Nonleptonic Weak Interactions in Unified Gauge Theories

Abstract

Weinberg has shown in general unified gauge theories that if (1) the strong interactions are described by a neutral-vector-gluon model, and (2) all quark masses are much smaller than all intermediate-massive-vector-boson masses, then the order-$\ensuremath{\alpha}$ effects of weak and electromagnetic corrections to the strong-interaction symmetries are just the conventional electromagnetic corrections plus corrections to the quark mass matrix which preserve parity, strangeness, charm, etc. In this paper we use his method to further show that if quark masses are also much smaller than Higgs scalar-boson masses, and some technical conditions stated in the text are satisfied, then to order ${G}_{F}{m}^{2}$ ($m=\mathrm{a}\mathrm{typical}\mathrm{quark}\mathrm{mass}$), only a certain part of vector-boson exchanges induces the dominant contribution to proper nonleptonic weak interactions which violate parity or strangeness or charm, etc., while the remaining part of vector-boson exchanges, all of scalar-boson exchanges, and all of tadpole diagrams can only produce corrections to the quark mass matrix, which preserve the quantum numbers of strong interactions. We also offer speculation on possible mechanisms to obtain the $\ensuremath{\Delta}I=\frac{1}{2}$ rule of nonleptonic decays.