New approach to nonleptonic weak interactions. I. Derivation of asymptotic selection rules for the two-particle weak ground-state-hadron matrix elements

Abstract

A new approach to nonleptonic weak interactions is presented. It is argued that the presence and violation of the $| \ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}} |=\frac{1}{2}$ rule as well as those of the quark-line selection rules can be explained in a unified way, along with other fundamental physical quantities [such as the value of ${g}_{A}(0)$ and the smallness of the isoscalar nucleon magnetic moments], in terms of a single dynamical asymptotic ansatz imposed at the level of observable hadrons. The ansatz prescribes a way in which asymptotic flavor $\mathrm{SU}(N)$ symmetry is secured levelwise for a certain class of chiral algebras in the standard QCD model. It yields severe asymptotic constraints upon the two-particle hadronic matrix elements of nonleptonic weak Hamiltonians as well as QCD currents and their charges. It produces for weak matrix elements the asymptotic $| \ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}} |=\frac{1}{2}$ rule and its charm counterpart for the ground-state hadrons, while for strong matrix elements quark-line-like approximate selection rules. However, for the less important weak two-particle vertices involving higher excited states, the $| \ensuremath{\Delta}\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}} |=\frac{1}{2}$ rule and its charm counterpart are in general violated, providing us with an explicit source of the violation of these selection rules in physical processes.