We study the profiles of the flux tube between a static quark and an antiquark in quenched SU(2) lattice gauge theory at temperatures around the deconfinement phase transition. The physical width of the flux tube and the string tension have been determined from the transverse profiles and the potential, respectively. Exploiting the computational power of a GPU accelerator in our flux tube investigation, we achieve a much higher statistics through which we can increase the signal to noise ratio of our observables in the simulation. This has allowed to investigate larger lattices as well as larger separations between the quarks than in our previous work. The improved accuracy gives us better results for the width and the string tension. The physical width of the flux tube is increasing with the temperature up to around Tc while keeping its increasing dependence on the separation. The string tension results have been compared for two different sizes of the lattice. As the lattice becomes larger and finer together with the precision improved, the temperature dependent string tension tends to have smaller value than the previous one.

We present results for screening masses of light and strange mesons in 2+1 flavour QCD using improved (p4fat3) staggered fermions on 6x24^3 lattices. We have studied the screening masses of scalar, pseudo-scalar, vector and axial-vector mesons along the line of constant physics, determined by a pion mass ~220 MeV and a kaon mass ~500 MeV. In order to investigate the cut-off and volume dependencies we have also performed studies of the meson screening correlators in the non-interacting theory using the p4 and the standard staggered discretizations.

The region of the Columbia plot with two light quark flavors is not yet conclusively understood. Non-perturbative effects, e.g. the magnitude of the anomalous U(1) axial symmetry breaking, decides on the nature of the phase transition in this region. We report on our study of this region of the Columbia plot using lattice techniques. We use gauge field ensembles generated within the Highly Improved Staggered Quark discretization scheme, with the strange quark mass fixed at its physical value and the light quark mass varied such that $m_l=m_s/27$ and $m_s/40$, where $m_l=m_s/27$ corresponds to the physical light quark mass. We study the eigenvalue spectrum of QCD using the overlap Dirac operator on these gauge field ensembles at finite temperature around the chiral transition temperature $T_c$, as the light quark masses approach the chiral limit, and infer about the fate of the anomalous $U_A(1)$ symmetry breaking.

We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon ($B$), strangeness ($S$), electric charge ($Q$), and isospin ($I$) chemical potentials $\mu_{X=B,Q,S,I}$. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as $ T_c(\mu_X) = T_c(0) \left[ 1 -\kappa_2^{X}(\mu_{X}/T_c(0))^2 -\kappa_4^{X}(\mu_{X}/T_c(0))^4 \right] $, we determined $\kappa_2^X$ and $\kappa_4^X$ from Taylor expansions of chiral observables in $\mu_X$. We obtained a precise result for $T_c(0)=(156.5\pm1.5)\;\mathrm{MeV}$. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., $\mu_{S}(T,\mu_{B})$ and $\mu_{Q}(T,\mu_{B})$ fixed from strangeness-neutrality and isospin-imbalance, we found $\kappa_2^B=0.012(4)$ and $\kappa_4^B=0.000(4)$. For $\mu_{B}\lesssim300\;\mathrm{MeV}$, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of $0.42(6)\;\mathrm{GeV/fm}^3$ and constant entropy density of $3.7(5)\;\mathrm{fm}^{-3}$.

We study the profiles of the flux tube between a static quark and an antiquark in quenched SU(2) lattice gauge theory at temperatures around the deconfinement phase transition. The physical width of the flux tube and the string tension have been determined from the transverse profiles and the q (q) over bar potential, respectively. Exploiting the computational power of a GPU accelerator in our flux tube investigation, we achieve much higher statistics through which we can increase the signal to noise ratio of our observables in the simulation. This has allowed the investigation of larger lattices as well as larger separations between the quarks than in our previous work. The improved accuracy gives us better results for the width and the string tension. The physical width of the flux tube increases with the temperature up to around T-c while keeping its increasing dependence on the q (q) over bar separation. The string tension results are compared for two different sizes of the lattice. As the lattice becomes larger and finer together with the improved precision, the temperature dependent string tension tends to have a smaller value than the previous one.

We present results for the ratios of mean (MB), variance (sigma(2)(B)), skewness (SB) and kurtosis(kappa B) of net baryon-number fluctuations obtained in lattice QCD calculations with physical values of light and strange quark masses. Using next-to-leading order Taylor expansions in baryon chemical potential we find that qualitative features of these ratios closely resemble the corresponding experimentally measured cumulant ratios of net proton-number fluctuations for beam energies down to root s(NN) >= 19.6 GeV. We show that the difference in cumulant ratios for the mean net baryon-number, M-B/sigma(2)(B) = chi(1)(B) (T, mu(B)) / chi(2)(B) (T, mu(B)), and the normalized skewness, S-B sigma(B) = chi(B)(3) (T, mu(B)) / chi(B)(2) (T, mu B), naturally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, S-B sigma(3)(B) / M-B = chi(B)(3) (T, mu(B)) / chi(B)(1) (T, mu(B)) and kappa(B)sigma(2)(B) = chi(B)(4) (T, mu(B)) /chi(B)(2) (T, mu(B)), valid at small values of the baryon chemical potential.

