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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
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