Choice Between Primary and Dynamical|ΔT|=12Rule in the Current-Current Picture for Nonleptonic Weak Decays

Abstract

The $P$-wave intrinsic structure of $K\to 3\pi$ decays is studied in the current-current picture for nonleptonic weak interactions, and it is shown that an accurate measurement of the asymmetry parameters of $K\to 3\pi$ decays could distinguish whether or not the $\left|\Delta \mathrm{T}\right|=\frac{1}{2}$ rule is primary or dynamical. In case of the former, as is expected, not only the rates, but also the asymmetry parameters of $K\to 3\pi$ decays should be consistent with a dominant (i.e., apart from electromagnetism) $\left|\Delta \mathrm{T}\right|=\frac{1}{2}$ rule, while for the latter, one should expect to observe a large violation of the $\left|\Delta \mathrm{T}\right|=\frac{1}{2}$ rule in the asymmetry parameters of $K\to 3\pi$ decays with or without a similar violation in the rates. Some comments are made concerning the general necessity of enhancement of nonleptonic modes regardless of whether the $\left|\Delta \mathrm{T}\right|=\frac{1}{2}$ rule is primary or dynamical.