MaximalCPviolation in the six-quark model

Abstract

Consideration is given to some experimental tests of the Kobayashi-Maskawa model of weak interactions for the case in which the $\mathrm{CP}$-violating effects could be expected to be maximal, that is, $\ensuremath{\delta}=\frac{\ensuremath{\pi}}{2}$. A reanalysis of the model is carried out to verify that $\ensuremath{\delta}=\frac{\ensuremath{\pi}}{2}$ is consistent with existing data. In addition to the usual contributions of the high-energy quark box diagram, this analysis takes into account low-energy dispersive terms, which depend on the energy boundary $\ensuremath{\mu}$. Double penguin diagrams are also shown to give a significant contribution to $\ensuremath{\Delta}m$, depending on $\ensuremath{\mu}$. Fitting of the result for $\ensuremath{\Delta}m(\ensuremath{\mu})$ to the measured mass difference leads to $\ensuremath{\mu}\ensuremath{\approx}1$ GeV, if the top-quark mass ${m}_{t}\ensuremath{\lesssim}45$ GeV. This places an upper limit on ${m}_{t}$ since, for larger ${m}_{t}$, the calculated $\ensuremath{\Delta}m$ is too high for all $\ensuremath{\mu}$. The results of the analysis are applied to the dilepton asymmetry in ${B}^{0}$, ${\overline{B}}^{0}$ production by ${e}^{+}{e}^{\ensuremath{-}}$ collisions and similar effects that can be obtained by comparing antineutrino with neutrino production of dileptons. When large asymmetries are found to occur, the rate is found to be hopelessly small because interference effects are suppressed. Large interference effects can occur if the parameters are chosen appropriately, but then the asymmetry is only 1 or 2%. It is also found that interference effects between ${T}^{0}$ and ${\overline{T}}^{0}$ are enormously suppressed for any choice of the parameters.