arXiv subjects

Alexander Rothkopf

Publications and source records attributed to Alexander Rothkopf.

At least 55 records · Page 3Linked to original sources

arXiv2020

Thermalization and dynamical spectral properties in the quark-meson model

We investigate the nonequilibrium evolution of the quark-meson model using two-particle irreducible effective action techniques. Our numerical simulations, which include the full dynamics of the order parameter of chiral symmetry, show how the model thermalizes into different regions of its phase diagram. In particular, by studying quark and meson spectral functions, we shed light on the real-time dynamics approaching the crossover transition, revealing e.g. the emergence of light effective fermionic degrees of freedom in the infrared. At late times in the evolution, the fluctuation-dissipation relation emerges naturally among both meson and quark degrees of freedom, confirming that the simulation successfully reaches thermal equilibrium.

hep-ph↗

arXiv2020

Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator

We develop a novel numerical scheme for the simulation of dissipative quantum dynamics following from two-body Lindblad master equations. All defining continuum properties of the Lindblad dynamics, hermiticity, positivity and in particular trace conservation of the evolved density matrix are preserved. The central ingredient is a new spatial difference operator, which not only fulfils the summation by parts (SBP) property but also implements a continuum reparametrization property. Using the time evolution of a heavy-quark anti-quark bound state in a hot thermal medium as an explicit example, we show how the reparametrization neutral summation-by-parts (RN-SBP) operator preserves the continuum properties of the theory.

physics.comp-ph↗

arXiv2020

Improved Gauss law model and in-medium heavy quarkonium at finite density and velocity

We explore the in-medium properties of heavy-quarkonium states at finite baryo-chemical potential and finite transverse momentum based on a modern complex-valued potential model. Our starting point is a novel, rigorous derivation of the generalized Gauss law for in-medium quarkonium, combining the non-perturbative physics of the vacuum bound state with a weak coupling description of the medium degrees of freedom. Its relation to previous models in the literature is discussed. We show that our approach is able to reproduce the complex lattice QCD heavy quark potential even in the non-perturbative regime, using a single temperature dependent parameter, the Debye mass $m_D$. After vetting the Gauss-law potential with state-of-the-art lattice QCD data, we extend it to the regime of finite baryon density and finite velocity, currently inaccessible to first principles simulations. In-medium spectral functions computed from the Gauss-law potential are subsequently used to estimate the $ψ'/J/ψ$ ratio in heavy-ion collisions at different beam energies and transverse momenta. We find qualitative agreement with the predictions from the statistical model of hadronization for the $\sqrt{s_{NN}}$ dependence and a mild dependence on the transverse momentum.

hep-ph↗

arXiv2020

Real-Time-Evolution of Heavy Quarks in the Glasma

We introduce a novel real-time formulation of lattice NRQCD designed for simulations in the background of an highly occupied gluon field. By evolving quarks in the background of a dynamically evolving gluon field we computed the time-evolution of heavy-quarkonium spectral functions as well as the static and for finitely heavy quarks generalised potential. We conclude that the back reaction of the quarks is necessary for any binding process. Here we discuss the methodology, our results and the origin of the absence of a binding process.

hep-lat↗

arXiv2020

Quarkonium production and suppression: Theory

Heavy quarkonium theory has seen significant progress over the past years. Not only has the community steadily improved the understanding of fully equilibrated quarkonium using first principles lattice QCD studies, but it has taken major steps towards developing a genuine dynamical understanding of quark-antiquark pairs immersed in a hot medium by embracing the paradigm of open quantum systems. We review recent developments, placing an emphasis on quarkonium real-time dynamics.

hep-ph↗

arXiv2019

Heavy Quarkonium in Extreme Conditions

In this report we review recent progress achieved in the understanding of heavy quarkonium under extreme conditions from a theory perspective. Its focus lies both on quarkonium properties in thermal equilibrium, as well as recent developments towards a genuine real-time description, valid also out-of-equilibrium. We will give an overview of the theory tools developed and deployed over the last decade, including effective field theories, lattice field theory simulations, modern methods for spectral reconstructions and the the open-quantum systems paradigm. The report will discuss in detail the concept of quarkonium melting, providing the reader with a contemporary perspective. In order to judge where future progress is needed we will also discuss recent results from experiments and phenomenological modeling of quarkonium in relativistic heavy-ion collisions.

hep-ph↗

arXiv2019

Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma

In this paper we study the real-time evolution of heavy quarkonium in the quark-gluon plasma (QGP) on the basis of the open quantum systems approach. In particular, we shed light on how quantum dissipation affects the dynamics of the relative motion of the quarkonium state over time. To this end we present a novel non-equilibrium master equation for the relative motion of quarkonium in a medium, starting from Lindblad operators derived systematically from quantum field theory. In order to implement the corresponding dynamics, we deploy the well established quantum state diffusion method. In turn we reveal how the full quantum evolution can be cast in the form of a stochastic non-linear Schrödinger equation. This for the first time provides a direct link from quantum chromodynamics (QCD) to phenomenological models based on non-linear Schrödinger equations. Proof of principle simulations in one-dimension show that dissipative effects indeed allow the relative motion of the constituent quarks in a quarkonium at rest to thermalize. Dissipation turns out to be relevant already at early times well within the QGP lifetime in relativistic heavy ion collisions.

