665 research outputs found
The Phase Structure of an SU(N) Gauge Theory with N_f Flavors
We investigate the chiral phase transition in SU(N) gauge theories as the
number of quark flavors, , is varied. We argue that the transition takes
place at a large enough value of so that it is governed by the infrared
fixed point of the function. We study the nature of the phase
transition analytically and numerically, and discuss the spectrum of the theory
as the critical value of is approached in both the symmetric and broken
phases. Since the transition is governed by a conformal fixed point, there are
no light excitations on the symmetric side. We extend previous work to include
higher order effects by developing a renormalization group estimate of the
critical coupling.Comment: 34 pages, 1 figure. More references adde
Dirac's Observables for the SU(3)XSU(2)XU(1) Standard Model
The complete, missing, Hamiltonian treatment of the standard SU(3)xSU(2)xU(1)
model with Grassmann-valued fermion fields in the Higgs phase is given. We
bypass the complications of the Hamiltonian theory in the Higgs phase,
resulting from the spontaneous symmetry breaking with the Higgs mechanism, by
studying the Hamiltonian formulation of the Higgs phase for the gauge
equivalent Lagrangian in the unitary gauge. A canonical basis of Dirac's
observables is found and the reduced physical Hamiltonian is evaluated. Its
self-energy part is nonlocal for the electromagnetic and strong interactions,
but local for the weak ones. Therefore, the Fermi 4-fermion interaction
reappears at the nonperturbative level.Comment: 90 pages, RevTeX, no figure
Limit on the fermion masses in technicolor models
Recently it has been pointed out that no limits can be put on the scale of
fermion mass generation in technicolor models, because the relation
between the fermion masses and depends on the dimensionality of the
interaction responsible for generating the fermion mass. Depending on this
dimensionality it may happens that does not depend on at all. We show
that exactly in this case may reach its largest value, which is almost
saturated by the top quark mass. We make few comments on the question of how
large can be a dynamically generated fermion mass.Comment: 5 pages, 1 figure, RevTeX
The Electroweak Chiral Lagrangian and CP-Violating Effects in Technicolor Theories
We estimate the CP-violating and anomalous form factors,
arising from CP-violating interactions in extended technicolor theories, and
discuss their future experimental detectability. The electric dipole moment of
the boson is found to be as large as {\cal O}(10^{-21}) \; \mbox{e cm}.
We connect the CP-odd and couplings to the corresponding
CP-violating electroweak chiral lagrangian operators. The electric dipole
moments of the neutron and the electron in technicolor theories are estimated
to be as large as {\cal O}(10^{-26}) \; \mbox{e cm} and {\cal O}(10^{-29})
\; \mbox{e cm} respectively. We also suggest the potential to observe large
CP-violating technicolor effects in the decay .Comment: 34 pages, YCTP-P9-94, LaTex. (minor changes in wording and notation,
the figures are appended at the end as one postscript file
A Comment on the Zero Temperature Chiral Phase Transition in Gauge Theories
Recently Appelquist, Terning, and Wijewardhana investigated the zero
temperature chiral phase transition in SU(N) gauge theory as the number of
fermions N_f is varied. They argued that there is a critical number of fermions
N^c_f, above which there is no chiral symmetry breaking and below which chiral
symmetry breaking and confinement set in. They further argued that that the
transition is not second order even though the order parameter for chiral
symmetry breaking vanishes continuously as N_f approaches N^c_f on the broken
side. In this note I propose a simple physical picture for the spectrum of
states as N_f approaches N^c_f from below (i.e. on the broken side) and argue
that this picture predicts very different and non-universal behavior than is
the case in an ordinary second order phase transition. In this way the
transition can be continuous without behaving conventionally. I further argue
that this feature results from the (presumed) existence of an infrared
Banks-Zaks fixed point of the gauge coupling in the neighborhood of the chiral
transition and therefore depends on the long-distance nature of the non-abelian
