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The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ N∗f ≲ 12. A reanalysis of already published O(a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.
The order of the chiral phase transition of lattice QCD with unimproved staggered fermions is known to depend on the number of quark flavours, their masses and the lattice spacing. Previous studies in the literature for Nf∈{3,4} show first-order transitions, which weaken with decreasing lattice spacing. Here we investigate what happens when lattices are made coarser to establish contact to the strong coupling region. For Nf∈{4,8} we find a drastic weakening of the transition when going from Nτ=4 to Nτ=2, which is consistent with a second-order chiral transition reported in the literature for Nf=4 in the strong coupling limit. This implies a non-monotonic behaviour of the critical quark or pseudo-scalar meson mass, which separates first-order transitions from crossover behaviour, as a function of lattice spacing.
According to perturbation theory predictions, QCD matter in the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential is expected to be in a superfluid Bardeen-Cooper-Schrieffer (BCS) phase of u and d¯ Cooper pairs. It is also expected, on symmetry grounds, that such phase connects via an analytical crossover to the phase with Bose-Einstein condensation (BEC) of charged pions at μI≥mπ/2. With lattice results, showing some indications that the deconfinement crossover also smoothly penetrates the BEC phase, the conjecture was made that the former connects continuously to the BEC-BCS crossover. We compute the spectrum of the Dirac operator, and use generalized Banks-Casher relations, to test this conjecture and identify signatures of the superfluid BCS phase.
The SU(3) pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global Z3 center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with Nf=2 degenerate standard Wilson fermions on Nτ∈{6,8,10} lattices, corresponding to lattice spacings a=0.12 fm, a=0.09 fm, a=0.07 fm, respectively. Significant cutoff effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate mcπ≈4 GeV with a remaining systematic error of ∼20%. Our results allow us to assess the accuracy of the leading-order and next-to-leading-order hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.
The magnetic fields generated in non-central heavy-ion collisions are among the strongest fields produced in the Universe, reaching magnitudes comparable to the scale of the strong interactions. Backed by model simulations, the resulting field is expected to be spatially modulated, deviating significantly from the commonly considered uniform profile. To improve our understanding of the physics of quarks and gluons under such extreme conditions, we use lattice QCD simulations with 2+1 staggered fermion flavors with physical quark masses and an inhomogeneous magnetic background for a range of temperatures covering the QCD phase transition. We assume a 1/cosh2 function to model the field profile and vary its strength to analyze the impact on the computed observables and on the transition. We calculate local chiral condensates, local Polyakov loops and estimate the size of lattice artifacts. We find that both observables show non-trivial spatial features due to the interplay between the sea and the valence effects.
We investigate the possible formation of a Bose-Einstein condensed phase of pions in the early Universe at nonvanishing values of lepton flavor asymmetries. A hadron resonance gas model with pion interactions, based on first-principle lattice QCD simulations at nonzero isospin density, is used to evaluate cosmic trajectories at various values of electron, muon, and tau lepton asymmetries that satisfy the available constraints on the total lepton asymmetry. The cosmic trajectory can pass through the pion condensed phase if the combined electron and muon asymmetry is sufficiently large: |le+lμ|≳0.1, with little sensitivity to the difference le−lμ between the individual flavor asymmetries. Future constraints on the values of the individual lepton flavor asymmetries will thus be able to either confirm or rule out the condensation of pions during the cosmic QCD epoch. We demonstrate that the pion condensed phase leaves an imprint both on the spectrum of primordial gravitational waves and on the mass distribution of primordial black holes at the QCD scale, e.g., the black hole binary of recent LIGO event GW190521 can be formed in that phase.