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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.
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.
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.
Lattice simulations employing reweighting and Taylor expansion techniques have predicted a (m;T)-phase diagram according to general expectations, with an analytic quark-hadron crossover at m =0 turning into a first order transition at some critical chemical potential mE. By contrast, recent simulations using imgainary m followed by analytic continuation obtained a critical structure in the fmu;d;ms;T;mg parameter space favouring the absence of a critical point and first order line. I review the evidence for the latter scenario, arguing that the various raw data are not inconsistent with each other. Rather, the discrepancy appears when attempting to extract continuum results from the coarse (Nt =4) lattices simulated so far, and can be explained by cut-off effects. New (as yet unpublished) data are presented, which for Nf = 3 and on Nt = 4 confirm the scenario without a critical point. Moreover, simulations on finer Nt = 6 lattices show that even if there is a critical point, continuum extrapolation moves it to significantly larger values of mE than anticipated on coarse lattices.
I review recent developments in determining the QCD phase diagram by means of lattice simulations.
Since the invention of methods to side-step the sign problem a few years ago, a number
of additional variants have been proposed, and progress has been made towards understanding
some of the systematics involved. All available techniques agree on the transition temperature
as a function of density in the regime mq/T <~1. There are by now four calculations with signals
for a critical point, two of them at similar parameter values and with consistent results. However,
it also emerges that the location of the critical point is exceedingly quark mass sensitive. At the
same time sizeable finite volume, cut-off and step size effects have been uncovered, demanding
additional investigations with exact algorithms on larger and finer lattices before quantitative conclusions
can be drawn. Depending on the sign of these corrections, there is ample room for the
eventual phase diagram to look as expected or also quite different, with no critical point at all.