Constraints on the parameters of the CKM matrix by End 1998

Abstract

A review of the current status of the Cabibbo-Kobayashi-Maskawa matrix (CKM) is presented. This paper is an update of the results published in [1]. The experimental constraints imposed by the measurements of \epsilon_K, V_{ub}/V_{cb}, \Delta m_d and from the limit on \Delta m_d are used. Values of the constraints and of the parameters entering into the constraints, which restrict the range of the \bar{\rho} and \bar{\eta} parameters, include recent measurements presented at 1998 Summer Conferences and progress obtained by lattice QCD collaborations. The results are: \bar{\rho}=0.202 ^{+0.053}_{-0.059},\bar{\eta}=0.340 \pm 0.035, from which the angles \alpha, \beta and \gamma of the unitarity triangle are inferred : \sin 2 \alpha = -0.26 ^{+ 0.29}_{-0.28} ,\sin 2 \beta = 0.725 ^{+0.050}_{-0.060} ,\gamma= (59.5^{+8.5}_{-7.5})^{\circ}. Without using the constraint from \epsilon_K, \sin 2 \beta has been obtained: \sin 2 \beta = 0.72 ^{+0.07}_{-0.11}. Several external measurements or theoretical inputs have been removed, in turn, from the constraints and their respective probability density functions have been obtained. Central values and uncertainties on these quantities have been compared with actual measurements or theoretical evaluations. In this way it is possible to quantify the importance of the different measurements and the coherence of the Standard Model scenario for CP violation. An important result is that \Delta m_s is expected to be between [12.0-17.6] ps^{-1} with 68% C.L. and <20 ps^{-1} at 95% C.L. Finally relations between the CKM parameters and the quark masses are examined within a given model.Comment: 26 page