Abstract:
This dissertation focuses on the calculation of transport coefficients in the matter created in a relativistic heavy-ion collision after the chemical freeze-out. This matter can be well approximated by a pion gas out of equilibrium. We describe the theoretical framework to obtain the shear and bulk viscosities, the thermal and electrical conductivities and the flavor diffusion coefficients of a meson gas at low temperatures. To describe the interactions of the degrees of freedom, we use effective field theories with chiral and heavy quark symmetries. We introduce the unitarization methods in order to obtain a scattering amplitude that satisfies the unitarity condition exactly. We perform the calculation of the transport properties of the low temperature phase of quantum chromodynamics -the hadronic medium- that can be used in the hydrodynamic simulations of a relativistic heavy-ion collision and its subsequent evolution. We show that the shear viscosity over entropy density exhibits a minimum in a phase transition by studying this coefficient in atomic Argon (around the liquid-gas phase transition) and in the linear sigma model in the limit of large number of scalar fields (that presents a chiral phase transition). Finally, we provide an experimental method to estimate the bulk viscosity in relativistic heavy-ion collisions by performing correlations of the fluctuating components of the stress-energy tensor.

Abstract:
We study the dynamical evolution of the so-called chiral magnetic effect in an electromagnetic conductor. To this end, we consider the coupled set of corresponding Maxwell and chiral anomaly equations, and we prove that these can be derived from chiral kinetic theory. After integrating the chiral anomaly equation over space in a closed volume, it leads to a quantum conservation law of the total helicity of the system. A change in the magnetic helicity density comes together with a modification of the chiral fermion density. We study in Fourier space the coupled set of anomalous equations and we obtain the dynamical evolution of the magnetic fields, magnetic helicity density, and chiral fermion imbalance. Depending on the initial conditions we observe how the helicity might be transferred from the fermions to the magnetic fields, or vice versa, and find that the rate of this transfer also depends on the scale of wavelengths of the gauge fields in consideration. We then focus our attention on the quark-gluon plasma phase, and analyze the dynamical evolution of the chiral magnetic effect in a very simple toy model. We conclude that an existing chiral fermion imbalance in peripheral heavy ion collisions would affect the magnetic field dynamics, and consequently, the charge dependent correlations measured in these experiments.

Abstract:
We use the recently developed kinetic theory with Berry curvature to describe the fermions and antifermions of a chiral relativistic plasma. We check that this transport approach allows to reproduce the chiral anomaly equation of relativistic quantum field theory at finite temperature. We also check that it allows to describe the anomalous gauge polarization tensor that appears in the Hard Thermal (and/or Dense) effective field theory. We also construct an energy density associated to the gauge collective modes of the chiral relativistic plasma, valid in the case of small couplings or weak fields, which can be the basis for the study of their dynamical evolution.

Abstract:
The drag force and diffusion coefficients for a D meson are calculated in hot dense matter composed of light mesons and baryons, such as it is formed in heavy-ion collisions. We use a unitarized approach based on effective models for the interaction of a D meson with hadrons, which are compatible with chiral and heavy quark symmetries. We study the propagation of the D meson in the hadron matter in two distinct cases. On the one hand, we analyze the propagation of D mesons in matter at vanishing baryochemical potential, which is relevant for high-energetic collisions at LHC or RHIC. On the other hand, we show the propagation of D mesons in the hadronic medium following isentropic trajectories, appropiate at FAIR and NICA heavy-ion experiments. We find a negligible baryon contribution to the transport coefficients at vanishing chemical potential. However at finite baryochemical potential we obtain a large correction to the transport coefficients with the inclusion of nucleons and Delta baryons. The relaxation time for D mesons is reduced a factor 2-3 in the later case, producing a more thermalized D meson-spectrum for FAIR physics than for the typical LHC energies. We finally present results for the spatial diffusion coefficient of a D meson in hadronic matter and the possible existence of a minimum near the phase transition to the quark-gluon plasma at zero and finite baryochemical potential.

