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.

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