Owe Philipsen

Static correlation lengths in QCD at high temperatures and finite densities

We use a perturbatively derived effective field theory and three-dimensional lattice simulations to determine the longest static correlation lengths in the deconfined QCD plasma phase at high temperatures (T greater than or similar to 2T(c)) and finite densities (mu less than or similar to 4T). For vanishing chemical potential, we refine a previous determination of the Debye screening length, and determine the dependence of different correlation lengths on the number of massless flavours as well as on the number of colours. For non-vanishing but small chemical potential, the existence of Debye screening allows us to carry out simulations corresponding to the full QCD with two (or three) massless dynamical flavours, in spite of a complex action. We investigate how the correlation lengths in the different quantum number channels change as the chemical potential is switched on

Static correlation lengths in QCD at high temperature and finite density

A brief review is given of the sign problem in finite density lattice QCD and various attempts to overcome it. To date there is still no solution to this problem which would work for realistic QCD. The main focus then is on the deconfined phase, where QCD can be described by a dimensionally reduced effective action. After summarizing derivation and validity of the effective theory, it is demonstrated that it can be simulated efficiently in the presence of a chemical potential for quarks μ/T ≲ 4. Direct comparison of simulations with imaginary and real μ suggests that equilibrium plasma properties could be analytically continued from 4d QCD simulations at imaginary μ.

String Breaking in Non-Abelian Gauge Theories with Fundamental Matter Fields

We present clear numerical evidence for string breaking in three-dimensional SU(2) gauge theory with fundamental bosonic matter through a mixing analysis between Wilson loops and meson operators representing bound states of a static source and a dynamical scalar. The breaking scale is calculated in the continuum limit. In units of the lightest glueball we find

The non-perturbative QCD Debye mass from a Wilson line operator

{r}_{mathrm{b}}{m}_{G}ensuremath{approx}13.6

THE SPECTRUM OF THE THREE-DIMENSIONAL ADJOINT HIGGS MODEL AND HOT SU(2) GAUGE THEORY

. The implications of our results for QCD are discussed.

Testing imaginary vs. real chemical potential in finite-temperature QCD

Abstract According to a proposal by Arnold and Yaffe, the non-perturbative g 2 T -contribution to the Debye mass in the deconfined QCD plasma phase can be determined from a single Wilson line operator in the three-dimensional pure SU(3) gauge theory. We extend a previous SU(2) measurement of this quantity to the physical SU(3) case. We find a numerical coefficient which is more accurate and smaller than that obtained previously with another method, but still very large compared with the naive expectation: the correction is larger than the leading term up to T ∼10 7 T c , corresponding to g 2 ∼0.4. At moderate temperatures T ∼2 T c , a consistent picture emerges where the Debye mass is m D ∼6 T , the lightest gauge invariant screening mass in the system is ∼3 T , and the purely magnetic operators couple dominantly to a scale ∼6 T . Electric (∼ gT ) and magnetic (∼ g 2 T ) scales are therefore strongly overlapping close to the phase transition, and the colour-electric fields play an essential role in the dynamics.

Adjoint string breaking in 4d SU(2) Yang–Mills theory

Abstract We compute the mass spectrum of the SU(2) adjoint Higgs model in 2+1 dimensions at several points located in the (metastable) confinement region of its phase diagram. We find a dense spectrum consisting of an almost unaltered repetition of the glueball spectrum of the pure gauge theory, and additional bound states of adjoint scalars. For the parameters chosen, the model represents the effective finite temperature theory for pure SU(2) gauge theory in four dimensions, obtained after perturbative dimensional reduction. Comparing with the spectrum of screening masses obtained in recent simulations of four-dimensional pure gauge theory at finite temperature, for the low-lying states we find quantitative agreement between the full and the effective theory for temperatures as low as T=2Tc. This establishes the model under study as the correct effective theory, and dimensional reduction as a viable tool for the description of thermodynamic properties. We furthermore compare the perturbative contribution ∼gT with the non-perturbative contributions ∼g2T and ∼g3T to the Debye mass. The latter turns out to be dominated by the scale g2T, whereas higher order contributions are small corrections.

Gauge-invariant scalar and field strength correlators in three dimensions

Abstract One suggestion for determining the properties of QCD at finite temperatures and densities is to carry out lattice simulations with an imaginary chemical potential whereby no sign problem arises, and to convert the results to real physical observables only afterwards. We test the practical feasibility of such an approach for a particular class of physical observables, spatial correlation lengths in the quark–gluon plasma phase. Simulations with imaginary chemical potential followed by analytic continuation are compared with simulations with real chemical potential, which are possible by using a dimensionally reduced effective action for hot QCD (in practice we consider QCD with two massless quark flavours). We find that for imaginary chemical potential the system undergoes a phase transition at |μ/T|≈π/3, and thus observables are analytic only in a limited range. However, utilising this range, relevant information can be obtained for the real chemical potential case.

STRING BREAKING IN SU(2) YANG MILLS THEORY WITH ADJOINT SOURCES

Abstract We compute the static potential of adjoint sources in SU(2) Yang–Mills theory in four dimensions by numerical Monte Carlo simulations. Following a recent calculation in 2+1 dimensions, we employ a variational approach involving string and gluelump operators and obtain clear evidence for string breaking and the saturation of the potential at large distances. For the string breaking scale we find r b ≈1.25 fm , 2.3r0, or in units of the lightest glueball, rbm0++≈9.7. We furthermore resolve the first excitation of the flux-tube and observe its breaking as well. The result for rb is in remarkable quantitative agreement with the three-dimensional one.

Cooling, physical scales and topology

Gauge-invariant non-local scalar and field strength operators have been argued to have significance, e.g., as a way to determine the behaviour of the screened static potential at large distances, as order parameters for confinement, as input parameters in models of confinement, and as gauge-invariant definitions of light constituent masses in bound-state systems. We measure such “correlators” in the 3d pure SU(2) and SU(2)+Higgs models on the lattice. We extract the corresponding mass parameters and discuss their scaling and physical interpretation. We find that the finite part of the MS scheme mass measured from the field strength correlator is large, more than half the glueball mass. We also determine the non-perturbative contribution to the Debye mass in the 4d finite T SU(2) gauge theory with a method due to Arnold and Yaffe, finding δmD ≈ 1.06(4)g2T.