Tau Polarization in Λb→Xcτνˉ \Lambda_b \to X_c \tau \bar{\nu} and B→XcτνˉB \to X_c \tau \bar{\nu}

We discuss the longitudinal and transverse $\tau$-polarization in inclusive decays of hadrons containing $b$-quarks. The calculation is performed by means of an OPE in HQET. Some mathematical difficulties in calculating transverse polarizations are explained. Numerical results are presented for longitudinal and for transverse polarizations, both in and perpendicular to the decay plane.Comment: LATEX, 20 pages, 5 Postscript figure

Generalized Action Invariants for Drift Waves-Zonal Flow Systems

Generalized action invariants are identified for various models of drift wave turbulence in the presence of the mean shear flow. It is shown that the wave kinetic equation describing the interaction of the small scale turbulence and large scale shear flow can be naturally written in terms of these invariants. Unlike the wave energy, which is conserved as a sum of small- and large- scale components, the generalized action invariant is shown to correspond to a quantity which is conserved for the small scale component alone. This invariant can be used to construct canonical variables leading to a different definition of the wave action (as compared to the case without shear flow). It is suggested that these new canonical action variables form a natural basis for the description of the drift wave turbulence with a mean shear flow

Teaching Index Numbers to economists

Economic statistics are frequently reported in the form of index numbers. This article considers how the field of Index Numbers should be approached in the teaching of a general economic degree. While the topic finds a natural home in statistics modules, it is emphasised that the area can also be referred to in the teaching of other areas of economics. It is also emphasised that the differences between Index Numbers theory and the practice of compiling economic statistics such as inflation can help students gain a better understanding of applied economic statistics. Methods for assessing learning in the area are also considered and available material to support teaching is also summarised

Quasi-Two-Dimensional Dynamics of Plasmas and Fluids

In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente

The Promising Process to Distinguish Supersymmetric Models with Large tanβ\beta from the Standard Model: B→Xsμ+μ−B\to X_s{\mu}^{+}{\mu}^{-}

It is shown that in supersymmetric models (SUSYMs) the large supersymmetric contributions to $B \to X_s{\mu}^{+}{\mu}^{-}$ come from the Feynman diagrams which consist of exchanging neutral Higgs bosons (NHBs) and the chargino-stop loop and are proportional to $m_b m_{\mu}$tan$^3\beta/m_{h}^2$ when tan$\beta$ is large and the mass of the lightest neutral Higgs boson m$_h$ is not too large (say, less than 150 Gev). Numerical results show that the branching ratios of $B \to X_s{\mu}^{+}{\mu}^{-}$ can be enhanced by more than 100% compared to the standard model (SM) and the backward-forward asymmetry of lepton is significantly different from that in SM when tan$\beta \geq 30$.Comment: 8 pages, including 2 figure

Exploring the influence of ancient and historic megaherbivore extirpations on the global methane budget

Globally, large-bodied wild mammals are in peril. Because “megamammals” have a disproportionate influence on vegetation, trophic interactions, and ecosystem function, declining populations are of considerable conservation concern. However, this is not new; trophic downgrading occurred in the past, including the African rinderpest epizootic of the 1890s, the massive Great Plains bison kill-off in the 1860s, and the terminal Pleistocene extinction of megafauna. Examining the consequences of these earlier events yields insights into contemporary ecosystem function. Here, we focus on changes inmethane emissions, produced as a byproduct of enteric fermentation by herbivores. Although methane is ∼200 times less abundant than carbon dioxide in the atmosphere, the greater efficiency of methane in trapping radiation leads to a significant role in radiative forcing of climate. Using global datasets of late Quaternary mammals, domestic livestock, and human population from the United Nations as well as literature sources, we develop a series of allometric regressions relating mammal body mass to population density and CH4 production, which allows estimation of methane production by wild and domestic herbivores for each historic or ancient time period. We find the extirpation ofmegaherbivores reduced global enteric emissions between 2.2–69.6 Tg CH4 y−1 during the various time periods, representing a decrease of 0.8–34.8% of the overall inputs to tropospheric input. Our analyses suggest that large-bodied mammals have a greater influence on methane emissions than previously appreciated and, further, that changes in the source pool from herbivores can influence global biogeochemical cycles and, potentially, climate

Ferredoxin C2 is required for chlorophyll biosynthesis and accumulation of photosynthetic antennae in Arabidopsis

Ferredoxins (Fd) are small iron-sulphur proteins, with sub-types that have evolved for specific redox functions. Ferredoxin C2 (FdC2) proteins are essential Fd homologues conserved in all photosynthetic organisms and a number of different FdC2 functions have been proposed in angiosperms. Here we use RNAi silencing in Arabidopsis thaliana to generate a viable fdC2 mutant line with near-depleted FdC2 protein levels. Mutant leaves have ~50% less chlorophyll a and b, and chloroplasts have poorly developed thylakoid membrane structure. Transcriptomics indicates upregulation of genes involved in stress responses. Although fdC2 antisense plants show increased damage at photosystem II (PSII) when exposed to high light, PSII recovers at the same rate as wild type in the dark. This contradicts literature proposing that FdC2 regulates translation of the D1 subunit of PSII, by binding to psbA transcript. Measurement of chlorophyll biosynthesis intermediates revealed a build-up of Mg-protoporphyrin IX, the substrate of the aerobic cyclase. We localise FdC2 to the inner chloroplast envelope and show that the FdC2 RNAi line has a disproportionately lower protein abundance of antennae proteins, which are nuclear-encoded and must be refolded at the envelope after import

Spectroscopy of Heavy Mesons Expanded in 1/m_Q

Operating just once with the naive Foldy-Wouthuysen-Tani transformation on the relativistic Fermi-Yang equation for $Q\bar q$ bound states described by the semi-relativistic Hamiltonian which includes Coulomb-like as well as confining scalar potentials, we have calculated heavy meson mass spectra of D and B together with higher spin states. Based on the formulation recently proposed, their masses and wave functions are expanded up to the second order in $1/m_Q$ with a heavy quark mass $m_Q$ and the lowest order equation is examined carefully to obtain a complete set of eigenfunctions for the Schr\"odinger equation. Heavy quark effective theory parameters, $\bar\Lambda$, $\lambda_1$, and $\lambda_2$, are also determined at the first and second order in $1/m_Q$.Comment: 49 pages, 5 epsf figure

Application of heavy-quark effective theory to lattice QCD: I. Power Corrections

Heavy-quark effective theory (HQET) is applied to lattice QCD with Wilson fermions at fixed lattice spacing a. This description is possible because heavy-quark symmetries are respected. It is desirable because the ultraviolet cutoff $1/a$ in current numerical work and the heavy-quark mass $m_Q$ are comparable. Effects of both short distances, a and $1/m_Q$, are captured fully into coefficient functions, which multiply the operators of the usual HQET. Standard tools of HQET are used to develop heavy-quark expansions of lattice observables and, thus, to propagate heavy-quark discretization errors. Three explicit examples are given: namely, the mass, decay constant, and semileptonic form factors of heavy-light mesons.Comment: 41 pp., no figs; Phys Rev D version, improving argument that an HQET holds for all m_Q