Search

We study the diffusion of charm and beauty in the early stage of high energy nuclear collisions at RHIC and LHC energies, considering the interaction of these heavy quarks with the evolving Glasma by means of the Wong equations. In comparison with previous works, we add the longitudinal expansion as well as we estimate the effect of energy loss due to gluon radiation. We find that heavy quarks diffuse in the strong transverse color fields in the very early stage (0.2-0.3 fm/c) and this leads to a suppression at low $p_T$ and enhancement at intermediate low $p_T$. The shape of the observed nuclear suppression factor obtained within our calculations is in qualitative agreement with the experimental results of the same quantity for $D-$mesons in proton-nucleus collisions. We compute the nuclear suppression factor in nucleus-nucleus collisions as well, for both charm and beauty, finding a substantial impact of the evolving Glasma phase on these, suggesting that initialization of heavy quarks spectra in the quark-gluon plasma phase should not neglect the early evolution in the strong gluon fields., Comment: 12 pages, 8+1 figures. Discussion on the scaling of parameters from three to two colors added in Appendix. Matches published version. arXiv admin note: text overlap with arXiv:1805.09617

We consider the SU(2) Glasma with gaussian fluctuations and study its evolution by means of classical Yang-Mills equations solved numerically on a lattice. Neglecting in this first study the longitudinal expansion we follow the evolution of the pressures of the system and compute the effect of the fluctuations in the early stage up to $t\approx 2$ fm/c, that is the time range in which the Glasma is relevant for high energy collisions. We measure the ratio of the longitudinal over the transverse pressure, $P_L/P_T$, and we find that unless the fluctuations carry a substantial amount of the energy density at the initial time, they do not change significantly the evolution of $P_L/P_T$ in the early stage, and that the system remains quite anisotropic. We also measure the longitudinal fields correlators both in the transverse plane and along the longitudinal direction: while at initial time fields appear to be anticorrelated in the transverse plane, this anticorrelation disappears in the very early stage and the correlation length in the transverse plane increases; on the other hand, we find that the longitudinal correlator decreases for a small longitudinal separation while being approximately constant for larger separation, which we interpret as a partial loss of longitudinal correlation induced by the dynamics., Comment: 14 pages, 10 figures. To appear on Phys. Rev. D. In V2 the discussion about isotropization has been resized, while a broad discussion about the gauge invariant correlators along the longitudinal direction and the breaking of the Glasma color strings has been added. In V3 a mistake about the definition of the parallel transporter has been corrected

We present results about photons production in relativistic heavy ion collisions. The main novelty of our study is the calculation of the contribution of the early stage photons to the photon spectrum. The initial stage is modeled by an ensemble of classical gluon fields which decay to a quark-gluon plasma via the Schwinger mechanism, and the evolution of the system is studied by coupling classical field equations to relativistic kinetic theory; photons production is then computed by including the pertinent collision processes into the collision integral. We find that the contribution of the early stage photons to the direct photon spectrum is substantial for $p_T \approx 2$ GeV and higher, the exact value depending on the collision energy; therefore we identify this part of the photon spectrum as the sign of the early stage. Moreover, the amount of photons produced during the early stage is not negligible with respect to those produced by a thermalized quark-gluon plasma: we support the idea that there is no dark age in relativistic heavy ion collisions., Comment: 11 pages, 9 figures. Matches published version

A new approach, combining the Ibragimov method and the one by Anco and Bluman, with the aim of algorithmically computing local conservation laws of partial differential equations, is discussed. Some examples of the application of the procedure are given. The method, of course, is able to recover all the conservation laws found by using the direct method; at the same time we can characterize which symmetry, if any, is responsible for the existence of a given conservation law. Some new local conservation laws for the Short Pulse equation and for the Fornberg Whitham equation are also determined., Comment: Submitted for publication on Journal of Mathematical physics (16/05/2016)

We study the influence of external electric, $E$, and magnetic, $B$, fields parallel to each other, and of a chiral chemical potential, $\mu_5$, on the chiral phase transition of Quantum Chromodynamics. Our theoretical framework is a Nambu-Jona-Lasinio model with a contact interaction. Within this model we compute the critical temperature of chiral symmetry restoration, $T_c$, as a function of the chiral chemical potential and field strengths. We find that the fields inhibit and $\mu_5$ enhances chiral symmetry breaking, in agreement with previous studies., Comment: 11 pages, 7 figures

