Non-perturbative Heavy Quark Effective Theory: a test and its matching to QCD

We give an introduction to the special problems encountered in a treatment of HQET beyond perturbation theory in the gauge coupling constant. In particular, we report on a recent test of HQET as an effective theory for QCD and discuss how HQET can be implemented on the lattice including the non-perturbative matching of the effective theory to QCD.Comment: 12 pages, Late

Non-perturbative Heavy Quark Effective Theory: Introduction and Status

We give an introduction to Heavy Quark Effective Theory (HQET). Our emphasis is on its formulation non-perturbative in the strong coupling, including the non-perturbative determination of the parameters in the HQET Lagrangian. In a second part we review the present status of HQET on the lattice, largely based on work of the ALPHA collaboration in the last few years. We finally discuss opportunities and challenges.Comment: 31 pages, 15 figures, Contribution to the Proceedings of the Final Meeting of DFG SFB-TR-9 (Durbach, Germany, Sept. 2014), to appear in Nucl. Phys. (Proc. Suppl.

Leptonic Decays of BB- and DD-Mesons

The present status of lattice calculations of $f_D$, $f_B$ and some mass splittings are discussed. When one includes the uncertainties due to discretization errors, the results do not yet have a sufficient precision to be relevant to phenomenological applications. There are, however, good prospects of cutting down the uncertainties by a factor of 2 or more soon.Comment: 8 pages, postscript included all figures, uuencode

Are marine diatoms favoured by high Si:N ratios?

Competition experiments were performed first with 4, then with 11 species of marine phytoplankton at various ratios of si1icate:nitrate and various light intensities. Diatoms became dominant at Si:N ratios >25:1 while flagellates were the superior competitors at lower ratios. The light supply did not influence the competitive position of diatoms and non-siliceous flagellates in general, while it was important in determining the outcome of competition at the species level. In the 11 species expenments, Stephanopyxis palmenana was the dominant diatom at high light intensities. It shared dominance with Lauderia annulata at medium and low light intensities and high Si.N ratios. Pseudonitzschia pungens was the dominant diatom at low light intensities and relatively low Si:N ratios. The green alga Dunaliella tertiolecta was the dominant flagellate at high light intensities, while at low light intensities the prymnesiophycean Chrysochromulina polylepis and the cryptophyte Rhodomonas sp. were also important

New Perspectives for B-Physics from the Lattice

We give an introduction to the problems faced on the way to a reliable lattice QCD computation of B-physics matrix elements. In particular various approaches for dealing with the large scale introduced by the heaviness of the b-quark are mentioned and promising recent achievements are described. We present perspectives for future developments.Comment: Invited talk at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 15 pages LaTeX. PSN FRAT07. Updated references and result of ref.[40

An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean PCA procedure, we show how PCA can be generalized to manifolds in an intrinsic way that does not resort to linearization of the data space. The underlying probability model is constructed by mapping a Euclidean stochastic process to the manifold using stochastic development of Euclidean semimartingales. The construction uses a connection and bundles of covariant tensors to allow global transport of principal eigenvectors, and the model is thereby an example of how principal fiber bundles can be used to handle the lack of global coordinate system and orientations that characterizes manifold valued statistics. We show how curvature implies non-integrability of the equivalent of Euclidean principal subspaces, and how the stochastic flows provide an alternative to explicit construction of such subspaces. We describe estimation procedures for inference of parameters and prediction of principal components, and we give examples of properties of the model on embedded surfaces

String breaking in SU(2) gauge theory with scalar matter fields

We investigate the static potential in the confinement phase of the SU(2) Higgs model on the lattice, where this model is expected to have properties similar to QCD. We observe that Wilson loops are inadequate to determine the potential at large distances, where the formation of two color-neutral mesons is expected. Introducing smeared fields and a suitable matrix correlation function, we are able to overcome this difficulty. We observe string breaking at a distance $r_b \approx 1.8 r_0$, where the length scale $r_0$ has a value $r_0 \approx 0.5 fm$ in QCD. The method presented here may lead the way towards a treatment of string breaking in QCD.Comment: 10 pages, eqs.(7),(9) corrected, small changes in numerics, new figure