235 research outputs found
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 -tagging at LEP I
We analyze the impact of using -tagged samples in studying non-Abelian
effects due to QCD in e^+e^-\ar 4jet events at , using
angular variable analyses and comparisons with e^+e^-\ar 3 \mbox{jet}\gamma
events. We find that QCD effects are largely enhanced in -quark samples with
respect to `unflavoured' ones, where energy-ordering is used to distinguish
between gluon and quark jets. We show that the -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.
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