Table of contents

The Extreme QCD 2012 conference, held at the George Washington University in August 2012, celebrated the 10th event in the series. It has been held annually since 2003 at different locations: San Carlos (2011), Bad Honnef (2010), Seoul (2009), Raleigh (2008), Rome (2007), Brookhaven (2006), Swansea (2005), Argonne (2004), and Nara (2003).

As usual, it was a very productive and inspiring meeting that brought together experts in the field of finite-temperature QCD, both theoretical and experimental. On the experimental side, we heard about recent results from major experiments, such as PHENIX and STAR at Brookhaven National Laboratory, ALICE and CMS at CERN, and also about the constraints on the QCD phase diagram coming from astronomical observations of one of the largest laboratories one can imagine, neutron stars. The theoretical contributions covered a wide range of topics, including QCD thermodynamics at zero and finite chemical potential, new ideas to overcome the sign problem in the latter case, fluctuations of conserved charges and how they allow one to connect calculations in lattice QCD with experimentally measured quantities, finite-temperature behavior of theories with many flavors of fermions, properties and the fate of heavy quarkonium states in the quark-gluon plasma, and many others.

The participants took the time to write up and revise their contributions and submit them for publication in these proceedings. Thanks to their efforts, we have now a good record of the ideas presented and discussed during the workshop. We hope that this will serve both as a reminder and as a reference for the participants and for other researchers interested in the physics of nuclear matter at high temperatures and density. To preserve the atmosphere of the event the contributions are ordered in the same way as the talks at the conference.

We are honored to have helped organize the 10th meeting in this series, a milestone that reflects the lasting interest in this research area and the steady progress in resolving the outstanding issues. Many challenges remain and we are confident that this series will continue well into the future. Next year, the meeting will be organized at the Albert Einstein Center for Fundamental Physics at the University of Bern. We expect to have another interesting and lively meeting and look forward to meeting you there.

February 23, 2013 Andrei Alexandru Alexei Bazavov Keh-Fei Liu

I summarize some constraints on the physics of neutron stars arising from X-ray observations of the surfaces of neutron stars, focusing on using models of low-magnetic-field neutron star atmospheres to interpret their X-ray spectra. I discuss observations of spectral lines, pulsation profiles, X-ray bursts, radius measurements of transiently accreting neutron stars in quiescence, crust and core cooling measurements of transiently accreting neutron stars, and cooling of young neutron stars. These observations have constrained the neutron star mass and radius (and thus the internal composition, and dense matter equation of state), the superfluidity and neutrino emissivity properties of the core, and the composition and superfluid state of the crust.

The three Υ states can be separated using the CMS experimental apparatus via their dimuon decays in both pp and heavy-ion collisions. A suppression of the Υ(1S), Υ(2S) and Υ(3S) mesons is observed in PbPb collisions at compared to the yield in pp collisions scaled by the number of inelastic nucleon-nucleon collisions. Furthermore, a suppression of the excited Υ states has been measured with respect to the Υ ground state, expressed as a double ratio [Υ(nS)/Υ(1S)]_PbPb / [Υ(nS)/Υ(1S)]_pp with n = 2, 3, and 2 + 3. The centrality dependence of the double ratio, as well as the nuclear modification factors (R_AA) of the Υ(1S) and Υ(2S) states are presented, based on the analysis of the full data sample collected during the 2011 PbPb run and the 2010 pp run, which corresponds to an integrated luminosity of 150 μb⁻¹ and 231 nb⁻¹ respectively. The three Υ states suppression pattern is ordered as

We discuss different static quark correlators, including Wilson loops in 2+1 flavor QCD at non-zero temperature and their relation to in-medium quarkonium properties. We present lattice results on static correlation functions obtained with highly improved staggered fermion action and their implications for potential models.

We review some recent results about the exploration of strong interactions in presence of external background fields by means of lattice QCD simulations. We discuss in particular studies concerning the influence of the external fields on the non-perturbative properties of the QCD vacuum and of the QCD phase diagram.

