Limit on the fermion masses in technicolor models

Abstract

Recently it has been pointed out that no limits can be put on the scale of fermion mass generation ͑M͒ in technicolor models, because the relation between the fermion masses (m f ) and M depends on the dimensionality of the interaction responsible for generating the fermion mass. Depending on this dimensionality it may happen that m f does not depend on M at all. We show that exactly in this case m f may reach its largest value, which is almost saturated by the top quark mass. We make a few comments on the question of how large a dynamically generated fermion mass can be. DOI: 10.1103/PhysRevD.68.077702 PACS number͑s͒: 12.60.Nz, 12.10.Dm The mechanism that breaks the electroweak gauge symmetry SU(2) L ϫU(1) Y down to the gauge symmetry of electromagnetism U(1) em is still the only obscure part of the standard model. It is known that up to the scale of 1 TeV some sign of this mechanism has to become manifest in future experiments. In the same way that an upper bound on the scale of electroweak symmetry breaking has been put forward ͑the 1 TeV scale͒, it was thought that the scale of fermion mass generation also had an upper bound, and that bound would be within the reach of the next generation of accelerators ͓1͔. Recently it was shown that no upper bound can be put on the scale of fermion mass generation beyond that on the scale of electroweak symmetry breaking ͓2͔. This result was obtained by considering the scattering of the same helicity fermions into a large number of longitudinal weak vector bosons in the final state, and it was also obtained in a more involved way in Ref. ͓3͔. This result is important and at the same time disappointing, because an upper bound on the scale of fermion mass generation would provide a target for future accelerators in order to understand the origin of fermion masses.The scale related to the origin of fermion masses cannot be bounded but the fermion mass itself is bounded. The bound on the fermion masses comes out from the upper limit on the Yukawa coupling ( y рͱ8) ͓4͔. In the standard scenario this is not very interesting because it also leads to a bound on the fermion masses of the order of 1 TeV. Therefore there is still space for a heavy new family ͑respecting the constraints provided by the high precision experiments͒. This problem becomes much more interesting in theories with dynamical symmetry breaking such as technicolor theories, where, in principle, some of the free parameters of the standard model are calculable as long as we know the symmetries of the underlying theory that is responsible for the mass generation. Let us recall some of the arguments about the nonexistence of a bound on the scale for fermion mass generation in technicolor ͑tc͒ models ͓2͔. In these models the fermion mass is given bywhere c is a constant and ͗ tc tc ͘ is the technifermion con- which gives the bound on the mass scale responsible for fermion mass generation. Nowadays it is known that composite operators like ͗ tc tc ͘ ͑and the technifermion selfenergy͒ may have a large anomalous di...

Light composite Higgs from an effective action for technicolor

“…The points that we have chosen in Fig. 6 correspond to extreme walking technicolor theories, and we expect the possible range of couplings and masses for other values to be located between these points and the standard model curve [7].…”

“…As two of us have pointed out in Ref. [7] only such kind of solution is naturally capable of generating a large mass to the third fermionic generation, which has a mass limit almost saturated by the top quark mass. This variation of the ansatz with is what makes our calculation a general one; it covers all possible solutions of the Schwinger-Dyson equation (or Bethe-Salpeter equation) for fermions forming the composite boson.…”

“…Actually we should say that this last case is not important and should not be considered, since a relevant contribution would come from heavy fermions, and as far as it is known up to now [7], such heavy mass could only be naturally generated in extreme walking gauge theories. Observe that the above Eqs.…”

“…The self-energy solution, in this specific limit, cannot generate large fermion masses [7] (without generating large flavor changing neutral currents). Therefore we can expect that ðm f ¼ m f ð1Þ % m u Þ or ðm f ¼ m f ð1Þ % m e Þ.…”

“…0 the self-energy is the one that appears in the extreme walking technicolor theo-ries [6]. Using this self-energy ansatz we can study several properties of the composite Higgs boson in a model independent way [7], as we choose the free parameter ( ) which defines the theory to be considered. Observe that Eq.…”