Aspects on Effective Theories and the QCD transition

We review recent advances in the understanding of the Quantum Chromodynamics (QCD) transition and its nature, paying special attention to the analysis of chiral symmetry restoration within different approaches based on effective theories. After presenting some of the main aspects of the current knowledge of the phase diagram from the theoretical, experimental and lattice sides, we discuss some recent problems where approaches relying on effective theories have been particularly useful. In particular, the combination of ideas such as Chiral Perturbation Theory, unitarity and Ward Identities allows us to describe successfully several observables of interest. This is particularly relevant for quantities expected to be dominated by the light meson components of the hadron gas such as the scalar and topological susceptibilities. In addition, ward identities and effective Lagrangians provide systematic results regarding chiral and $U(1)_A$ partner degeneration properties which are of great importance for the interplay between those two transitions and the nature of chiral symmetry restoration. Special attention is paid to the connection of this theoretical framework with lattice simulations.Comment: Invited review paper submitted to Symmetry Journal, special issue "Effective Field Theories - Chiral Perturbation Theory and Non-relativistic QFT". 28 pages, 15 figures. Version accepted for publication. Various comments and one reference adde

Light quarks at finite temperature: chiral restoration and the fate of the U(1)AU(1)_A symmetry

We review recent results on the role of light quark states within the QCD phase diagram. In particular, we will discuss how the combined use of theoretical techniques such as Effective Theories, Unitarization and Ward Identities helps to shed light on several important issues regarding chiral symmetry restoration, building bridges with recent lattice analyses. Special attention will be paid to the role of chiral and $U(1)_A$ partners in the interplay between those symmetries, which is crucial to properly understand the transition pattern. Light scalar mesons at finite temperature will be shown to be responsible for the description of susceptibilities encoding chiral and $U(1)_A$ restoration properties.Comment: Invited review paper submitted to European Physical Journal Special Topics. 18 pages, 11 figures. Version accepted for publicatio

Chiral Symmetry restoration from the hadronic regime

We discuss recent advances on QCD chiral symmetry restoration at finite temperature, within the theoretical framework of Effective Theories. $U(3)$ Ward Identities are derived between pseudoscalar susceptibilities and quark condensates, allowing to explain the behaviour of lattice meson screening masses. Unitarized interactions and the generated $f_0(500)$ thermal state are showed to play an essential role in the description of the transition through the scalar susceptibilityComment: 10 pages, 9 figures. Proceedings of "XII Quark Confinement and the Hadron Spectrum

On the effective lagrangian at nonzero isospin chemical potential

We revisit the most general effective lagrangian within Chiral Perturbation Theory at nonzero isospin chemical potential. In addition to the contributions already considered in the literature, we discuss the effects of new terms allowed by the symmetries, derived within the external source method including spurion fields, as well as of linear-field corrections. We study the influence of those new contributions on the energy density at zero temperature and observables derived from it, such as the pion and quark condensates and the isospin density. Corrections are shown to be compatible with lattice results, which favor a nonzero value for the only undetermined low-energy constant (LEC) to leading order ${\cal O}(p^2)$, rendering in particular a shift of the critical value for Bose-Einstein condensation. To ${\cal O}(p^4)$ we study the physical constraints on the new LEC, which renormalize the energy density and whose numerical effect is estimated within natural values. The new ${\cal O}(p^4)$ corrections give rise to more significant deviations than those previously considered and remain compatible with lattice results.Comment: 19 pages, 9 figure