F-theory Yukawa couplings and supersymmetric quantum mechanics

The localized fermions on the intersection curve Σ of D7-branes, are connected to a N=2 supersymmetric quantum mechanics algebra. Due to this algebra the fields obey a global U(1) symmetry. This symmetry restricts the proton decay operators and the neutrino mass terms. Particularly, we find that several proton decay operators are forbidden and the Majorana mass term is the only one allowed in the theory. A special SUSY QM algebra is studied at the end of the paper. In addition we study the impact of a non-trivial holomorphic metric perturbation on the localized solutions along each matter curve. Moreover, we study the connection of the localized solutions to an N=2 supersymmetric quantum mechanics algebra when background fluxes are turned on.     

Infra-red stable fixed points of Yukawa couplings in supersymmetric models

We provide the solutions of the fixed point conditions of the Yukawa sector for a large class of N = 1 supersymmetric theories including the minimal and next-to-minimal supersymmetric standard models and their grand unified and other extensions. We also introduce a test which can discriminate between infra-red stable, infra-red unstable and saddle point solutions, and illustrate our methods with the example of the next-to-minimal supersymmetric standard model. We show that in this case, the fixed point prediction of the top quark mass is equivalent to that of the minimal supersymmetric standard model, supporting previous numerical analyses.     

Predictions for Higgs and supersymmetry spectra from SO(10) Yukawa unification with mu > 0

We use t, b, tau Yukawa unification to constrain supersymmetry parameter space. We find a narrow region survives for mu>0 (suggested by b-->sgamma and the anomalous magnetic moment of the muon) with A0 approximately -1.9m(16), m(10) approximately 1.4m(16), m(16) approximately 1200-3000 GeV and muM(1/2) approximately 100-500 GeV. Demanding Yukawa unification thus makes definite predictions for Higgs and sparticle masses.     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

Neutron-antineutron oscillations and SO (10) grand unification

Within the framework of the survival hypothesis for Higgs scalars we comprehensively examine the following question: could there be neutron-antineutron oscillations in SO(10) grand unified theories which would be detectable in the forthcoming experiments? In the process of answering this, we critically discuss and supplement the existing knowledge of the relevant patterns of SO(10) symmetry breakdown in relation to the said oscillations. However, our conclusions are negative with the oscillation period being 10²⁵ years or higher.     

Higgs bosons in SO(10) and partial unification

The implications of the existence of a partial unification, previous to the grand unification into SO(10) are studied. Special emphasis is given to the influence of the Higgs bosons in the theory. We calculate their contribution to the β-functions of the partialunification roups of most phenomenological interest and it is found that the results previously calculated for the partial and grand unification masses are in general drastically changed. After making an extended “survival hypothesis” about the masses of the Higgses, we find that the partial unification mass (PUM) should be typically 10^10?11 GeV. The masses of the neutrinos are related to the PUM and we obtain m_ντ ～ 1–10 eV. Neutron oscillations can appear, but at a negligible rate. Proton decay may occur at the expected rate, although in some models it is highly suppressed. The result for the ratio m_b/m_τ is smaller than in SU(5) and the simplest SO(10) version.