arXiv subjects
Publications and source records attributed to Cristina Manuel.
We explore the effects of an applied strong external magnetic field in the structure and magnitude of the color superconducting diquark condensate of a three massless flavor theory. The long-range component of the B field that penetrates the superconductor enhances the condensates formed by quarks charged with respect to this electromagnetic field.
We discuss some low energy properties of color-flavor locked (CFL) superconductors. First, we study how an external magnetic field affects their Goldstone physics in the chiral limit, stressing that there is a long-range component of the field that penetrates the superconductor. We note that the most remarkable effect of the applied field is giving a mass to the charged pions and kaons. By estimating this effect, we see that for values $e B \sim 2 f_πΔ$, where $Δ$ is the quark gap, and $f_π$ the pion decay constant, the charged Goldstone bosons become so heavy, that they turn out to be unstable. The symmetry breaking pattern is then changed, agreeing with that of the magnetic color-flavor locked (MCFL) phase, recently proposed in hep-ph/0503162. Finally, we discuss the physics of the superfluid phonon of the CFL phase, compare it with that of the phonon of a Bose-Einstein condensate, and discuss transport phenomena at low temperature. Astrophysical implications of all the above low energy properties are also commented.
We explore the effects of an applied strong external magnetic field in a three flavour massless colour superconductor. The long-range component of the B field that penetrates the superconductor enhances some quark condensates, leading to a different condensation pattern. The external field also reduces the flavour symmetries in the system, and thus it changes drastically the corresponding low energy physics. Our considerations are relevant for the study of highly magnetized compact stars.
We compute the mean free path and shear viscosity in the color-flavor locked (CFL) phase of dense quark matter at low temperature T, when the contributions of mesons, quarks and gluons to the transport coefficients are Boltzmann suppressed. CFL quark matter displays superfluid properties, and transport phenomena in such cold regime are dominated by phonon-phonon scattering. We study superfluid phonons within thermal field theory and compute the mean free path associated to their most relevant collision processes. Small-angle processes turn out to be more efficient in slowing transport phenomena in the CFL matter, while the mean free path relevant for the shear viscosity is less sensitive to collinear scattering due to the presence of zero modes in the Boltzmann equation. In analogy with superfluid He4, we find the same T power law for the superfluid phonon damping rate and mean free path. Our results are relevant for the study of rotational properties of compact stars, and correct wrong estimates existing in the literature.
We investigate the effects of an external magnetic field in the gap structure of a color superconductor with three massless quark flavors. Using an effective theory with four-fermion interactions, inspired by one-gluon exchange, we show that the long-range component $\widetilde{B}$ of the external magnetic field that penetrates the color-flavor locked (CFL) phase modifies its gap structure, producing a new phase of lower symmetry. A main outcome of our study is that the $\widetilde{B}$ field tends to strengthen the gaps formed by $\widetilde{Q}$-charged and $\widetilde{Q}$-neutral quarks that coupled among themselves through tree-level vertices. These gaps are enhanced by the field-dependent density of states of the $\widetilde{Q}$-charged quarks on the Fermi surface. Our considerations are relevant for the study of highly magnetized compact stars.
Using explicit solutions of the QCD transport equations, we construct an effective potential for an anisotropic quark-gluon plasma which under plausible assumptions holds beyond the Hard Loop approximation. The configurations, which are unstable in the linear response approach, are characterized by a negative quadratic term of the effective potential. The signs of higher order terms can be either negative or positive, depending on the parton momentum distribution. In the case of a Gaussian momentum distribution, the potential is negative and unbound from below. Therefore, the modes, which are unstable for gauge fields of small amplitude, remain unstable for arbitrary large amplitudes. We also present an example of a momentum distribution which gives a negative quadratic term of the effective potential but the whole potential has a minimum and it grows for sufficiently large gauge fields. Then, the system is weakly unstable. The character of the instability is important for the dynamical evolution of the plasma system.
Parton-parton collisions do not neutralize local color charges in the quark-gluon plasma as they only redistribute the charges among momentum modes. We discuss color diffusion and color conductivity as the processes responsible for the neutralization of the plasma. For this purpose, we first compute the conductivity and diffusion coefficients in the plasma that is significantly colorful. Then, the time evolution of the color density due to the conductivity and diffusion is studied. The conductivity is shown to be much more efficient than the diffusion in neutralizing the plasma at the scale longer than the screening length. Estimates of the characteristic time scales, which are based on close to global equilibrium computations, suggest that first the plasma becomes white and then the momentum degrees of freedom thermalize.