nucl-th↗

arXiv2019

Towards the nucleon hadronic tensor from lattice QCD

We present the first calculation of the hadronic tensor on the lattice for the nucleon. The hadronic tensor can be used to extract the structure functions in deep inelastic scatterings and also provide information for the neutrino-nucleon scattering which is crucial to the neutrino-nucleus scattering experiments at low energies. The most challenging part in the calculation is to solve an inverse problem. We have implemented and tested three algorithms using mock data, showing that the Bayesian Reconstruction method has the best resolution in extracting peak structures while the Backus-Gilbert and Maximum Entropy methods are somewhat more stable for the flat spectral function. Numerical results are presented for both the elastic case (clover fermions on domain wall configuration with $m_π\sim$ 370 MeV and $a\sim$ 0.06 fm) and a case (anisotropic clover lattice with $m_π\sim$ 380 MeV and $a_t\sim$ 0.035 fm) with large momentum transfer. For the former case, the reconstructed Minkowski hadronic tensor gives precisely the vector charge which proves the feasibility of the approach. While for the latter case, the nucleon resonances and possibly shallow inelastic scattering contributions around $ν=1$ GeV are clearly observed but no information is obtained for higher excited states with $ν>2$ GeV. A check of the effective masses of $ρ$ meson with different lattice setups indicates that, in order to reach higher energy transfers, using lattices with smaller lattice spacings is essential.

hep-ph↗

arXiv2019

Quarkonium Phenomenology from a Generalised Gauss Law

We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum potential with a weak-coupling description of the QCD medium. The resulting Gauss-law parametrisation is able to reproduce full lattice QCD data by using only a single temperature dependent parameter, the Debye mass $m_D$. Using this parametrisation we model the in-medium potential at finite baryo-chemical potential, which allows us to estimate the $Ψ^\prime$/$J/Ψ$ ratio in heavy-ion collisions at different beam energies.

hep-ph↗

arXiv2019

Quarkonium Production in the QGP

We report on recent theory progress in understanding the production of heavy quarkonium in heavy-ion collisions based on the in-medium heavy-quark potential extracted from lattice QCD simulations. On the one hand, the proper in-medium potential allows us to study the spectral properties of heavy quarkonium in thermal equilibrium, from which we estimate the $ψ^\prime$ to $J/ψ$ ratio in heavy-ion collisions. On the other hand, the potential provides a central ingredient in the description of the real-time evolution of heavy-quarkonium formulated in the open-quantum-systems framework.

hep-ph↗

arXiv2019

Spectral properties of light and charm mesons from $N_f=2+1$ anisotropic lattice QCD

We compute temporal correlators and spectral functions for light, open charm and charmonium mesons in the pseudoscalar and vector channel for a range of temperatures below and above the deconfinement transition. The study is carried out using anisotropic lattice QCD with 2+1 dynamical flavours, $a_s=0.123\,$fm and $a_s/a_τ=3.5$. The high-temperature results are benchmarked by comparing them to reconstructed correlators obtained by direct summation of the zero temperature correlator. We use two Bayesian methods to reconstruct the spectral functions: the maximum entropy method and the more recent BR method.

hep-lat↗

arXiv2019

Bayesian techniques and applications to QCD

Realizing the full potential of interconnecting the large amounts of data created in physics experiments, phenomenological models and theory simulations requires robust tools for statistical inference. Here I review a particularly promising branch, Bayesian statistics, which over the past decade has found manifold use in high-energy physics. After a brief introduction to Bayesian statistics I will present two concrete examples, where Bayesian thinking has led to progress in understanding strongly interacting matter: unfolding problems in the form of lattice QCD spectral functions (in spirit similar to detector corrections), as well as the efficient estimation of quark-gluon-plasma parameters from a systematic comparison of experimental heavy-ion collision data and phenomenological models.

hep-ph↗

arXiv2019

In-medium heavy quarkonium from lattice NRQCD

We present the final results from a multi-year study of the in-medium spectral properties of heavy quarkonium bound states on the lattice. In this work we combine high statistics $N_f=2+1$ ensembles from the HotQCD collaboration with the effective theory NRQCD and improved Bayesian spectral reconstruction methods. We corroborate with high precision the hierarchical in-medium modification of quarkonium states with respect to their vacuum binding energy and provide updated values on melting temperatures. In particular we are able to understand previous disagreements between different Bayesian methods as resulting from underestimated systematic uncertainties. The main quantitative result is a robust determination of the in-medium mass shifts of quarkonium ground states, which we find are negative, consistent with the behavior observed in strongly coupled pNRQCD potential based computations.