We study microscopic processes responsible for chirality flips in the thermal bath of Quantum Chromodynamics at finite temperature and zero baryon chemical potential. We focus on the temperature range where the crossover from chirally broken phase to quark-gluon plasma takes place, namely $T \simeq (150, 200)$ MeV. The processes we consider are quark-quark scatterings mediated by collective excitations with the quantum number of pions and $\sigma$-meson, hence we refer to these processes simply as \sugg{to} one-pion (one-$\sigma$) exchange\sugg{s}. We use a Nambu-Jona-Lasinio model to compute equilibrium properties of the thermal bath, as well as the relevant scattering kernel to be used in the collision integral to estimate the chiral relaxation time $\tau$. We find $\tau\simeq 0.1 \div 1$ fm/c around the chiral crossover., Comment: 16 pages, 8 figures. One figure (lower panel of Fig. 6) added in comparison with V1. New version to appear on Phys. Rev. D

In this article we study spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field $\bm E$ and magnetic field $\bm B$. We use a Nambu-Jona-Lasinio model with a local kernel interaction to compute the relevant quantities to describe chiral symmetry breaking at finite temperature for a wide range of $E$ and $B$. We study the effect of this background on inverse catalysis of chiral symmetry breaking for $E$ and $B$ of the same order of magnitude. We then focus on the effect of equilibration of chiral density, $n_5$, produced dynamically by axial anomaly on the critical temperature. The equilibration of $n_5$, a consequence of chirality flipping processes in the thermal bath, allows for the introduction of the chiral chemical potential, $\mu_5$, which is computed self-consistently as a function of temperature and field strength by coupling the number equation to the gap equation, and solving the two within an expansion in $E/T^2$, $B/T^2$ and $\mu_5^2/T^2$. We find that even if chirality is produced and equilibrates within a relaxation time $\tau_M$, it does not change drastically the thermodynamics, with particular reference to the inverse catalysis induced by the external fields, as long as the average $\mu_5$ at equilibrium is not too large., Comment: 12 pages, 10 figures. Matches the published version

In this article we study restoration of chiral symmetry at finite temperature for quark matter with a chiral chemical potential, $\mu_5$, by means of a nonlocal Nambu-Jona-Lasinio model. This model allows to introduce in the simplest way possible a Euclidean momentum, $p_E$, dependent quark mass function which decays (neglecting logarithms) as $1/p_E^2$ for large $p_E$, in agreement with asymptotic behaviour expected in QCD in presence of a nonperturbative quark condensate. We focus on the critical temperature for chiral symmetry restoration in the chiral limit, $T_c$, versus $\mu_5$, as well as on the order of the phase transition. We find that $T_c$ increases with $\mu_5$, and that the transition remains of the second order for the whole range of $\mu_5$ considered., Comment: Section 3.2 added. To appear on Journal of Physics G

This document was prepared by the community that is active in Italy, within INFN (Istituto Nazionale di Fisica Nucleare), in the field of ultra-relativistic heavy-ion collisions. The experimental study of the phase diagram of strongly-interacting matter and of the Quark-Gluon Plasma (QGP) deconfined state will proceed, in the next 10-15 years, along two directions: the high-energy regime at RHIC and at the LHC, and the low-energy regime at FAIR, NICA, SPS and RHIC. The Italian community is strongly involved in the present and future programme of the ALICE experiment, the upgrade of which will open, in the 2020s, a new phase of high-precision characterisation of the QGP properties at the LHC. As a complement of this main activity, there is a growing interest in a possible future experiment at the SPS, which would target the search for the onset of deconfinement using dimuon measurements. On a longer timescale, the community looks with interest at the ongoing studies and discussions on a possible fixed-target programme using the LHC ion beams and on the Future Circular Collider., Comment: 99 pages, 56 figures

