Abstract. We compute the charm drag and diffusion coefficients in a hot pion gas, such as is formed in a Heavy Ion Collision after the system cools sufficiently to transit into the hadron phase. We fully exploit Heavy Quark Effective Theory (with both D and D * mesons as elementary degrees of freedom during the collision) and Chiral Perturbation Theory, and employ standard unitarization to reach higher temperatures. We find that a certain friction and shear diffusion coefficients are almost p 2 -independent at fixed temperature which simplifies phenomenological analysis. At the higher end of reliability of our calculation, T ≃ 150 MeV, we report a charm relaxation length λc ≃ 40 fm, in agreement with the model estimate of He, Fries and Rapp.

We calculate the time evolution of the X(3872) abundance in the hot hadron gas produced in the late stage of heavy ion collisions. We use effective field Lagrangians to obtain the production and dissociation cross sections of X(3872). In this evaluation we include diagrams involving the anomalous couplings πD * D * and XD * D * and also the couplings of the X(3872) with charged D and D * mesons. With these new terms the X(3872) interaction cross sections are much larger than those found in previous works. Using these cross sections as input in rate equations, we conclude that during the expansion and cooling of the hadronic gas, the number of X(3872), originally produced at the end of the mixed QGP/hadron gas phase, is reduced by a factor of 4.

The Nambu-Jona-Lasinio (NJL) model is one of the most frequently used four-fermion models in the study of dynamical symmetry breaking. In particular, the NJL model is convenient for that analysis at finite temperature, chemical potential and size effects, as has been explored in the last decade. With this motivation, we investigate the finite-size effects on the phase structure of the NJL model in D = 3 Euclidean dimensions, in the situations that one, two and three dimensions are compactified. In this context, we employ the zeta-function and compactification methods to calculate the effective potential and gap equation. The critical lines that separate trivial and non-trivial fermion mass phases in a second order transition are obtained. We also analyze the system at finite temperature, considering the inverse of temperature as the size of one of the compactified dimensions.The last decades witnessed significant investigations on the phase structure of quantum field theories, in particular on the chiral symmetry phase transitions in Quantum Cromodynamics (QCD). However, due to its complex structure, effective models have been largely employed to simplify that analysis. Among them, one of the most frequently used is the four-fermion theory known as Nambu-Jona-Lasinio (NJL) model [1]. The NJL model is specially convenient for the investigation of dynamical symmetries when the system is under certain conditions, like finite temperature, finite chemical potential, external gauge field, gravitation field and others [2,3,4].Finite-size effects on the phase transitions of four-fermion models have also attracted a great interest [5,6,7]. This question emerges when the system has a finite size and it is not clear if it is large enough to apply the thermodynamic limit in a usual way; frequently it is necessary to take into account the fluctuations due to finite-size effects. In particular, Ref.[6] performed a numerical investigation of a three-dimensional four-fermion model in a finite-size scaling analysis, where the finite-size effects act as an external field. On the other hand, Ref.[7] studied the NJL model in the framework of the multiple reflection expansion, where in terms of a modified density of states finite-size effects are included (see also Ref. [8]). The critical temperature was suggested to decrease as the system is reduced.In this paper, we investigate finite-size effects on the dynamical symmetry breaking in a different way. We study the Euclidean three-dimensional NJL model in the framework of zeta-function and compactification methods [9]. This procedure in principle allows us to explore the mentioned model with one, two or three compactified dimensions with antiperiodic boundary conditions [17] and compare their effects in the phase diagram of the model. With the choice of all dimensions being spatial, the system is considered confined between two parallel planes a distance L apart, confined to a infinity cylinder having a square transversal section of area L 2 , and to a cubic box of volume L 3 , for ...

Phase transitions and critical behavior of complex systems for magnetic shape-memory AIP Conf.We investigate the critical behavior of the N-component Euclidean 4 model, in the large N limit, in three situations: confined between two parallel planes a distance L apart from one another; confined to an infinitely long cylinder having a square transversal section of area L 2 ; and to a cubic box of volume L 3 . Taking the mass term in the form m 0 2 = ␣͑T − T 0 ͒, we retrieve Ginzburg-Landau models which are supposed to describe samples of a material undergoing a phase transition, respectively, in the form of a film, a wire and of a grain, whose bulk transition temperature ͑T 0 ͒ is known. We obtain equations for the critical temperature as functions of L and of T 0 , and determine the limiting sizes sustaining the transition.

In this work we evaluate the B-meson drag and diffusion coefficients in a hot medium constituted of light mesons (π, K,K and η). We treat the B-meson and B * -meson interaction with pseudoGoldstone bosons in chiral perturbation theory at next-to-leading order within the constraints from heavy quark symmetry, and employ standard unitarization techniques of NLO amplitudes in order to account for dynamically generated resonances (leading to a more efficient heavy-flavor diffusion) and thus reach higher temperatures. We estimate individual meson contributions from the gas to the transport coefficients and perform a comparison with other findings in literature. We report a bottom relaxation length of about 80 fm at a temperature of 150 MeV and for typical momenta of 1 GeV, at which our approach is reliable. Compared to a charm relaxation length of 40 fm in the same conditions, we conclude that the B mesons provide a cleaner probe of the early stages of a heavy-ion collision.

We study the size dependence of the dynamical symmetry breaking in the fourdimensional Nambu-Jona-Lasinio model. We show that the presence of boundaries reduces the chiral breaking region, and this effect is strengthened for a larger number of compactified dimensions. A critical value for the length of the compactified dimensions exists, below which the dynamical symmetry breaking is not possible. Considering finite temperature and chemical potential, the chiral phase structure for the system with compactified dimensions is obtained. A gradual decreasing of the chiral breaking region with increasing of chemical potential is found. Also, at fixed chemical potential, the decreasing of the size of the system changes the order of the chiral phase transition.

We investigate finite-size effects on the chiral transition at finite temperature and density in the framework of the Nambu-Jona-Lasinio model in the presence of an external magnetic field. The thermodynamic potential and the gap equation are derived in the mean-field approximation and analyzed under the changing of the relevant parameters.

We investigate finite-size effects on the phase structure of chiral and difermion condensates at finite temperature and density in the framework of the two-dimensional large-N Nambu-Jona-Lasinio model. We take into account size-dependent effects by making use of zeta-function and compactification methods. The thermodynamic potential and the gap equations for the chiral and difermion condensed phases are then derived in the mean-field approximation. Size-dependent critical lines separating the different phases are obtained considering antiperiodic boundary conditions for the spatial coordinate.