gauge force.Comment: 7 pages, 2 figure
Fermion Masses and Mixing in Extended Technicolor Models
We study fermion masses and mixing angles, including the generation of a
seesaw mechanism for the neutrinos, in extended technicolor (ETC) theories. We
formulate an approach to these problems that relies on assigning right-handed
quarks and charged leptons to ETC representations that are conjugates
of those of the corresponding left-handed fermions. This leads to a natural
suppression of these masses relative to the quarks, as well as the
generation of quark mixing angles, both long-standing challenges for ETC
theories. Standard-model-singlet neutrinos are assigned to ETC representations
that provide a similar suppression of neutrino Dirac masses, as well as the
possibility of a realistic seesaw mechanism with no mass scale above the
highest ETC scale of roughly TeV. A simple model based on the ETC group
SU(5) is constructed and analyzed. This model leads to non-trivial, but not
realistic mixing angles in the quark and lepton sectors. It can also produce
sufficiently light neutrinos, although not simultaneously with a realistic
quark spectrum. We discuss several aspects of the phenomenology of this class
of models.Comment: 74 pages, revtex with embedded figure
Beta Functions of Orbifold Theories and the Hierarchy Problem
We examine a class of gauge theories obtained by projecting out certain
fields from an N=4 supersymmetric SU(N) gauge theory. These theories are
non-supersymmetric and in the large N limit are known to be conformal. Recently
it was proposed that the hierarchy problem could be solved by embedding the
standard model in a theory of this kind with finite N. In order to check this
claim one must find the conformal points of the theory. To do this we calculate
the one-loop beta functions for the Yukawa and quartic scalar couplings. We
find that with the beta functions set to zero the one-loop quadratic
divergences are not canceled at sub-leading order in N; thus the hierarchy
between the weak scale and the Planck scale is not stabilized unless N is of
the order 10^28 or larger. We also find that at sub-leading orders in N
renormalization induces new interactions, which were not present in the
original Lagrangian.Comment: 21 pages, LaTeX, 6 figures. Minor clarifications, references adde
First-order Phase Transition in Three-dimensional QED with Chern--Simons Term
We have studied the chiral phase transition in three-dimensional QED in the
presence of a Chern--Simons term for the gauge field. There exists a phase
where the chiral symmetry is broken dynamically and we have determined the
critical line for this symmetry breaking as a function of the effective
coupling and the strength of the additional Chern--Simons term. In the presence
of a Chern--Simons term, the chiral phase transition turns out to be first
order, in sharp contrast to the phase transition in pure three-dimensional QED.Comment: 8 pages, LaTeX, final version, to be published in Phys. Rev. Let
Discrete Anomaly and Dynamical Mass in 2+1 dimensional Model
We note that in (2+1)-dimensional gauge theories with even number of massless
fermions, there is anomalous symmetry if theory is regularized in a
parity-invariant way. We then consider a parity invariant
model, which induces a mutual Chern-Simons term in the effective action due to
anomaly. The effect of the discrete anomaly is studied in the induced
spin and in the dynamical fermion mass.Comment: 14 pages, latex, two figures (available upon request
Z -> b\bar{b} Versus Dynamical Electroweak Symmetry Breaking involving the Top Quark
In models of dynamical electroweak symmetry breaking which sensitively
involve the third generation, such as top quark condensation, the effects of
the new dynamics can show up experimentally in Z->b\bar{b}. We compare the
sensitivity of Z->b\bar{b} and top quark production at the Tevatron to models
of the new physics. Z->b\bar{b} is a relatively more sensitive probe to new
strongly coupled U(1) gauge bosons, while it is generally less sensitive a
probe to new physics involving color octet gauge bosons as is top quark
production itself. Nonetheless, to accomodate a significant excess in
Z->b\bar{b} requires choosing model parameters that may be ruled out within run
I(b) at the Tevatron.Comment: LaTex file, 19 pages + 2 Figs., Fermilab-Pub-94/231-
- …