In this study we model early times dynamics of the system produced in relativistic heavy ion collisions by an initial color electric field which then decays to a plasma by the Schwinger mechanism, coupling the dynamical evolution of the initial color field to the dynamics of the many particles system produced by the decay. The latter is described by relativistic kinetic theory in which we fix the ratio $\eta/s$ rather than insisting on specific microscopic processes. We study isotropization and thermalization of the system produced by the field decay for a static box and for a $1+1$D expanding geometry. We find that regardless of the viscosity of the produced plasma, the initial color electric field decays within $1$ fm/c; however in the case $\eta/s$ is large, oscillations of the field are effective along all the entire time evolution of the system, which affect the late times evolution of the ratio between longitudinal and transverse pressure. In case of small $\eta/s$ ($\eta/s\lesssim0.3$) we find $\tau_{isotropization}\approx 0.8$ fm/c and $\tau_{thermalization}\approx 1$ fm/c in agreement with the common lore of hydrodynamics. Moreover we have investigated the effect of turning from the relaxation time approximation to the Chapman-Enskog one: we find that this improvement affects mainly the early times evolution of the physical quantities, the effect being milder in the late times evolution., Comment: 12 pages, 9 figures

We study the evolution of a gluon system under conditions of density and temperature similar to those explored in the early stage of ultra-relativistic heavy-ion collisions. We first describe the implementation of Relativistic Boltzmann-Nordheim (RBN) transport approach that includes in the collision integral the quantum effects of Bose-Einstein Statistics. Then, we describe the evolution of a spatially uniform gluon system in a box under elastic collisions solving the RBN for various initial conditions. We discuss the critical phase-space density that leads to the onset of a Bose-Einstein condensate (BEC) and the time scale for this process to occur. In particular, thanks to the fact that RBN allows to relax the small angle approximation, we study the effect at both small and large screening mass $ m_{D} $. For small $ m_{D}\ll T $ we see that our solution of RBN is in agreement with the recent extensive studies within a Fokker-Planck scheme in small angle approximation. For the same total cross section but with large $ m_{D}\simeq 2\, T $ (large angle scatterings), we see a significant time speed-up of the onset of BEC respect to small $m_{D}\ll T$. This further strengthen the possibility that at least a transient BEC is formed in the early stage of ultra-relativistic heavy-ion collisions., Comment: 12 pages, 15 figures

In this article we study chiral symmetry breaking for quark matter in a magnetic background, $\bm B$, at finite temperature and quark chemical potential, $\mu$, making use of the Ginzburg-Landau effective action formalism. As a microscopic model to compute the effective action we use the renormalized quark-meson model. Our main goal is to study the evolution of the critical endpoint, ${\cal CP}$, as a function of the magnetic field strength, and investigate on the realization of inverse magnetic catalysis at finite chemical potential. We find that the phase transition at zero chemical potential is always of the second order; for small and intermediate values of $\bm B$, ${\cal CP}$ moves towards small $\mu$, while for larger $\bm B$ it moves towards moderately larger values of $\mu$. Our results are in agreement with the inverse magnetic catalysis scenario at finite chemical potential and not too large values of the magnetic field, while at larger $\bm B$ direct magnetic catalysis sets in., Comment: 6 pages, 2 figures

The primordial nucleosinthesys of the element can be influenced by the transitions of phase that take place after the Big Bang, such as the QCD transition. In order to study the effect of this phase transition, in this work we compute the time evolution of thermodynamical quantities of the early universe, focusing on temperature and energy density fluctuations, by solving the relevant equations of motion using as input the lattice QCD equation of state to describe the strongly interacting matter in the early universe plasma. We also study the effect of a primordial strong magnetic field by means of a phenomenological equation of state. Our results show that small inhomogeneities of strongly interacting matter in the early Universe are moderately damped during the crossover., Comment: 4 pages, 2 figures. Talk given at Sventh European Summer School on Experimental Nuclear Astrophysics, 15-27 September 2013, Santa Tecla (CT) - Italy

A current goal of relativistic heavy ion collisions experiments is the search for a Color Glass Condensate as the limiting state of QCD matter at very high density. In viscous hydrodynamics simulations, a standard Glauber initial condition leads to estimate $4\pi \eta/s \sim 1$, while a Color Glass Condensate modeling leads to at least a factor of 2 larger $\eta/s$. Within a kinetic theory approach based on a relativistic Boltzmann-like transport simulation, we point out that the out-of-equilibrium initial distribution proper of a Color Glass Condensate reduces the efficiency in building-up the elliptic flow. Our main result at RHIC energy is that the available data on $v_2$ are in agreement with a $4\pi \eta/s \sim 1$ also for Color Glass Condensate initial conditions, opening the possibility to describe self-consistently also higher order flow, otherwise significantly underestimated, and to pursue further the search for signatures of the Color Glass Condensate., Comment: 6 pages, 4 figures. // Title changed, some discussion added, main conclusions unchanged. Version accepted for publication on Phys. Lett. B

