M. Asakawa
Focusing Effect and Transverse Rapidity Dependence of the Proton-Antiproton Ratio as a Signature of the QCD Critical Endpoint
The presence of a critical endpoint in the QCD phase diagram can deform the trajectories describing the evolution of the expanding fireball in the $\mu_B-T$ phase diagram. The deformation of the hydrodynamic trajectories will change the transverse rapidity ($y_{\rm T}$) dependence of the proton-antiproton ratio when the fireball passes in the vicinity of the critical endpoint. An unusual $y_{\rm T}$-dependence of the $\bar{p}/p$ ratio in a narrow beam energy window would thus signal the presence of the critical endpoint.

J.-P. Blaizot
xxxx

D. Blaschke
The critical endpoint in nonlocal chiral quark models
Studies of the high-temperature and low-density part of the QCD phase diagram are provided by Lattice QCD (lQCD) simulations. Recent progress in reproducing lQCD results with phenomenological models has been made when a Polyakov-loop generalization of the Nambu--Jona-Lasinio (PNJL) modeling of the chiral quark dynamics had been introduced [1-3]. In the present contribution, we report on the response of the QCD phase diagram and in particular the critical endpoint to extensions of this type of models when (1) the effects of nonlocality, (2) color neutrality constraints and (3) Dyson-Schwinger-type chiral dynamics are taken into account [4,5]. We also discuss the issue of the BEC-BCS crossover in quark matter [6], which is a natural consequence of the coexistence of dynamical chiral symmetry breaking and color superconductivity in the phase diagram and which occurs, e.g., when color neutrality is enforced in the PNJL model [5]. The final point of discussion concerns some steps towards a unified treatment of the hadron-to-quark matter transition with particular emphasis on the low-temperature and high-density region of the phase diagram, to be probed in upcoming heavy-ion collision programs (RHIC Low-Energy, CBM @ FAIR, NICA-MPD) and by observational constraints from compact stars [7].

J. Braun
Chiral Phase Boundary from Quark-Gluon Dynamics
I discuss the chiral phase transition in QCD with its underlying mechanisms in terms of quarks and gluons and present results for the chiral phase boundary in the plane of temperature and number of (massless) quark flavors obtained from a functional renormalization group approach. In addition, first results for the dependence of the chiral phase transition temperature on small quark chemical potentials are discussed. The last part of the talk deals with the deconfinement phase transition in Yang-Mills theory. The order-parameter potential for SU(3) Yang-Mills theory, namely the Polyakov-loop potential, obtained from a functional renormalization group study is shown.

H. Caines for the STAR Collaboration
STAR and the RHIC Energy Scan
  I will discuss STAR's current activities and plans for the proposed RHIC energy scan. STAR's large acceptance is ideal for such a study as we can obtain significant statistics with minimal running of the accelerator, thus allowing us to truly scan a range of collision energies. I will present results from STAR's studies to understand how the detector, triggering  and accelerator will operate at lower collision energies. Included in these studies are analyses of the data taken by STAR during RHIC's 2008 sqrt(s)= 9 GeV Au-Au collisions test run. Finally I will describe some of the measurements we propose to locate the QCD critical point.

J.-W. Chen
Phase Transitions and the Perfectness of Fluids
We calculate the ratio eta/s, the shear viscosity (eta) to entropy density (s), which characterizes how perfect a fluid is, in weakly coupled real scalar field theories with different types of phase transitions. The resulting eta/s behaviors agree with the empirical observations in atomic and molecular systems such as water, He and N. These behaviors are expected to be the same in N component scalar theories with an O(N) symmetry. We speculate these eta/s behaviors are general properties of fluid shared by QCD and cold atoms. Finally, we clarify some issues regarding counterexamples of the conjectured universal eta/s bound found in literature.

P. de Forcrand
asdasas

S. Ejiri
Numerical study of the critical point in lattice QCD at high temperature and density
We study the critical point in lattice QCD at high temperature and density by Monte-Carlo simulations. We propose two methods to probe the nature of the phase transition. One is based on the investigation of an effective potential as a function of the average plaquette. The other is a method by constructing the canonical partition function for each quark number. We analyze the data obtained by a simulation of two-flavor QCD with p4-improved staggered quarks, and find that a first order phase transition line appears in the high density regime.

