Quark Mass Hierarchies, Flavor Mixing and Maximal Cp –violation

Flavor mixing and the quark mass spectrum are intimately related. In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for B physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense. At the magnificient Boston Museum of Fine Arts one can see a big stone brought in from Northern Africa, covered with strange hieroglyphes. More than 2000 years ago it was located in the Great Temple of Amun at the old City of Jebel Barkal in the kingdom of Nubia and is assumed to describe the rulership of king Tanyidamani. The text is written in the Meroitic language, which is still underdeciphered. Neither the grammar of that language nor the content of the text on the Stone of Amun is known, only the letters. In particle physics today one is facing a similar problem, as far as the masses of the leptons and quarks are concerned. After the discovery of the t–quark the spectrum of these masses (apart from the yet unknown neutrino masses) is known. It is a rather wild spectrum, extending over 5 orders of magnitude, from the tiny electron mass to the huge t–mass, but the actual dynamics behind this spectrum remains mysterious. Nature speaks to us in some kind of Meroitic language. The letters of this language, i. e. the masses and flavor mixing parameters, are known, but the grammar and the content of the underlying text are unknown. Of course, in these lectures I cannot offer a complete solution of the mass problem, but I shall describe what I would like to define as the grammar of patterns and rules, which are not only very simple, but seem to come out very well, if confronted with the experimental results. The phenomenon of flavor mixing, which is intrinsically linked to CP – violation, is an important ingredient of the Standard Model of Basic Interactions. Yet unlike other features of the Standard Model, e. g. the mixing of the neutral electroweak gauge bosons, it is a phenomenon which can merely be described. A deeper …