We study the interpretation of Lattice data about the thermodynamics of the deconfinement phase of SU(3) Yang-Mills theory, in terms of gluon quasiparticles propagating in a background of a Polyakov loop. A potential for the Polyakov loop, inspired by the strong coupling expansion of the QCD action, is introduced; the Polyakov loop is coupled to tranverse gluon quasiparticles by means of a gas-like effective potential. This study is useful to identify the effective degrees of freedom propagating in the gluon medium above the critical temperature. A main general finding is that a dominant part of the phase transition dynamics is accounted for by the Polyakov loop dynamics, hence the thermodynamics can be described without the need for diverging or exponentially increasing quasiparticle masses as $T \rightarrow T_c$, at variance respect to standard quasiparticle models., Comment: 8 pages, 9 figures

The interplay of deconfinement and chiral symmetry restoration are considered in terms of effective theories. We generalize the earlier model studies by considering fermions in higher representations, and study the finite temperature phase diagrams of SU(2) and SU(3) gauge theories with two fermion flavors in fundamental, adjoint or two-index symmetric representations. We discuss our results in relation to recent lattice simulations on these theories and outline possible applications in the context of dynamical electroweak symmetry breaking., Comment: 13 pages, 6 figures

We discuss the QCD phase diagram from two different point of view. We first investigate the phase diagram structure in the strong coupling lattice QCD with Polyakov loop effects, and show that the the chiral and Z_{N_c} deconfinement transition boundaries deviate at finite mu as suggested from large N_c arguments. Next we discuss the possibility to probe the QCD critical point during prompt black hole formation processes. The thermodynamical evolution during the black hole formation would result in quark matter formation, and the critical point in isospin asymmetric matter may be swept. (T,mu_B) region probed in heavy-ion collisions and the black hole formation processes covers most of the critical point locations predicted in recent lattice Monte-Carlo simulations and chiral effective models., Comment: 10 pages, 4 figures. Talk presented at the HIC for FAIR workshop & 28th Max Born Symposium on Three days on Quarkyonic Island, Wroclaw, Poland, May 19-21, 2011

We discuss the possibility to probe the QCD critical point during the dynamical black hole formation from a gravitational collapse of a massive star, where the temperature and the baryon chemical potential become as high as T ~ 90 MeV and $\mu_B$ ~ 1300 MeV. Comparison with the phase boundary in chiral effective models suggests that quark matter is likely to be formed before the horizon is formed. Furthermore, the QCD critical point may be probed during the black hole formation. The critical point is found to move in the lower temperature direction in asymmetric nuclear matter, and in some of the chiral models it is found to be in the reachable region during the black hole formation processes., Comment: 7 pages, 3 figures

An efficient, joint transmission delay and channel parameter estimation algorithm is proposed for uplink asynchronous direct-sequence code-division multiple access (DS-CDMA) systems based on the space-alternating generalized expectation maximization (SAGE) framework. The marginal likelihood of the unknown parameters, averaged over the data sequence, as well as the expectation and maximization steps of the SAGE algorithm are derived analytically. To implement the proposed algorithm, a Markov Chain Monte Carlo (MCMC) technique, called Gibbs sampling, is employed to compute the {\em a posteriori} probabilities of data symbols in a computationally efficient way. Computer simulations show that the proposed algorithm has excellent estimation performance. This so-called MCMC-SAGE receiver is guaranteed to converge in likelihood., Comment: 5 pages, 3 figures, 10th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 2009

We construct nontopological solitonic solutions in (3+1)-dimensional Minkowski spacetime carrying a conserved global U(1) charge and nonvanishing angular momentum in a supersymmetric extension of the standard model with low-energy, gauge-mediated symmetry breaking., Comment: 6 pages, 2 figures, paragraph added, version published in Phys. Rev. D

We investigate the three flavor Nambu-Jona Lasinio model of neutral quark matter at zero temperature and finite density, keeping into account the scalar, the pseudoscalar and the Kobayashi-Maskawa-'t Hooft interactions as well as the repulsive vector plus axial-vector interaction terms (vector extended NJL, VENJL in the following). We focus on the effect of the vector interaction on the chiral restoration at finite density in neutral matter. We also study the evolution of the charged pseudoscalar meson energies as a function of the quark chemical potential., Comment: 19 pages, Revtex4. Enlarged discussion of the new kaon excitation at large $mu$, revised Introduction, some reference added. Version to appear on Phys. Rev. D

