Measurement of the branching ratio and form factor of K(L)-->mu(+)mu(-)gamma

We report on the analysis of the rare decay K(L)-->mu(+)mu(-)gamma the 1997 data from the KTeV experiment at Fermilab. A total of 9327 candidate events are observed with 2.4% background, representing a factor of 40 increase in statistics over the current world sample. We find that B(K(L)-->mu(+)mu(-)gamma) = (3.62 +/- 0.04(stat) +/- 0.08(syst)) x 10(-7). The form factor parameter alpha(K*) is measured to be alpha(K*) = -0.160(+0.026)(-0.028). In addition, we make the first measurement of the parameter alpha from the D'Ambrosio-Isidori-Portolés form factor, finding alpha = -1.54 +/- 0.10. In that model, this alpha measurement limits the Cabibbo-Kobayashi-Maskawa parameter rho>-0.2.     

On the construction of the three dimensional polymer measure

Summary The three dimensional polymer measure was first constructed by Westwater in 1980 with a very complicated proof. We give an alternative construction for small coupling parameter which is based on the approach by Brydges-Fröhlich-Sokal in quantum field theory and Bovier-Felder-Fröhlich, using skeleton inequalities. The main new features are the proof of convergence which had been open in the Brydges-Fröhlich-Sokal construction, and the construction of the measure on the space of paths with fixed time length.     

Über metall-alkyl-verbindungen: XIV. Die kristallstrukturen von K[In(CH3)4], Rb[In(CH3)4] und Cs[In(CH3)4]

The crystal structure of KInMe₄ and CsInMe₄ have been determined from single crystal diffractometer data. Lattice parameters of RbInMe₄ obtained by powder methods are given. KInMe₄ and RbInMe₄ are isostructural (space group I4₁/amd), containing four formula units in the unit cell. CsInMe₄ belongs to space group P4? 2m with one formula unit per unit cell. Lattice parameters in Å: KInMe₄:a=9.904(2), c=8.132(2); RbInMe₄:a=10.208(2), c=8.146(2); CsInMe₄:a=7.459(1), c=4.163(1). All compounds consist of isolated alkali cations and tetrahedral InMe₄-anions. InC distances are 2.239(3) in KInMe₄ and 2.26(2) in CsInMe₄. The appearance of three different structure types of alkali metal tetramethyl indates is explained by the increasing alkali ion radii.     

Minimal extensions of graphs to absolute retracts

A graph H is an absolute retract if for every isometric embedding h of, into a graph G an edge-preserving map g from G to H exists such that g · h is the identity map on H. A vertex v is embeddable in a graph G if G ? v is a retract of G. An absolute retract is uniquely determined by its set of embeddable vertices. We may regard this set as a metric space. We also prove that a graph (finite metric space with integral distance) can be isometrically embedded into only one smallest absolute retract (injective hull). All graphs in this paper are finite, connected, and without multiple edges.