Thermal 2-loop master spectral function at finite momentum

When considering NLO corrections to thermal particle production in the “relativistic” regime, in which the invariant mass squared of the produced particle is K2 ~ (πT)2, then the production rate can be expressed as a sum of a few universal “master” spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K2 ~(8πT)2, whereas the zero-momentum approximation works surprisingly well. Once the simpler masters have been similarly resolved, NLO results for quantities such as the right-handed neutrino production rate from a Standard Model plasma or the dilepton production rate from a QCD plasma can be assembled for K2 ~ (πT)2.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.

NLO thermal dilepton rate at non-zero momentum

The vector channel spectral function and the dilepton production rate from a QCD plasma at a temperature above a few hundred MeV are evaluated up to next-to-leading order (NLO) including their dependence on a non-zero momentum with respect to the heat bath. The invariant mass of the virtual photon is taken to be in the range K2 ~ (πT)2 ~ (1GeV)2, generalizing previous NLO results valid for K2 ≫ (πT)2. In the opposite regime 0 < K2 ≪ (πT)2 the loop expansion breaks down, but agrees nevertheless in order of magnitude with a previous result obtained through resummations. Ways to test the vector spectral function through comparisons with imaginary-time correlators measured on the lattice are discussed.

Charm mass effects in bulk channel correlations

The bulk viscosity of thermalized QCD matter at temperatures above a few hundred MeV could be significantly influenced by charm quarks because their contribution arises four perturbative orders before purely gluonic effects. In an attempt to clarify the challenges of a lattice study, we determine the relevant imaginary-time correlator (of massive scalar densities) up to NLO in perturbation theory, and compare with existing data. We find discrepancies much larger than in the vector channel; this may hint, apart from the importance of taking a continuum limit, to larger non-perturbative effects in the scalar channel. We also recall how a transport peak related to the scalar density spectral function encodes non-perturbative information concerning the charm quark chemical equilibration rate close to equilibrium.

Hard thermal loop benchmark for the extraction of the nonperturbative QQ[over ¯] potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the Wilson loop. General arguments tell us that the lowest lying spectral peak encodes, through its position and shape, the real and imaginary parts of this complex potential. Here we benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. In other words, we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real and imaginary parts and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. Access to the full spectrum allows an investigation of spectral features that do not contribute to the potential but can pose a challenge to numerical attempts of an analytic continuation from imaginary time data. Differences in these contributions between the Wilson loop and gauge fixed Wilson line correlators are discussed. To better understand the difficulties in a numerical extraction we deploy the maximum entropy method with extended search space to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary parts are reproduced. Possible venues for improvement of the extraction strategy are discussed.

Temporal mesonic correlators at NLO for any quark mass

We present NLO results for thermal imaginary-time correlators in the vector and scalar channels as a function of the quark mass. The range of quark masses for which a non-relativistic approximation works in the temperature range considered is estimated, and charm quarks turn out to be a borderline case. Comparing with simulation data from fine lattices, we find good agreement in the vector channel but a substantial discrepancy in the scalar one. An explanation for the discrepancy is suggested in terms of physics of the quark-antiquark threshold region. Perturbative predictions for the bottom scalar spectral function around the threshold are also briefly reviewed.

Benchmarking the Bayesian reconstruction of the non-perturbative heavy ǪǬ potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the real-time Wilson loop. Through its position and shape, the lowest lying spectral peak encodes the real and imaginary part of this complex potential. We benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. I.e. we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real- and imaginary part and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. We deploy a novel Bayesian approach to the reconstruction of spectral functions to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary part are reproduced. Finally we apply the method to quenched lattice QCD data and perform an improved estimate of both real and imaginary part of the non-perturbative heavy ǪǬ potential.

Nonperturbative estimate of the heavy quark momentum diffusion coefficient

We estimate the momentum diffusion coefficient of a heavy quark within a pure SU(3) plasma at a temperature of about 1.5Tc. Large-scale Monte Carlo simulations on a series of lattices extending up to 1923×48 permit us to carry out a continuum extrapolation of the so-called color-electric imaginary-time correlator. The extrapolated correlator is analyzed with the help of theoretically motivated models for the corresponding spectral function. Evidence for a nonzero transport coefficient is found and, incorporating systematic uncertainties reflecting model assumptions, we obtain κ=(1.8–3.4)T3. This implies that the “drag coefficient,” characterizing the time scale at which heavy quarks adjust to hydrodynamic flow, is η−1D=(1.8–3.4)(Tc/T)2(M/1.5  GeV)  fm/c, where M is the heavy quark kinetic mass. The results apply to bottom and, with somewhat larger systematic uncertainties, to charm quarks.

Polaronic metal state at the LaAlO₃/SrTiO₃ interface

Interplay of spin, charge, orbital and lattice degrees of freedom in oxide heterostructures results in a plethora of fascinating properties, which can be exploited in new generations of electronic devices with enhanced functionalities. The paradigm example is the interface between the two band insulators LaAlO3 and SrTiO3 that hosts a two-dimensional electron system. Apart from the mobile charge carriers, this system exhibits a range of intriguing properties such as field effect, superconductivity and ferromagnetism, whose fundamental origins are still debated. Here we use soft-X-ray angle-resolved photoelectron spectroscopy to penetrate through the LaAlO3 overlayer and access charge carriers at the buried interface. The experimental spectral function directly identifies the interface charge carriers as large polarons, emerging from coupling of charge and lattice degrees of freedom, and involving two phonons of different energy and thermal activity. This phenomenon fundamentally limits the carrier mobility and explains its puzzling drop at high temperatures.

A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.