Transport coefficients of dense quark matter are needed to study properties of compact stars. They can tell us about the cooling, vibrational and rotational properties of the star. We report below a computation of the shear viscosity in the CFL phase at low temperature T. CFL quark matter behaves as a superfluid, and at low T its transport properties are dominated by the collisions of superfluid phonons.
Within kinetic theory, we look for local equilibrium configurations of the quark-gluon plasma by maximizing the local entropy. We use the well-established transport equations in the Vlasov limit, supplemented with the Waldmann-Snider collision terms. Two different classes of local equilibrium solutions are found. The first one corresponds to the configurations that comply with the so-called collisional invariants. The second one is given by the distribution functions that cancel the collision terms, representing the most probable binary interactions with soft gluon exchange in the t-channel. The two sets of solutions agree with each other if we go beyond these dominant processes and take into account subleading quark-antiquark annihilation/creation and gluon number non-conserving processes. The local equilibrium state appears to be colorful, as the color charges are not locally neutralized. Properties of such an equilibrium state are analyzed. In particular, the related hydrodynamic equations of a colorful fluid are derived. Possible neutralization processes are also briefly discussed.
Transport theory is an efficient approach to derive an effective theory for the soft modes of QCD at high temperature. It is known that the leading order operators of this theory can be obtained from (semi-classical) kinetic equations of quasiparticles carrying classical or quantum color charges. Higher order operators can also be obtained. Discrepancy between these quasiparticle models starts for dimension 4 operators, which converge in the limit of high dimensional color representations. These quasiparticle models are reviewed and compared.
We solve the collisionless transport equations of a quark-gluon plasma interacting through mean chromodynamic fields. The system is assumed to be translation invariant in one or more space-time directions. We present exact solutions that hold if the vector gauge fields in the direction of the translation invariance commute with their covariant derivatives. We also solve the equations perturbatively when the commutation condition is relaxed. Further, we derive the color current and the associated effective action. For the static quasi-equilibrium system, our results reproduce the full one-loop effective action of QCD in the presence of constant background fields, where the above mentioned commutation condition is satisfied.
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 Langevin-type 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-dense-loop 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.
It is known that non-Abelian classical kinetic theory reproduces the Hard Thermal/Dense Loop (HTL/HDL) effective action of QCD, obtained after integrating out the hardest momentum scales from the system, as well as the first higher dimensional operator beyond the HTL/HDL level. We discuss here its applicability at still higher orders, by comparing the exact classical effective action obtained in the static limit, with the 1-loop quantum effective potential. We remark that while correct types of operators arise, the classical colour algebra reproduces correctly the prefactor of the 4-point function $tr A_0^4$ only for matter in asymptotically high dimensional colour representations.
In a color superconductor the diquark condensates break spontaneously both the color and ordinary electromagnetism, leaving a remanining 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.
We imagine shining light on a lump of cold dense quark matter, in the CFL phase and therefore a transparent insulator. We calculate the angles of reflection and refraction, and the intensity of the reflected and refracted light. Although the only potentially observable context for this phenomenon (reflection of light from and refraction of light through an illuminated quark star) is unlikely to be realized, our calculation casts new light on the old idea that confinement makes the QCD vacuum behave as if filled with a condensate of color-magnetic monopoles.
QCD with two light quark flavors at high baryonic density and low temperature is a color superconductor. The diquark condensate partially breaks the SU(3) gauge symmetry down to an SU(2) subgroup. We study thermal fluctuations of the superconductor for temperatures below the gap. These are described by a simple transport equation, linked to a quasiparticle behavior of the thermal excitations of the condensate. When solved in the collisionless limit and close to equilibrium, it gives rise to the ``hard superconducting loop'' (HSL) effective theory for the unbroken SU(2) gauge fields with momenta smaller than the gap. This theory describes Debye screening and Landau damping of the gauge fields in the presence of the diquark condensate. We also explain how our effective theory follows to one-loop order from quantum field theory. Our approach provides a convenient starting point for the computation of transport coefficients of the two-flavor color superconductor.
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 Weinberg's sum rules, we compute the decay constant $f_π$ of the Goldstone modes and find agreement with previous derivations. Using Das's 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.
We review the non-Fermi or marginal liquid behavior of a relativistic QED plasma. In this medium a quasiparticle has a damping rate that depends linearly on the distance between its energy and the Fermi surface. We stress that this dependence is due to the long-range character of the magnetic interactions in the medium. Finally, we study how the quark damping rate modifies the gap equation of color superconductivity, reducing the value of the gap at the Fermi surface.