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

A Note on the Morse Index Theorem for Geodesics between Submanifolds in semi-Riemannian Geometry

The computation of the index of the Hessian of the action functional in semi-Riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint. Using this observation, we give an elementary proof of the Morse Index Theorem for Riemannian geodesics with two variable endpoints, in the spirit of the original Morse's proof. This approach reduces substantially the effort required in the proofs of the Theorem given in previous articles on the subject. Exactly the same argument works also in the case of timelike geodesics between two submanifolds of a Lorentzian manifold. For the extension to the lightlike Lorentzian case, just minor changes are required and one obtains easily a proof of the focal index theorems of Beem, Ehrlich and Kim.Comment: 12 pages, LaTeX2e, amsart style. To appear on the Journal of Mathematical Physic

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.