On Scalar Meson Dominance in Semi- and Non-Leptonic Weak Pseudoscalar Meson Decays

Introduction. The theoretical description of leptonic, semiand non-leptonic weak decays of pseudoscalar mesons has been known to be extremly rewarding since at least 5 decades [1] in particular due to technical and numerical challenges in the description of strong interactions on the basis Quantum Chromodynamics (QCD) [2]. The experimental and theoretical study of non-leptonic K-meson decays has for instance a long tradition [1, 3, 4, 5, 6], yet the theoretical issues concerning these decays are far from settled [7, 8, 9]. To use the words of G. Colangelo [9]: “. . . The calculation of the K → ππ amplitude in the Standard Model still remains one of the most difficult and yet unsolved problems of today’s particle physics, despite many years of efforts and progress in our understanding of various related physics aspects. Indeed we lack yet a satisfactory explanation of the ∆I = 1/2 rule, and do not yet have a calculation of ε ′/ε in the Standard Model which would make a comparison to the measured value somewhat useful — the typical size of the theoretical uncertainties attached to any of the calculations available in the literature is around 50 % . . .. A recurring disussion in the literature on calculations of K → ππ concerns the role of final state interactions (FSI) . . .”. In view of the outlined situation we want to recall that a growing amount of meson production data available from charm/bottom quark factories allows for the first time a direct view [10] to the nature and properties of light scalar mesons which up now were only hardly accessable in elastic meson-meson scattering due to the unfortunate presence of Adler-zeros [11] and were taken into account in QCD-based formalisms to meson weak decays only indirectly as hardly quantifiable non-perturbative effects. The very existence of light scalar mesons draws renewed attention to the strongly neglected Partial Conservation of flavour-changing Vector Current (PCVC) which has coexisted with often celebrated Partial Conservation of Axialvector Current (PCAC) for about 4 decades [12]. We shall here report shortly on first results of a “Scalar Meson Dominance” (SMD) approach to pseudoscalar meson weak decays taking into account PCVC manifestly by including scalar mesons, rather than guessing PCVC non-perturbatively like in QCD.