Extension dimensional approximation theorem

Let $L$ be a countable CW-complex and $F\colon X\to Y$ be upper semicontinuous $UV^{[L]}$-valued mapping of a paracompact space $X$ to a complete metric space $Y$. We prove that if $X$ is a C-space of extension dimension \ed X \le [L], then $F$ admits single-valued graph approximations. For $L=S^n$ our result implies well-known approximation theorem for $UV^{n-1}$-valued mappings of $n$-dimensional spaces. And for $L=\{\rm point\}$ our theorem implies a theorem of Ancel on approximations of $UV^\infty$-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 $f\colon X\to Y$ of $k$-space $X$ onto paracompact $C$-space $Y$: if for finite $CW$-complex $M$ we have \ed Y\le [M] and for every point $y\in Y$ and every compactum $Z$ with \ed Z\le [M] we have \ed(f^{-1}(y)\times Z)\le [L] for some $CW$-complex $L$, 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 $\mu_r$. For example, by using the conventional way of setting $\mu_r \in [m_t/2,2m_t]$, one obtains the total $t \bar{t}$ production cross-section $\sigma_{t \bar{t}}$ 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 $t \bar t$ cross-section $\sigma_{t\bar{t}}$ at the Tevatron and LHC colliders. It is found that $\sigma_{t\bar{t}}$ remains almost unchanged by varying $\mu^{\rm init}_r$ within the region of $[m_t/4,4m_t]$. The convergence of the expansion series is greatly improved. For the $(q\bar{q})$-channel, which is dominant at the Tevatron, its NLO PMC scale is much smaller than the top-quark mass in the small $x$-region, and thus its NLO cross-section is increased by about a factor of two. In the case of the $(gg)$-channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than $m_t$ for $\sqrt{s}\lesssim 1$ TeV, and the resulting NLO cross-section is increased by $\sim 20$. As a result, a larger $\sigma_{t\bar{t}}$ is obtained in comparison to the conventional scale-setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting $m_t=172.9\pm 1.1$ GeV, we predict $\sigma_{\rm Tevatron,\;1.96\,TeV} = 7.626^{+0.265}_{-0.257}$ pb, $\sigma_{\rm LHC,\;7\,TeV} = 171.8^{+5.8}_{-5.6}$ pb and $\sigma_{\rm LHC,\;14\,TeV} = 941.3^{+28.4}_{-26.5}$ 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 $e^\pm e^-$ 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 $\gamma^* \gamma^* \to X$ in the region dominated by BFKL hard Pomeron exchange and report the predicted cross sections at present and future $e^\pm e^-$ colliders. I also discuss exclusive $\gamma \gamma$ reactions in QCD as a measure of hadron distribution amplitudes and a new method for measuring the anomalous magnetic and quadrupole moments of the $W$ and $Z$ 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 $\gamma^{*}Q$ cross sections in the case of arbitrary values of the heavy quark mass. Then the azimuth-dependent ${\cal O}(\alpha_{s})$ lepton-quark DIS is calculated in the helicity basis. Finally, we investigate numerically the properties of the $\cos\phi$ and $\cos2\phi$ 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 $\cos2\phi$-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