We model magnetars as hybrid stars, which have a core of quark matter surrounded by hadronic matter. For this purpose, we use an extended version of the SU(3) non-linear realization of the sigma model in which the degrees of freedom change naturally from hadrons to quarks as the temperature/density increases. The presence of a variable magnetic field allows us to study in detail the influence of Landau quantization and the anomalous magnetic moment on the particle population of the star, more precisely on particles with different spin projections. This allows us to calculate the polarization of the system throughout different phases of the star, hadronic, quark and also a mixed phase.

I present a simple matrix model for the deconfined phase of SU(N) theories at temperatures just above T_c. The model is designed to reproduce the anomaly, in particular the flatness of (e − 3p)/T² above ∼ 1.2T_c observed by lattice simulations with up to six colors. Furthermore, it predicts the existence of an adjoint Higgs phase where the masses of diagonal and off-diagonal gluons split and that the phase transition of SU(N) with three or more colors, and for exceptional groups with a trivial center such as G(2), is generically of first order. For G(2) gauge group, a small value of the Polyakov loop at T⁻_c can be obtained with a non-perturbative potential summed over the roots of SU(7) rather than G(2), which implements the principle of maximal eigenvalue repulsion.

By using the lattice Monte-Carlo simulation, we investigate the finite temperature chiral phase transition in color SU(3) gauge theories with various species of fundamental fermions, and discuss the signals of the (pre-)conformality at large N_f (number of flavors) via their comparisons. With increasing N_f, we confirm stronger fermion screening which results from a larger fermion multiplicity. We investigate a finite T step-scaling which is attributed to the uniqueness of the critical temperature (T_c) at each N_f, then the vanishing step-scaling signals the emergence of the conformality around N*_f ∼ 10−12. Further, motivated by the recent functional renormalization group analyses, we examine the N_f dependence of T_c, whose vanishing behavior indicates that the conformal phase sets in around N*_f ∼ 9 − 10.

Because of the sign problem, it is difficult to study finite-density QCD. In order to circumvent the sign problem, we prove that the phase-quenched approximation is exact to O(N_f/N_c) for any physical observables in a certain region of the phase diagram. We also find a quantitative evidence for the validity of the phase quenching from existing lattice QCD results at N_c = 3. Our results show that the phase-quenched approximation is good already at N_c = 3, and the 1/N_c correction can be incorporated by the phase reweighting method without suffering from a severe overlap problem. The same equivalence holds in effective models and holographic models. It gives us a theoretical understanding of the empirical facts (exactness of the phase quenching in the mean-field approximation) found in model calculations.

The early thermalization is crucial to the quark-gluon plasma as a perfect liquid and results from many-body scattering. We calculate squared amplitudes for elastic parton-parton-parton scattering in perturbative QCD. Transport equations with the squared amplitudes are established and solved to obtain the thermalization time of initially produced quark-gluon matter and the initial temperature of quark-gluon plasma. We find that the thermalization times of quark matter and gluon matter are different.

We discuss some issues in our previous works in quantum kinetic approach to chiral anomaly, chiral magnetic and vortical effects. The Wigner function for massless fermions in a constant background electromagnetic field is solved in a power expansion. Chiral magnetic and vortical effects emerge naturally. The conservation equations with anomaly are derived in details.

The quark-gluon plasma behaves as a relativistic viscous fluid in high-energy heavy ion collisions. I develop a causal dissipative hydrodynamic model at finite baryon density for RHIC and LHC to estimate the net baryon rapidity distribution. The net baryon number is found to be carried to forward rapidity by the flow, effectively enhancing the transparency of the collisions. This suggests that the energy available for the production of a hot medium could be larger than that naively implied from experimental data. Also the distribution can be sensitive to baryon dissipation as much as to shear and bulk viscosity.

Recent results on fluctuations of conserved charges are reviewed and compared between different collaborations, where good agreement is found. Uncertainties of the lattice QCD simulations involved are discussed. Dedicated simulations addressing some of these uncertainties are shown, which indicate that, in the parameter regions studied so far, they are under control.

