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.

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.

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.

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.

A relation between screening masses and real-time rates

Thermal screening masses related to the conserved vector current are determined for the case that the current carries a non-zero Matsubara frequency, both in a weak-coupling approach and through lattice QCD. We point out that such screening masses are sensitive to the same infrared physics as light-cone real-time rates. In particular, on the perturbative side, the inhomogeneous Schrödinger equation determining screening correlators is shown to have the same general form as the equation implementing LPM resummation for the soft-dilepton and photon production rates from a hot QCD plasma. The static potential appearing in the equation is identical to that whose soft part has been determined up to NLO and on the lattice in the context of jet quenching. Numerical results based on this potential suggest that screening masses overshoot the free results (multiples of 2πT) more strongly than at zero Matsubara frequency. Four-dimensional lattice simulations in two-flavour QCD at temperatures of 250 and 340 MeV confirm the non-static screening masses at the 10% level. Overall our results lend support to studies of jet quenching based on the same potential at T ≳ 250 MeV.

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.

Lattice NRQCD study of in-medium bottomonium states using Nf = 2+1, 48³ × 12 HotQCD configurations

The behavior of bottomonium state correlators at non-zero temperature, 140.4(β = 6.664) ≤ T ≤ 221(β = 7.280) (MeV), where the transition temperature is 154(9) (MeV), is studied, using lattice NRQCD on 48³ ×12 HotQCD HiSQ action configurations with light dynamical Nf = 2+1 (mu,s/ms = 0.05) staggered quarks. In order to understand finite temperature effects on quarkonium states, zero temperature behavior of bottomonium correlators is compared based on 32⁴ (β = 6.664,6.800 and 6.950) and 48³ ×64 (β = 7.280) lattices. We find that temperature effects on S-wave bottomoniumstates are small but P-wave bottomoniumstates show a noticeable temperature dependence above the transition temperature.

Measurement of event-plane correlations in √s_NN=2.76 TeV lead-lead collisions with the ATLAS detector

A measurement of event-plane correlations involving two or three event planes of different order is presented as a function of centrality for 7 μb −1 Pb+Pb collision data at √s NN =2.76 TeV, recorded by the ATLAS experiment at the Large Hadron Collider. Fourteen correlators are measured using a standard event-plane method and a scalar-product method, and the latter method is found to give a systematically larger correlation signal. Several different trends in the centrality dependence of these correlators are observed. These trends are not reproduced by predictions based on the Glauber model, which includes only the correlations from the collision geometry in the initial state. Calculations that include the final-state collective dynamics are able to describe qualitatively, and in some cases also quantitatively, the centrality dependence of the measured correlators. These observations suggest that both the fluctuations in the initial geometry and the nonlinear mixing between different harmonics in the final state are important for creating these correlations in momentum space.

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

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 β c is reproduced to better than one percent from a one-coupling effective theory on N τ = 4 lattices while up to five couplings are needed on N τ = 8 for the same accuracy.

Parton energy loss and momentum broadening at NLO in high temperature QCD plasmas

We present an overview of a perturbative-kinetic approach to jet propagation, energy loss, and momentum broadening in a high temperature quark–gluon plasma. The leading-order kinetic equations describe the interactions between energetic jet-particles and a non-abelian plasma, consisting of on-shell thermal excitations and soft gluonic fields. These interactions include ↔ scatterings, collinear bremsstrahlung, and drag and momentum diffusion. We show how the contribution from the soft gluonic fields can be factorized into a set of Wilson line correlators on the light-cone. We review recent field-theoretical developments, rooted in the causal properties of these correlators, which simplify the calculation of the appropriate Wilson lines in thermal field theory. With these simplifications lattice measurements of transverse momentum broadening have become possible, and the kinetic equations describing parton transport have been extended to next-to-leading order in the coupling g.