L. Ferroni
The compressible hadron gas: a simple idea for the cross-over transition.
We formulate a simple model for a gas of extended hadrons at zero chemical potential by taking inspiration from the compressible bag model. We show that the massless gas behavior observed in lattice QCD at high temperatures can be mimicked by such a system without the need of any actual phase transition.

M. Forbes
asdasas

H. Fujii
Spectral functions near the QCD critical point in chiral models
Critical mode appears near the continuous phase transition. We present the results of the mode spectrum in the NJL model as well as the sigma model with the omega field, and discuss the general feature of the critical mode associated to the QCD critical point.

K. Fukushima
What can we learn from the model studies on the QCD critical point?
The PNJL model (Nambu--Jona-Lasinio model with the Polyakov loop coupling) is quite successful reproducing the thermodynamics of QCD matter at finite temperature and zero density. Supposing the finite density effect enters only through the quark chemical potential, we can give model predictions. I will report what we can learn from the three-flavor PNJL model on the QCD critical point. In my talk I will emphasize: Some of the model parameters are not under theoretical control and thus even the existence or non-existence is not clear yet. Assuming the critical point, the model-predicted EoS gives the adiabatic path, from which we see the focusing effect, which turns out to be not a wide effect.

C. Greiner
Quick Chemical Equilibration Time in an Expanding Hadronic Fireball
It has been suggested that hadrons are ``born" into equilibrium following the Quark Gluon Plasma phase because of long chemical equilibration times needed to explain particle ratios in the hadron gas phase in relativistic heavy ion collisions. However, after developing a dynamical scheme of rate equations used to describe Hagedorn states that catalyze fast chemical equilibration of (anti-)baryons and (anti-)kaons inside a hadron gas just below the critical temperature, we find that hadrons can reach chemical equilibrium within the lifetime of a hadronic fireball. Furthermore, we are able to develop analytical time scale estimates using the master equations. Considering a Bjorken expansion, the baryons and kaons as well as the bath of pions and Hagedorn states are able to quickly equilibrate for various initial conditions. Additionally, our results for $(B+\bar{B})/\pi$ and $K/\pi$ ratios at RHIC match experimental data points well.

S. Gupta
New results in QCD at finite chemical potential

J. Han
asdasas

T. Hell
Thermodynamics of a nonlocal PNJL model
The synthesis of Polyakov loop dynamics and the Nambu and Jona-Lasinio (NJL) model in the form of the PNJL model has become a promising approach to the description of the thermodynamics of strongly interaction quark-gluon matter. The NJL model offers a schematic but nonetheless realistic picture of the basic dynamics behind spontaneous chiral symmetry breaking, while the Polyakov loop is introduced as the order parameter describing the confinement-deconfinement transition in pure-gauge QCD. On the other hand, the price paid for the simplicity of the NJL model with its local point coupling between quarks is the necessity of introducing a momentum cutoff to regularize loop integrals. In order to circumvent deficiencies arising from this cutoff, a nonlocal covariant extension of the two-flavour NJL model is constructed with built-in constraints from the running coupling of QCD at high-momentum and instanton physics at low-momentum scales. The momentum-dependent dynamical quark mass derived from this approach is in agreement with results from Dyson-Schwinger equations and lattice QCD. At finite temperature, inclusion of the Polyakov loop and its gauge invariant coupling to quarks reproduces the dynamical entanglement of the chiral and deconfinement crossover transitions as in the (local) PNJL model. Steps beyond the mean-field approximation are made including mesonic correlations through quark-antiquark ring summations, leading to a pressure, energy density and other thermodynamical quantities which include pion contributions that dominate below the critical temperature.

K. Homma
Fluctuations and Search for the QCD Critical Point
PHENIX analyses on multiplicity fluctuations from both integrated [1] and differential [2] view points are presented in detail. In addition to a peculiar centrality dependence of a quantity related with susceptibility of density fluctuations via two point correlation of fluctuations advocated in [2], I introduce suggestive centrality dependences of other observables like; meson-meson and meson-baryon fluctuations, a sudden flip of deviations of baryon and meson v_2 from quark number scaled universal curves of v_2 at low KE_T region (possibly related with light sigma field [3]), a sudden jump of amplitude and width of two particle correlation in eta direction by START collaboration[4].

