Scalar Mesons in B-decays

We summarize some persistent problems in scalar spectroscopy and discuss what could be learned here from charmless B-decays. Recent experimental results are discussed in comparison with theoretical expectations: a simple model based on penguin dominance leads to various symmetry relations in good agreement with recent data; a factorisation approach yields absolute predictions of rates. For more details, see Ref. 1.Comment: Plenary talk (W.O.) at XI International Conference on Hadron Spectroscopy (Hadron05), Rio de Janeiro, Aug. 21-26, 2005, to be publ. by AIP, 13 pages, 4 figure

Gluonic Meson Production

The existence of glueballs is predicted in QCD, the lightest one with quantum numbers J^{PC}=0^{++}, but different calculations do not well agree on its mass in the range below 1800 MeV. Several theoretical schemes have been proposed to cope with the experimental data which often have considerable uncertainties. Further experimental studies of the scalar meson sector are therefore important and we discuss recent proposals to study leading clusters in gluon jets and charmless B-decays to serve this purpose.Comment: Talk at Ringberg Workshop "New Trens in HERA Physics 2003", Sept.28-Oct.3, 2003 (by W.O.), to appear in Proceedings, 12 pages, 2 figure

Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search strategy, we obtain a flexible algorithm for which we prove (subsequential) convergence to a stationary point under weak assumptions on the growth of the model function error. Special instances of the algorithm with a Euclidean distance function are, for example, Gradient Descent, Forward--Backward Splitting, ProxDescent, without the common requirement of a "Lipschitz continuous gradient". In addition, we consider a broad class of Bregman distance functions (generated by Legendre functions) replacing the Euclidean distance. The algorithm has a wide range of applications including many linear and non-linear inverse problems in signal/image processing and machine learning