Journal Article•
Strangeness-Neutral Equation of State for QCD with a Critical Point
TL;DR: In this paper, a strangeness-neutral equation of state for QCD was proposed that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$B/T/T$$n.
Abstract: We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$\\mu _B/T$$
. It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trajectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.
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TL;DR: Finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied).
Abstract: The standard model of particle physics predicts two phase transitions that are relevant for the evolution of the early Universe. One, the quantum chromodynamics transition, involves the strong force that binds quarks into protons and neutrons. Despite much theoretical effort, the nature of this transition remains ambiguous. Now Aoki et al. report computationally demanding calculations that suggest that there was no true phase transition. Instead, an analytic crossover took place, involving a rapid, continuous change with temperature as opposed to a jump. This means that it will be difficult to find experimental evidence of a transition from astronomical observations. The standard model of particle physics predicts two transitions that are relevant for the evolution of the early Universe. Computationally demanding calculations now reveal that a real phase transition did not occur, but rather an analytic crossover, involving a rapid change (as opposed to a jump) as the temperature varies. Quantum chromodynamics (QCD) is the theory of the strong interaction, explaining (for example) the binding of three almost massless quarks into a much heavier proton or neutron—and thus most of the mass of the visible Universe. The standard model of particle physics predicts a QCD-related transition that is relevant for the evolution of the early Universe. At low temperatures, the dominant degrees of freedom are colourless bound states of hadrons (such as protons and pions). However, QCD is asymptotically free, meaning that at high energies or temperatures the interaction gets weaker and weaker1,2, causing hadrons to break up. This behaviour underlies the predicted cosmological transition between the low-temperature hadronic phase and a high-temperature quark–gluon plasma phase (for simplicity, we use the word ‘phase’ to characterize regions with different dominant degrees of freedom). Despite enormous theoretical effort, the nature of this finite-temperature QCD transition (that is, first-order, second-order or analytic crossover) remains ambiguous. Here we determine the nature of the QCD transition using computationally demanding lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities. No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.
1,606 citations
TL;DR: In this article, the 2+1 flavor QCD equation of state has been extended to even finer lattices and now includes ensembles with Nt = 6,8,10,12 up to 16.
947 citations
TL;DR: In this paper, the phase transition restoring chiral symmetry at finite temperatures is considered in a linear σ-sigma model. But the model is not suitable for the case of massless flavors.
Abstract: The phase transition restoring chiral symmetry at finite temperatures is considered in a linear $\ensuremath{\sigma}$ model. For three or more massless flavors, the perturbative $\ensuremath{\epsilon}$ expansion predicts the phase transition is of first order. At high temperatures, the ${\mathrm{U}}_{A}(1)$ symmetry will also be effectively restored.
897 citations
University of Iowa1, Los Alamos National Laboratory2, University of Utah3, Central China Normal University4, Indiana University5, American Physical Society6, Bielefeld University7, Brookhaven National Laboratory8, Lawrence Livermore National Laboratory9, University of Regensburg10, University of California, Santa Barbara11
TL;DR: In this paper, the authors present results for the equation of state in ($2+1$)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent.
Abstract: We present results for the equation of state in ($2+1$)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent ${N}_{\ensuremath{\tau}}=6$, 8, 10, and 12. We show that these data can be reliably extrapolated to the continuum limit and obtain a number of thermodynamic quantities and the speed of sound in the temperature range 130--400 MeV. We compare our results with previous calculations and provide an analytic parameterization of the pressure, from which other thermodynamic quantities can be calculated, for use in phenomenology. We show that the energy density in the crossover region, $145\text{ }\text{ }\mathrm{MeV}\ensuremath{\le}T\ensuremath{\le}163\text{ }\text{ }\mathrm{MeV}$, defined by the chiral transition, is ${\ensuremath{\epsilon}}_{c}=(0.18--0.5)\text{ }\text{ }\mathrm{GeV}/{\mathrm{fm}}^{3}$, i.e., $(1.2--3.1)\text{ }{\ensuremath{\epsilon}}_{\text{nuclear}}$. At high temperatures, we compare our results with resummed and dimensionally reduced perturbation theory calculations. As a byproduct of our analyses, we obtain the values of the scale parameters ${r}_{0}$ from the static quark potential and ${w}_{0}$ from the gradient flow.
885 citations