Highest weight modules and polarized embeddings of shadow spaces

Let Gamma be the K-shadow space of a spherical building Delta. An embedding V of Gamma is called polarized if it affords all "singular" hyperplanes of Gamma. Suppose that Delta is associated to a Chevalley group G. Then Gamma can be embedded into what we call the Weyl module for G of highest weight lambda_K. It is proved that this module is polarized and that the associated minimal polarized embedding is precisely the irreducible G-module of highest weight lambda_K. In addition a number of general results on polarized embeddings of shadow spaces are proved. The last few sections are devoted to the study of specific shadow spaces, notably minuscule weight geometries, polar grassmannians, and projective flag-grassmannians. The paper is in part expository in nature so as to make this material accessible to a wide audience.Comment: Improvement in exposition of Sections 1-3 and . Notation improved. References added. Main results unchange

Nonperturbative Corrections to Inclusive Beauty and Charm Decays: QCD versus Phenomenological Models

We present a selfconsistent method for treating nonperturbative effects in inclusive nonleptonic and semileptonic decays of heavy flavour hadrons. These effects give rise to powerlike corrections $\propto 1/m_Q^n\,$, $n \ge 2$ with $m_Q$ denoting the heavy quark mass.The leading correction to the semileptonic branching ratio occurs for n=2. It is expressed in terms of the vector-pseudoscalar mass splitting: \delta BR\ind{sl}/BR\ind{sl} \simeq BR\ind{nl}\, \cdot \,6\,(\,(M_V^2-M_P^2)/m_Q^2)\cdot (c_+^2 - c_-^2)/2N_c and yields a {\it reduction} of BR\ind{sl}. This nonperturbative correction contributes to the nonleptonic width with a sign opposite to that of the perturbative terms that are non-leading in $1/N_c$. In beauty decays the former reduces the latter by 20 \% whereas in charm decays they more or less cancel. This leads to a {\it reduction} of BR\ind{sl} by no more than 10 \% in beauty decays and by a factor of roughly two in charm decays. We confront these results with those obtained from phenomenological models of heavy flavour decays and find that such models are unable to mimic these leading corrections by a specific choice of quark masses or by invoking Fermi motion.Comment: 11 pages (2 figs are not included), Latex file, FERMILAB-PUB-92/158-T UND-HEP-92-BIG04 TPI-MINN-92/30-

Coulomb scattering of quantum dipoles in QED

We calculate the total scattering cross-section of a dynamical quantum electrically neutral dipole in QED of the infinitely heavy charge and of the infinitely heavy dipole in the leading order in electromagnetic coupling constant.Comment: 7 pages, no figure

The Case Against Warm or Self-Interacting Dark Matter as Explanations for Cores in Low Surface Brightness Galaxies

Warm dark matter (WDM) and self-interacting dark matter (SIDM) are often motivated by the inferred cores in the dark matter halos of low surface brightness (LSB) galaxies. We test thermal WDM, non-thermal WDM, and SIDM using high-resolution rotation curves of nine LSB galaxies. We fit these dark matter models to the data and determine the halo core radii and central densities. While the minimum core size in WDM models is predicted to decrease with halo mass, we find that the inferred core radii increase with halo mass and also cannot be explained with a single value of the primordial phase space density. Moreover, if the core size is set by WDM particle properties, then even the smallest cores we infer would require primordial phase space density values that are orders of magnitude smaller than lower limits obtained from the Lyman alpha forest power spectra. We also find that the dark matter halo core densities vary by a factor of about 30 from system to system while showing no systematic trend with the maximum rotation velocity of the galaxy. This strongly argues against the core size being directly set by large self-interactions (scattering or annihilation) of dark matter. We therefore conclude that the inferred cores do not provide motivation to prefer WDM or SIDM over other dark matter models.Comment: Accepted to ApJL; additions to Figs 3 and 4; minor changes to tex

Improving control of duponchelia fovealis (Lepidoptera: Pyralidae) by rooting media related strategies

Soil-dwelling predatory mites can be very effective as biological control agents against larvae of the lepidopteral pest Duponchelia fovealis. Some growing media were reported to have natural high level and stable populations of predatory mite. The objective of this experiment was to define conditions to establish stable predatory mite populations in the rooting medium and to assess the direct effect of the rooting media on pest development. Eight rooting media were prepared, including a range of degradabilities as measured with the Oxygen Uptake Rate method (OUR). The OUR range was created by mixing peat products, coir dust, bark, perlite, compost and wood fiber. Each treatment was split: half with and half without a commercially used mulch to create a drier top layer. Kalanchoës were grown on these rooting media. After one week soil-dwelling predatory mites (Hypoaspis miles) were added. Adults of the pest Duponchelia fovealis were released during a number of weeks. Both populations were counted. Results show that the OUR range was successfully achieved. The commercial mulch, a cork based fine granulate, reduced the numbers of Duponchelia by 32%. The number of predatory mites was related to the oxygen uptake of the rooting media (R2=0.87). The predatory mite reduced the numbers of Duponchelia larvae on average by 58%. Thus, biological control by soil-dwelling predatory mites can be improved by offering rooting media with an increased degradability as measured by the oxygen uptake rate. The combined effects of using predatory mite and mulch layers are discussed

The Bose-Einstein Correlations and the strong coupling constant at low energies

It is shown that $\alpha_s(E)$, the strong coupling constant, can be determined in the non-perturbative regime from Bose-Einstein correlations (BEC). The obtained $\alpha_s(E)$ is in agreement with the prescriptions dealt with in the Analytic Perturbative Theory approach. It also extrapolates smoothly to the standard perturbative $\alpha_s(E)$ at higher energies. Our results indicate that BEC dimension can be considered as an alternative approach to the short range measure between hadrons.Comment: 7 pages, 4 figure