After briefly reviewing recent progress by the HotQCD collaboration in studying the 2+1 flavor QCD equation of state, we will focus on results on fluctuations of conserved charges by the BNL-Bielefeld and HotQCD collaborations. Higher order cumulants of the net-charge distributions are increasingly dominated by a universal scaling behavior, which arises due to a critical point of QCD in the chiral limit. Considering cumulants up to the 6^th order, we observe that they generically behave as expected from universal scaling laws, which is quite different from cumulants calculated within the hadron resonance gas model. Taking ratios of these cumulants, we obtain volume independent results that can be compared to the experimental measurements. We will argue that the freeze-out chemical potentials and the freeze-out temperature, usually obtained by a HRG model fit to the measured hadronic yields, can also be obtained in a model independent way from ab-initio lattice QCD calculations by utilizing observables related to conserved charge fluctuations. Further, we will show that the freeze-out strangeness and electric charge chemical potentials can be fixed by imposing strangeness neutrality and isospin asymmetry constraints in the lattice QCD calculations, in order to accommodate conditions met in heavy ion collisions. All results have been obtained with the highly improved staggered quark action (HISQ) and almost physical quark masses on lattices with temporal extent of N_τ = 6, 8, 10, 12.

We study the temperature dependence of bottomonium for temperatures in the range 0.4T_e < T < 2.1T_c, using non-relativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for N_f = 2 light flavors. We consider the behaviour of the correlators in Euclidean space, we analyze the associated spectral functions and we study the dependence on the momentum. Our results are amenable to a successful comparison with effective field theories. They help build a coherent picture of the behaviour of bottomonium in the plasma, consistent which the current LHC results.

I review recent calculations of the suppression of bottomonium states in heavy ion collisions. A non-relativistic potential is used which is complex valued. This allows one to extract the binding energies and decay widths of the ground and excited states of bottomonium as a function of the typical plasma particle momentum and momentum-space anisotropy. The decay widths determined are used as input and integrated over space-time taking into account the dynamical evolution of the typical particle momentum and momentum-space anisotropy. The suppression of Υ(1s), Υ(2s), Υ(3s), χ_b1, and χ_b2 is obtained as a function of centrality, rapidity, and transverse momentum. The obtained results are compared with data from the STAR and CMS collaborations.

We present preliminary results for the curvature of the pseudocritical line and susceptibilities in N_f = 2 + 1 flavor QCD. The computations are carried out on lattice sizes of 16³ × 4, at matching parameters of early work of the Bielefeld group. Emphasis is placed on the control of systematic errors, by cross-validating results obtained by use of the Taylor expansion and measurements at imaginary chemical potential. To this end, we generalize the magnetic equation of state to the analysis of the number density, and we extend it to imaginary values of the chemical potential.

We show, in a model-independent manner, that the QCD critical point can appear only inside the pion condensation phase of the phase-quenched QCD as long as the contribution of flavor-disconnected diagrams is negligible. The sign problem is known to be maximally severe in this region, implying that the QCD critical point is reachable by the present lattice QCD techniques only if there is an enhancement of the flavor-disconnected contribution at finite baryon chemical potential.

The study of the QCD chiral phase transition on the lattice has been hampered in the past by the lack of a chiral-invariant fermion formulation. Only recently has it become possible to perform fully dynamical simulations with chiral formulations such as domain-wall and overlap fermions. Here we present results for various chiral observables at finite temperature that were obtained using domain-wall fermions. We also present results showing that the axial anomaly is still present even above the chiral phase transition. Lastly, we show our results for the Dirac spectrum at finite temperature and speculate on the mechanism of U(1)_A breaking beyond the chiral phase transition.

A new lattice action is proposed for the overlap Dirac matrix with nonzero chemical potential. It is shown to preserve the full chiral invariance for all values of lattice spacing exactly. It is further demonstrated to arise in the domain wall formalism by coupling the chemical potential only to the physically relevant wall modes.

I present recent results from lattice simulations of SU(2) gauge theory with N_f = 2 Wilson quark flavors, at non-zero quark chemical potential μ. The thermodynamic equation of state is discussed along with the nature of the high density matter which forms. It is conjectured that deconfinement may mean different things for bulk and Fermi surface phenomena.

