# High precision effective modelling of the QCD phase diagram

Modern technology has allowed Humanity a glimpse into an extraordinary world of particle interactions which are at the base of the reality that surrounds us. The Standard Model of particle physics, one of the greatest scientific achievements of the last century, serves as the fundamental theoretical bedrock upon which the scientific knowledge of Electromagnetic, Weak (collectively known as Electroweak) and Strong interactions is built. Full unification would imply the inclusion of the theory of gravity which is not possible without considering extensions of this model. Small deviations from Standard Model predictions in Electroweak Precision Observables are in fact being actively pursued, a fact which is in itself a testament to the high degree of agreement already achieved between theoretical predictions and experimental observations at this point in the Electroweak sector. A different scenario appears when considering Strong interactions. Moving away from the comfortable grounds of the high energy perturbative regime, where QCD - Quantum ChromoDynamics (the Standard Model sector pertaining strong interactions) has already proven its worth, one is forced to deal with a non-perturbative regime. This low energy, non-perturbative regime is nevertheless responsible for the vast majority of the reality which we deem familiar. The origin of the vast majority of the mass of the matter that surrounds us as well the confinement of quarks in hadrons are phenomena a full understanding of which beckons us to venture into these troubled waters. As a consequence of this, several different approaches are being pursued in an attempt to gain a deeper knowledge of the underlying mechanisms at play. Even the “ab initio”, although computationally challenging, approach of lattice QCD (lQCD) which tackles the problem resorting to the discretization of the space-time continuum runs is subject to complication at finite chemical potential. A popular alternative approach is the use of effective models which capture the fundamental symmetry content of the theory in a simplified and schematic fashion. The ample expertise of our workgroup in this field, particularly in extensions of Nambu-Jona-Lasinio type models, has allowed the development of advanced effective models which can be of undeniable value in the interpretation of experimental data. When considering the Phase Diagram for Strongly Interacting Matter two main features are usually considered: the partial restoration of chiral symmetry and deconfinement. Both these features can be modelled by our simple approach. One particular point of interest is the possible existence of a Critical End Point in the chiral transition. At vanishing chemical potential a temperature induced crossover transition is obtained using, for instance, lQCD calculations. It is widely expected that at some critical chemical potential this transition changes nature into a first order one. In limit of which we would then have this Critical Endpoint. The existence, location and search of this feature has motivated ample theoretical and experimental effort. Experimental signatures that signal this behavior can be devised using our effective model approach thus guiding the experimental effort. The effective models by us constructed can be constrained by vacuum properties of hadronic matter and by lQCD data obtained at vanishing chemical potential thus enabling the extrapolation of this knowledge into finite chemical potential regime. Another set of observational constraints comes from the area of compact stars where our group also has extensive expertise. With the recent observation of gravitational waves and the wealth of information which come from them (with constraints for radius, mass and tidal deformability), the interplay between these different sources of constraints has become even more interesting with the physics of strong interactions acting as a bridge between these different fields. It is also of particular relevance in this field the inclusion of the effect of a background magnetic field, a subject where our team has a large experience. There is furthermore an ongoing collaboration with the purpose of computationally testing the robustness of these models predictions by exploring the parameter space. The evaluation of transport coefficients has also been the focus of intense research and is of great practical relevance in wide range of physical scenarios ranging from heavy ion collisions to supernova collapse. The models by us developed will also be employed in the evaluation of these coefficients.

**Status**: Running

**Starting date**: 1/Aug/2020

**End date**: 31/Jul/2022

**Financing**: 20000 Euros

**Financing entity**: FCT

**Project ID**: CERN/FIS-PAR/0040/2019

**Person*month**: 34.7

**Group person*month**: 3