Abstract:
We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.

Abstract:
In this work we evaluate the B-meson drag and diffusion coefficients in a hot medium constituted of light mesons (pions, kaons and eta mesons). We treat the B-meson and B*-meson interaction with pseudo-Goldstone 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.

Abstract:
Heavy hadrons containing heavy quarks (for example, Upsilon-mesons) feature a scale separation between the heavy quark mass (about 4.5 GeV for the b-quark) and the QCD scale (about 0.3 GeV}) that controls effective masses of lighter constituents. Therefore, as in ordinary molecules, the de-excitation of the lighter, faster degrees of freedom leaves the velocity distribution of the heavy quarks unchanged, populating the available decay channels in qualitatively predictable ways. Automatically an application of the Franck-Condon principle of molecular physics explains several puzzling results of Upsilon(5S) decays as measured by the Belle collaboration, such as the high rate of Bs*-anti Bs* versus Bs*-anti Bs production, the strength of three-body B-anti B + pion decays, or the dip in B momentum shown in these decays. We argue that the data is showing the first Sturm-Liouville zero of the Upsilon(5S) quantum mechanical squared wavefunction, and providing evidence for a largely b-anti b composition of this meson.

Abstract:
We apply the three-flavor (Polyakov-)Nambu-Jona-Lasinio model to generate baryons as quark-diquark bound states using many-body techniques at finite temperature. All the baryonic states belonging to the octet and decuplet flavor representations are generated in the isospin-symmetric case. For each state we extract the melting temperature at which the baryon may decay into a quark-diquark pair. We seek for an evidence of the strangeness dependence of the baryon melting temperature as suggested by the statistical thermal models and supported by lattice-QCD results. A clear and robust signal for this claim is found, pointing to a flavor dependence of the hadronic deconfinement temperature.

Abstract:
The interaction and propagation of anti-B mesons with light mesons, N and Delta baryons is studied within a unitarized approach based on effective models that are compatible with chiral and heavy-quark symmetries. We find several heavy-quark spin doublets in the open-bottom sectors, where anti-B and anti-B* mesons are present. In the meson sector we find several resonant states, among them, a B0 and a B1 with masses 5530 MeV and 5579 MeV as well as Bs0* and Bs1* narrow states at 5748 MeV and 5799 MeV, respectively. They form two doublets with no experimental identification yet, the first one being the bottom counterpart of the D0(2400) and D1(2430) states, and the second bottom doublet associated to the ubiquitous Ds0* (2317) and the Ds1 (2460). In the baryon sector, several Lambda_b and Sigma_b doublets are identified, among them the one given by the experimental Lambda_b(5910) and Lambda*_b(5921). Moreover, one of our states, the Sigma_b*(5904), turns out to be the bottom counterpart of the Sigma*(1670) and Sigma_c*(2549), which is a case for discovery. We finally analyze different transport coefficients for the anti-B meson in hot matter, such as formed in heavy-ion collisions at RHIC and LHC. For RHIC/LHC energies, the main contribution to the coefficients comes from the interaction of anti-B mesons with pions. However, we also include the effects of baryonic density which might be sizable at temperatures T < 100 MeV, as the chemical potential is expected to increase in the last stages of the expansion. We conclude that although the relaxation time decreases with larger baryonic densities, the anti-B meson does not thermalize at RHIC/LHC energies, representing an ideal probe for the initial bottom distribution.

Abstract:
Hydrodynamic fluctuations have been studied in a wide variety of physical, chemical, and biological phenomena in the past decade. In high energy heavy ion collisions, there will be intrinsic fluctuations even if the initial conditions are fixed. Fluctuations will be greatly enhanced if the trajectory in the plane of temperature versus chemical potential passes near a critical point. We construct a model for the thermal conductivity which diverges at the critical point with the correct critical exponents, and use it in a simple illustrative model of a heavy ion collision. The proton correlation function is sensitive to the presence of the critical point.