3,626 research outputs found
Extension dimensional approximation theorem
Let be a countable CW-complex and be upper
semicontinuous -valued mapping of a paracompact space to a
complete metric space . We prove that if is a C-space of extension
dimension \ed X \le [L], then admits single-valued graph approximations.
For our result implies well-known approximation theorem for
-valued mappings of -dimensional spaces. And for
our theorem implies a theorem of Ancel on approximations of -valued
mappings of C-spaces.Comment: 7 pages, final version, minor correction
Hurewicz theorem for extension dimension
We prove a new selection theorem for multivalued mappings of C-space. Using
this theorem we prove extension dimensional version of Hurewicz theorem for a
closed mapping of -space onto paracompact -space
: if for finite -complex we have \ed Y\le [M] and for every point
and every compactum with \ed Z\le [M] we have
\ed(f^{-1}(y)\times Z)\le [L] for some -complex , then \ed X\le [L]
Application of the Principle of Maximum Conformality to Top-Pair Production
A major contribution to the uncertainty of finite-order perturbative QCD
predictions is the perceived ambiguity in setting the renormalization scale
. For example, by using the conventional way of setting , one obtains the total production cross-section
with the uncertainty \Delta \sigma_{t \bar{t}}/\sigma_{t
\bar{t}}\sim ({}^{+3%}_{-4%}) at the Tevatron and LHC even for the present
NNLO level. The Principle of Maximum Conformality (PMC) eliminates the
renormalization scale ambiguity in precision tests of Abelian QED and
non-Abelian QCD theories. In this paper we apply PMC scale-setting to predict
the cross-section at the Tevatron and LHC
colliders. It is found that remains almost unchanged by
varying within the region of . The convergence
of the expansion series is greatly improved. For the -channel,
which is dominant at the Tevatron, its NLO PMC scale is much smaller than the
top-quark mass in the small -region, and thus its NLO cross-section is
increased by about a factor of two. In the case of the -channel, which is
dominant at the LHC, its NLO PMC scale slightly increases with the subprocess
collision energy , but it is still smaller than for
TeV, and the resulting NLO cross-section is increased by
. As a result, a larger is obtained in comparison
to the conventional scale-setting method, which agrees well with the present
Tevatron and LHC data. More explicitly, by setting GeV, we
predict pb,
pb and pb. [full abstract can be found in the
paper.]Comment: 15 pages, 11 figures, 5 tables. Fig.(9) is correcte
Perturbative QCD relations inspired by hypothetical tau leptons
We review our recent works on tests of perturbative QCD, inspired by the
relation between the hadronic decay of the tau lepton and the e+ e-
annihilation into hadrons. First, we present a set of commensurate scale
relations that probe the self-consistency of leading-twist QCD predictions for
any observable which defines an effective charge. These tests are independent
of the renormalization scheme and scale, and are applicable over wide data
ranges. As an example we apply this approach to R_{e+ e-}. Second, using a
differential form of these conmensurate scale relations, we present a method to
measure the QCD Gell-Mann--Low Psi function.Comment: To appear in the proceedings of the QCD 99 Euroconference, 7-13th
July 1999 Montpellier, France 4 pages, uses espcrc2.sty (included
High Energy Photon-Photon and Electron-Photon Collisions
The advent of a next linear collider and back-scatterd laser
beams will allow the study of a vast array of high energy processes of the
Standard Model through the fusion of real and virtual photons and other gauge
bosons. As examples, I discuss virtual photon scattering in the region dominated by BFKL hard Pomeron exchange and report the
predicted cross sections at present and future colliders. I also
discuss exclusive reactions in QCD as a measure of hadron
distribution amplitudes and a new method for measuring the anomalous magnetic
and quadrupole moments of the and gauge bosons to high precision in
polarized electron-photon collisions.Comment: LaTex, 12 page
Azimuthal Dependence of the Heavy Quark Initiated Contributions to DIS
We analyze the azimuthal dependence of the heavy-quark-initiated
contributions to the lepton-nucleon deep inelastic scattering (DIS). First we
derive the relations between the parton level semi-inclusive structure
functions and the helicity cross sections in the case of
arbitrary values of the heavy quark mass. Then the azimuth-dependent lepton-quark DIS is calculated in the helicity basis. Finally,
we investigate numerically the properties of the and
distributions caused by the photon-quark scattering (QS) contribution. It turns
out that, contrary to the basic photon-gluon fusion (GF) component, the QS
mechanism is practically -independent. This fact implies that
measurements of the azimuthal distributions in charm leptoproduction could
directly probe the charm density in the proton.Comment: 11 pages, 4 figures, revtex4, published versio
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