Probing CKM parameters through unitarity, \epsilon_K and \Delta m_{B_{d,s}}

The unitarity based analysis carried out in hep-ph/0106161, involving the evaluation of Jarlskog's rephasing invariant parameter J and the angles of the unitarity triangle is extended to include the effects of K^0-\bar K^0 and B^0-\bar B^0 mixings. The present analysis attempts to evaluate CP violating phase \delta, V_{td} and the angles of the unitarity triangle by invoking the constraints imposed by unitarity, K^0 -\bar K^0 and B^0 -\bar B^0 mixings separately as well as collectively, using the "full scanning" of input parameters. Interestingly, our results indicate that the lower limit of \delta is mostly determined by unitarity, while the upper limit is governed by constraints from \Delta m_{B_d}. Our analysis yields sin2\beta=0.50-0.88, which is in agreement with the BABAR results, however has marginal overlap only with the lower limit of recent BELLE results.