Eur. Phys. J. C 25, 427-443 (2002)
DOI: 10.1007/s10052-002-0967-1
Kl3 form factors at order p6 of chiral perturbation theory
P. Post and K. SchilcherInstitut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, 55099 Mainz, Germany
(Received: 8 January 2002 / Revised version: 27 March 2002 / Published online: 20 September 2002)
Abstract
This paper describes the calculation of the
semileptonic
Kl3 decay form factors at order
p6 of chiral perturbation
theory,
which is the next-to-leading order correction to the well-known
p4
result achieved by Gasser and Leutwyler. At order
p6 the
chiral
expansion contains one- and two-loop diagrams which are discussed
in detail. The
irreducible two-loop graphs of the sunset topology are calculated
numerically.
In addition, the chiral Lagrangian
produces
direct
couplings with the
W bosons. Due to these unknown couplings,
one can
always add linear terms in
q2 to the predictions of the
form factor
f-(q2) . For the form factor
f+(q2), this ambiguity
involves
even quadratic terms. Making use of the fact that the pion electromagnetic
form factor involves the same
q4 counterterm, the
q4
ambiguity
can be resolved. Apart from the possibility of adding an arbitrary
linear
term in
q2 our calculation shows that chiral perturbation
theory
converges very well in this application, as the
corrections are small. Comparing the predictions of chiral perturbation
theory with the recent CPLEAR data, it is seen that the experimental
form
factor
f+(q2) is well described by a linear fit, but
that the slope
is smaller by about 2 standard deviations than
the
prediction. The unavoidable
q2 counterterm of the
corrections allows one to bring the predictions of chiral
perturbation
theory into perfect agreement with experiment.
© Società Italiana di Fisica, Springer-Verlag 2002