Physics beyond the standard model of electroweak interactions that violates lepton number will, in general, induce operators involving the quark and lepton fields that violate lepton number. I point out that some matrix elements of particular operators are known. In the limit of exact SU(3) flavor symmetry the operator $ū{\gamma }_{\mu }\left(1\mathrm{}-{\gamma }_5\right)dū{\gamma }_{\mu }\left(1\mathrm{}-{\gamma }_5\right)d$ is part of the $27$ representation responsible for $\Delta I=\frac{3}{2}$ strangeness changing decays in the standard model. At leading order in the chiral expansion there is only one coupling constant that describes the weak interactions of the pseudo-Goldstone bosons induced by the $27$ representation. The observed branching fraction for $K^{+}\to {\pi }^{+}{\pi }^0$ determines this coupling constant. Contributions of the form $m_s\ln m_s$ are used to estimate SU(3) breaking corrections to the relation between $K^{+}\to {\pi }^{+}{\pi }^0$ and the ${\pi }^{-}\to {\pi }^{+}{e}^{-}{e}^{-}$ interaction.

• Received 15 December 1998

DOI:https://doi.org/10.1103/PhysRevC.59.2293