Jens Langelage

The QCD deconfinement transition for heavy quarks and all baryon chemical potentials

A bstractUsing combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to Nτ ~ 6 at finite temperature. For nonzero quark chemical potentials, the effective theory has a fermionic sign problem which is mild enough to carry out simulations up to large chemical potentials. Moreover, by going to a flux representation of the partition function, the sign problem can be solved. As an application, we determine the deconfinement transition and its critical end point as a function of quark mass and all chemical potentials.

Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks

Lattice QCD at finite density suffers from a severe sign problem, which has so far prohibited simulations of the cold and dense regime. Here we study the onset of nuclear matter employing a three-dimensional effective theory derived by combined strong coupling and hopping expansions, which is valid for heavy but dynamical quarks and has a mild sign problem only. Its numerical evaluations agree between a standard Metropolis and complex Langevin algorithm, where the latter is free of the sign problem. Our continuum extrapolated data approach a first order phase transition at μ(B) ≈ m(B) as the temperature approaches zero. An excellent description of the data is achieved by an analytic solution in the strong coupling limit.

Heavy dense QCD and nuclear matter from an effective lattice theory

A bstractA three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, κ, whose action is correct to κnum with n + m = 4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state in the limit of heavy baryons. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as a gap between the onset of isospin and baryon condensation.

The deconfinement transition of finite density QCD with heavy quarks from strong coupling series

Starting from Wilson’s action, we calculate strong coupling series for the Polyakov loop susceptibility in lattice gauge theories for various small Nτ in the thermodynamic limit. Analysing the series with Padé approximants, we estimate critical couplings and exponents for the deconfinement phase transition. For SU(2) pure gauge theory our results agree with those from Monte-Carlo simulations within errors, which for the coarser Nτ = 1, 2 lattices are at the percent level. For QCD we include dynamical fermions via a hopping parameter expansion. On a Nτ = 1 lattice with Nf = 1, 2, 3, we locate the second order critical point where the deconfinement transition turns into a crossover. We furthermore determine the behaviour of the critical parameters with finite chemical potential and find the first order region to shrink with growing μ. Our series moreover correctly reflects the known Z(N) transition at imaginary chemical potential.

Strong coupling expansion for finite temperature Yang-Mills theory in the confined phase

We perform Euclidean strong coupling expansions for Yang Mills theory on the lattice at finite temperature. After setting up the formalism for general SU(N), we compute the first few terms of the series for the free energy density and the lowest screening mass in the case of SU(2). To next-to-leading order the free energy series agrees with that of an ideal gas of glueballs. This demonstrates that in the confined phase the quasi-particles indeed correspond to the T = 0 hadron excitations, as commonly assumed in hadron resonance gas models. Our result also fixes the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method. In accord with Monte Carlo results, we find screening masses to be nearly temperature independent in the confined phase. This and the exponential smallness of the pressure can be understood as genuine strong coupling effects. Finally, we analyse Pade approximants to estimate the critical couplings of the phase transition, which for our short series are only ~ 25% accurate. However, up to these couplings the equation of state agrees quantitatively with numerical results on Nt = 1−4 lattices.

Colour-electric spectral function at next-to-leading order

The spectral function related to the correlator of two colour-electric fields along a Polyakov loop determines the momentum diffusion coefficient of a heavy quark near rest with respect to a heat bath. We compute this spectral function at next-to-leading order,

Towards a non-perturbative measurement of the heavy quark momentum diffusion coefficient

\mathcal{O}\left( {\alpha_s^2} \right)

Numerical corrections to the strong coupling effective Polyakov-line action for finite T Yang-Mills theory

, in the weak-coupling expansion. The high-frequency part of our result (ω ≫ T), which is shown to be temperature-independent, is accurately determined thanks to asymptotic freedom; the low-frequency part of our result (ω ≪ T), in which Hard Thermal Loop resummation is needed in order to cure infrared divergences, agrees with a previously determined expression. Our result may help to calibrate the overall normalization of a lattice-extracted spectral function in a perturbative frequency domain T ≪ ω ≪ 1/a, paving the way for a non-perturbative estimate of the momentum diffusion coefficient at ω → 0. We also evaluate the colour-electric Euclidean correlator, which could be directly compared with lattice simulations. As an aside we determine the Euclidean correlator in the lattice strong-coupling expansion, showing that through a limiting procedure it can in principle be defined also in the confined phase of pure Yang-Mills theory, even if a practical measurement could be very noisy there.

Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature

We report on a lattice investigation of heavy quark diffusion within pure SU(3) plasma above the deconfinement transition, with the quarks treated to leadin g order in the heavy mass expansion. Using a multilevel algorithm, several volumes and lattice spacings, as well as tree-level improvement and perturbative renormalization, we measure the relevant “colour-electric” Euclidean correlator, finding that it clearly exceeds its perturbative co unterpart. Even without analytic continuation, this suggests that at temperatures just above the cri tical one, non-perturbative interactions felt by the heavy quarks are stronger than within the weak-coupling expansion. After introducing rough modelling of the spectral shape, diffusion coefficien ts down to D∼ 0.5/T appear possible.

Strong-coupling effective action(s) for SU(3) Yang-Mills

We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase structure, with a sign problem mild enough to allow simulations also at finite density. In this work we present a numerical method to determine improved values for the effective couplings directly from correlators of 4d Yang-Mills theory. For values of the gauge coupling up to the vicinity of the phase transition, the dominant short range effective coupling are well described by their corresponding strong coupling series. We provide numerical results also for the longer range interactions, Polyakov lines in higher representations as well as four-point interactions, and discuss the growing significance of non-local contributions as the lattice gets finer. Within this approach the critical Yang-Mills coupling βc is reproduced to better than one percent from a one-coupling effective theory on Nτ = 4 lattices while up to five couplings are needed on Nτ = 8 for the same accuracy.