The $\Delta I = 1/2 $ Rule in the Light of Two-Dimensional QCD

Abstract

We calculate in QCD$_2$ the ratios of baryonic matrix elements of $\Delta I = 2$ and $\Delta I = 0$ four-fermion operators, with a view to understanding better the mechanism of $\Delta I = 1/2$ enhancement in QCD$_4$. We find relatively small suppressions of both the scalar-scalar and vector-vector $\Delta I = 2$ four-fermion operators. We discuss the possible implications of these results, in view of a suggestion that gluon condensation may be an important contributing factor in the $\Delta I = 1/2$ enhancement seen in QCD$_4$. At the technical level, our calculation of the vector-vector operator matrix element requires a treatment of the time dependence of the QCD$_2$ soliton which had not been developed in previous phenomenological calculations within this model.