Aspects of the gauge hierarchy of the standard model

  • The standard model (SM) is a huge success, being able to explain particle physics phenomenology up to the energy scales accessible nowadays (up to 13 TeV). Albeit this huge feat, the SM is not considered to provide an ultimate description of nature. Many extensions of the standard model have been motivated by the so-called hierarchy problem. While this does not characterize an incosistency of the standard model, it rather refers to the aesthetics of the theory, or its naturalness. This issue is often paraphrased as: How can the Higgs mass stay small compared to an UV cutoff while it receives radiative corrections which are naively of order cutoff squared?
  • In this work functional renormalization group techinques are employed to provide a new perspective on the gauge hierarchy of various toy models mimicking parts of the standard model. First a Z2-symmetric toy model containing one real scalar field and one Dirac fermion is studied, especially focussing on the dependence of the scale separation on the IR observables top mass and Higgs mass. Then a model containing Nf = 6 Fermions transforming in the fundamental representation of SU(3), gauge bosons, and one scalar SU(2) doublet is investigated. The strong interaction forces spontaneous chiral symmetry breaking which will be accounted for by partial bosonization of the theory, in addition to the the usual electroweak symmetry breaking in the scalar sector. The hierarchy of the emerging scales is studied, namely the UV cutoff, the electroweak scale and in the latter model also the QCD scale for different values of the parameters of the models. The goal is to study the phase transition or crossover of this standard-model-like system from a “deeply-Higgsed” into a pure QCD-type phase. From the renormalization group perspective, the rapidness of this transition is quantitatively related to the severity of the naturalness problem.

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