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- Computation of hybrid static potentials in SU(3) lattice gauge theory (2018)
- 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.

- Updates on the Columbia plot and its extended/alternative versions (2018)
- 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).

- Strong coupling expansion for Yang-Mills theory at finite temperature (2007)
- 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.

- Towards corrections to the strong coupling limit of staggered lattice QCD : the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10 - 16, 2011, Squaw Valley, Lake Tahoe, California (2011)
- 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).

- Screened perturbation theory for 3d Yang-Mills theory and the magnetic modes of hot QCD : International Workshop on QCD Green’s Functions, Confinement, and Phenomenology - QCD-TNT09, September 07 - 11 2009, ECT Trento, Italy (2009)
- 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.

- Lattice calculations at non-zero chemical potential: the QCD phase diagram (2009)
- 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.

- Towards a determination of the chiral critical surface of QCD (2009)
- 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.

- The finite-temperature phase structure of lattice QCD with twisted-mass Wilson fermions (2008)
- We report progress in our exploration of the finite-temperature phase structure of two-flavour lattice QCD with twisted-mass Wilson fermions and a tree-level Symanzik-improved gauge action for a temporal lattice size Nt = 8. Extending our investigations to a wider region of parameter space we gain a global view of the rich phase structure. We identify the finite temperature transition/ crossover for a non-vanishing twisted-mass parameter in the neighbourhood of the zerotemperature critical line at sufficiently high b . Our findings are consistent with Creutz’s conjecture of a conical shape of the finite temperature transition surface. Comparing with NLO lattice cPT we achieve an improved understanding of this shape.

- Exploring the QCD phase diagram (2007)
- 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.

- QCD equation of state and dark matter (2006)
- The QCD equation of state is not often discussed in cosmology. However, the relic density of weakly interacting massive particles (WIMPs) depends on the entropy and the expansion rate of the Universe when they freeze out, at a temperature in the range 400 MeV – 40GeV, where QCD corrections are still important. We use recent analytic and lattice calculations of the QCD pressure to produce a new equation of state suitable for use in relic density calculations. As an example, we show that relic densities calculated by the dark matter package DarkSUSY receive corrections of several per cent, within the observational accuracy of the Planck CMB mission, due for launch in 2007.