The Phase Diagram of the U(2)×U(2)U(2)\times U(2) Sigma Model

We study the phase diagram of the $U(2) \times U(2)$ scalar model in $d=4$ dimensions. We find that the phase transition is of first order in most of the parameter space. The theory can still be relevant to continuum physics (as an effective theory) provided the transition is sufficiently weakly first order. This places restrictions on the allowed coupling constants.Comment: 3 pages (Latex), 2 eps figures, uses espcrc2.sty, epsf, talk given at LATTICE9

Twist-4 Gluon Recombination Corrections for Deep Inelastic Structure Functions

We calculate twist--4 coefficient functions for the deep inelastic structure function $F_2(x,Q^2)$ associated to 4--gluon operator matrix elements for general values of the Bjorken variable $x$ and study the numerical effect on the slope $\partial F_2(x,Q^2)/\partial \log Q^2$. It is shown that these contributions diminish the strongly rising twist--2 terms towards small values of $x$.Comment: 10 pages LATEX, 2 style file, 3 eps-file

Proton structure function at small Q^2

A fit is made to the data for the proton structure function up to Q^2=10 GeV^2, including the real gamma p total cross-section. It is economical and simple, and its form is motivated by physical principles. It is extrapolated down to very small values of x. Data for the ratio (nu W_2^n/nu W_2^p) are also fitted. A FORTRAN program for the fit to (nu W_2^p) is available by email on request Figure 5 from the original version has been deleted.Comment: 10 pages plus 9 figure

The Distribution of Constituent Charm Quarks in the Hadron

Using a statistical approach in the framework of non-covariant perturbation theory the distributions for light and charmed quarks in the hadron have been derived, taking into account the mass of the charmed quark. The parameters of the model have been extracted from the comparison with NA3 data on hadroproduction of J/psi particles. A reanalysis of the EMC data on charm production in muon-nucleon scattering has been performed. It has been found in comparison with the conventional source of charmed quarks from photon-gluon fusion, that the EMC data indicate the presence of an additional contribution from deep-inelastic scattering on charmed quarks at large x. The resulting admixture of the Fock states, containing charmed quarks in the decomposition of the proton wave function is of the order of 1%. The approach presented for the excitation of the Fock states with charmed quarks can also be applied to states with beauty quarks as well as to the hadronic component of the virtual photon (resolved photon component).Comment: 23 pages, 4 PostScript figures, Latex2e. In revised version in comparison with the original one all (?) mistypings have been corrected, one more thank has been added and the comparison of the pion and the proton J/psi production is described in more detai

The phase diagram of the U(2)×U(2)U(2) \times U(2) Sigma Model and its Implications for Chiral Hierarchies

Motivated by the issue of whether it is possible to construct phenomenologically viable models where the electroweak symmetry breaking is triggered by new physics at a scale $\Lambda \gg 4\pi v$, where $v$ is the order parameter of the transition ($v\sim 250$ GeV) and $\Lambda$ is the scale of new physics, we have studied the phase diagram of the $U(2) \times U(2)$ model. This is the relevant low energy effective theory for a class of models which will be discussed below. We find that the phase transition in these models is first order in most of parameter space. The order parameter can not be made much smaller than the cut-off and, consequently a large hierarchy does not appear sustainable. In the relatively small region in the space of parameters where the phase transition is very weakly first order or second order the model effectively reduces to the O(8) theory for which the triviality considerations should apply.Comment: LaTeX file. 32 pages, 10 appended PostScript files, uses epsfig.st

Confinement in the Deconfined Phase: A numerical study with a cluster algorithm

We have previously found analytically a very unusual and unexpected form of confinement in SU(3) Yang-Mills theory. This confinement occurs in the deconfined phase of the theory. The free energy of a single static test quark diverges, even though it is contained in deconfined bulk phase and there is no QCD string present. This phenomenon occurs in cylindrical volumes with a certain choice of spatial boundary conditions. We examine numerically an effective model for the Yang-Mills theory and, using a cluster algorithm, we observe this unusual confinement. We also find a new way to determine the interface tension of domain walls separating distinct bulk phases.Comment: LaTex, 14 pages, 4 figure

Monte Carlo and Renormalization Group Effective Potentials in Scalar Field Theories

We study constraint effective potentials for various strongly interacting $\phi^4$ theories. Renormalization group (RG) equations for these quantities are discussed and a heuristic development of a commonly used RG approximation is presented which stresses the relationships among the loop expansion, the Schwinger-Dyson method and the renormalization group approach. We extend the standard RG treatment to account explicitly for finite lattice effects. Constraint effective potentials are then evaluated using Monte Carlo (MC) techniques and careful comparisons are made with RG calculations. Explicit treatment of finite lattice effects is found to be essential in achieving quantitative agreement with the MC effective potentials. Excellent agreement is demonstrated for $d=3$ and $d=4$, O(1) and O(2) cases in both symmetric and broken phases.Comment: 16 pages, 4 figures appended to end of this fil

The Non-Trivial Effective Potential of the `Trivial' lambda Phi^4 Theory: A Lattice Test

The strong evidence for the `triviality' of (lambda Phi^4)_4 theory is not incompatible with spontaneous symmetry breaking. Indeed, for a `trivial' theory the effective potential should be given exactly by the classical potential plus the free-field zero-point energy of the shifted field; i.e., by the one-loop effective potential. When this is renormalized in a simple, but nonperturbative way, one finds, self-consistently, that the shifted field does become non-interacting in the continuum limit. For a classically scale-invariant (CSI) lambda Phi^4 theory one finds m_h^2 = 8 pi^2 v^2, predicting a 2.2 TeV Higgs boson. Here we extend our earlier work in three ways: (i) we discuss the analogy with the hard-sphere Bose gas; (ii) we extend the analysis from the CSI case to the general case; and (iii) we propose a test of the predicted shape of the effective potential that could be tested in a lattice simulation.Comment: 22 pages, LaTeX, DE-FG05-92ER40717-

Hot Gauge Theories and ZNZ_{N} Phases

In this paper the several aspects of the $Z_{N}$ symmetry in gauge theories at high temperatures are discussed. The metastable $Z_{N}$ bubbles in the $SU(N)$ gauge theories with fermions may have, generically, unacceptable thermodynamic behavior. Their free energy $F \propto T^4$ with a positive proportionality constant. This leads not only to negative pressure but also to negative specific heat and, more seriously, to negative entropy. We argue that although such domains are important in the Euclidean theory, they cannot be interpreted as physical domains in Minkowski space. The related problem is connected with the analysis of the high-temperature limit of the confining phase. Using the two-dimensional QCD with adjoint fermions as a toy model we shall demonstrate that in the light fermion limit in this theory there is no breaking of the $Z_{N}$ symmetry in the high-temperature limit and thus there are no $Z_{N}$ bubbles.Comment: preprint PUPT-1415, 21

Effective potential and vacuum stability

By following previous work on this subject, we investigate the issue of the instability of the electroweak vacuum against the top loop corrections by performing an accurate analysis of a Higgs-Yukawa model. We find that, when the physical cutoff is properly implemented in the theory, the potential does not exhibit any instability. Moreover, contrary to recent claims, we show that this instability cannot be understood in terms of the very insightful work of Wu and Weinberg on the non-convexity of the one-loop effective potential of a scalar theory. Some of the theoretical and phenomenological consequences of our results are briefly discussed.Comment: 10 pages, 4 figure