Abstract
In this talk we describe examples of renormalizable strongly interacting field theories where chiral symmetry, broken at the UV cutoff by the presence of some irrelevant d > 4 operators in the fundamental Lagrangian, is recovered at low energy owing to the tuning of certain Lagrangian parameters. The interference of UV effects with IR features coming from the spontaneous breaking of the recovered chiral symmetry yields non perturbatively generated elementary fermion masses parametrically expressed by formulae of the kind mq ~ Cq(α)ΛRGI with α the gauge coupling constant and ΛRGI the RGI scale of the theory. Upon introducing EW interactions, this mechanism can be extended to give mass to EW bosons and leptons and can thus be used as an alternative to the Higgs scenario. In order to give the top quark and the weak gauge bosons a mass of the phenomenologically correct order of magnitude, the model must necessarily include (yet unobserved) super-strongly interacting massive fermions endowed, besides ordinary Standard Model interactions, with super-strong interactions with a RGI scale, ΛT ΛQCD in the few TeV range. Though limited in its scope (here we ignore hypercharge and leptons and discuss only the case of one family neglecting weak isospin splitting), the model opens the way to a solution of the naturalness problem and an understanding of the fermion mass hierarchy.
Highlights
We show in this talk that in strongly interacting field theories where chiral symmetry, broken at the UV cuto↵ by the presence of some irrelevant d > 4 operators of the Wilson type in the fundamental Lagrangian, is recovered at low energy owing to the tuning of certain Lagrangian parameters, mass terms for elementary fermions are dynamically generated
They are a consequence of a sort of “interference” between such UV chiral breaking terms and nonperturbative (NP) e↵ects coming from the spontaneous breaking of the chiral symmetry occurring in the Nambu–Goldstone (NG) phase of the theory. and are standardly induced by the strong interaction dynamics [1, 2]
As an alternative to the Higgs mechanism, masses can be NP-ly generated in a strongly interacting theory where chiral symmetry, broken at the UV cuto↵ level by irrelevant Wilson-like terms, is recovered at low energy owing to the tuning of certain Lagrangian parameters
Summary
We show in this talk that in strongly interacting field theories where chiral symmetry, broken at the UV cuto↵ by the presence of some irrelevant d > 4 operators of the Wilson type in the fundamental Lagrangian, is recovered at low energy owing to the tuning of certain Lagrangian parameters, mass terms for elementary fermions are dynamically generated. The second is that the modulation of the Yukawa couplings that in the SM is introduced by hand to fit the values of fermion masses, here, as we said before, is controlled to leading order by the magnitude of the gauge coupling of the strongest among the interactions the particle feels. We conclude from this analysis that the NP scenario for mass generation we advocate here can be considered as a valid alternative to the Higgs mechanism, with the extra advantage that, as we shall see, we will not have to deal with power divergencies in the Higgs mass. In ref. [9] it has been shown that with a reasonable choice of the elementary particle content, a theory extending the SM with the inclusion of the new super-strong sector leads to gauge coupling unification at a ⇠ 1018 GeV scale, yielding a proton life-time comfortably larger than the present limit ⌧prot > 1.7 ⇥ 1034 years
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