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Register a new userBounds on Higgs And Top Quark Masses From The Other Degenerate Vacua Near The Planck Scale With Gravitational Contributions
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Based on the weak coupling expansion of gravity, we calculate the gravitational contributions to yukawa coupling, scalar quartic coupling as well as gauge couplings with general Landau-DeWitt gauge-fixing choice and a gauge preserving (of SM gauge group) cut off regularization scheme. We find that the results depend on the Landau-DeWitt gauge-fixing parameter. Based on the two loop RGE of SM couplings with one loop full gravitational contributions in harmonic gauge, we study the constraints on the higgs and top quark mass from the requirement of existing the other degenerate vacua at the Planck-dominated region. Our numerical calculations show that nature will not develop the other degenerate vacua at the Planck-dominated region with current higgs and top quark masses. On the other hand, requiring the existence of the other degenerate vacua at the Planck-dominated region will constrain the higgs and top mass to lie at approximately 130 and 174 GeV, respectively.
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We propose a scenario in which the Planck scale is dynamically linked to the electroweak scale induced by top condensation. The standard model field content, without the Higgs, is promoted to a 5D warped background. There is also an additional 5D fermion with the quantum numbers of the right-handed top. Localization of the zero-modes leads, at low energies, to a Nambu-Jona-Lasinio model that also stabilizes the radion field dynamically thus explaining the hierarchy between the Planck scale and v_EW = 174 GeV. The top mass arises dynamically from the electroweak breaking condensate. The other standard model fermion masses arise naturally from higher-dimension operators, and the fermion mass hierarchies and flavor structure can be explained from the localization of the zero-modes in the extra dimension. If any other contributions to the radion potential except those directly related with electroweak symmetry breaking are engineered to be suppressed, the KK scale is predicted to be about two orders of magnitude above the electroweak scale rendering the model easily consistent with electroweak precision data. The model predicts a heavy (composite) Higgs with a mass of about 500 GeV and standard-model-like properties, and a vector-like quark with non-negligible mixing with the top quark and mass in the 1.6 - 2.9 TeV range. Both can be within the reach of the LHC. It also predicts a radion with a mass of a few GeV that is very weakly coupled to standard model matter.
In N=1 supergravity the scalar potential may have supersymmetric (SUSY) and non-supersymmetric Minkowski vacua (associated with supersymmetric and physical phases) with vanishing energy density. In the supersymmetric Minkowski (second) phase some breakdown of SUSY may be induced by non-perturbative effects in the observable sector that give rise to a tiny positive vacuum energy density. Postulating the exact degeneracy of the physical and second vacua as well as assuming that at high energies the couplings in both phases are almost identical, one can estimate the dark energy density in these vacua. It is mostly determined by the SUSY breaking scale M_S in the physical phase. Exploring the two-loop renormalization group (RG) flow of couplings in these vacua we find that the measured value of the cosmological constant can be reproduced if M_S varies from 20 TeV to 400 TeV. We also argue that this prediction for the SUSY breaking scale is consistent with the upper bound on M_S in the higgsino dark matter scenario.
We argue that the exact degeneracy of vacua in N=1 supergravity can shed light on the smallness of the cosmological constant. The presence of such vacua, which are degenerate to very high accuracy, may also result in small values of the quartic Higgs coupling and its beta function at the Planck scale in the phase in which we live.
It is shown how pure Dirac neutrino masses can naturally occur at low energies even in the presence of Planck scale lepton number violation. The geometrical picture in five dimensions assumes that the lepton number symmetry is explicitly broken on the Planck brane while the right-handed neutrino is localised on the TeV brane. This physical separation in the bulk causes the global lepton number to be preserved at low energies. A small wavefunction overlap between the left-handed and right-handed neutrinos then naturally leads to a small Dirac Yukawa coupling. By the AdS/CFT correspondence there exists a purely four-dimensional dual description in which the right-handed neutrino is a composite CFT bound state. The global lepton number is violated at the Planck scale in a fundamental sector whose mixing into the composite sector is highly suppressed by CFT operators with large anomalous dimensions. A similar small mixing is then also responsible for generating a naturally small Dirac Yukawa coupling between the fundamental left-handed neutrino and the composite right-handed neutrino.
We consider fermions on an extra dimensional interval. We find the boundary conditions at the ends of the interval that are consistent with the variational principle, and explain which ones arise in various physical circumstances. We apply these results to higgsless models of electroweak symmetry breaking, where electroweak symmetry is not broken by a scalar vacuum expectation value, but rather by the boundary conditions of the gauge fields. We show that it is possible to find a set of boundary conditions for bulk fermions that would give a realistic fermion mass spectrum without the presence of a Higgs scalar, and present some sample fermion mass spectra for the standard model quarks and leptons as well as their resonances.
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