Cristina Manuel

Semi-classical transport theory for non-Abelian plasmas

We review a semi-classical transport theory for non-Abelian plasmas based on a classical picture of coloured point particles. Within this formalism, kinetic equations for the mean particle distribution, the mean fields and their fluctuations are obtained using an ensemble-average in phase space. The framework permits the integrating-out of fluctuations in a systematic manner. This leads to the derivation of collision integrals, noise sources and fluctuation-induced currents for the effective transport equations of QCD. Consistency with the non-Abelian gauge symmetry is established, and systematic approximation schemes are worked out. In particular, the approach is applicable to both in- and out-of-equilibrium plasmas. The formalism is applied explicitly to a hot and weakly coupled QCD plasma slightly out of equilibrium. The physics related to Debye screening, Landau damping or colour conductivity is deduced in a very simple manner. Effective transport equations are computed to first and second order in moments of the fluctuations. To first order, they reproduce the seminal hard-thermal-loop effective theory. To second order, the fluctuations induce collisions amongst the quasi-particles, leading to a Langevintype transport equation. A complementary Langevin approach is discussed as well. Finally, we show how the approach can be applied to dense quark matter systems. In the normal phase, the corresponding kinetic equations lead to the hard-denseloop effective theory. At high density and low temperature diquark condensates are formed, changing the ground state of QCD. In the superconducting phase with two massless quark flavours, a transport equation for coloured excitations is given as well. Possible future applications are outlined.

Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

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.

Masses of the Goldstone modes in the CFL phase of QCD at finite density

Abstract We construct the U L (3)× U R (3) effective lagrangian which encodes the dynamics of the low energy pseudoscalar excitations in the Color-Flavor-Locking superconducting phase of QCD at finite quark density. We include the effects of instanton-induced interactions and study the mass pattern of the pseudoscalar mesons. A tentative comparison with the analytical estimate for the gap suggests that some of these low energy momentum modes are not stable for moderate values of the quark chemical potential μ .

Dynamical evolution of the chiral magnetic effect: applications to the quark-gluon plasma

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.

Effective transport equations for non-Abelian plasmas

Abstract Starting from classical transport theory, we derive a set of covariant equations describing the dynamics of mean fields and their statistical fluctuations in a non-Abelian plasma in or out of equilibrium. A general procedure is detailed for integrating out the fluctuations as to obtain the effective transport equations for the mean fields. In this manner, collision integrals for Boltzmann equations are obtained as correlators of fluctuations. The formalism is applied to a hot non-Abelian plasma close to equilibrium. We integrate out explicitly the fluctuations with typical momenta of the Debye mass, and obtain the collision integral in a leading logarithmic approximation. We also identify a source for stochastic noise. The resulting dynamical equations are of the Boltzmann–Langevin type. While our approach is based on classical physics, we also give the necessary generalizations to study the quantum plasmas. Ultimately, the dynamical equations for soft and ultra-soft fields change only in the value for the Debye mass.

Photon self-energy in a color superconductor

In a color superconductor the diquark condensates break spontaneously both the color and ordinary electromagnetism, leaving a remaining rotated U(1) symmetry unbroken. The gauge interactions associated to this rotated symmetry may be considered as the in-medium electromagnetism. We compute the in-medium photon self-energy in the presence of diquark condensates at high baryonic density and weak coupling. This is done to one-loop order for the cases of two and three quark flavors. For vanishing temperature, a detailed discussion is given of the low momentum behavior of the photon polarization tensor. A simple physical picture for the propagation of light in color superconducting media is obtained. The main new effect is due to the diquark condensates, which lead to a strong dielectric constant of the medium. The magnetic permeability remains unchanged, because the primary condensates have vanishing spin and angular momentum. In the two flavor case, an additional contribution arises due to gapless quarks and electrons, which is responsible for Debye screening effects. We also discuss the low energy effective theory for the three flavor case in the presence of electromagnetic interactions.

DISPERSION RELATIONS IN ULTRADEGENERATE RELATIVISTIC PLASMAS

The propagation of excitation modes in a relativistic ultradegenerate plasma is modied by their interactions with the medium. These modications can be computed by evaluating their on-shell self-energy, which gives (gaugeindependent) dispersion relations. For modes with momentum close to the Fermi momentum, the one-loop fermion self-energy is dominated by a diagram with a soft photon in the loop. We nd the one-loop dispersion relations for quasiparticles and antiquasiparticles, which behave dierently as a consequence of their very dierent phase-space restrictions when they scatter with the electrons of the Fermi sea. In a relativistic system, the unscreened magnetic interactions spoil the normal Fermi liquid behavior of the plasma. For small values of the Fermi velocity, we recover the non-relativistic dispersion relations of condensed matter systems.

Sum rules in the CFL phase of QCD at finite density

Abstract We study the asymmetry between the vector current and axial-vector current correlators in the colour–flavour locking (CFL) phase of QCD at finite density. Using Weinbergs sum rules, we compute the decay constant f π of the Goldstone modes and find agreement with previous derivations. Using Dass sum rule, we also estimate the contribution of electromagnetic interactions to the mass of the charged modes. Finally, we comment on low temperature corrections to the effective field theory describing the Goldstone bosons.

Lifetime effects in color superconductivity at weak coupling

Present computations of the gap of color superconductivity in weak coupling assume that the quarks which participate in the condensation process are infinitely long-lived. However, the quasiparticles in a plasma are characterized by having a finite lifetime. In this article we take into account this fact to evaluate its effect in the computation of the color gap. By first considering the Schwinger-Dyson equations in weak coupling, when one-loop self-energy corrections are included, a general gap equation is written in terms of the spectral densities of the quasiparticles. To evaluate lifetime effects, we then model the spectral density by a Lorentzian function. We argue that the decay of the quasiparticles limits their efficiency to condense. The value of the gap at the Fermi surface is then reduced. To leading order, these lifetime effects can be taken into account by replacing the coupling constant of the gap equation by a reduced effective one.

Shear viscosity due to phonons in superfluid neutron stars

We compute the contribution of phonons to the shear viscosity