Recent results of the BNL-CCNU-Bielefeld collaboration on the Taylor expansion of the pressure up to sixth order in the baryon, strangeness and electric charge chemical potentials are presented, with the focus on the QCD equation of state. The calculations have been performed with the Highly Improved Staggered Quark action on lattices with aspect ratio $4$ and temporal extents ranging from $6$ to $16$, i.e. at four different values of the lattice spacing. The strange quark mass has been tuned to its physical value, and two ratios of the light to the strange mass, $m_l/m_s = 1/20$ and $1/27$ have been investigated. The comparison of sixth order Taylor expansion in the chemical potentials with fourth order ones shows that the truncation errors are small at least up to baryon chemical potential of $\mu_B/T \simeq 2$.

We calculated the QCD equation of state using Taylor expansions that include contributions from up to sixth order in the baryon strangeness and electric charge chemical potentials. Calculations have been performed with the Highly Improved Staggered Quark action in the temperature range T epsilon [135 MeV 330 MeV] using up to four different sets of lattice cutoffs corresponding to lattices of size N sigma 3x N tau with aspect ratio N sigma/N tau = 4 and N tau=6-16. The strange quark mass is tuned to its physical value and we use two strange to light quark mass ratios ms/ml = 20 and 27 which in the continuum limit correspond to a pion mass of about 160 and 140 MeV respectively. Sixth order results for Taylor expansion coefficients are used to estimate truncation errors of the fourth order expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature (mu(B) <= 2T). The fourth order equation of state thus is suitable for the modeling of dense matter created in heavy ion collisions with center of mass energies down to root SNN similar to 12 GeV. We provide a parametrization of basic thermodynamic quantities that can be readily used in hydrodynamic simulation codes. The results on up to sixth order expansion coefficients of bulk thermodynamics are used for the calculation of lines of constant pressure energy and entropy densities in the T mu(B) plane and are compared with the crossover line for the QCD chiral transition as well as ith xperimental results on freeze out parameters in heavy ion collisions. These coefficients also provide estimates for the location of a possible critical point. We argue that results on sixth order expansion coefficients disfavor the existence of a critical point in the QCD phase diagram for B= T <= 2 and T/Tc(mu(B) = 0) > 0.9.

We investigate the phase structure of QCD with three degenerate quark flavors as a function of the degenerate quark masses at vanishing baryon number density. We use the highly improved staggered quarks on lattices with temporal extent N-tau = 6 and perform calculations for six values of quark masses, which in the continuum limit correspond to pion masses in the range 80 MeV less than or similar to m(pi) less than or similar to 230 MeV. By analyzing the volume and temperature dependence of the chiral condensate and chiral susceptibility, we find no direct evidence for a first-order phase transition in this range of pion mass values. Relying on the universal scaling behaviors of the chiral observables near an anticipated chiral critical point, we estimate an upper bound for the critical pion mass, m(pi)(c) less than or similar to 50 MeV, below which a region of first-order chiral phase transition is favored.

The magnitude of the UA(1) symmetry breaking is expected to affect the nature of N f = 2 QCD chiral phase transition. The explicit breaking of chiral symmetry due to realistic light quark mass is small, so it is important to use chiral fermions on the lattice to understand the effect of UA(1) near the chiral crossover temperature, Tc. We report our latest results for the eigenvalue spectrum of 2+1 flavour QCD with dynamical Mobius domain wall fermions at finite temperature probed using the overlap operator on 323 × 8 lattice. We check how sensitive the low-lying eigenvalues are to the sea-light quark mass. We also present a comparison with the earlier independent results with domain wall fermions.

The nature of chiral phase transition for two flavor QCD is an interesting but unresolved problem. One of the most intriguing issues is whether or not the anomalous U(1) symmetry in the flavor sector is effectively restored along with the chiral symmetry. This may determine the universality class of the chiral phase transition. Since the physics near the chiral phase transition is essentially non-perturbative, we employ first principles lattice techniques to address this issue. We use overlap fermions, which have exact chiral symmetry on the lattice, to probe the anomalous U(1) symmetry violation of 2+1 flavor dynamical QCD configurations with domain wall fermions. The latter also optimally preserves chiral and flavor symmetries on the lattice, since it is known that the remnant chiral symmetry of the light quarks influences the scaling of the chiral condensate in the crossover transition region. We observe that the anomalous U(1) is not effectively restored in the chiral crossover region. We perform a systematic study of the finite size and cut-off effects since the signals of U(1) violation are sensitive to it. We also provide a glimpse of the microscopic topological structures of the QCD medium that are responsible for the strongly interacting nature of the quark gluon plasma phase. We study the effect of these microscopic constituents through our first calculations for the topological susceptibility of QCD at finite temperature, which could be a crucial input for the equation of state for anomalous hydrodynamics.