R. Karabowicz
The Critical Point in the CBM Experiment
The Compressed Baryonic Matter (CBM) is the heavy ion experiment in the future FAIR facility located by the GSI. Contrary to the present trends (RHIC and LHC) towards using more and more energetic beams to obtain baryon free high temperature medium, CBM is focusing at production of a hot fireball with large baryon density. Monte Carlo simulations of the heavy ion collisions at the FAIR energies of about 30 AGeV show that for a short while the created medium in the hottest phase exists as the Quark Gluon Plasma. The come-back trajectory on the QCD phase diagram is situated in the vicinity of the QCD critical point. The CBM Collaboration aims at designing and building an experimental setup that will allow gathering large statistics of high quality data. The high interaction rate of 107 collisions per second delivered by the SIS300 accelerator is of particular importance for the observation of rare probes, like charm mesons or leptonic decay channels of light vector mesons.

F. Karsch
Lattice results on the QCD critical point

B. Klein
Scaling and finite-size scaling analysis of critical behavior in lattice QCD
The exact nature of the QCD phase transition is still not determined conclusively, and there are contradictory results from lattice QCD simulations about the scaling behavior, even for two quark flavors. Ultimately, this issue can be resolved only by a careful scaling and finite-size scaling analysis of the lattice results. We use renormalization group methods to obtain scaling functions and finite-size scaling functions and discuss how to apply these results to a scaling analysis of the lattice QCD data.

D. Kresan
asdasas

R. Lacey
asdasas

A. Li
asdasas

J. Liao
Magnetic Scenario for sQGP and QCD Phase Diagram from E-M Duality Perspective
Based on monopoles and generic E-M duality, we have recently suggested a ``magnetic scenario'' [PRC75:054907,2007] for quark-gluon plasma in 1-2$T_c$ region (known as sQGP) --- a plasma in which monopoles become light, weakly coupled, and dominant d.o.f near $T_c$, while electric particles (quarks and gluons) are forced to become heavy and strongly coupled, eventually confined. This picture has been supported by several independent lattice results. In particular our ``magnetic scenario'' predicted that electric/magnetic effective coupling should run in opposite direction as temperature changes. This was confirmed in our paper [arXiv:0804.0255[hep-ph]] by analyzing recent accurate data about lattice monopoles. This scenario is also shown to be able to explain both the ``perfect liquid'' transport properties observed at RHIC and nontrivial $T$-dependence of static $\bar Q Q$ potentials calculated on lattice. (see [PRC75:054907,2007], [Phys. Rev. C 77: 064905, 2008] and [arXiv:0804.4890 [hep-ph]]) In the same spirit, we generalized the E-M duality perspective to the whole $T$-$\mu$ plane, leading to a new view on the QCD phase diagram. Different from the tranditional one which focuses on the phase transition lines, we concentrate on the competition for dominance between the electric and magnetic sector. Comparison between the two views and possible connection to the QCD critical point will be discussed.

K.-F. Liu
Lattice Calculation of the Critital Point with the Canonical Ensemble
Lattice calculation with an exact Monte Carlo algorithm to simulate finite density and finite temperature is carried out with Wilson and Clover fermions. We show that the two-flavor case is not a first order phase transition down to 0.83 T_c and it is a first order phase transition for the four-flavor case below T_c for finite density. We will report progress on the more interesting three-flavor case where the phase boundaries in the $\mu-\rho$ plane are determined via the Maxwell construction in order to determine the critical point.

M. Lombardo
asdasas

L. McLerran
The Phase Diagram of QCD at Large N_c
I discuss the phase diagram at large N_c. The phases are characterized by two order parameters, the Wilson Line and the Baryon Number Density, N_B. I argue that in addition to the Hadronic and Deconfined Phases, there is third phase, the Quarkyonic, which has finite N_B and is confined. The Hadronic phase has N_B = 0 and the Deconfined has N_B finite. Also at large N_C and large numbers of Fermions, confinement is no longer a good order parameter, but there is maintained a transitions between the Hadronic and Quarkyonic Phases. I discuss the gross properties of these phases, and implications for the phase diagram of QCD.

