Bd0-B-bard0 mixing and the prediction of the top-quark mass in an independent particle potential model.

Abstract

Considering ${B}_{d}^{0}\ensuremath{-}{\overline{B}}_{d}^{0}$ mixing in a potential model of independent quarks by taking the effective interaction Hamiltonian of the standard Salam-Weinberg-Glashow model and subsequently diagonalizing the corresponding mass matrix with respect to ${B}_{d}^{0}$ and ${\overline{B}}_{d}^{0}$ states, we obtain an expression for the mass difference $\ensuremath{\Delta}{M}_{{B}_{d}^{0}}$ in terms of the $t$-quark mass ${m}_{t}$. Using the recent observation of the mixing parameter ${x}_{d}=0.72\ifmmode\pm\else\textpm\fi{}0.15$ by the ARGUS Collaboration, we predict the lower bound on the top-quark mass as ${m}_{t}\ensuremath{\ge}149$ GeV. Further, a consideration of experimental mass difference $\ensuremath{\Delta}{M}_{{B}_{d}^{0}}=(4.0\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ GeV also leads to ${m}_{t}={167}_{\ensuremath{-}17}^{+16}$ GeV which is in agreement with the recent experimental bound as well as other theoretical predictions. However, such a prediction of ${m}_{t}$ that utilizes the experimental value of the CKM matrix element $|{V}_{\mathrm{td}}|$ may not appear convincing in view of the large uncertainties in the measurement of $|{V}_{\mathrm{td}}|$ so far reported. Therefore using the range of ${m}_{t}$ values within its bounds predicted from other independent works, we make a reasonable estimation of $|{V}_{\mathrm{td}}|$.