Implications of the Top Quark Mass Measurement for the CKM Parameters, $x_s$ and CP Asymmetries

Abstract

Motivated by the recent determination of the top quark mass by the CDF collaboration, $\mt =174 \pm 10 ^{+13}_{-12}$ GeV, we review and update the constraints on the parameters of the quark flavour mixing matrix $V_{CKM}$ in the standard model. In performing our fits, we use inputs from the measurements of the following quantities: (i) $\abseps$, the CP-violating parameter in $K$ decays, (ii) $\delmd$, the mass difference due to the \bdbdbar\ mixing, (iii) the matrix elements $\absvcb$ and $\absvub$, and (iv) $B$-hadron lifetimes. We find that the allowed region of the unitarity triangle is very large, mostly due to theoretical uncertainties. (This emphasizes the importance of measurements of CP-violating rate asymmetries in the $B$ system.) Nevertheless, the present data do somewhat restrict the allowed values of the coupling constant product $f_{B_d}\sqrt{\hat{B}_{B_d}}$ and the renormalization-scale invariant bag constant $\hat{B}_K$. With the updated CKM matrix we present the currently-allowed range of the ratio $\vert V_{td}/V_{ts} \vert$, as well as the standard model predictions for the \bsbsbar\ mixing parameter $\xs$ and the quantities $\sin 2α$, $\sin 2β$ and $\sin^2γ$, which characterize the CP-asymmetries in $B$-decays. The ALEPH collaboration has recently reported a significant improvement on the lower limit on the $\bs$-$\bsb$ mass difference, $ΔM_s/ΔM_d > 11.3$ (95\% C.L.). This has interesting consequences for the CKM parameters which are also worked out. NOTE: this is a revised and updated version of our previous paper.