We describe Scalar-Pseudoscalar partner degeneration at the QCD chiral transition in terms of the dominant low-energy physical states for the light quark sector. First, we obtain within modelindependent one-loop Chiral Perturbation Theory (ChPT) that the QCD pseudoscalar susceptibility is proportional to the quark condensate at low T . Next, we show that this chiral-restoring behaviour for χP is compatible with recent lattice results for screening masses and gives rise to degeneration between the scalar and pseudoscalar susceptibilities (χS, χP ) around the transition point, consistently with an O(4)-like current restoration pattern. This scenario is clearly confirmed by lattice data when we compare χS(T ) with the quark condensate, expected to scale as χP (T ). Finally, we show that saturating χS with the σ/f0(500) broad resonance observed in pion scattering and including its finite temperature dependence, allows to describe the peak structure of χS(T ) in lattice data and the associated critical temperature. This is carried out within a unitarized ChPT scheme which generates the resonant state dynamically and is also consistent with partner degeneration.

We analyze the isospin-breaking corrections to quark condensates within oneloop SU(2) and SU(3) chiral perturbation theory including m u = m d as well as electromagnetic (EM) contributions. The explicit expressions are given and several phenomenological aspects are studied. We analyze the sensitivity of recent condensate determinations to the EM low-energy constants (LEC). If the explicit chiral symmetry breaking induced by EM terms generates a ferromagnetic-like response of the vacuum, as in the case of quark masses, the increasing of the order parameter implies constraints for the EM LEC, which we check with different estimates in the literature. In addition, we extend the sum rule relating quark condensate ratios in SU(3) to include EM corrections, which are of the same order as the m u = m d ones, and we use that sum rule to estimate the vacuum asymmetry within ChPT. We also discuss the matching conditions between the SU(2) and SU(3) LEC involved in the condensates, when both isospin-breaking sources are taken into account.

We analyze quark condensates and chiral (scalar) susceptibilities including isospin-breaking effects at finite temperature T. These include m u Þ m d contributions as well as electromagnetic (e Þ 0) corrections, both treated in a consistent chiral Lagrangian framework to leading order in SUð2Þ and SUð3Þ chiral perturbation theory, so that our predictions are model-independent. The chiral restoration temperature extracted from h " qqi ¼ h " uu þ " ddi is almost unaffected, while the isospin-breaking order parameter h " uu À " ddi grows with T for the three-flavor case SUð3Þ. We derive a sum rule relating the condensate ratio h " qqiðe Þ 0Þ=h " qqiðe ¼ 0Þ with the scalar susceptibility difference ðTÞ À ð0Þ, directly measurable on the lattice. This sum rule is useful also for estimating condensate errors in staggered lattice analysis. Keeping m u Þ m d allows one to obtain the connected and disconnected contributions to the susceptibility, even in the isospin limit, whose temperature, mass, and isospin-breaking dependence we analyze in detail. The disconnected part grows linearly, diverging in the chiral (infrared) limit as T=M , while the connected part shows a quadratic behavior, infrared regular as T 2 =M 2 , and coming from 0 mixing terms. This smooth connected behavior suggests that isospin-breaking correlations are weaker than critical chiral ones near the transition temperature. We explore some consequences in connection with lattice data and their scaling properties, for which our present analysis for physical masses, i.e. beyond the chiral limit, provides a useful model-independent description for low and moderate temperatures.

We investigate the charged-neutral difference in the pion self-energy at finite temperature T. Within chiral perturbation theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self-energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at T ¼ 0 due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to OðT 2 Þ ∼ OðM 2 π Þ. Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly ρ and a 1 exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being OðT 2 M 2 π =M 2 R Þ with M R the involved resonance masses.

Abstract. 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 susceptibility.