Phase diagram of the U(2)×U(2) σ model and its implications for chiral hierarchies

In the minimal version of the standard model of electroweak interactions the same mechanism ~a one-doublet complex scalar field! gives masses simultaneously to the W and Z gauge bosons and to the fermionic matter fields~other than the neutrino!. This remains so in many extensions of the minimal standard model, such as those consisting of more scalar doublet fields or even fields in other representations of SU(2) L . On the contrary, the mechanism that gives masses to the W and Z bosons and to the matter fields remains somewhat distinct in models of dynamical symmetry breaking ~such as technicolor theories @1#!. In these models, there are interactions that become strong, typically at the scale 4 pv (v 5250 GeV!, breaking the global SU(2) L3SU(2)R symmetry to its diagonal subgroup SU(2) V and producing Goldstone bosons which eventually become the longitudinal degrees of freedom of the W 6 and Z. Yet to transmit this