ar X iv : h ep - p h / 99 12 25 7 v 1 7 D ec 1 99 9 December 1999 PAR - LPTHE 99 / 46 MASS HIERARCHIES AND MIXING ANGLES

The misalignment of strong interactions with spontaneously broken electroweak interactions can produce mixing-angle-dependent mass hierarchies for asymptotic states. A framework of computation of the two types of parameters is presented. The origin of mass hierarchies still appears as an unsolved problem of today's particle physics, and equally puzzling is the one of mixing angles [1]. I uncover, in a precise framework, a connection between the two, and show that they can be determined as solutions of a system of equations minimizing, in a sense to be specified, the scalar potential of a spontaneously broken electroweak gauge theory misaligned with flavour independent strong interactions 1. It relies on the reasonable hypothesis that strong interactions, supposed to be flavour independent, are the ones which tend to determine asymptotic states for mesons, the latter being usually fitted into representations of flavour U (N) (N/2 is the number of generations). It restricts to particles undergoing two types of " competing " interactions and thus excludes leptons unless they undergo a still undetected hyper-weak interaction. The first remark is that electroweak symmetry breaking introduces a drastic mass hierarchy between the three associated goldstone bosons and other massive states. Secondly, one wishes to use the flavour misalignment of electroweak interactions to trigger a violation of flavour symmetry for asymptotic mesons. For that purpose, one uses the property that the associated three goldstones, together with their Higgs partner, can be considered to transform like (linear combinations of) composite quark-antiquark pseudoscalars and scalar, and thus be incorporated into the same framework as the J = 0 mesons [2]. Since, unlike mesons, they are electroweak eigenstates, the Cabibbo-Kobayashi-Maskawa [1] rotation is expected to play a crucial role. In practice, the misalignment of the two considered interactions is translated into the one of two subgroups, the electroweak group SU (2) L × U (1) of electroweak interactions and the diagonal flavour group U (N) of the larger chiral group U (N) R × U (N) L 2. In this framework:-the three goldstones appear as linear combinations of flavour eigenstates;-like other mesons, they are expected to undergo strong interactions in addition to electroweak interactions;-the spontaneous breakdown of electroweak symmetry naturally introduces a breaking of the flavour symmetry. The questions that we then wish to answer are:-what is the effect on asymptotic states (flavour eigenstates) of the competition between strong interactions and spontaneously broken electroweak interactions?-are there values of the mixing angles …