We discuss the next-to-leading order Taylor expansion of ratios of cumulants of net-baryon number fluctuations. We focus on the relation between the skewness ratio, S-B sigma(B) = chi(B)(3)/chi(B)(1) and the kurtosis ratio, KBol = chi(B)(4)/chi(B)(4). We show that differences in these two cumulant ratios are small for small values of the baryon chemical potential. The next-to-leading order correction to kappa(B)sigma(2)(B) however is approximately three times larger than that for S-B sigma(B). The former thus drops much more rapidly with increasing beam energy, root S-NN. We argue that these generic patterns are consistent with current data on cumulants of net-proton number fluctuations measured by the STAR Collaboration at root(SNN) >= 19.6 GeV.

We calculate the mean and variance of net-baryon number and net-electric charge distributions from quantum chromodynamics (QCD) using a next-to-leading order Taylor expansion in terms of temperature and chemical potentials. We compare these expansions with experimental data from STAR and PHENIX, determine the freeze-out temperature in the limit of vanishing baryon chemical potential, and, for the first time, constrain the curvature of the freeze-out line through a direct comparison between experimental data on net-charge fluctuations and a QCD calculation. We obtain a bound on the curvature coefficient, kappa(f)(2) < 0.011, that is compatible with lattice QCD results on the curvature of the QCD transition line.

We investigate the low-lying eigenmodes of the Dirac matrix with the aim to gain more insight into the temperature dependence of the anomalous U-A(1) symmetry in QCD. We use the overlap operator to probe dynamical QCD configurations generated with (2 + 1)-flavors of highly improved staggered quarks. We find no evidence of a gap opening up in the infrared region of the eigenvalue spectrum even at 1.5T(c), T-c being the chiral crossover temperature. Instead, we observe an accumulation of near-zero eigenmodes. We argue that these near-zero eigenmodes are primarily responsible for the anomalous breaking of the axial symmetry still being effective. At 1.5T(c), these near-zero eigenmodes remain localized and their distribution is consistent with the dilute instanton gas picture. At this temperature, the average size of the instantons is 0.223(8) fm and their density is 0.147(7) fm(-4).

Recent results obtained from numerical computations in lattice regularized QCD are summarized. The write-up of the talk concentrates on the liberation of strange quarks in the vicinity of the chiral QCD transition and on certain ratios of cumulants of net electric charge fluctuations which can be used to determine freeze-out parameters by a comparison of experimental data from heavy ion collisions with lattice QCD results.

A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, 4 E. Laermann, Y. Maezawa, Swagato Mukherjee, H. Ohno, 5 P. Petreczky, C. Schmidt, S. Sharma, W. Soeldner, and M. Wagner Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52240, USA Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany Physics Department, Indiana University, Bloomington, Indiana 47405, USA

In this project we study the effect of the $U_A(1)$ anomaly for (2+1)-flavour QCD at high temperature. We apply the overlap operator as a tool to probe the topological properties of gauge field configurations which have been generated within the Highly Improved Staggered Quark (HISQ) discretization scheme on lattices of size $32^3\times 8$ with $m_l/m_s=1/20$, commonly used for the study of QCD thermodynamics. Although we have at present, only results for one value of the quark masses and thus cannot monitor the change of the eigenvalue distributions with the light quark mass, the distribution of the low-lying eigenvalues of the overlap operator suggests that the $U_A(1)$ is not restored effectively even at 1.5 times the pseudo critical temperature. The corresponding low-lying eigenmodes show localization properties.

We present results on the thermodynamic and continuum limit of meson screening masses in the deconfined phase, using standard staggered and non-perturbatively clover-improved Wilson fermions in the quenched approximation with light quark masses. For two temperatures, 1.5 Tc and 3.0 Tc, it is found that on finite lattices screening masses differ between the actions. We study if both actions reproduce the same masses in the continuum by employing different methods of extrapolation to the thermodynamic and continuum limit.

An overview is presented of transverse momentum distributions of particles at the LHC using the Tsallis distribution.The use of a thermodynamically consistent form of this distribution leads to an excellent description of charged and identified particles.The values of the Tsallis parameter q are truly remarkably consistent.