at order p 6 of chiral perturbation theory


This paper describes the calculation of the semileptonic Kl3 decay form factors at order p of chiral perturbation theory which is the nextto-leading order correction to the well-known p result achieved by Gasser and Leutwyler. At order p the chiral expansion contains 1and 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 to the predictions of the form factor f−(q ). For the form factor f+(q ), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q counter term, the q-ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q our calculation shows that chiral perturbation theory converges very well in this application, as the O(p6)-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 ) is well described by a linear fit, but that the slope λ+ is smaller by about 2 standard deviations than the O(p4) prediction. The unavoidable q counter term of the O(p6) corrections allows to bring the predictions of chiral perturbation theory into perfect agreement with experiment. 1Now at Fraunhofer Gesellschaft, Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, D-53754 Sankt Augustin, Germany, E-mail: 2Supported in part by Bundesministerium für Bildung und Forschung, Bonn, Germany, under Contract 05 HT9UMB 4, E-mail:

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@inproceedings{Post2008atOP, title={at order p 6 of chiral perturbation theory}, author={Paul-Philipp Post and Karl Schilcher}, year={2008} }