K_l3 form factors at order p^6 in chiral perturbation theory

This paper describes the calculation of the semileptonic K_l3 decay form factor at order p^6 of chiral perturbation theory which is the next-to-leading order correction to the well-known p^4 result achieved by Gasser and Leutwyler. At order p^6 the chiral expansion contains 1- and 2-loop diagrams which are discussed in detail. The irreducible 2-loop graphs of the sunset topology are calculated numerically. In addition, the chiral Lagrangian L^6 produces direct couplings with the W-bosons. Due to these unknown couplings, one can always add linear terms in q^2 to the predictions of the form factor f_-(q^2). For the form factor f_+(q^2), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q^4 counter term, the q^4-ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q^2 our calculation shows that chiral perturbation theory converges very well in this application, as the O(p^6) corrections are small. Comparing the predictions of chiral perturbation theory with the recent CPLEAR data, it is seen that the experimental form factor f_+(q^2) is well described by a linear fit, but that the slope lambda_+ is smaller by about 2 standard deviations than the O(p^4) prediction. The unavoidable q^2 counter term of the O(p^6) corrections allows to bring the predictions of chiral perturbation theory into perfect agreement with experiment.Comment: 32 pages, 7 figure

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

How far can Tarzan jump?

The tree-based rope swing is a popular recreation facility, often installed in outdoor areas, giving pleasure to thrill-seekers. In the setting, one drops down from a high platform, hanging from a rope, then swings at a great speed like "Tarzan", and finally jumps ahead to land on the ground. The question now arises: How far can Tarzan jump by the swing? In this article, I present an introductory analysis of the Tarzan swing mechanics, a big pendulum-like swing with Tarzan himself attached as weight. The analysis enables determination of how farther forward Tarzan can jump using a given swing apparatus. The discussion is based on elementary mechanics and, therefore, expected to provide rich opportunities for investigations using analytic and numerical methods.Comment: 8 pages, 4 figure

K0 form factor at order p^6 of chiral perturbation theory

This paper describes the calculation of the electromagnetic form factor of the K0 meson at order p^6 of chiral perturbation theory which is the next-to-leading order correction to the well-known p^4 result achieved by Gasser and Leutwyler. On the one hand, at order p^6 the chiral expansion contains 1- and 2-loop diagrams which are discussed in detail. Especially, a numerical procedure for calculating the irreducible 2-loop graphs of the sunset topology is presented. On the other hand, the chiral Lagrangian L^6 produces a direct coupling of the K0 current with the electromagnetic field tensor. Due to this coupling one of the unknown parameters of L^6 occurs in the contribution to the K0 charge radius.Comment: 22 pages Latex with 8 figures, Typos corrected, one reference adde

Geschiedenis van het doopsgezinde kerklied (1793-1973): Van particularisme naar oecumeniciteit

Visser, P. [Promotor]Cossee, E.H. [Copromotor