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, $\text{mt}=174\pm 10_{-12}^{+13}$ 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) $\text{abseps}$, the CP-violating parameter in $K$ decays, (ii) $\text{delmd}$, the mass difference due to the \bdbdbar\ mixing, (iii) the matrix elements $\text{absvcb}$ and $\text{absvub}$, 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 $|V_{td}/V_{ts}|$, as well as the standard model predictions for the \bsbsbar\ mixing parameter $\text{xs}$ and the quantities $\sin 2\alpha$, $\sin 2\beta$ and ${\sin }^2\gamma$, which characterize the CP-asymmetries in $B$-decays. The ALEPH collaboration has recently reported a significant improvement on the lower limit on the $\text{bs}$-$\text{bsb}$ mass difference, $\Delta M_s/\Delta M_d>11.3$ (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.

Comments: LaTeX, 27 pages, 16 uuencoded figures (enclosed), CERN-TH.7398/94, UdeM-GPP-TH-94-06