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Lattice QCD and functional methods are making significant progress in constraining the QCD phase diagram. As an important milestone, the chiral phase transition with massless u, d-quarks at zero density is now understood to be of second order for all strange quark masses, and a smooth crossover as soon as mu,d, ≠ 0. Together with information on fluctuations and refined reweighted simulations, this bounds a possible critical point to be at µB/T ≲3. On the other hand, an approximately chiral-spin symmetric temperature window has been discovered above the chiral crossover, Tch<T ≳3Tch, with distinct correlator multiplet patterns and a pion spectral function suggesting resonance-like degrees of freedom, which dissolve graduallly with temperature.
The QCD equation of state at finite baryon density is studied in the framework of a Cluster Expansion Model (CEM), which is based on the fugacity expansion of the net baryon density. The CEM uses the two leading Fourier coefficients, obtained from lattice simulations at imaginary μB, as the only model input and permits a closed analytic form. Excellent description of the available lattice data at both μB = 0 and at imaginary μB is obtained. We also demonstrate how the Fourier coefficients can be reconstructed from baryon number susceptibilities.
Spectral functions encode a wealth of information about the dynamics of any given system, and the determination of their non-perturbative characteristics is a long-standing problem in quantum field theory. Whilst numerical simulations of lattice QCD provide ample data for various Euclidean correlation functions, the inversion required to extract spectral functions is an ill-posed problem. In this work, we pursue previously established constraints imposed by field locality at finite temperature T, namely that spectral functions possess a non-perturbative representation which generalises the well-known Källén-Lehmann spectral form to T > 0. Using this representation, we analyse lattice QCD data of the spatial pseudo-scalar correlator in the temperature range 220–960 MeV, and obtain an analytic expression for the corresponding spectral function, with parameters fixed by the data. From the structure of this spectral function we find evidence for the existence of a distinct pion state above the chiral pseudo-critical temperature Tpc, and contributions from its first excitation, which gradually melt as the temperature increases. As a non-trivial test, we find that the extracted spectral function reproduces the corresponding temporal lattice correlator data for T = 220 MeV.
In quantum field theories at finite temperature spectral functions describe how particle systems behave in the presence of a thermal medium. Although data from lattice simulations can in principle be used to determine spectral function characteristics, existing methods rely on the extraction of these quantities from temporal correlators, which requires one to circumvent an illposed inverse problem. In these proceedings we report on a recent approach that instead utilises the non-perturbative constraints imposed by field locality to extract spectral function information directly from spatial correlators. In particular, we focus on the application of this approach to lattice QCD data of the spatial pseudo-scalar meson correlator in the temperature range 220−960 MeV, and outline why this data supports the conclusion that there exists a distinct pion state above the chiral pseudo-critical temperature Tpc.
Lattice constraints on the QCD chiral phase transition at finite temperature and baryon density
(2021)
The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.
The thermodynamics of QCD with sufficiently heavy dynamical quarks can be described by a three-dimensional Polyakov loop effective theory, obtained after a truncated character and hopping expansion. We investigate the resulting phase diagram for low temperatures by mean field methods. Taking into account chemical potentials for both baryon number and isospin, we obtain clear signals for a liquid-gas type transition to baryon matter at μI=0 and a Bose-Einstein condensation transition at μB=0, as well as for their connection when both chemical potentials are non-zero.
Recently, an approximate SU(4) chiral spin-flavour symmetry was observed in multiplet patterns of QCD meson correlation functions, in a temperature range above the chiral crossover. This symmetry is larger than the chiral symmetry of massless QCD, and can only arise effectively when colour-electric quark-gluon interactions dynamically dominate the quantum effective action. At temperatures about three times the crossover temperature, these patterns disappear again, indicating the screening of colour-electric interactions, and the expected chiral symmetry is recovered. In this contribution we collect independent evidence for such an intermediate temperature range, based on screening masses and the pion spectral function. Both kinds of observables behave non-perturbatively in this window, with resonance-like peaks for the pion and its first excitation disappearing gradually with temperature. Using symmetry arguments and the known behaviour of screening masses at small densities, we discuss how this chiral spin symmetric band continues into the QCD phase diagram.
Effective three-dimensional Polyakov loop theories derived from QCD by strong coupling and hopping expansions are valid for heavy quarks and can also be applied to finite chemical potential μ, due to their considerably milder sign problem. We apply the Monte-Carlo method to the Nf=1,2 effective theories up to O(κ4) in the hopping parameter at μ=0 to determine the critical quark mass, at which the first-order deconfinement phase transition terminates. The critical end point obtained from the effective theory to order O(κ2) agrees well with 4-dimensional QCD simulations with a hopping expanded determinant by the WHOT-QCD collaboration. We also compare with full QCD simulations and thus obtain a measure for the validity of both the strong coupling and the hopping expansion in this regime.
The global center symmetry of quenched QCD at zero baryonic chemical potential is broken spontaneously at a critical temperature Tc leading to a first-order phase transition. Including heavy dynamical quarks breaks the center symmetry explicitly and weakens the first-order phase transition for decreasing quark masses until it turns into a smooth crossover at a Z(2)-critical point. We investigate the Z(2)-critical quark mass value towards the continuum limit for Nf=2 flavors using lattice QCD in the staggered formulation. As part of a continued study, we present results from Monte-Carlo simulations on Nτ=8,10 lattices. Several aspect ratios and quark mass values were simulated in order to obtain the critical mass from a fit of the Polyakov loop to a kurtosis finite size scaling formula. Moreover, the possibility to develop a Ginzburg-Landau effective theory around the Z(2)-critical point is explored.