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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.
We compute hybrid static potentials in SU(3) lattice gauge theory. We present a method to automatically generate a large set of suitable creation operators with defined quantum numbers from elementary building blocks. We show preliminary results for several channels and discuss, which structures of the gluonic flux tube seem to be realized by the ground states in these channels.
From the colour glass condensate to filamentation: systematics of classical Yang–Mills theory
(2019)
The non-equilibrium early time evolution of an ultra-relativistic heavy ion collision is often described by classical lattice Yang–Mills theory, starting from the colour glass condensate (CGC) effective theory with an anisotropic energy momentum tensor as initial condition. In this work we investigate the systematics associated with such studies and their dependence on various model parameters (IR, UV cutoffs and the amplitude of quantum fluctuations) which are not yet fixed by experiment. We perform calculations for SU() and SU(), both in a static box and in an expanding geometry. Generally, the dependence on model parameters is found to be much larger than that on technical parameters like the number of colours, boundary conditions or the lattice spacing. In a static box, all setups lead to isotropisation through chromo-Weibel instabilities, which is illustrated by the accompanying filamentation of the energy density. However, the associated time scale depends strongly on the model parameters and in all cases is longer than the phenomenologically expected one. In the expanding system, no isotropisation is observed for any parameter choice. We show how investigations at fixed initial energy density can be used to better constrain some of the model parameters.
The quark gluon plasma produced in heavy ion collisions behaves like an almost ideal fluid described by viscous hydrodynamics with a number of transport coefficients. The second order coefficient κ is related to a Euclidean correlator of the energy-momentum tensor at vanishing frequency and low momentum. This allows for a lattice determination without maximum entropy methods or modelling, but the required lattice sizes represent a formidable challenge. We calculate κ in leading order lattice perturbation theory and simulations on 1203 × 6, 8 lattices with a < 0.1 fm. In the temperature range 2Tc − 10Tc we find κ = 0.36(15)T2. The error covers both a suitably rescaled AdS/CFT prediction as well as, remarkably, the result of leading order perturbation theory. This suggests that appropriate noise reduction methods on the lattice and NLO perturbative calculations could provide an accurate QCD prediction in the near future.
Lattice QCD with heavy quarks reduces to a three-dimensional effective theory of Polyakov loops, which is amenable to series expansion methods. We analyse the effective theory in the cold and dense regime for a general number of colours, Nc. In particular, we investigate the transition from a hadron gas to baryon condensation. For any finite lattice spacing, we find the transition to become stronger, i.e. ultimately first-order, as Nc is made large. Moreover, in the baryon condensed regime, we find the pressure to scale as p ∼ Nc through three orders in the hopping expansion. Such a phase differs from a hadron gas with p ∼ N0c, or a quark gluon plasma, p ∼ N2c, and was termed quarkyonic in the literature, since it shows both baryon-like and quark-like aspects. A lattice filling with baryon number shows a rapid and smooth transition from condensing baryons to a crystal of saturated quark matter, due to the Pauli principle, and is consistent with this picture. For continuum physics, the continuum limit needs to be taken before the large Nc limit, which is not yet possible in practice. However, in the controlled range of lattice spacings and Nc-values, our results are stable when the limits are approached in this order. We discuss possible implications for physical QCD.
LatticeQCD using OpenCL
(2011)
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.
We present unambiguous evidence from lattice simulations of Nf = 3 QCD for two tricritical points in the (T;m) phase diagram at fixed imaginary m=T = ip=3 mod. 2p=3, one in the light and one in the heavy quark regime. Together with similar results in the literature for Nf = 2 this implies the existence of a chiral and of a deconfinement tricritical line at those values of imaginary chemical potentials. These tricritical lines represent the boundaries of the analytically continued chiral and deconfinement critical surfaces, respectively, which delimit the parameter space with first order phase transitions. It is demonstrated that the shape of the deconfinement critical surface is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. A qualitatively similar effect holds for the chiral critical surface.
Perturbation theory for non-abelian gauge theories at finite temperature is plagued by infrared
divergences which are caused by magnetic soft modes ~ g2T, corresponding to gluon fields of
a 3d Yang-Mills theory. While the divergences can be regulated by a dynamically generated
magnetic mass on that scale, the gauge coupling drops out of the effective expansion parameter
requiring summation of all loop orders for the calculation of observables. Some gauge invariant
possibilities to implement such infrared-safe resummations are reviewed. We use a scheme based
on the non-linear sigma model to estimate some of the contributions ~ g6 of the soft magnetic
modes to the QCD pressure through two loops. The NLO contribution amounts to ~ 10% of the
LO, suggestive of a reasonable convergence of the series.