The sunset diagram in SU(3) chiral perturbation theory

A general procedure for the calculation of a class of two-loop Feynman diagrams is described. These are two-point functions containing three massive propagators, raised to integer powers, in the denominator, and arbitrary polynomials of the loop momenta in the numerator. The ultraviolet divergent parts are calculated analytically, while the remaining finite parts are obtained by a one-dimensional numerical integration, both below and above the threshold. Integrals of this type occur, for example, in chiral perturbation theory at order p^6.Comment: 13 pages, LATEX, 2 LATEX figure

QCD effects and bb-tagging at LEP I

We analyze the impact of using $b$-tagged samples in studying non-Abelian effects due to QCD in e^+e^-\ar 4jet events at $\sqrt s=M_{Z^0}$, using angular variable analyses and comparisons with e^+e^-\ar 3 \mbox{jet}\gamma events. We find that QCD effects are largely enhanced in $b$-quark samples with respect to `unflavoured' ones, where energy-ordering is used to distinguish between gluon and quark jets. We show that the $b$-quark mass influences the angular distributions significantly and should not be neglectedComment: 16 pages, latex, 11 figures appended (tarred and uuencoded), the complete paper is available via anonymous ftp at ftp://cpt1.dur.ac.uk/pub/preprints/dtp94/dtp94104/ (get dtp94104_*.ps

Calculation of Infrared-Divergent Feynman Diagrams with Zero Mass Threshold

Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with zero mass thresholds is applied. On the other hand, a numerical method based on a two-fold integral representation is used. The application of the latter method is possible by using lightcone coordinates in the parallel space. The numerical data obtained with the two methods are in impressive agreement.Comment: 20 pages, Latex with epsf-figures, References updated, to appear in Z.Phys.