar squared mass ratio around 1/12, both LL and RR insertions with decent sizes, and low tanβ.