Box diagrams and mixings with heavy external quarks.

Abstract

We present, within the standard model, an exact calculation of the effective Hamiltonian generated by the box diagrams when both the external and internal quarks are arbitrarily heavy. We use this result to calculate the mixings of the neutral hadrons involving one fourth-generation quark. Large ${B}_{b}^{\ensuremath{'}}\ensuremath{-}{\overline{B}}_{b}^{\ensuremath{'}} ({B}_{b}^{\ensuremath{'}}\ensuremath{\equiv}{b}^{\ensuremath{'}}\overline{b})$ mixing is predicted for a wide range of ${b}^{\ensuremath{'}}$-, $t$-, and ${t}^{\ensuremath{'}}$-quark masses.