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Approaching the continuum limit of the deconfinement critical point for Nf=2 staggered fermions
(2022)
Quenched QCD at zero baryonic chemical potential undergoes a first-order deconfinement phase transition at a critical temperature Tc, which is related to the spontaneous breaking of the global center symmetry. The center symmetry is broken explicitly by including dynamical quarks, which weaken the first-order phase transition for decreasing quark masses. At a certain critical quark mass, which corresponds to the Z(2)-critical point, the first-order phase transition turns into a smooth crossover. We investigate the Z(2)-critical quark mass for Nf=2 staggered fermions on Nτ=8,10 lattices, where larger Nτ correspond to finer lattices. Monte-Carlo simulations are performed for several quark mass values and aspect ratios in order to extrapolate to the thermodynamic limit. We present final results for Nτ=8 and preliminary results for Nτ=10 for the critical mass, which are obtained from fitting to a kurtosis finite size scaling formula of the absolute value of the Polyakov loop.
Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions.
Quenched QCD at zero baryonic chemical potential undergoes a first-order deconfinement phase transition at a critical temperature Tc, which is related to the spontaneous breaking of the global center symmetry. Including heavy, dynamical quarks breaks the center symmetry explicitly and weakens the first-order phase transition. For decreasing quark masses the first-order phase transition turns into a smooth crossover at a Z2-critical point. The critical quark mass corresponding to this point has been examined with Nf=2 Wilson fermions for several Nτ in a recent study within our group. For comparison, we also locate the critical point with Nf=2 staggered fermions on Nτ=8 lattices. For this purpose we perform Monte Carlo simulations for several quark mass values and various aspect ratios in order to extrapolate to the thermodynamic limit. The critical mass is obtained by fitting to a finite size scaling formula of the kurtosis of the Polyakov loop. Our results indicate large discretization effects, requiring simulations on lattices with Nτ>8.
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.
We report on the status of ongoing investigations aiming at locating the deconfinement critical point with standard Wilson fermions and Nf = 2 flavors towards the continuum limit (standard Columbia plot); locating the tricritical masses at imaginary chemical potential with unimproved staggered fermions at Nf = 2 (extended Columbia plot); identifying the order of the chiral phase transition at μ = 0 for Nf = 2 via extrapolation from non integer Nf (alternative Columbia plot).
Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory
at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions
have a finite radius of convergence and thus are valid only for b <bc, where bc denotes the nearest
singularity of the free energy on the real axis. The accessible temperature range is thus the
confined regime up to the deconfinement transition. We have calculated the first few orders of
these expansions of the free energy density as well as the screening masses for the gauge groups
SU(2) and SU(3). The resulting free energy series can be summed up and corresponds to a glueball
gas of the lowest mass glueballs up to the calculated order. Our result can be used to fix
the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via
the integral method, and shows from first principles that in the confined phase this constant is
indeed exponentially small. Similarly, our results also explain the weak temperature dependence
of glueball screening masses below Tc, as observed in Monte Carlo simulations. Possibilities and
difficulties in extracting bc from the series are discussed.
We report on the first steps of an ongoing project to add gauge observables and gauge corrections
to the well-studied strong coupling limit of staggered lattice QCD, which has been shown earlier
to be amenable to numerical simulations by the worm algorithm in the chiral limit and at finite
density. Here we show how to evaluate the expectation value of the Polyakov loop in the framework
of the strong coupling limit at finite temperature, allowing to study confinement properties
along with those of chiral symmetry breaking. We find the Polyakov loop to rise smoothly, thus
signalling deconfinement. The non-analytic nature of the chiral phase transition is reflected in the
derivative of the Polyakov loop. We also discuss how to construct an effective theory for non-zero
lattice coupling, which is valid to O(b).
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.
The so-called sign problem of lattice QCD prohibits Monte Carlo simulations at finite baryon
density by means of importance sampling. Over the last few years, methods have been developed
which are able to circumvent this problem as long as the quark chemical potential is m=T <~1.
After a brief review of these methods, their application to a first principles determination of the
QCD phase diagram for small baryon densities is summarised. The location and curvature of the
pseudo-critical line of the quark hardon transition is under control and extrapolations to physical
quark masses and the continuum are feasible in the near future. No definite conclusions can as
yet be drawn regarding the existence of a critical end point, which turns out to be extremely quark
mass and cut-off sensitive. Investigations with different methods on coarse lattices show the lightmass
chiral phase transition to weaken when a chemical potential is switched on. If persisting on
finer lattices, this would imply that there is no chiral critical point or phase transition for physical
QCD. Any critical structure would then be related to physics other than chiral symmetry breaking.
The chiral critical surface is a surface of second order phase transitions bounding the region of
first order chiral phase transitions for small quark masses in the fmu;d;ms;mg parameter space.
The potential critical endpoint of the QCD (T;m)-phase diagram is widely expected to be part of
this surface. Since for m = 0 with physical quark masses QCD is known to exhibit an analytic
crossover, this expectation requires the region of chiral transitions to expand with m for a chiral
critical endpoint to exist. Instead, on coarse Nt = 4 lattices, we find the area of chiral transitions
to shrink with m, which excludes a chiral critical point for QCD at moderate chemical potentials
mB < 500 MeV. First results on finer Nt = 6 lattices indicate a curvature of the critical surface
consistent with zero and unchanged conclusions. We also comment on the interplay of phase
diagrams between the Nf = 2 and Nf = 2+1 theories and its consequences for physical QCD.