Low Energy Constants from Kℓ4 Form-Factors

Abstract

We have calculated the form-factors F and G in K → ππℓν decays (Kℓ4) to two-loop order in Chiral Perturbation Theory (ChPT). Combining this together with earlier two-loop calculations an updated set of values for the L r i, the ChPT constants at O(p 4), is obtained. We discuss the uncertainties in the determination and the changes compared to previous estimates. PACS numbers: 13.20.Eb, 11.30.Rd, 12.39.Fe, 12.38.Aw 1. The theoretical study of K → ππlν decays, Kℓ4 decays, provides an interesting possibility to test our understanding of the long-distance dynamics of the strong sector in the Standard Model. Perturbative QCD can not be applied at energies lower than the spontaneous symmetry scale, Λχ ∼ mρ. One has to resort to an effective approach to the full theory, Chiral Perturbation Theory (ChPT) [1], to obtain a reliable model independent description of physical processes. The main purpose in the study of Kℓ4 decays is twofold: i) This decay is one of the cleanest sources of ππ pairs at low-energies and thus provides us with the possibility to check ππ-scattering near threshold. ii) The form-factors themselves are also directly of interest. They provide a direct test