Phenomenological constraints due to CP violation in the K-E system and the extent of B-B mixing are used to determine the constraints on the various parameters of the Cabibbo-Kobayashi-Maskawa (CKM) matrix given the Ansatz is symmetric. An existing parametrization for the CKM matrix is shown to be the most general parametrization for the symmetric Ansatz. This Ansatz implies that the mass of the t quark is at least 180 GeV. The standard electroweak model, despite its immense success, is somewhat arbitrary in that the Yukawa couplings of the fermions with the Higgs field are not constrained by any symmetry. The only way to determine the mixing angles and fermion masses is by empirical methods, although various constraints on the form of the mass matrices or the mixing angles have been advocated towards a partial solution of the problem. However, the phenomenological validity of such Ansiitze are not guaranteed a priori, and comparisons with experimental results have to be explicitly made in each case.In this paper we pursue the investigation of symmetric quark mixing [i.e., a symmetric (CKM) matrix [1,2]] in conjunction with CP-violation in the neutral-kaon system and the extent of the B~-E mixings. Such a study is of particular interest for the following reasons. By defining the asymmetry parameter (where the latter equalities follow from unitarity in the three-generation case) it may be shown that the condition for the symmetric C K M parametrization implies that A = O [2]. This actually implies that the C K M matrix is of symmetric modulus; by use of the rephasing freedom one can make it symmetric. Within (the quite small) limits of error the values of / V12 and that of V2, I are identical [3] and range between 0.217 and 0.223. This strongly suggests the possibility that the C K M matrix is symmetric. By comparing the constraint of the symmetric C K M matrix and the results of B-B mixing and measurement of cK (the parameter associated with CP-violation in the KO-RO system) we show that a symmetric C K M matrix is consistent with experiment only if the top-quark mass m, is higher than 180 GeV. For any given m,, the value of q = V13 / / 1 and the CP-violating phase 6 is strongly constrained. For the three-generation C K M matrix, we adovt the =I v31 12-I v 1 3 l2(1) parametrization [3,41where cij =cosOij; sij =sineij. The ansatz of a symmetric C K M mixing matrix can be studied by either constraining a nonsymmetric parametrization (such as the one given above) or by using the most general manifestly symmetric parametrization possible. This latter parametrization has only recently been explored [1,2]. Although in this paper we shall make use of the parametrization (2) above in deriving the limits on m,, the parametrization of Ref.[ l ] is more useful in comparing our results to those of Refs. [5,6] where a more restricted symmetry on the C K M matrix was imposed. We shall employ it at the end of our paper for this purpose. While is very accurately determined from Ke3 and hyperon decays, $2, and 013 are rather poor...
