No abstract

No abstract

The constraints obtained in I for the asymptotic two-body meson matrix elements of the weak nonleptonic Hamiltonian are related to the physical K --tar and D--tKa decay amplitudes by using a soft-pion approximation in the infinite-momentum frame of the parent particle. In this new milder extrapolation, a part of the so-called surface terms survives in addition to the usual equal-timecommutator term and plays a significant role, especially for the D-Kr decays. However, to the approximation in which only the ground-state-meson contribution is kept in the surface terms, the + 1 / A I / = rule for the K-27 decays and the 6@ 6* rule [in exact SU(3) symmetry] for the D-KT decays are shown to hold exactly and the amplitudes predict a reasonable value for the ratio of the rates, r (~; + a +~-) / r (~O t~-p + ) .A semiquantitative scenario is also drawn, which suggests that the L = 1 meson contribution to the surface terms plays an important role for the violation of these selection rules and yields the right order of magnitude for the violation of the I AT 1 = rule in K -2 r decays. For the D-Ea decays it leads to a more significant violation of the 6@ 6* rule.

A concept of asymptotic symmetry is formulated and applied to the determination of mixing parameters between the 7r°, TJ°, and r)'°(958) in broken SU(3) and SU(2) symmetries. One of the solutions gives rise to a rather large violation of the | Al |=\ rule in the K lZ decays which is not inconsistent with present experiment.This paper aims to discuss the particle mixing effects by taking the view of asymptotic symmetry which assumes that the SU(3) and SU(2) symmetries are well realized among particles of extremely high momenta. A similar assumption has been used in deriving several successful sum rules from the chiral SU(3)®SU(3) algebra. 1 ' 2 To derive our result by a short-cut (but instructive) computation, we express the requirement of asymptotic SU(3) symmetry in a simple form. Let us consider the pseudoscalar nonet and denote their annihilation operators as a a (k) 1 where a stands for TT*' 0 , K + »°, K + *°, r]°, and 7?' 0 (958), and k denotes their momenta. It should be noted that a a (k) are not the Heisenberg operators but the operators of the physical (i.e., incoming) particles with mass m a . Denoting the SU(3) generators by V i9 the transformation of physical particles in broken SU(3) symmetry can be expressed