Pionic matrix elements in neutrinoless double-β decay

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 (u) over bar gamma(mu)(1 - gamma(5))d (u) over bar gamma(mu)(1 - gamma(5))d is part of the 27 representation responsible for Delta I = 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+ --> 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+ --> pi(+) pi(0) and the pi(-)-->pi(+)e(-)e(-) interaction. [S0556-2813(99)03304-X].