Kℓ3 form factors and the algebra of charges

Abstract

Starting from the algebra of vector and axial vector charges, we obtain information about the Kl3 form factors by approximating the commutation relations with the one particle intermediate states. We assume a once subtracted dispersion relation for the weak form factors appearing in the calculation. The subtraction constants can then be uniquely determined as a function of the weak decay constants ƒπ, ƒK and ƒK of the mesons contributing in the intermediate states. The momentum transfer dependence of the Kl3 form factors is characterized by the particle masses, the above mentioned decay constants and the two additional constants gπKκ and ƒK∗gπKK∗, where gπKκ∗ and gπKK∗ are strong coupling constants, and ƒK∗ is the weak decay constant of the K∗ meson. Assuming unsubtracted dispersion relations for the various form factors, we are able to make some numerical predictions.