703 research outputs found
Duality and Superconvergence Relation in Supersymmetric Gauge Theories
We investigate the phase structures of various N=1 supersymmetric gauge
theories including even the exceptional gauge group from the viewpoint of
superconvergence of the gauge field propagator. Especially we analyze in detail
whether a new type of duality recently discovered by Oehme in gauge
theory coupled to fundamental matter fields can be found in more general gauge
theories with more general matter representations or not. The result is that in
the cases of theories including matter fields in only the fundamental
representation, Oehme's duality holds but otherwise it does not. In the former
case, superconvergence relation might give good criterion to describe the
interacting non-Abelian Coulomb phase without using some information from dual
magnetic theory.Comment: 20 pages, LaTe
The Riemann Surface of a Static Dispersion Model and Regge Trajectories
The S-matrix in the static limit of a dispersion relation is a matrix of a
finite order N of meromorphic functions of energy in the plane with
cuts . In the elastic case it reduces to N functions
connected by the crossing symmetry matrix A. The scattering of
a neutral pseodoscalar meson with an arbitrary angular momentum l at a source
with spin 1/2 is considered (N=2). The Regge trajectories of this model are
explicitly found.Comment: 5 pages, LaTe
Analytic Approach to Perturbative QCD
The two-loop invariant (running) coupling of QCD is written in terms of the
Lambert W function. The analyticity structure of the coupling in the complex
Q^2-plane is established. The corresponding analytic coupling is reconstructed
via a dispersion relation. We also consider some other approximations to the
QCD beta-function, when the corresponding couplings are solved in terms of the
Lambert function. The Landau gauge gluon propagator has been considered in the
renormalization group invariant analytic approach (IAA). It is shown that there
is a nonperturbative ambiguity in determination of the anomalous dimension
function of the gluon field. Several analytic solutions for the propagator at
the one-loop order are constructed. Properties of the obtained analytical
solutions are discussed.Comment: Latex-file, 19 pages, 2 tables, 51 references, to be published in
Int. J. Mod. Phys.
Glueballs in a Hamiltonian Light-Front Approach to Pure-Glue QCD
We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it.
The renormalization procedure is designed to produce a Hamiltonian that will
yield physical states that rapidly converge in an expansion in free-particle
Fock-space sectors. To make this possible, we use light-front field theory to
isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to
force its free-state matrix elements to quickly decrease as the difference of
the free masses of the states increases. The cutoff violates a number of
physical principles of light-front pure-glue QCD, including Lorentz covariance
and gauge covariance. This means that the operators in the Hamiltonian are not
required to respect these physical principles. However, by requiring the
Hamiltonian to produce cutoff-independent physical quantities and by requiring
it to respect the unviolated physical principles of pure-glue QCD, we are able
to derive recursion relations that define the Hamiltonian to all orders in
perturbation theory in terms of the running coupling. We approximate all
physical states as two-gluon states, and use our recursion relations to
calculate to second order the part of the Hamiltonian that is required to
compute the spectrum. We diagonalize the Hamiltonian using basis-function
expansions for the gluons' color, spin, and momentum degrees of freedom. We
examine the sensitivity of our results to the cutoff and use them to analyze
the nonperturbative scale dependence of the coupling. We investigate the effect
of the dynamical rotational symmetry of light-front field theory on the
rotational degeneracies of the spectrum and compare the spectrum to recent
lattice results. Finally, we examine our wave functions and analyze the various
sources of error in our calculation.Comment: 75 pages, 17 figures, 1 tabl
Quarkonia in Hamiltonian Light-Front QCD
A constituent parton picture of hadrons with logarithmic confinement
naturally arises in weak coupling light-front QCD. Confinement provides a mass
gap that allows the constituent picture to emerge. The effective renormalized
Hamiltonian is computed to , and used to study charmonium and
bottomonium. Radial and angular excitations can be used to fix the coupling
, the quark mass , and the cutoff . The resultant hyperfine
structure is very close to experiment.Comment: 9 pages, 1 latex figure included in the text. Published version (much
more reader-friendly); corrected error in self-energ
Coupling Reduction and the Higgs Mass
Assuming the existence of a functional relation among the Standard Model (SM)
couplings gauge and quartic , we determine the mass of the
Higgs particle. Similar considerations for the top and bottom Yukawa couplings
in the minimal supersymmetric SM lead to the prediction of a narrow window for
, one of the main parameters that determine the light Higgs mass.Comment: 17 pages, 16 figure
The anomalous threshold, confinement, and an essential singularity in the heavy-light form factor
The analytic behavior of the heavy-light meson form factor is investigated
using several relativistic examples including unconfined, weakly confined, and
strongly confined mesons. It is observed that confinement erases the anomalous
threshold singularity and also induces an essential singularity at the normal
annihilation threshold. In the weak confinement limit, the "would be" anomalous
threshold contribution is identical to that of the real singularity on its
space-like side.Comment: Latex 2.09 with epsf.sty. 24 pages of text and 8 postscript figures.
Postscript version of complete paper will also be available soon at
http://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-983 or at
ftp://phenom.physics.wisc.edu/pub/preprints/1997/madph-97-98
Wilsonian Matching of Effective Field Theory with Underlying QCD
We propose a novel way of matching effective field theory with the underlying
QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive
Wilsonian matching conditions between current correlators obtained by the
operator product expansion in QCD and those by the hidden local symmetry (HLS)
model. This determines without much ambiguity the bare parameters of the HLS at
the cutoff scale in terms of the QCD parameters. Physical quantities for the pi
and rho system are calculated by the Wilsonian RGE's from the bare parameters
in remarkable agreement with the experiment.Comment: 13 pages, 4 figures, Minor corrections. This is the version to appear
in Physical Review
Reduction of Couplings and Finiteness in Realistic Supersymmetric GUTs
Reduction of couplings in supersymmetric GUTs is achieved by searching for
renormalization group invariant (RGI) relations among couplings which hold
beyond the unification scale. Finiteness is due to the fact that there exist
RGI relations among couplings that guarantee the vanishing of the
beta-functions of a N=1 supersymmetric GUT even to all orders in perturbation
theory. Of particular interest are the relations among gauge and Yukawa
couplings which lead to very interesting predictions of the top quark massComment: 25 pages, 1 figure. To appear in the proceedings of the Buckow
Symposium 199
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