We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio (PNJL) model at finite density within the adopted mean field approximation. Also we point out how usual assumption about the diagonal form of the Wilson loop may fail in the presence of the diquark condensate on several grounds., Comment: 8 pages, 1 figure. Introduction enlarged, several comments about the adopted mean field approximation and the relation with Elitzur's theorem added. Version to appear on Phys. Rev. D

We study aspects of the pion condensation in two-flavor neutral quark matter using the Nambu--Jona-Lasinio model of QCD at finite density. We investigate the role of electric charge neutrality, and explicit symmetry breaking via quark mass, both of which control the onset of the charged pion $(\pi^c)$ condensation. We show that the equality between the electric chemical potential and the in-medium pion mass, $\mu_{e}=M_{\pi^-}$, as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion condensed phase is of the second order. Moreover, we find that the pion condensate in neutral quark matter is extremely fragile to the symmetry breaking effect via a current quark mass $m$, and is ruled out for $m$ larger than the order of 10 keV., Comment: 6 pages, 4 figures, RevTex4, (v2) title changed, Fig. 1 replaced, fourth section enlarged, references added, version accepted for publication in Phys. Rev. D, (v3) typos corrected, published version

I discuss recent results obtained by our group within the Nambu-Jona Lasinio model with the Polyakov loop. I focus on the two flavor version of the model, discussing the phase diagram in the $\mu-T$ plane in the case in which electrical neutrality is required. One of the results is that pion condensation is not observed in our model when a physical mass for the light quarks is considered., Comment: 6 pages, 3 figures. Invited talk at the YITP international symposium on ``Fundamental Problems in Hot and/or Dense QCD'', Kyoto, Japan, 3-6 Mar 2008

We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a non local Nambu-Jona Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a $\mu$ dependent scale, case III. In the cases I and II, at high chemical potential $\mu$ and low temperature $T$ the main contribution to the free energy is due to the Z(3)-neutral three-quark states, mimicking the quarkyonic phase of the large $N_c$ phase diagram. On the other hand in the case III the quarkyonic window is shrunk to a small region. Finally we comment on the relations of these results to lattice studies and on possible common prospects. We also briefly comment on the coexistence of quarkyonic and color superconductive phases., Comment: 16 pages, 7 figures, RevTeX4. Some typos corrected, references added

We study how the charge neutrality affects the phase structure of three-flavor PNJL model. We point out that, within the conventional PNJL model at finite density the color neutrality is missing because the Wilson line serves as an external ``colored'' field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality one has then to allow non vanishing color chemical potentials. We study how the quark matter phase diagram in $(T,m_s^2/\mu)$-plane is affected by imposing neutrality and by including the Polyakov loop dynamics. Although these two effects are correlated in a nonlinear way, the impact of the Polyakov loop turns out to be significant in the $T$ direction, while imposing neutrality brings a remarkable effect in the $m_s^2/\mu$ direction. In particular, we find a novel unlocking transition, when the temperature is increased, even in the chiral SU(3) limit. We clarify how and why this is possible once the dynamics of the colored Polyakov loop is taken into account. Also we succeed in giving an analytic expression for $T_c$ for the transition from two-flavor pairing (2SC) to unpaired quark matter in the presence of the Polyakov loop., Comment: 11 pages, REVTex4, 10 eps figures; v2: added two notes, added a reference; version to appear in Phys. Rev. D

We study the phase diagram and the pion modes in the electrically neutral two flavor PNJL model. One of the main result of this paper is that when electrical neutrality is required, pions do not condense in the ground state of the model: the isospin chemical potential $\mu_I = -\mu_e/2$ is always smaller than the value required for pion condensation to occur. Moreover we investigate on the pions and $\sigma$ mass spectra. We find that the qualitative behavior of the masses resembles that obtained in the NJL model. We close this paper by studying the intriguing possibility that a bound state with the quantum numbers of the pions can be formed above the chiral phase transition., Comment: 8 pages, 8 figures, RevTeX4 style. One figure added, role of the bare quark mass clarified, some reference added. To appear on Phys. Rev. D