Recent measurements of the azimuthal anisotropy of direct photons in heavy-ion collisions at the energies of RHIC showed that it is of the same order as the hadronic one. This finding appears to contradict the expected dominance of photon production from a quark-gluon plasma at an early stage of a heavy-ion collision. A possible explanation of the strong azimuthal anisotropy of the photons, given recently, is based on the presence of a large magnetic field in the early phase of a collision. In this talk, we consider a novel photon production mechanism stemming from the conformal anomaly of QCDxQED and the existence of strong (electro)magnetic fields in heavy ion collisions. Using the hydrodynamical description of the bulk modes of QCD plasma, we show that this mechanism leads to the photon production yield that is comparable to the yield from conventional sources. The comparison of the results to the data from the PHENIX collaboration, show that this mechanism might be the most responsible for the observed azimuthal anisotropy of photons.

Major nonperturbative phenomena in QCD – confinement and chiral symmetry breaking – are known to be related with certain topological objects. Recent lattice advances into the domain of many N_f = O(10) fermion flavors have shown that both phase transitions had shifted in this case to much stronger coupling. We discuss confinement in terms of monopole Bose condensation, and discuss how it is affected by fermions "riding" on the monopoles, ending with the N_f dependence of the critical line. Chiral symmetry breaking is discussed in terms of the (anti)selfdual dyons, the instanton constituents. The fermionic zero modes of those have a different meaning and lead to strong interaction between dyons and antidyons. We report some qualitative consequences of this theory and also some information about our first direct numerical study of the dyonic ensemble, in respect to both chiral symmetry breaking and confinement (via back reaction to the holonomy potential).

At nonzero quark chemical potential lattice QCD simulations with dynamical quarks are hampered by the sign problem caused by the complex fermion determinant. In this talk we discuss the relation between QCD and random matrix theory and present a novel solution to the sign problem in dynamical random matrix simulations. The sign problem is solved by gathering matrices in subsets, whose sums of complex determinants are real and positive. Markov chains of relevant subsets were generated in Monte Carlo simulations and various observables, like the chiral condensate and quark number, were accurately computed. The subset formula, which is at the basis of the positivity proof for the subset weights, also provides a simple solution to the Silver Blaze puzzle.

Lattice four-fermion models containing N flavors of staggered fermions, that are invariant under Z₂ and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. In this talk, we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.

Recently, we have introduced a novel approach to deal with the sign problem that prevents the Monte Carlo simulations of a class of quantum field theories (QFTs). The idea is to formulate the QFT on a Lefschetz thimble. Here we review the formulation of our approach and describe the Aurora Monte Carlo algorithm that we are currently testing on a scalar field theory with a sign problem.

Systems of non-zero isospin chemical potential are studied from a canonical approach by computing correlation functions with the quantum numbers of N π⁺'s (C_Nπ). In order to reduce the number of contractions required in calculating C_Nπ for a large N in the Wick's theorem, we constructed a few new algorithms. With these new algorithms, systems with isospin charge up to 72 are investigated on three anisotropic gauge ensembles with a pion mass of 390 MeV, and with lattice spatial extents L ∼ 2.0, 2.5, 3.0 fm. The largest isospin density of ρ_I ≈ 9 fm⁻³ is achieved in the smallest volume, and the QCD phase diagram is investigated at a fixed low temperature at varying isospin chemical potentials, m_π ≤ μ_I ≤ 4.5 m_π. By investigating the behaviour of the extracted energy density of the system at different isospin chemical potentials, we numerically identified the conjectured transition to a Bose-Einstein condensation state at μ_I ≥ m_π.

I report on the current status of QCD phase diagram at vanishing baryon density. I focus on the QCD phase diagram with three degenerate quark flavor using Highly Improved Staggered Quarks on N_T = 6 lattices. No evidence of a first order phase transition in the pion mass window of 80 ≲ m_π ≲ 230 MeV is found. The pion mass at the critical point where the chiral first order phase transition ends is estimated to be m_π^c ≲ 45 MeV.

