Resonances in the weak chiral lagrangian

Abstract

We consider the weak interaction of the octet of pseudoscalar mesons with meson resonances with spin 0,1 to lowest order in the derivative expansion. We determine the resonance contributions to the O(p 4 ) weak coupling constants. In general, the resonance contributions imply only relations between these constants. If additional assumptions such as factorization or weak deformation are imposed, a more detailed comparison with experiment becomes possible. In contrast to the strong sector, available data do not suggest that all the weak couplings of the p 4 -Lagrangian are dominated by resonance exchange in the factorization approximation. We also give a treatment of singlet external fields.

The decays K→πl+l− beyond leading order in the chiral expansion

“…Note that for typical values of η V (but for η V ≃ 1/2) the local vector meson contribution is dominant. A relation equivalent to (21) was obtained in [10] under the factorization assumption (the result of [10] is obtained from (21) with the substitution η V → k F ). As discussed in [10], the separate predictions of a S and a + involve an additional unknown coupling which is difficult to interpret in the framework of VMD.…”

“…In the following we shall employ the Vector Meson Dominance (VMD) hypothesis to estimate W pol + + W pol S . The vector meson contributions to the low-energy constants of the O(p 4 ) weak Lagrangian have been discussed in [10,12]. Employing the vector field formulation of Ref.…”

General structure of relativistic vector condensation

“…[8], or the antisymmetric tensor field of Ref. [23]. Or one can introduce the massive vector fields following the method outlined in [19,20].…”

Strong isospin-breaking effects in K→2π at next-to-leading order in the chiral expansion

“…[17,18] (or the equivalent reduced forms of Refs. [19,20], which take into account constraints associated with the Cayley-Hamilton theorem and the leading order equation of motion). We work with the version in which the weak mass term present in the most general form of the leading (second) order part of L W , L (2) W , has been removed by a field redefinition, and the NLO part of…”