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Abstract
| This paper describes the calculation of the semileptonic K/sub l3/ decay form factors at order p/sup 6/ of chiral perturbation theory, which is the next-to-leading order correction to the well-known p/sup 4/ result achieved by Gasser and Leutwyler. At order p/sup 6/ 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 L/sup (6)/ produces direct couplings with the W bosons. Due to these unknown couplings, one can always add linear terms in q /sup 2/ to the predictions of the form factor f/sub -/(q/sup 2/). For the form factor f/sub +/(q/sup 2/), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q/sup 4/ counterterm, the q/sup 4/ ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q/sup 2/ our calculation shows that chiral perturbation theory converges very well in this application, as the O (p/sup 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/sub +/(q/sup 2/) is well described by a linear fit, but that the slope lambda /sub +/ is smaller by about 2 standard deviations than the O(p/sup 4/) prediction. The unavoidable q/sup 2/ counterterm of the O(p/sup 6/) corrections allows one to bring the predictions of chiral perturbation theory into perfect agreement with experiment. (23 refs). |