On the universality of weak interactions

Abstract

In classical physics the electromagnetic interactions can be introduced, on account of their universality, by the well-known formal procedure: pμ→pμ−(e/c)Aμ. The universal gravitational interaction is also introduced formally as a change in metric: δμν→gμν=δμν+χμν. In analogy with these classical examples of universal interactions we shall propose here to introduce the universal leptonic interactions by a similar formal procedure of replacing baryonic currents Jμ, Yμ (strangeness-conserving and violating currents) and boson-field operators ∂μπ and ∂μK appearing in the non-leptonic interaction Lagrangian: ℒ=l[Jμ+∂μK+Yμ+∂μπ+h. c.] by Jμ→Jμ+αLμ, Yμ→Yμ+βLμ, and ∂μπ→∂μπ+αr0Lμ, ∂μK→∂μK+βr0Lμ, where \(L_\mu = [(\bar e + \bar \mu )\gamma _\mu (1 + \gamma _5 )v]\) is the usual leptonic current, r0=1.4·10−13 cm; α and β are constants which can be determined as α=1/4 and β=1. Then almost all leptonic interactions are introduced by this formal procedure and the predictions from the new Lagrangian are compared with experiments. The agreements are satisfactory, e.g., the well-known small probabilities of the leptonic decays of hyperons are reproduced by our new Lagrangian.