The mass difference of the neutral K-mesons and the validity of the pertubation expansion in the theory of weak interactions

Abstract

In the conventionalV - A theory of weak interactions, the selection rule †S≤ 1 requires that the mass difference of the neutral K-mesons must be a second order effect in the weak interactions. This mass difference has actually been established by several experimental groups and it constitutes the single clear-cut piece of information on such higher order effects available at present. The experimental value of the mass difference could thus possibly give an estimate of the size of the cut-off entering the theory of weak interactions in order to make the individual terms in the perturbation expansion finite. Earlier attempts to determine the size of this cut-off have only established upper limits and in-contrast to the mass splitting †m(K01 —K02)the results from the processes considered so far all critically depend on which version of the theory of weak interactions one applies. The theoretical interpretation of results from processes involving bosons are, however, partly obscured by the presence of strong interactions. One expects that the effective cut-off for such processes will be influenced by the strong interaction cut-off, which is of the order of the nucleon mass. It will be shown that the cut-off compatible with the observed value of |†m(K01 — K02) is of the order of a few nucleon masses within two different schemes for the theory of weak interactions and the possible implications of these results are discussed. The two schemes both lead to the result that the K02 meson is heavier than theK01 meson. So far the sign of the mass difference has not been determined experimentally.