Swagato Mukherjee

Chiral and deconfinement aspects of the QCD transition

We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2 + 1 flavors of quarks using the p4, asqtad, and HISQ/tree actions. Lattices with temporal extent N-tau = 6, 8, and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using O(N) scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is T-c = 154 +/- 9 MeV.

Equation of State for physical quark masses

We calculate the QCD equation of state for temperatures corresponding to the transition region with physical mass values for two degenerate light quark flavors and a strange quark using an improved staggered fermion action (p4-action) on lattices with temporal extent N{sub {tau}=}8. We compare our results with previous calculations performed at twice larger values of the light quark masses as well as with results obtained from a resonance gas model calculation. We also discuss the deconfining and chiral aspects of the QCD transition in terms of renormalized Polyakov loop, strangeness fluctuations, and subtracted chiral condensate. We show that compared to the calculations performed at twice larger value of the light quark mass the transition region shifts by about 5 MeV toward smaller temperatures.

Fluctuations and correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model

We calculate the quadratic fluctuations of net baryon number, electric charge and strangeness as well as correlations among these conserved charges in (2+1)-flavor lattice QCD at zero chemical potential. Results are obtained using calculations with tree level improved gauge and the highly improved staggered quark (HISQ) actions with almost physical light and strange quark masses at three different values of the lattice cut-off. Our choice of parameters corresponds to a value of 160 MeV for the lightest pseudo scalar Goldstone mass and a physical value of the kaon mass. The three diagonal charge susceptibilities and the correlations among conserved charges have been extrapolated to the continuum limit in the temperature interval 150 MeV <T < 250 MeV. We compare our results with the hadron resonance gas (HRG) model calculations and find agreement with HRG model results only for temperatures T<= 150 MeV. We observe significant deviations in the temperature range 160 MeV < T < 170 MeV and qualitative differences in the behavior of the three conserved charge sectors. At T < 160 MeV quadratic net baryon number fluctuations in QCD agree with HRG model calculations while, the net electric charge fluctuations in QCD are about 10% smaller and net strangeness fluctuations are about 20% larger. These findings are relevant to the discussion of freeze-out conditions in relativistic heavy ion collisions.

Phase boundary for the chiral transition in (2+1) -flavor QCD at small values of the chemical potential

We determine the chiral phase transition line in (2+1)-flavor QCD for small values of the light quark chemical potential. We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. To do so we extend earlier studies of the magnetic equation of state in (2+1)-flavor QCD to finer lattice spacings, aT = 1/8. We use these universal scaling properties of the chiral order parameter to extract the curvature of the transition line at two values of the cut-off, aT = 1/4 and 1/8. We find that cut-off effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain Tc(µq)/Tc(0) = 1 0.059(2)(4)(µq/T) 2 + O(µ 4).

QCD phase transition in a strong magnetic background

We investigate the properties of the deconfining/chiral restoring transition for two flavor QCD in presence of a uniform background magnetic field. We adopt a standard staggered discretization of the fermion action and a lattice spacing of the order of 0.3 fm. We explore different values of the bare quark mass, corresponding to pion masses in the range 200 - 480 MeV, and magnetic fields up to |e|B ~ 0.75 GeV^2. The deconfinement and chiral symmetry restoration temperatures remain compatible with each other and rise very slightly (< 2 % for our largest magnetic field) as a function of the magnetic field. On the other hand, the transition seems to become sharper as the magnetic field increases.

Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics

We present a determination of freeze-out conditions in heavy ion collisions based on ratios of cumulants of net electric charge fluctuations. These ratios can reliably be calculated in lattice QCD for a wide range of chemical potential values by using a next-to-leading order Taylor series expansion around the limit of vanishing baryon, electric charge and strangeness chemical potentials. From a computation of up to fourth order cumulants and charge correlations we first determine the strangeness and electric charge chemical potentials that characterize freeze-out conditions in a heavy ion collision and confirm that in the temperature range 150 MeV ≤ T ≤ 170 MeV the hadron resonance gas model provides good approximations for these parameters that agree with QCD calculations on the 5%-15% level. We then show that a comparison of lattice QCD results for ratios of up to third order cumulants of electric charge fluctuations with experimental results allows us to extract the freeze-out baryon chemical potential and the freeze-out temperature.

QCD Phase Transition with Chiral Quarks and Physical Quark Masses

Tanmoy Bhattacharya, Michael I. Buchoff, 3 Norman H. Christ, H.-T. Ding, Rajan Gupta, Chulwoo Jung, F. Karsch, 7 Zhongjie Lin, R. D. Mawhinney, Greg McGlynn, Swagato Mukherjee, David Murphy, P. Petreczky, Chris Schroeder, R A. Soltz, P. M. Vranas, and Hantao Yin Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA Physics Division, Lawrence Livermore National Laboratory, Livermore CA 94550, USA Institute for Nuclear Theory, Box 351550, Seattle, WA 98195-1550, USA Physics Department, Columbia University, New York, NY 10027, USA Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China Physics Department, Brookhaven National Laboratory,Upton, NY 11973, USA Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany

Thermodynamics of Strong-Interaction Matter from Lattice QCD

We review results from lattice QCD calculations on the thermodynamics of strong-interaction matter with emphasis on input these calculations can provide to the exploration of the phase diagram and properties of hot and dense matter created in heavy ion experiments. This review is organized in sections as follows: (1) Introduction, (2) QCD thermodynamics on the lattice, (3) QCD phase diagram at high temperature, (4) Bulk thermodynamics, (5) Fluctuations of conserved charges, (6) Transport properties, (7) Open heavy flavors and heavy quarkonia, (8) QCD in external magnetic fields, (9) Summary.

Magnetic equation of state in (2 + 1)-flavor QCD

A first study of critical behavior in the vicinity of the chiral phase transition of (2+1)-flavor QCD is presented. We analyze the quark mass and volume dependence of the chiral condensate and chiral susceptibilities in QCD with two degenerate light quark masses and a strange quark. The strange quark mass (m(s)) is chosen close to its physical value; the two degenerate light quark masses (m(l)) are varied in a wide range 1/80 < m(l)/m(s)< 2/5, where the smallest light quark mass value corresponds to a pseudoscalar Goldstone mass of about 75 MeV. All calculations are performed with staggered fermions on lattices with temporal extent N-tau=4. We show that numerical results are consistent with O(N) scaling in the chiral limit. We find that in the region of physical light quark mass values, m(l)/m(s)similar or equal to 1/20, the temperature and quark mass dependence of the chiral condensate is already dominated by universal properties of QCD that are encoded in the scaling function for the chiral order parameter, the magnetic equation of state. We also provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. At temperatures below, but close to the chiral phase transition at vanishing quark mass, this leads to a characteristic dependence of the light quark chiral condensate on the square root of the light quark mass.

Strangeness at high temperatures: from hadrons to quarks

Appropriate combinations of up to fourth order cumulants of net strangeness fluctuations and their correlations with net baryon number and electric charge fluctuations, obtained from lattice QCD calculations, have been used to probe the strangeness carrying degrees of freedom at high temperatures. For temperatures up to the chiral crossover, separate contributions of strange mesons and baryons can be well described by an uncorrelated gas of hadrons. Such a description breaks down in the chiral crossover region, suggesting that the deconfinement of strangeness takes place at the chiral crossover. On the other hand, the strangeness carrying degrees of freedom inside the quark gluon plasma can be described by a weakly interacting gas of quarks only for temperatures larger than twice the chiral crossover temperature. In the intermediate temperature window, these observables show considerably richer structures, indicative of the strongly interacting nature of the quark gluon plasma.