Interplay of chiral transitions in the standard model

We investigate nonperturbative aspects of the interplay of chiral transitions in the standard model in the course of the renormalization flow. We focus on the chiral symmetry breaking mechanisms provided by the QCD and the electroweak sectors, the latter of which we model by a Higgs-top-bottom Yukawa theory. The interplay becomes quantitatively accessible by accounting for the fluctuation-induced mixing of the electroweak Higgs field with the mesonic composite fields of QCD. In fact, our approach uses dynamical bosonization and treats these scalar fields on the same footing. Varying the QCD scale relative to the Fermi scale we quantify the mutual impact of the symmetry-breaking mechanisms, specifically the departure from the second order quantum phase transition of the pure Yukawa sector in favor of a crossover upon the inclusion of the gauge interactions. This allows to discuss the “naturalness” of the standard model in terms of a pseudo-critical exponent which we determine as a function of the ratio of the QCD and the Fermi scale. We also estimate the minimum value of the W boson mass in absence of the Higgs mechanism.