Constraints on charge23quark masses

We have investigated the constraints on the masses of the top quark and the corresponding member of a conjectured fourth generation, which are imposed by the $K_L-K_S$ mass difference and the $K_L\to {\mu }^{+}{\mu }^{-}$ decay rate, in the context of the standard model. It was found that the top-quark mass is bounded above, as previously shown by Buras for the case of three generations, but by an increasing function of the mass of the fourth charge $\frac{2}{3}$ quark. Viewed differently, the mass of any additional charge $\frac{2}{3}$ quark is bounded below by a function of the top-quark mass. The constraints were found to be quite sensitive to the value of the $K^0-{\overline{K}}^0$ matrix element of the $\Delta S=2\mathrm{}$ four-quark operator, as in the three-generation case, and numerical results are presented for a range of values for this model-dependent matrix element, including the MIT-bag-model prediction.