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Register a new userThe Planck Scale from Top Condensation
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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.
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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.
Models of top condensation can provide both a compelling solution to the hierarchy problem as well as an explanation of why the top-quark mass is large. The spectrum of such models, in particular topcolor-assisted technicolor, includes top-pions, top-rhos and the top-Higgs, all of which can easily have large top-charm or top-up couplings. Large top-up couplings in particular would lead to a top forward-backward asymmetry through $t$-channel exchange, easily consistent with the Tevatron measurements. Intriguingly, there is destructive interference between the top-mesons and the standard model which conspire to make the overall top pair production rate consistent with the standard model. The rate for same-sign top production is also small due to destructive interference between the neutral top-pion and the top-Higgs. Flavor physics is under control because new physics is mostly confined to the top quark. In this way, top condensation can explain the asymmetry and be consistent with all experimental bounds. There are many additional signatures of topcolor with large tu mixing, such as top(s)+jet(s) events, in which a top and a jet reconstruct a resonance mass, which make these models easily testable at the LHC.
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 explore the possibility that well known properties of the parity operator, such as its idempotency and unitarity, might break down at the Planck scale. Parity might then do more than just swap right and left polarized states and reverse the sign of spatial momentum ${bf k}$: it might generate superpositions of right and left handed states, as well as mix momenta of different magnitudes. We lay down the general formalism, but also consider the concrete case of the Planck scale kinematics governed by $kappa$-Poincare symmetries, where some of the general features highlighted appear explicitly. We explore some of the observational implications for cosmological fluctuations. Different power spectra for right handed and left handed tensor modes might actually be a manifestation of deformed parity symmetry at the Planck scale. Moreover, scale-invariance and parity symmetry appear deeply interconnected.
We show that quadratic divergences in top-quark condensation are cancelled when the tadpoles cancel. This latter cancellation is naturally implemented as the cancellation among the top-quark, Goldstone and Higgs contributions. We also calculate the bosonic correction terms to Gribovs mass formula for the Higgs boson. These reduce the prediction for M_H from 167 GeV to 132 GeV. The tadpole cancellation condition by itself is an independent condition on the mass of the Higgs boson which, in Gribovs U(1)_Y scenario, yields M_H approx 117 GeV with large theoretical uncertainty. More generally, we are able to obtain all three masses, M_W, m_t and M_H, in 100 MeV to 10 TeV energy range as a function of the cut-off scale and the gauge couplings only.
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