Thanks to 2D and maybe even beyond: 115 GeV and 140 GeV almost Standard Model Higgs without problems

I address: (1) dynamical, likely local Higgs mass generation as resolution to the 4D hierarchy and vacuum energy problems, (2) possibility that top condensation may be explained by an interplay among the gluon and scalar sectors, (3) the Higgs Mass Zero Crossing (HMZC) scale, most likely equal to {\Lambda}_EWSB, in accord with standard cosmology or classic inflation, and (4) two preferred Higgs regions centered at 116.5 GeV and 140.5 GeV with related high energy models. I show that SM in 2D could simultaneously satisfy (a) complete radiative generation of the Higgs mass via top loop and (b) cancelation of the remaining leading order corrections to the scalar propagator. The Higgs mass, m_H, parameterized with k=1 (2), in the leading order is 113.0{\pm}1.0 GeV (143.4{\pm}1.3 GeV). I show that the SM top condensation is consistent with the gluon and Higgs mediated top-anti top interactions at tree level. I predict the QCD fine structure constant with the mean value only 0.25% away from the world average value at {\sqrt}s=M_Z. The SM driven theory at energies larger than the HMZC scale necessary includes effective tachyonic Higgs (Popovic 2001). Here, I map the SM physical Higgs mass to the low energy HMZC scale (0.8-1.8 TeV). I show that the very "long lived" SM necessitates Higgs lighter than 146.5{\pm}2 GeV such that there is a single HMZC scale at energies smaller than the Planck mass. I present candidate m_H=138.1{\pm}1.8 GeV for the SM valid up to an energy scale, nearly equal Planck mass, obtained from a conjecture which minimizes the parameters of the Higgs potential. I introduce a class of models potentially exactly removing tachyons. I analyze Composite Particles Models (CPM) (Popovic 2002) where top quark is composite, composed of 3 fundamental fermions, and Higgs scalar is composite, composed of 2 fundamental fermions, with m_H=2/3 m_t=115.4{\pm}0.9 GeV.Comment: 52 Pages, 11 Figures, 1 Table, 155 References, document created on July 24, 2010, document submitted to the Physical Review D on July 25, 201

Statistical ensembles in Hamiltonian formulation of hybrid quantum-classical systems

General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible physically distinguishable statistical ensembles of hybrid systems. Nevertheless, statistical operators associated with the hybrid system and with the quantum subsystem can be consistently defined. Dynamical equations for the statistical operators representing the mixed states of the hybrid system and its quantum subsystem are derived and analyzed. In particular, these equations irreducibly depend on the total probability density on the hybrid phase space.Comment: This is the published version of the paper with an added note with an observation made after the paper was accepted. The main conclusions are as in the published version but the final formula is considerably simplife