C. Miao
asdasas

M. Mitrovski
Energy and system size dependence of hadron yields and spectra from NA49
Final NA49 results on the energy dependence of hadron production in central Pb+Pb collisions will be shown and discussed with respect to possible indications for the onset of deconfinement. Around 30 $A$GeV a rapid change of the energy dependence of pion and kaon yields as well as of the mean transverse mass is observed. Furthermore preliminary data on the system size dependence of hadron production at 158 $A$ and 40 $A$GeV will be shown. Besides the inclusive hadron production also the directed and elliptic flow of hadrons has been measured for pions, kaons and protons at 40 $A$GeV. At 158 $A$GeV we measured in addition the v2 of $K^{0}_{s}$ and $\Lambda$. The observation of significant elliptic flow and its mass dependence suggests strong collective behavior of the matter produced in collisions of heavy nuclei already at the SPS. Scaling properties of elliptic flow of different particle species have been tested at 158 $A$ GeV. Moreover, the HBT-radii of the pion emitting source is obtained from the study of the corresponding Bose-Einstein correlations in central Pb+Pb collisions. Together with results from AGS and RHIC experiments we observe only a weak energy or no dependence of the radii over the full energy range. Microscopic (e.g. UrQMD) and hadron gas models are compared to data where possible.

K. Mitsutani
A possible quasi-particle picutre of the quark neat T_c and its effect on the dilepton production rate
We have investigated the quasi-particle picutre of the quark near T_c in terms of the spectral function and the pole structure of the propagator. Now we study the effect of the novel spectral property found there on the dilepton production rate using a Yukawa model. In this report, we show the numerical results and its physical interpretation.

U. Mosel
asdasas

M. Nahrgang
asdasas

T. Nayak
asdasas

R. Neufeld
asdasas

C. Nonaka
Hydrodynamic expansion with the QCD critical point in heavy ion collisions
Using a combined fully three-dimensional macroscopic/microscopic transport approach (3D hydro + UrQMD model), we discuss the existence of the QCD critical point and how to find consequence of it in relativistic heavy ion collisions.

G. Odyniec
asdasas

K. Rajagopal
asdasdas
asdasdasdadad

J. Randrup
asdasdas
asdasdasdadad

C. Ratti
Phases of QCD, Polyakov loop and quasiparticles
We investigate the QCD phase diagram and thermodynamics in the framework of the PNJL model, which incorporates both the chiral and the deconfinement phase transition. The position of the critical point is discussed, including its dependence on the degrees of freedom involved in the system.

K. Redlich
asdasas

S. Roessner
The interplay of flavour- and Polyakov-loop- degrees of freedom --- A PNJL model analysis
Flavour dependent quark number susceptibilities are considered to be a sensitive probe of the QCD thermodynamics around the chiral and deconfinement transitions. We point out that isovector susceptibilities are influenced by the $C$-odd combination $\langle \Phi^*-\Phi \rangle$ of the Polyakov loop. The mixing effects of colour and flavour are investigated using a 2-flavour Polyakov loop extended Nambu and Jona-Lasinio (PNJL) model. Perturbations induced by the difference of $\langle \Phi^* \rangle$ and $\langle \Phi \rangle$ at finite quark chemical potential are systematically implemented in the model. The applied perturbative approach allows to demonstrate the origin of the colour-flavour interrelation. We study the influence of the Polyakov loop effective potential on the colour and flavour mixing strength and discuss its effects on the up-down quark number susceptibility $\chi_{ud}$.

