1,721,045 research outputs found
From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma
Full text linkThe in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound states at finite temperature through a Schrödinger equation with an instantaneous potential. Here we review recent progress in devising a comprehensive approach to define such a potential from first principles QCD and extract its, in general complex, values from non-perturbative lattice QCD simulations. Based on the theory of open quantum systems we will show how to interpret the role of the imaginary part in terms of spatial decoherence by introducing the concept of a stochastic potential. Shortcomings as well as possible paths for improvement are discussed
Hard thermal loop benchmark for the extraction of the nonperturbative QQ[over ¯] potential
No full textThe 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
Improved Maximum Entropy Analysis with an Extended Search Space
No full textRothkopf A. Improved Maximum Entropy Analysis with an Extended Search Space. Journal of Computational Physics. 2013;238:106-114.The standard implementation of the Maximum Entropy Method (MEM) follows Bryanand deploys a Singular Value Decomposition (SVD) to limit the dimensionality ofthe underlying solution space apriori. Here we present arguments based on theshape of the SVD basis functions and numerical evidence from a mock dataanalysis, which show that the correct Bayesian solution is not in generalrecovered with this approach. As a remedy we propose to extend the search basissystematically, which will eventually recover the full solution space and thecorrect solution. In order to adequately approach problems where anexponentially damped kernel is used, we provide an open-source implementation,using the C/C++ language that utilizes high precision arithmetic adjustable atrun-time. The LBFGS algorithm is included in the code in order to attackproblems without the need to resort to a particular search space restriction
Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories
No full textWe 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
Light-cone Wilson loop in classical lattice gauge theory
Full text linkThe transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity
In medium static quark anti-quark potential from lattice QCD
Full text linkPhD thesis in Mathematics and PhysicsIn this thesis we present recent progress in the quest to study the properties of the quark gluon plasma in relativistic heavy ion collisions through a better understanding of the binding of heavy quark and anti-quark pairs (quarkonium). We present two studies investigating the complex binding potential between heavy quarks using non-perturbative lattice QCD simulations and modern data analysis techniques that were contributed to and performed as a part of this PhD project. The first study utilizes state of the art simulations with 2+1 flavours of dynamical light HISQ quarks. This study revealed a complex potential with an unscreened real part. Its results were in stark contrast to previous studies on quenched and full QCD lattices which had all shown a complex potential with a screened real part. This unusual result motivated a second study, where we re-investigated the potential on high resolution quenched lattices to confirm their robustness using the same methods deployed in the full QCD study. We found that the analysis techniques applied to the raw correlators confirms previous results, i.e. resulting in a complex potential with a screened real part. Applying the same analysis after performing a recently proposed subtraction procedure leads instead to an unscreened potential akin to the first study on HISQ lattices.The Norwegian research foundatio
Benchmarking the Bayesian reconstruction of the non-perturbative heavy ǪǬ potential
Full text linkThe 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
A new Bayesian approach to the reconstruction of spectral functions
Full text linkWe 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
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