We study numerically a class of non-topological solitons, the Q-balls, arising in supersymmetric extension of the Standard Model with low-energy, gauge-mediated symmetry breaking. % Taking into account the exact form of the supersymmetric potential giving rise to Q-balls, we find that there is a lower limit on the value of the charge $Q$ in order to make them classically stable: $Q \gtrsim 5 \times 10^2 Q_{\rm cr}$, where $Q_{\rm cr}$ is constant depending on the parameters defining the potential and can be in the range $1 \lesssim Q_{\rm cr} \lesssim 10^{8 \div 16}$.If $Q$ is the baryon number, stability with respect to the decay into protons requires $Q \gtrsim 10^{17} Q_{\rm cr}$, while if the gravitino mass is greater then $m_{3/2} \gtrsim 61 \MeV$, no stable gauge-mediation supersymmetric Q-balls exist. Finally, we find that energy and radius of Q-balls can be parameterized as $E \sim \xi_E Q^{3/4}$ and $R \sim \xi_R Q^{1/4}$, where $\xi_E$ and $\xi_R$ are slowly varying functions of the charge., Comment: 6 pages, 2 columns, 6 figures. To appear on Phys. Rev. D

We study the phase diagram of the three flavor Polyakov-Nambu-Jona Lasinio (PNJL) model and in particular the interplay between chiral symmetry restoration and deconfinement crossover. We compute chiral condensates, quark densities and the Polyakov loop at several values of temperature and chemical potential. Moreover we investigate on the role of the Polyakov loop dynamics in the transition from nuclear matter to quark matter., Comment: 10 pages, 4 figures, RevTeX4 style

We consider the Polyakov Nambu Jona Lasinio model with three massless quarks at high density and moderate temperature in the superconductive color flavor locking phase. We compute the critical temperature $T_c$ as a function of the baryonic chemical potential for the phase transition from the superconductive state to the normal phase. We find that $T_c$ is higher by a factor 1.5 -2 in comparison to the model containing no Polyakov loop. We also compute the specific heat $C_v$ near the second order phase transition and we show that the inclusion of the Polyakov loop does not change the value of the critical exponent., Comment: 7 pages, 2 figures, RevTeX4 style

We study the bosonic excitations in the favorite cubic three flavor crystalline LOFF phases of QCD. We calculate in the Ginzburg-Landau approximation the masses of the eight pseudo Nambu-Goldstone Bosons (NGB) present in the low energy theory. We also compute the decay constants of the massless NGB Goldstones associated to superfluidity as well as those of the eight pseudo NGB. Differently from the corresponding situation in the Color-Flavor-Locking phase, we find that meson condensation phases are not expected in the present scenario., Comment: 10 pages, RevTeX4 class. Section IIIA enlarged, to appear on Phys. Rev. D

In this talk I discuss the inhomogeneous (LOFF) color superconductive phases of Quantum Chromodynamics (QCD). In particular, I show the effect of a core of LOFF phase on the cooling of a compact star., Comment: 4 pages, 1 figure, uses aiproc style. Talk given at "Quark confinement and the hadron spectrum", Ponta Delgada, Acores, Portugal, 2-7 September 2006

This paper is devoted to the study of some aspects of the instability of two flavor color superconductive quark matter. We find that, beside color condensates, the Goldstone boson related to the breaking of $U(1)_A$ suffers of a velocity instability. We relate this wrong sign problem, which implies the existence of a Goldstone current in the ground state or of gluonic condensation, to the negative squared Meissner mass of the $8^{th}$ gluon in the g2SC phase. Moreover we investigate the Meissner masses of the gluons and the squared velocity of the Goldstone in the multiple plane wave LOFF states, arguing that in such phases both the chromo-magnetic instability and the velocity instability are most probably removed. We also do not expect Higgs instability in such multiple plane wave LOFF. The true vacuum of gapless two flavor superconductors is thus expected to be a multiple plane wave LOFF state., Comment: 16 pages, RevTe3X4 style

We present a self-consistent evaluation of the constituent quark masses in the three flavor Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phases of QCD, employing an improved Nambu-Jona Lasinio model. This result allows to determine the window for values of the baryonic chemical potential where the LOFF state is energetically favored., Comment: 17 pages, 5 figures, JHEP3 style. A second treatment of the ultraviolet cutoff added. Three figures adapted to the new cutoff. Two references added. Version accepted for publication on JHEP

