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The present paper concludes our investigation on the QCD equation of state with 2+1 staggered flavors and one-link stout improvement. We extend our previous study [JHEP 0601:089 (2006)] by choosing even finer lattices. Lattices with $N_t=6,8$ and 10 are used, and the continuum limit is approached by checking the results at $N_t=12$. A Symanzik improved gauge and a stout-link improved staggered fermion action is utilized. We use physical quark masses, that is, for the lightest staggered pions and kaons we fix the $m_\pi/f_K$ and $m_K/f_K$ ratios to their experimental values. The pressure, the interaction measure, the energy and entropy density and the speed of sound are presented as functions of the temperature in the range $100 ...1000 \textmd{MeV}$. We give estimates for the pion mass dependence and for the contribution of the charm quark. We compare our data to the equation of state obtained by the "hotQCD" collaboration.Comment: Minor changes: Figure 1 added; Figure 15, Figure 17 and Table 5 changed. Accepted for publication in JHE

Prethermalization of the equation of state and the kinetic temperature to their equilibrium values occurs on time scales dramatically shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collisions of heavy nuclei or other nonequilibrium phenomena in complex quantum and classical many body systems. We also compare the chemical equilibration time with other characteristic time scales.

We extend our previous study [Phys. Lett. B643 (2006) 46] of the crossover temperatures (T c ) of QCD. We improve our zero temperature analysis by using physical quark masses and finer lattices. In addition to the kaon decay constant used for scale setting we determine four quantities (masses of the Ω baryon, K * (892) and φ(1020) mesons and the pion decay constant) which are found to agree with experiment. This implies that -independently of which of these quantities is used to set the overall scale-the same results are obtained within a few percent. At finite temperature we use finer lattices down to a < ∼ 0.1 fm (N t = 12 and N t = 16 at one point). Our new results confirm completely our previous findings. We compare the results with those of the 'hotQCD' collaboration.

The present paper concludes our investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement. 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. The new results on this broad cross-over are in complete agreement with our earlier ones. We compare our findings with the published results of the hotQCD collaboration. 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. The findings of the hotQCD collaboration can be recovered by using a distorted spectrum which takes into account lattice discretization artifacts and heavier than physical quark masses. This analysis provides a simple explanation for the observed discrepancy in the transition temperatures between our and the hotQCD collaborations.

The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically different universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of 300 kilo-electron volts, which is greater than 0 by 5 standard deviations. We also determine the splittings in the Σ, Ξ, D, and Ξcc isospin multiplets, exceeding in some cases the precision of experimental measurements.

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