T. Schaefer
The Phase Diagram of QCD at finite baryon density

T. Schuster
Energy and system size dependence of fluctuations: NA49 results and NA61 plans
Measurements of the event-by-event fluctuations of hadrons produced in heavy-ion collisions are predicted to convey signals of the phase transition between hadron gas and quark-gluon plasma. In particular, they may help to learn about the nature of the transition and thus provide evidence for the existence of the critical point of strongly interacting matter. In the NA49 experiment, hadron production in central Pb+Pb collisions in the CERN-SPS energy range (6.1 < sqrt(s_NN) < 17.2 GeV) has been studied, and the fluctuations of different quantities were extracted. Multiplicity, net charge, mean transverse momentum fluctuations and the balance function show no significant energy dependence. In contrast, the dynamical fluctuations of the K/pi ratio rise towards low SPS energies, a behavior that is not described by the string-hadronic model UrQMD and that was proposed as a signal for the onset of deconfinement. Furthermore, the dependence of fluctuations on the size of the colliding system has been studied in peripheral Pb+Pb collisions at sqrt(s_NN) = 17.2 GeV. An enhancement of multiplicity fluctuations was observed in peripheral collisions the cause of which is still a subject of discussion. Together with indications for the onset of deconfinement seen in the yields and spectra of inclusive hadron production, the fluctuation results of the NA49 energy and system size scan motivate a new ion physics program at the CERN-SPS: NA61 (SHINE). The status and plans of the NA61 collaboration will be presented: starting from 2009, hadronic collisions will be studied in a finely grained energy and system size scan with the aim to further investigate the onset of deconfinement and to find a signature of the critical point.

E. Shuryak
asdasas

P. Sorensen
asdasas

P. Stankus
Critical Point Searches at Full RHIC Energy
Matter created at mid-rapidities in A+A collisions at full RHIC energies is thought to exhibit a very low baryon chemical potential. The most-often-mentioned approach to accessing other regions of the (T,\mu_B) plane is to examine A+A collisions at lower beam energies. However, there are a number of practical technical drawbacks to running A+A collisions at low energies in RHIC, particularly in luminosity and triggering. We will discuss how well the (T,\mu_B) plane can be explored while remaining at full (or near-full) RHIC energy and instead (i) varying the rapidity range of observations, (ii) changing the size of the colliding nuclei, and (iii) allowing for asymmetric ion collisions.

G. Stephens
asdasdas

H. Stoecker
asdasas

J. Stroth
asdasas

M. Tachibana
Spectral Continuity of Hadrons in Dense QCD
The vector mesons in three-flavor quark matter with chiral and diquark condensates are studied using the in-medium QCD sum rules. The diquark condensate leads to a mass splitting between the flavor-octet and flavor-singlet channels. At high density, the singlet vector meson disappears from the low-energy spectrum, while the octet vector mesons survive as light excitations with a mass comparable to the fermion gap. A possible connection between the light gluonic modes and the flavor-octet vector mesons at high density is also discussed.

J. Verbaarschot
Phase of the Fermion Determinand and the Phase Diagram of QCD
The phase of the fermion determinant has a strong effect on physical observables, and even though it severely impedes computations, there is no choice but to take it into account. The physics of the average phase factor is explained in terms of the ratio of the QCD partition function and the phase quenched QCD partition function. Using chiral perturbation theory we obtain the volume dependence of the average phase factor in the chemical potential-temperature plane. These results are used to determine regions of the phase diagram where lattice QCD can be simulated reliably. We also find an analytical expression for the distribution of the phase as a function of the chemical potential. Comparisons with lattice results are made. In the microscopic limit our results reduce to the random matrix expression for the average phase factor. Singularities that occur in the quenched approximation are discussed.

G. Westfall
asdasas

N. Xu
asdasas

Z. Zhang
Another chiral critical end-point induced by neutral color superconductivity
We investigate the effect of the electric charge neutrality in $\beta$-equilibrium on the chiral phase transition by solving the chiral and diquark condensates in the two-flavor Nambu--Jona-Lasinio model. We demonstrate that the electric charge neutrality plays a similar role as the repulsive vector interaction on the chiral phase transition, which weakens the first-order chiral phase transition. The important feature is that the effect of the neutrality is temperature dependent: The first-order chiral phase transition at high density is not affected at high temperatures where the diquark condensate melts. The chiral phase transition could be second-order at intermediate temperatures when the diquark effects surpass the chiral dynamics, while the first-order transition may survive at low temperatures. The number of the chiral critical end-points can thus vary from zero to three depending on the relative strength of the chiral and diquark couplings. We systematically study the possibility of the multi-end-point structure of the QCD phase diagram.