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Register a new userSupersymmetric grandunification and fermion masses
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Authors
Borut Bajc
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A short review of the status of supersymmetric grand unified theories and their relation to the issue of fermion masses and mixings is given.
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Within the scenario of chiral freedom we compute the quark and lepton masses of the first two generations in terms of their chiral couplings. This allows us to make a rough estimate of the size of the chiral couplings, narrowing down the uncertainty in the chiron contribution to low energy observables, like the anomalous magnetic moment of the muon. We also extract information about the chiron mass which determines the size of possible chiron effects at the LHC.
We consider the supersymmetric extension of the Standard Model with neutrino Yukawa interactions and R-parity violation. We found that R-parity breaking term lambda u H_u H_d leads to an additional F-type contribution to the Higgs scalar potential, and thus to the masses of supersymmetric Higgs bosons. The most interesting consequence is the modification of the tree-level expression for the lightest neutral supersymmetric Higgs boson mass. It appears that due to this contribution the bound on the lightest Higgs mass may be shifted upwards, thus slightly opening the part of the model parameter space excluded by non-observation of the light Higgs boson at LEP in the framework of the Minimal Supersymmetric Standard Model.
The boson and fermion particle masses are calculated in a finite quantum field theory. The field theory satisfies Poincare invariance, unitarity and microscopic causality, and all loop graphs are finite to all orders of perturbation theory. The infinite derivative nonlocal field interactions are regularized with a mass (length) scale parameter $Lambda_i$. The $W$, $Z$ and Higgs boson masses are calculated from finite one-loop self-energy graphs. The $W^{pm}$ mass is predicted to be $M_W=80.05$ GeV, and the higher order radiative corrections to the Higgs boson mass $m_H=125$ GeV are damped out above the regulating mass scale parameter $Lambda_H=1.57$ TeV. The three generations of quark and lepton masses are calculated from finite one-loop self-interactions, and there is an exponential spacing in mass between the quarks and leptons.
Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution $P({cal Q})$ of a physical quantity $cal Q$ (with nonnegative dimension) tends to peak (diverge) at ${cal Q}=0$ as a signature of string theory. In the Racetrack Kahler uplift model, where $P(Lambda)$ of the cosmological constant $Lambda$ peaks sharply at $Lambda=0$, the electroweak scale (not the electroweak model) naturally emerges when the median $Lambda$ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution $P(m)$ that diverges at $m=0$, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be $sum m_{ u} simeq 0.0592$ eV, with an upper bound $sum m_{ u} <0.066$ eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.
Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.
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