The Standard Model (SM) of particle physics is the best present description of the fundamental laws of Nature: The model has been spectacularly verified, the discovery of the Higgs boson being its crowning completion. However, in spite of this extraordinary success, there are a number of questions about the nature of fundamental interactions which remain unanswered, among which we mention the strong CP problem (related to the symmetry under the combined action of particle-antiparticle exchange and spatial reflections), the matter-antimatter asymmetry, the origin of dark matter. Some of these problems are also interrelated, think for instance of axions, which are candidate new particles which could solve the CP problem and the dark matter problem at the same time.
A full completion of our knowledge about the world around us has been a primary goal for humankind since ever, disseminating history with a series of pure knowledge breakthroughs, inducing also technological progress afterwards. In this perspective, pure research efforts trying to solve the open questions above are of fundamental importance for society as a whole.
Part of the open problems above emerge in regimes where some of the interaction couplings get large and perturbation theory is not applicable, thus demanding for a non-perturbative (NP) approach. A notable example is represented by Quantum Chromodynamics (QCD), the theory describing the interactions among quarks and gluons and how they bind together to form the hadrons we observe: the study of many aspects of QCD needs a NP approach. Many theories which are being considered as possible extensions of the SM are also characterized by NP regimes. The method of choice, in this case, are numerical lattice simulations, which are based only on first principles and are systematically improvable.
Within this context, we addressed a number of specific timely theoretical and phenomenological questions, mostly related to the spectrum of strongly coupled quantum gauge theories (within the SM or beyond) and to the dependence of QCD on the topological angle theta, whose small phenomenological value represents in fact the strong CP problem:
a) we made substantial progress towards a comprehensive determination of the spectrum of QCD and of QCD-like theories, in particular glueballs and flux tubes, which could be observed by future experiments, or be used as an input for theories beyond the SM;
b) we made progress towards setting more stringent values on the theta angle through a NP determination, by lattice QCD simulations, of the neutron electric dipole moment (nEDM). At the same time, we have addressed the problem of determining the dependence on the theta angle of many observables in QCD and QCD-like theories, with a particular focus on quantities related to axion phenomenology.
In order to reach the objectives above, we have also developed a number of side products which will seed future progress in various directions, in particular regarding numerical codes for High Performance Computing and machine learning techniques.
