Effects of technicolor on standard model running couplings

We discuss the running couplings in the standard model, SU(3$)_C \times$SU(2$)_L \times$U(1$)_Y$, when the Higgs sector is replaced by SU($N_{TC})$ technicolor. Particular attention is given to the running of the couplings at momentum scales where technicolor is nonperturbative, and in this region we apply a relativistic constituent technifermion model. This model has been tested against the known running of the QED coupling due to nonperturbative QCD. An understanding of this low momentum running allows the calculation of the couplings at a higher scale, $\Lambda_{pert}$, where technicolor becomes perturbative. We provide numerical values for the changes in the three standard model couplings between $m_Z$ and $\Lambda_{pert}$ due to technicolor, assuming separately ``one doublet'' and ``one family'' technicolor models. The distinction between a running and walking technicolor coupling is also considered.Comment: 14 pages of LaTeX, UTPT-94-

Charged Vacuum Bubble Stability

A type of scenario is considered where electrically charged vacuum bubbles, formed from degenerate or nearly degenerate vacuua separated by a thin domain wall, are cosmologically produced due to the breaking of a discrete symmetry, with the bubble charge arising from fermions residing within the domain wall. Stability issues associated with wall tension, fermion gas, and Coulombic effects for such configurations are examined. The stability of a bubble depends upon parameters such as the symmetry breaking scale and the fermion coupling. A dominance of either the Fermi gas or the Coulomb contribution may be realized under certain conditions, depending upon parameter values.Comment: 16 pages,revtex; accepted for publication in Phys.Rev.

CP Violation from the Neutrino Sector: A Case for the Superweak Model

We discuss how CP violation originating in the right-handed neutrino sector can feed into the quark sector, in an otherwise CP invariant theory. The dominant effects are superweak, and we suggest that this may yield a natural resolution of the strong CP problem. This work builds on and extends a previously proposed model of quark and lepton masses, based on a new strong flavor interaction above the weak scale.Comment: 15 pages, LaTeX, version to be published in PR

Chiral Symmetry Breaking via Multi-fermion Green Functions

Previous results on fermion chirality-flipping four-point functions are extended to $SU(N)$ gauge theories. The problem is purely non-perturbative, and it is approached by truncating the Schwinger-Dyson hierarchy. The large-$N$ limit also simplifies the problem substantially. The resulting equation is solved numerically by relaxation techniques and an estimate of the critical coupling and momentum behavior is obtained. We also comment on the behavior of chirality-flipping $2n$-point functions for general $n$.Comment: 17 pages, LaTeX + 3 figures, version to be publishe

Are Four-Fermion Operators Relevant for the Fermion Mass Problem?

Four-fermion operators may have large anomalous scaling and become relevant operators in some strongly interacting gauge theories. We present a detailed model which illustrates some of the implications of such operators for the generation of quark and lepton masses. Such operators would originate at high scales where quarks and leptons experience a new strong interaction, but no unbroken technicolor interaction is required. The breakdown of both the new gauge symmetry and electroweak gauge symmetry is associated with a dynamical TeV mass for fourth family quarks. Among the new physics signatures are anomalous (chromo)magnetic moments and their flavor-changing counterparts.Comment: 23 pages, postscript, version to be published in PRD, PDF file is available at http://miteymac.physics.utoronto.ca/bh/papers/papers.htm

Critical Behavior of a Four-Fermion Schwinger-Dyson Equation

We study the Schwinger-Dyson equation associated with a chirality- changing fermion 4-point function in a strongly-coupled $U(1)$ gauge theory. After making appropriate simplifications, we solve the equation numerically via a relaxation method. Our analysis provides an estimate of the critical coupling and it gives some indication as to the general momentum dependence of the 4-point function.Comment: version to be published, postscript fil

Derivation of the Effective Chiral Lagrangian for Pseudoscalar Mesons from QCD

We formally derive the chiral Lagrangian for low lying pseudoscalar mesons from the first principles of QCD considering the contributions from the normal part of the theory without taking approximations. The derivation is based on the standard generating functional of QCD in the path integral formalism. The gluon-field integration is formally carried out by expressing the result in terms of physical Green's functions of the gluon. To integrate over the quark-field, we introduce a bilocal auxiliary field Phi(x,y) representing the mesons. We then develop a consistent way of extracting the local pseudoscalar degree of freedom U(x) in Phi(x,y) and integrating out the rest degrees of freedom such that the complete pseudoscalar degree of freedom resides in U(x). With certain techniques, we work out the explicit U(x)-dependence of the effective action up to the p^4-terms in the momentum expansion, which leads to the desired chiral Lagrangian in which all the coefficients contributed from the normal part of the theory are expressed in terms of certain Green's functions in QCD. Together with the existing QCD formulae for the anomaly contributions, the present results leads to the complete QCD definition of the coefficients in the chiral Lagrangian. The relation between the present QCD definition of the p^2-order coefficient F_0^2 and the well-known approximate result given by Pagels and Stokar is discussed.Comment: 16 pages in RevTex, some typos are corrected, version for publication in Phys. Rev.

A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions

Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2) Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4 dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for publication in the EPJ

Planck-Scale Unification and Dynamical Symmetry Breaking

We explore the possibility of unification of gauge couplings near the Planck scale in models of extended technicolor. We observe that models of the form G X SU(3)_c X SU(2)_L X U(1)_Y cannot be realized, due to the presence of massless neutral Goldstone bosons (axions) and light charged pseudo-Goldstone bosons; thus, unification of the known forces near the Planck scale cannot be achieved. The next simplest possibility, G X SU(4)_{PS} X SU(2)_L X U(1)_{T_{3R}}, cannot lead to unification of the Pati-Salam and weak gauge groups near the Planck scale. However, superstring theory provides relations between couplings at the Planck scale without the need for an underlying grand-unified gauge group, which allows unification of the SU(4)$_{PS}$ and SU(2)$_L$ couplings.Comment: LaTeX, 12 pages, FERMILAB-PUB-93/262-

Leptophobic U(1)'s and the R_b - R_c Crisis

In this paper, we investigate the possibility of explaining both the R_b excess and the R_c deficit reported by the LEP experiments through Z-Z' mixing effects. We have constructed a set of models consistent with a restrictive set of principles: unification of the Standard Model (SM) gauge couplings, vector- like additional matter, and couplings which are both generation-independent and leptophobic. These models are anomaly-free, perturbative up to the GUT scale, and contain realistic mass spectra. Out of this class of models, we find three explicit realizations which fit the LEP data to a far better extent than the unmodified SM or MSSM and satisfy all other phenomenological constraints which we have investigated. One realization, the \eta-model coming from E_6, is particularly attractive, arising naturally from geometrical compactifications of heterotic string theory. This conclusion depends crucially on the inclusion of a U(1) kinetic mixing term, whose value is correctly predicted by renormalization group running in the E_6 model given one discrete choice of spectra.Comment: LaTeX, 26 pages, 5 embedded EPSF figures. Version to be published in Phys. Rev.