Anatomy of a Weak Matrix Element

Abstract

Although the weak nonleptonic amplitudes of the Standard Model are notoriously difficult to calculate, we have produced a modified weak matrix element which can be analyzed using reliable methods. This hypothetical nonleptonic matrix element is expressible in terms of the isovector vector and axialvector spectral functions $ρ_{\rm V}(s)$ and $ρ_{\rm A}(s)$, which can be determined in terms of data from tau lepton decay and $e^+ e^-$ annihilation. Chiral symmetry and the operator product expansion are used to constrain the spectral functions respectively in the low energy and the high energy limits. The magnitude of the matrix element thus determined is compared with its `vacuum saturation' estimate, and in the future may be accessible with lattice calculations.