Quark mixing and Kaon transitions

Abstract

The phenomenological applications of strangeness changing neutral currents, particularly the Kº - Kº transition, are reviewed. In the Standard Model there are three possible contributions to this transition: the box diagram, the double penguin and the long distance dispersive amplitudes. The results obtained from a phenomenological study of the Kº - Kº amplitude are shown to depend critically on the assumptions made about the relative magnitudes of each of these contributions. Upper and lower bounds on the size of the hadronic matrix element (B) of the box diagram, amplitude are derived, assuming that this amplitude is the dominant contribution to the Kº - Kº transition. No interesting upper bound can be derived under other assumptions. Measurements of the B-meson lifetime and partial decay widths are used to restrict the allowed ranges for the parameters Ɵ-(_2) and Ɵ(_3) of the quark mixing matrix. This information is used, together with an analysis (under various assumptions) of the Kº - Kº mass matrix, to derive lower bounds on the mass of the t-quark (m(_t)) as a function of the parameter B. These bounds can also be regarded as lower bounds on B as a function of m(_t). The information from B-meson decays is used to determine the box diagram contribution to the K(_L)-K(_S) mass difference. For B < 1 this is significantly less than the experimental result. The double penguin amplitude is also estimated and a possibly large contribution to δm is found. There is no compelling phenomenological reason to include a substantial contribution to δm from long distance dispersive amplitudes.