In this note we summarize the results from a longer article on obtaining the QCD phase diagram as a function of the temperature and chemical potential at large N_c and large N_f in the weak coupling limit λ → 0, and the strong coupling limit λ → ∞. The weak coupling phase diagram is obtained from the Polyakov line order parameter, and the quark number, calculated using 1-loop perturbation theory for QCD formulated on S¹ × S³. The strong coupling phase diagram is obtained from the same observables calculated at leading order in the lattice strong coupling and hopping parameter expansions. We show that the matrix models in these two limits agree at temperatures and chemical potentials which are not too high, such that observables in the strongly-coupled theory can be obtained from the observables in the weakly-coupled theory, and vice versa, using a simple transformation of variables.

We propose a simple model with the ₃ symmetry in order to answer whether the symmetry is a good concept in QCD with light quark mass. The model is constructed by imposing the flavor-dependent twisted boundary condition (TBC) on the three-flavor Polyakov-loop extended Nambu-Jona-Lasinio model. In the model, the ₃ symmetry is preserved below some temperature T_c, but spontaneously broken above T_c. Dynamics of the simple model is similar to that of the original PNJL model without the TBC, indicating that the ₃ symmetry is a good concept. We also investigate the interplay between the ₃ symmetry and the emergence of the quarkyonic phase.

We suggest a novel charge structure inside nucleons in electromagnetic field due to the chiral anomaly. We use Skyrmions, where nucleons appear as solitons of mesons, to calculate the charge distributions in a single nucleon and find that an additional non-integer charge proportional to the magnetic field would be produced. This might look surprising, but the magnitude of the induced charge is evaluated to be tiny enough to have not been observed yet.

We propose a practical way of circumventing the sign problem in lattice QCD simulations with the theta-vacuum term. This method is the reweighting method for QCD Lagrangian after the U_A(1) transformation. In the Lagrangian, the P-odd mass term as a cause of the sign problem is minimized. In order to find out a good reference system in the reweighting method, we estimate the average reweighting factor by using the two-flavor NJL model and eventually find a good reference system.

Due to the presence of light pions in the theory, lattice QCD at finite densities suffers from issues with noise in both grand canonical and canonical formulations. We study two different formulations of the Nambu-Jona-Lasinio model reduced to 2+1 dimensions at large N, where N is the number of flavors. At finite chemical potential one formulation has a severe sign problem and a fermion correlator which displays a broad probability distribution with small mean. In the other we find no sign problem and a distribution amenable to the cumulant expansion techniques developed in Ref. [1, 2, 3].

With combined hopping parameter and strong coupling expansions, we calculate a dimensionally reduced Polyakov-loop effective theory valid for heavy quarks at nonzero temperature and arbitrary chemical potential. We numerically compute the critical endpoint of the deconfinement transition as a function of quark masses and number of flavours. We also investigate the applicability of the model to the low-T and high density region, specifically in terms of baryon condensation phenomena.

It has recently been found that dynamics of pure glue QCD supports the low energy band of Dirac modes with local chiral properties qualitatively different from that of a bulk: while bulk modes suppress chirality relative to statistical independence between left and right, the band modes enhance it. The width of such chirally polarized zone – chiral polarization scale ∧_ch – has been shown to be finite in the continuum limit at fixed physical volume. Here we present evidence that ∧_ch remains non-zero also in the infinite volume, and is therefore a dynamical scale in the theory. Our experiments in N_f = 2+1 QCD support the proposition that the same holds in the massless limit, connecting ∧_ch to spontaneous chiral symmetry breaking. In addition, our results suggest that thermal agitation in quenched QCD destroys both chiral polarization and condensation of Dirac modes at the same temperature T_ch > T_c.

Acknowledgements This conference would not have been possible without the generous support from Brookhaven National Laboratory and the George Washington University INS and IMPACT institutes, Columbian College of Arts and Sciences, the Office of Vice-President for Research, and the Department of Physics. We thank them wholeheartedly.

We are also very grateful for the support of our colleagues on the local organizing committee, Walter Freeman and Frank Lee, and on the International Advisory Committee: Simon Hands, Tetsuo Hatsuda, Frithjof Karsch, Maria Paola Lombardo, Tereza Mendes, Atsushi Nakamura, Owe Philipsen, Claudia Ratti, Paul Romatschke, Misha Stephanov, and Nu Xu.

List of participants

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.