We discuss specific heat and neutrino emissivity due to direct Urca processes for quark matter in the color superconductive Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of Quantum-Chromodynamics. We assume that the three light quarks $u, d, s$ are in a color and electrically neutral state and interact by a four fermion Nambu-Jona Lasinio coupling. We study a LOFF state characterized by a single plane wave for each pairing. From the evaluation of neutrino emissivity and fermionic specific heat, the cooling rate of simplified models of compact stars with a quark core in the LOFF state is estimated., Comment: 16 pages, 5 figures, revtex4 style. Version accepted for publication in Phys. Rev. D

We study in the Ginzburg-Landau approximation, the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors and one plane wave, including terms of order O(1/mu). We show that the LOFF window is slightly enlarged, and actually splits into two different regions, one characterized by u-s and d-u pairings and the other with d-u pairs only., Comment: 8 pages, 3 figures

We compute in the Ginzburg-Landau approximation the gluon Meissner masses for the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors in the kinematical range where it is energetically favored. We find real Meissner masses and therefore chromomagnetic stability., Comment: 13 pages, 2 figures

We compute the effect of a non-zero lepton chemical potential on the structure of the three flavor Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase of QCD at finite temperature. We show that, as in the BCS case, the lepton chemical potential favors two-species color superconductivity and disfavors the three species pairing. We stress that this study could be relevant for the cooling of a proto-neutron star with a FFLO core, if the temperatures are higher than the un-trapping temperature., Comment: 12 pages, 2 figures, RevTeX4 class. Changed Fig. 2 (see text) and some reference added

In the framework of HDET, we discuss an averaging procedure of the NJL quark-quark interaction lagrangian, treated in the mean field approximation, for the two flavor LOFF phase of QCD. This procedure gives results which are valid in domains where Ginzburg-Landau results may be questionable. We compute and compare the free energy for different LOFF crystalline structures., Comment: 10 pages; contribution to QCD@Workshop

We explore, using a Ginzburg-Landau expansion of the free energy, the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase of QCD with three flavors, using the NJL four-fermion coupling to mimic gluon interactions. We find that, below the point where the QCD homogeneous superconductive phases should give way to the normal phase, Cooper condensation of the pairs u-s and d-u is possible, but in the form of the inhomogeneous LOFF pairing., Comment: 8 pages, 4 figures. Eq. (20) corrected. As a consequence figures have been modified to show only the solution with parallel total momenta of the us, ud pairs, as the other configurations are suppressed. Main conclusions of the paper are unchanged

We calculate the Meissner masses of gluons in neutral three-flavor color superconducting matter for finite strange quark mass. In the CFL phase the eissner masses are slowly varying function of the strange quark mass. For large strange quark mass, in the so called gCFL phase, the Meissner masses of gluons with colors $a=1,2,3$ and 8 become imaginary, indicating an instability., Comment: New Fig. 1 shows that also the masses of the gluons 3 and 8 are imaginary

We compute, at the first order in the fine structure constant, the parameters of the electromagnetic Lagrangian for the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell phase in Quantum Chromodynamics (QCD) and in condensed matter. In particular we compute for QCD with two flavors the dielectric and the magnetic permeability tensors, and for condensed matter superconductors the penetration depth of external magnetic fields., Comment: 12 pages

We present an approximate gap equation for different crystalline structures of the LOFF phase of high density QCD at T=0. This equation is derived by using an effective condensate term obtained by averaging the inhomogeneous condensate over distances of the order of the crystal lattice size. The approximation is expected to work better far off any second order phase transition. As a function of the difference of the chemical potentials of the up and down quarks, $\delta\mu$, we get that the octahedron is energetically favored from $\delta\mu=\Delta_0/\sqrt 2$ to $0.95\Delta_0$, where $\Delta_0$ is the gap for the homogeneous phase, while in the range $0.95\Delta_0-1.32\Delta_0$ the face centered cube prevails. At $\delta\mu=1.32\Delta_0$ a first order phase transition to the normal phase occurs., Comment: 11 pages, 5 figures

We describe some topics related to massive two and three flavors color superconductivity (CSC), obtained in the framework of high density effective theory (HDET); moreover we present a {\em modified} Nambu-Jona Lasinio model with running - as opposite to fixed - ultraviolet cutoff, discussing the troubles that one encounters with the former when discussing QCD at high density., Comment: Talk at (or Contribution to) the International Workshop on QCD: QCD@Work 2003 - Conversano (Italy) 14-18 June 2003 (eConf C030614)