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We report on a continuum extrapolated result (arXiv:1309.5258) for the equation of state (EoS) of QCD with $N_f=2+1$ dynamical quark flavors and discuss preliminary results obtained with an additional dynamical charm quark ($N_f=2+1+1$). For all our final results, the systematics are controlled, quark masses are set to their physical values, and the continuum limit is taken using at least three lattice spacings corresponding to temporal extents up to $N_t=16$.
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The QCD transition is studied on lattices up to $N_t=16$. The chiral condensate is presented as a function of the temperature, and the corresponding transition temperature is extracted. The equation of state is determined on lattices with $N_t=6,8,10$ and at some temperature values with $N_t=12$. The pressure and the trace anomaly are presented as functions of the temperature in the range 100 ...1000 MeV . Using the same configurations we determine the continuum extrapolated phase diagram of QCD on the $mu-T$ plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility.
It has proven a significant challenge to experiment and phenomenology to extract precise values of the nucleon sigma terms. This difficulty opens the window for lattice QCD simulations to lead the field in resolving this aspect of nucleon structure. Here we report on recent advances in the extraction of nucleon sigma terms in lattice QCD. In particular, the strangeness component is now being resolved to a precision that far surpasses best phenomenological estimates.
We study the effects of the addition of the charm quark on the QCD equation of state at zero and nonzero chemical potential on lattices with $N_t=6$. Our ensembles are quenched with respect to charm and the charm quark is a valence staggered quark. Along the trajectory of constant physics the ratio $m_s/m_c$ is kept constant after tuning the charm quark mass at a lattice spacing of about 0.09 fm. We find that the charm quark has a significant contribution to the equation of state at zero chemical potential already at temperatures between about $1.2T_c$ and $2T_c$. The additional contribution at nonzero chemical potential vanishes within the current statistical uncertainty.
We present an N_t=4 lattice study for the equation of state of 2+1 flavour staggered, dynamical QCD at finite temperature and chemical potential. We use the overlap improving multi-parameter reweighting technique to extend the equation of state for non-vanishing chemical potentials. The results are obtained on the line of constant physics and our physical parameters extend in temperature and baryon chemical potential upto approx 500-600 MeV.
We present our most recent investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement [JHEP 1009:073, 2010]. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices ($N_t$=16) and we work again with physical quark masses. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum in these analytic calculations. A comparison with the results of the hotQCD collaboration is also discussed.
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