hep-lat↗

arXiv2019

Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks

The computation of the parton distribution functions (PDF) or distribution amplitudes (DA) of hadrons from first principles lattice QCD constitutes a central open problem. In this study, we present and evaluate the efficiency of a selection of methods for inverse problems to reconstruct the full $x$-dependence of PDFs. Our starting point are the so called Ioffe time PDFs, which are accessible from Euclidean time calculations in conjunction with a matching procedure. Using realistic mock data tests, we find that the ill-posed incomplete Fourier transform underlying the reconstruction requires careful regularization, for which both the Bayesian approach as well as neural networks are efficient and flexible choices.

hep-lat↗

arXiv2018

Reconstructing the gluon

We reconstruct the gluon spectral function in Landau gauge QCD from numerical data for the gluon propagator. The reconstruction relies on two novel ingredients: Firstly we derive analytically the low frequency asymptotics of the spectral function. Secondly we construct a functional basis from a careful consideration of the analytic properties of the gluon propagator in Landau gauge. This allows us to reliably capture the non-perturbative regime of the gluon spectrum. We also compare different reconstruction methods and discuss the respective systematic errors.

hep-ph↗

arXiv2018

Quarkonium in-medium properties from realistic lattice NRQCD

We present the final results of our high statistics study on the properties of bottomonium and charmonium at finite temperature. We focus on the temperature range around the crossover transition $150\leq T\leq 410$MeV, relevant for current heavy ion collision experiments. The QCD medium degrees of freedom which consist of dynamical u,d, and s quarks and gluons are captured by realistic state-of-the art ($m_π\approx 161$MeV) lattice QCD simulations of the HotQCD collaboration. For the heavy quarks we deploy the non-relativistic effective field theory of QCD, NRQCD. The in-medium properties of quarkonium are deduced from their spectral functions, which are reconstructed using improved and novel Bayesian approaches. Through a systematic analysis we shed light on the origin of the discrepancies in melting temperatures previously reported in the literature, showing that they are owed to underestimated methods uncertainties of the deployed spectral reconstructions. Our simulations corroborate a picture of sequential in-medium modification, ordered according to the vacuum binding energy of the states. As a central quantitative result, our study reveals how the mass of the heavy quarkonium ground state reduces as temperature increases. The observed spectral modifications are interpreted in the light of, and compared to previous studies based on the complex lattice potential for heavy quarkonium. Thus for the first time we provide a robust picture of in-medium heavy quarkonium modification in the quark-gluon plasma consistent among different non-relativistic methods. We also critically discuss the perspectives for improving on these results.

hep-lat↗

arXiv2018

Realistic in-medium heavy-quark potential from high statistics lattice QCD simulations

We present our first results on a direct computation of the complex in-medium heavy quark potential from realistic lattice QCD simulations. Ensembles with $N_τ=12$ from the HotQCD and TUMQCD collaboration offer unprecedented high statistics, those with $N_τ=16$ unprecedented time resolution, making possible a robust extraction of the real part from the spectral functions of Wilson line correlators. To this end we deploy a combination of a Bayesian reconstruction (BR method), as well as a Padé-like approximation. We corroborate findings made on less realistic lattices that ${\rm Re}[V]$ smoothly transitions from a confining to a screened behavior at high temperatures and its values lie close to the color singlet free energies. A finite value of the ${\rm Im}[V]$ is observed in the quark-gluon-plasma phase.

hep-lat↗

arXiv2018

Bayesian study of relativistic open and hidden charm in anisotropic lattice QCD

We present the first combined study of correlators and spectral properties of charmonium and open-charm-mesons at finite temperature using a fully relativistic lattice QCD approach. The QCD medium is captured by second generation anisotropic 24^3xN_t lattices from the FASTSUM collaboration, including 2+1 flavors of clover discretized quarks with m_pi~380 MeV. Two Bayesian methods are deployed to reconstruct the spectral functions, the recent BR method as well as the Maximum Entropy Method with Fourier basis. We take particular care to disentangle genuine in-medium effects from method artifacts with the help of the reconstructed correlator. Consistent with the direct inspection of correlators, we observe no significant in-medium modification for J/Psi and eta_c around the crossover, while the chi_c states on the other hand show clear changes around the transition. At the highest temperature, T=352 MeV, J/Psi and eta_c also exhibit discernible changes compared to the vacuum. For D mesons around $T_c$, no significant modifications are observed, but we find clear indications that no bound state survives at the highest temperature of T=352 MeV. Above T_c we discover a significant difference between D and D* mesons, the latter being much more strongly affected by the medium.

hep-lat↗