A Basis Independent Formulation of the Connection Between Quark Mass Matrices, CP Violation and Experiment

In the standard electroweak model, with three families, a one-to-one correspondence between certain determinants involving quark mass matrices (m and m' for charge 2/3 and 1 / 3 quarks respectively) and the presence/absence of CP violation is given. In an arbitrary basis for mass matrices, the quantity Imde t 1-ram +, m ' m '+3 appropriately normalized is introduced as a measure of CP violation. By this measure, CP is not maximally violated in any transition in Nature. Finally, constraints on quark mass matrices are derived from experiment. Any model of mass matrices, with the ambition to explain Nature, must satisfy these conditions. nection with CP-violation in a basis independent fashion. The organization of this paper is as follows. In Sect. 2 the commutators of functions of quark mass matrices and their intimate connection with CP-violation are discussed in the hermitian basis. In Sect. 3, it is shown that such an intimate connection exists in any basis provided appropriate commutators are considered. Basis independent constraints on mass matrices are derived, from experiment, in Sect. 4 and in Sect. 5, CP-asymmetry parameters are introduced and the question of maximal CP-violation is discussed. Finally, the conclusions are presented in Sect. 6.