We show that the pseudogap of the quark density of states is formed in hot quark matter as a precursory phenomenon of the color superconductivity on the basis of a low-energy effective theory. We clarify that the soft mode of the di-quark pair field gives rise to a peculiar behavior of the quark dispersion relation and a short life-time of the quasiparticles near the Fermi surface, both of which make a depression of the density of states of quarks. Our result suggests that the appearance of the pseudogap is a universal phenomenon of strong coupling superconductors, irrespective of the dimensionality.Comment: 4 pages, 4 figures, PTPTeX; Proceedings of Finite Density QCD at Nara July 10-12 2003 Nara Prefecture Public Hall Big Roof Nara Japan; v2:errors in affiliation are correcte

The third moments of conserved charges, the baryon and electric charge numbers, and energy, as well as their mixed moments, carry more information on the state around the QCD phase boundary than previously proposed fluctuation observables and higher order moments. In particular, their signs give plenty of information on the location of the state created in relativistic heavy ion collisions in the temperature and baryon chemical potential plane. We demonstrate this with an effective model.

No abstract

Baryon number cumulants are invaluable tools to diagnose the primordial stage of heavy ion collisions if they can be measured. In experiments, however, proton number cumulants have been measured as substitutes. In fact, proton number fluctuations are further modified in the hadron phase and are different from those of the baryon number. We show that the isospin distribution of nucleons at kinetic freeze-out is binomial and factorized. This leads to formulas that express the baryon number cumulants solely in terms of proton number fluctuations, which are experimentally observable.PACS numbers: 12.38. Mh, 25.75.Nq, 24.60.Ky The order of the phase transition of quantum chromodynamics (QCD) at nonzero temperature (T ) is believed to change from crossover [1] to first order at a nonzero baryon chemical potential (µ B ). The existence of the QCD critical point is thus expected in the phase diagram on the T -µ B plane [2]. Experiments to explore the phase structure at nonzero µ B , especially the existence of the critical point, are now ongoing in the energy scan program at the Relativistic Heavy Ion Collider (RHIC) [3,4], and will also be performed in future facilities [5,6]. Much attention has also been paid to this problem from numerical experiments on the lattice [1,7]. The establishment of the QCD phase structure at nonzero µ B is an important issue, not only to deepen our knowledge of the matter described by QCD, but also to gain understanding of a wide array of topics in physics which share the concepts of phase transitions and techniques to treat strongly correlated many-body systems.Fluctuations, which are experimentally measured by event-by-event analyses in heavy ion collisions, are promising observables to probe the properties of created fireballs [8], as their behaviors are sensitive to the state of the matter. For example, because of the singularity at the critical point, fluctuations of various physical quantities, including skewness and kurtosis, behave anomalously near the critical point [9][10][11]. One can also argue that ratios between the cumulants of conserved charges are sensitive to the magnitudes of the charge carried by the quasiparticles composing the system, and hence they behave differently in the hadronic and quark-gluon phases [12][13][14]. Recently, it was also pointed out that some higher-order cumulants of conserved charges change signs around the phase boundary of QCD, which would serve as clear experimental signatures to determine the location of the matter in the phase diagram [15][16][17].Among the fluctuation observables, those of conserved charges can reflect fluctuations produced in earlier stages during the time evolution of fireballs, than non-conserved ones [18]. This is because the variation of a conserved charge in a volume is achieved only through diffusion, which makes the relaxation to equilibrium slower. In fact, it is argued that if the rapidity range of a detector is taken to be sufficiently large, whereas the range should be kept narrow enough so that the rest of ...

The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with β = 6.287-7.500 corresponding to the lattice spacing a = 0.013-0.061 fm. The spatial (temporal) sizes are chosen to be Ns = 64, 96, 128 (Nτ = 12,16,20,22,24) with the aspect ratio, 5.33 ≤ Ns/Nτ ≤ 8. Double extrapolation, a → 0 (the continuum limit) followed by t → 0 (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.

We investigate the effects of the dynamical formation of the chiral condensates on color superconducting phases under the electric and color neutrality constraints at vanishing temperature. We shall show that the phase appearing next to the color-flavor-locked (CFL) phase down in density depends on the strength of the diquark coupling. In particular, the gapless CFL (gCFL) phase is realized only in a weak coupling regime. We give a qualitative argument on why the gCFL phase in the weak coupling region is replaced by some other phases in the strong coupling, once the competition between dynamical chiral symmetry breaking and the Cooper pair formation is taken into account. 25.75.Nq On the basis of the asymptotic-free nature of QCD and the attraction between quarks due to gluon exchanges, we now believe that the ground state of the quark matter composed of u, d and s quarks at extremely high densities is a special type of color superconducting phases [1,2]; that is the color-flavor locked (CFL) phase where all the quarks equally participate in pairing [3,4].In reality, nature may not, however, allow such an extremely high-density matter to exist, even in the core of neutron stars and in possible quark stars. In such systems at relatively low density corresponding to the quark chemical potential of, say, 500 MeV, the following two ingredients become important for the fate of the CFL phase and determining the pattern of color superconductivities [5,6,7]: Firstly, one can not neglect the effect of the strange quark mass M s which ranges from around 100 MeV to 500 MeV depending on the quark density. Secondly, the constraints of the color and electric neutrality must be satisfied as well as β-equilibrium under the weak interaction. The former causes Fermi-momentum mismatch [8,9,10], and the latter pulls up or down the Fermi momentum of each species of quarks [6,7]; as the density goes lower, the symmetric CFL pairing would cease to be the ground state at some critical density, and some phases other than the CFL phase would appear.One of the recent findings of such novel pairing patterns is the gapless CFL (gCFL) phase [11,12], which is a non-BCS state having some quarks with gapless dispersions despite the same symmetry breaking pattern as the CFL phase. Historically, a possible realization of the stable gapless state was first discussed for the two-flavor color superconducting phase [13]: It was shown that the local charge neutrality gives a so strong constraint that such an exotic state, called the g2SC phase, exists stably; this is in contrast with the case of the electronic superconductivity in metals [14], where the possible gapless state is unstable against the spatial separation into the Pauli-paramagnetic and superconducting phases because of the absence of a long-range force mediated by gauge fields. The gCFL phase is the three flavor analogue of the g2SC phase. Successive detailed studies have revealed a rich phase structure of superconducting quark matter at zero and nonzero temperatures [15,16]. It shoul...

We explore the quark properties at finite temperature near but above the critical temperature of the chiral phase transition. We investigate the effects of the precursory soft mode of the phase transition on the quark dispersion relation and the spectral function. It is found that there appear novel excitation spectra of quasi-quarks and quasi-antiquarks with a three-peak structure, which are not attributed to the hard-thermal-loop approximation. We show that the new spectra originate from the mixing between a quark (anti-quark) and an anti-quark hole (quark hole) caused by a "resonant scattering" of the quasi-fermions with the thermally-excited soft mode which has a small but finite excitation energy.

We investigate the time evolution of higher order cumulants of conserved charges in a volume with the diffusion master equation. Applying the result to the diffusion of non-Gaussian fluctuations in the hadronic stage of relativistic heavy ion collisions, we show that the fourth-order cumulant of net-electric charge at LHC energy is suppressed compared with the recently observed second-order cumulant at ALICE, if the higher order cumulants at hadronization are suppressed compared with their values in the hadron phase in equilibrium. The significance of the experimental information on the rapidity window dependence of various cumulants in investigating the history of the dynamical evolution of the hot medium created in relativistic heavy ion collisions is emphasized.