*mgr Michał Szymański*

**Promotor:** *Dr hab. Chihiro Sasaki*

### Investigating QCD phase transitions with effective theory approach

**I recenzent:** *Prof dr hab. Maciej A. Nowak*

**II recenzent:** *Prof. dr hab. Wojciech Broniowski*

Understanding the phase diagram of quantum chromodynamics (QCD) is one of the key objectives of high-energy physics. A lot of effort, on both theoretical and experimental sides, have been put to achieve this goal, but the task is far from being complete. The phase structure of QCD is expected to be very rich. Phase transitions which are particularly interesting from the perspective of phenomenology of heavy-ion collisions are deconfinement and chiral phase transition. Theoretical investigation of QCD phase transitions is very difficult as it requires nonperturbative methods. The most accurate predictions are obtained from numerical lattice simulations (LQCD). In particular, it was found that chiral transition and deconfinement are smooth crossovers. These methods, however, are currently not capable of describing QCD thermodynamics at large chemical potential because of the numerical sign problem and thus other approaches are necessary. Very useful for this purpose are effective theories of QCD. In the effective approach, one considers simplified models of QCD which share its particular features, for example symmetries, while having considerably simpler structure. Effective models are useful for several reasons. First, they may be used to explore the QCD phase diagram in the range of parameters for which LQCD methods are not applicable, and thus serve as the extrapolation tool. Particularly, many models predict the existence of the critical point (CP) in the QCD phase diagram. Moreover, with effective models one can investigate the role of different parameters or interactions and, thus, they may serve as explanatory tools, complementary to more advanced methods. The goal of this thesis is to extend our knowledge on deconffinement and chiral phase transition. To this end, we use the effective approach. In particular, we investigate the effects of magnetic field and baryon chemical potential on these phenomena. To study deconffinement, we use an effective Polyakov loop model. We explore the consequences of both spontaneous and explicit Z(3) symmetry breaking on Polyakov loop and its fluctuations. We compute ratios of Polyakov loop susceptibilities and show that the essential features of these observables, seen in LQCD, can be successfully captured by the effective approach. We also argue that ratio observables are sensitive to the strength of explicit center symmetry breaking. Next, we generalize the model to finite magnetic field and study the impact of this parameter on deconfinement of heavy quarks by calculating Polyakov loop and its fluctuations. We demonstrate that the strength of the explicit center symmetry breaking increases with the magnetic field. In consequence, increasing magnetic field tends to decrease the (pseudo) critical temperature and leads to shrinking of the first-order region in the phase diagram. We also study how Polyakov loop and its susceptibilities are affected when the magnetic field and quark chemical potential are considered simultaneously. When light quarks are considered, chiral physics cannot be neglected. It is known that many chiral models tend to predict the opposite trend on the magnetic field dependence on the deconfinement and chiral transition temperatures, than observed in lattice QCD. We demonstrate how the correct trend on the former can be achieved in our model by considering an improved constituent quark mass function. To show the importance of in-medium effects, we study the screening of four-quark interaction by the ring diagram in an effective chiral quark model, inspired by Coulomb gauge QCD. In consequence, the medium-dependent coupling is obtained, which naturally reduces the chiral transition temperature in a class of models and generates an inverse magnetic catalysis. The QCD phase diagram can also be explored experimentally with the means of relativistic heavy-ion collisions. One of the goals of these experiments is to search for the conjectured QCD critical point. Large fluctuations associated with the critical point are expected to affect various experimentally measurable quantities. An important class of observables sensitive to the critical point are fluctuations of conserved charges. We study the effect of the critical point on net-proton number fluctuations using the phenomenological model in which fluctuations of the critical mode are coupled to protons and anti-protons. We calculate net proton-number cumulants along the phenomenological freeze-out line and discuss how our results depend on the model parameters and the proximity of the chemical freeze-out line to the CP.