Chaotic Dynamics of the Renormalization Group Flow and Standard Model Parameters

Bringing closure to the host of open questions posed by the current Standard Model for particle physics (SM) continues to be a major challenge for theoretical physics community. Motivated by recent advances in the study of complex systems, our work suggests that the pattern of particle masses and gauge couplings emerges from the critical dynamics of renormalization group equations. Using the ε-expansion method along with the universal path to chaos in unimodal maps, we find that the observed hierarchies of SM parameters amount to a series of scaling ratios depending on the Feigenbaum constant.