Global fits to the Cabibbo-Kobayashi-Maskawa matrix: unitarity condition method versus standard unitarity triangles approach

Abstract

The aim of the paper is to make a comparison between the unitarity condition method and the standard version of the unitarity triangle approach by using as parameters four independent moduli $|U_{ij}|$. This choice is motivated by the measurability property and leads to a simple criterion for the separation of unistochastic matrices from the double stochastic ones, whose fulfillment is the key point of any global fit for the CKM entries. In our formulation both the methods are exact, do not depend on any assumption as the smallness of some parameter and both can be used to global fits in the quark and fermion sectors. Monte Carlo simulations show that the separation criterion puts very strong conditions requiring a fine tuning of all the CKM matrix elements.