The prediction of new physics beyond the Standard Model might crucially rely on the understanding of the lightness of the Higgs mass, and of the apparent absence of new particles at the TeV scale. This accidental approximate scale invariance, which gets translated in the almost vanishing of the renormalization group flow of the Standard Model at high-energy scales, calls for models able to predict and explain such a feature. Field theories of this kind have to be ultraviolet complete, in the sense of being controlled by ultraviolet renormalization-group fixed points. The construction of minimalistic and physically viable models of this kind, in absence of gravity, within and beyond perturbative approaches, is the main objective of the present proposal. This goal is pursued along two directions, corresponding to asymptotically free and asymptotically safe scenarios. On the one hand, we will address the generalization of the recent discovery of novel asymptotically free trajectories in several toy models of the Standard Model, to the full Standard Model augmented with higher-dimensional operators. On the other hand, we will explore several proposed asymptotic safety scenarios in four-dimensional field theories by means of semi-analytic nonperturbative methods, addressing their soundness and physical viability. These explorations will be confronted with phenomenological constraints, and special attention will be devoted to possible solutions of the gauge hierarchy problem in the different models under consideration. In particular, we will consider the Coleman-Weinberg mechanism of dynamical generation of the Higgs mass in these models, and the possibility to have an attenuation of the gauge hierarchy problem due to non-canonical scaling dimensions at nontrivial fixed points.

Luca Zambelli - INFN BOLOGNA
Luca Zambelli is a researcher at INFN Bologna Unit. He is an expert of renormalization-group and functional methods at weak and at strong coupling, and their applications to model building for physics beyond the Standard Model. Before joining INFN he worked as a researcher and teacher at three universities: in Austin (TX, USA), Bologna, and Jena (Germany). He co-organized workshops in Germany and Italy and had collaborations with groups from 5 countries. He has been co-advisor of PhD students, grant-project reviewer, co-writer of grant-winning research-network projects, member of selection committees, and referee for international journals.