arXiv subjects

Alexander Rothkopf

Publications and source records attributed to Alexander Rothkopf.

At least 91 records · Page 5Linked to original sources

arXiv2015

Quarkonium at finite temperature: Towards realistic phenomenology from first principles

We present the finite temperature spectra of both bottomonium and charmonium, obtained from a consistent lattice QCD based potential picture. Starting point is the complex in-medium potential extracted on full QCD lattices with dynamical u,d and s quarks, generated by the HotQCD collaboration. Using the generalized Gauss law approach, vetted in a previous study on quenched QCD, we fit ${\rm Re}[V]$ with a single temperature dependent parameter $m_D$, the Debye screening mass, and confirm the up to now tentative values of ${\rm Im}[V]$. The obtained analytic expression for the complex potential allows us to compute quarkonium spectral functions by solving an appropriate Schrödinger equation. These spectra exhibit thermal widths, which are free from the resolution artifacts that plague direct reconstructions from Euclidean correlators using Bayesian methods. In the present adiabatic setting, we find clear evidence for sequential melting and derive melting temperatures for the different bound states. Quarkonium is gradually weakened by both screening (${\rm Re}[V]$) and scattering (${\rm Im}[V]$) effects that in combination lead to a shift of their in-medium spectral features to smaller frequencies, contrary to the mass gain of elementary particles at finite temperature.

hep-ph↗

arXiv2015

In-medium heavy-quarkonium from lattice QCD spectral functions

We discuss recent progress in the study of in-medium heavy quarkonium using first-principles lattice QCD calculations and effective field theory. In particular our focus lies on real-time information carried by QCD spectral functions and we report on a novel strategy for their extraction from Euclidean-time simulations. Combining an effective description for heavy quarks with finite temperature lattice QCD we compute in-medium spectra providing insight in heavy quarkonium melting in a static thermal medium. On the other hand we use spectral information to extract the complex in-medium potential which provides the basis for a dynamical description of quarkonium real-time evolution via the Schrödinger equation.

hep-lat↗

arXiv2015

Lattice NRQCD study of S- and P-wave bottomonium states in a thermal medium with $N_f=2+1$ light flavors

We investigate the properties of S-and P-wave bottomonium states in the vicinity of the deconfinement transition temperature. The light degrees of freedom are represented by dynamical lattice QCD configurations of the HotQCD collaboration with $N_f = 2 + 1$ flavors. Bottomonium correlators are obtained from bottom quark propagators, computed in nonrelativistic quantum chromodynamics (NRQCD) under the background of these gauge field configurations. The spectral functions for the $^3S_1$ ($Υ$) and $^3P_1$ ($χ_{b1}$) channel are extracted from the Euclidean time correlators using a novel Bayesian approach in the temperature region $140 {\rm MeV} \le T \le 249 {\rm MeV}$ and the results are contrasted to those from the standard maximum entropy method. We find that the new Bayesian approach is far superior to the maximum entropy method. It enables us to study reliably the presence or absence of the lowest state signal in the spectral function of a certain channel, even under the limitations present in the finite temperature setup. We find that $χ_{b1}$ survives up to $T=249 {\rm MeV}$, the highest temperature considered in our study and put stringent constraints on the size of the medium modification of $Υ$ and $χ_{b1}$ states.

hep-lat↗

arXiv2015

A gauge invariant Debye mass and the complex heavy-quark potential

Following the original idea of Debye, we define and extract a gauge-invariant screening mass from the complex static in-medium heavy-quark potential $V_{Q\bar{Q}}$, recently obtained from lattice QCD. To this end we derive a field theoretically motivated analytic formula that faithfully reproduces both the screened real- as well as the imaginary part of the lattice potential with a single temperature dependent fit parameter $m_D(T)$. Using values of the real part of $V_{Q\bar{Q}}$ in a gluonic medium, we obtain Debye masses compatible with predictions from HTL perturbation theory.

hep-ph↗

arXiv2015

A first look at Bottomonium melting via a stochastic potential

We investigate the phenomenon of Bottomonium melting in a thermal quark-gluon plasma using three-dimensional stochastic simulations based on the concept of open-quantum systems. In this non-relativistic framework, introduced in [Phys.Rev. D85 (2012) 105011], which makes close contact to the potentials derived in effective field theory, the $b\bar{b}$ system evolves unitarily under the incessant kicks by the constituents of the surrounding heat bath. In particular thermal fluctuations and the presence of a complex potential in the EFT are naturally related. An intricate interplay between state mixing and thermal excitations emerges as we show how non-thermal initial conditions of Bottomonium states evolve over time. We emphasize that the dynamics of these states gives us access to information beyond what is encoded in the thermal Bottomonium spectral functions. Assumptions underlying our approach and their limitations, as well as the refinements necessary to connect to experimental measurements under more realistic conditions are discussed.

hep-ph↗

arXiv2014

Quark-gluon plasma phenomenology from anisotropic lattice QCD

The FASTSUM collaboration has been carrying out simulations of N_f=2+1 QCD at nonzero temperature in the fixed-scale approach using anisotropic lattices. Here we present the status of these studies, including recent results for electrical conductivity and charge diffusion, and heavy quarkonium (charm and beauty) physics.

nucl-th↗

arXiv2014

Lattice NRQCD study on in-medium bottomonium spectra using a novel Bayesian reconstruction approach

We present recent results on the in-medium modification of S- and P-wave bottomonium states around the deconfinement transition. Our study uses lattice QCD with $N_f=2+1$ light quark flavors to describe the non-perturbative thermal QCD medium between $140$MeV$<T<249$MeV and deploys lattice regularized non-relativistic QCD (NRQCD) effective field theory to capture the physics of heavy quark bound states immersed therein. The spectral functions of the $^3S_1$ $(Υ)$ and $^3P_1$ $(χ_{b1})$ bottomonium states are extracted from Euclidean time Monte Carlo simulations using a novel Bayesian prescription, which provides higher accuracy than the Maximum Entropy Method. Based on a systematic comparison of interacting and free spectral functions we conclude that the ground states of both the S-wave $(Υ)$ and P-wave $(χ_{b1})$ channel survive up to $T=249$MeV. Stringent upper limits on the size of the in-medium modification of bottomonium masses and widths are provided.

hep-lat↗

arXiv2014

The Bayesian reconstruction of the in-medium heavy quark potential from lattice QCD and its stability

We report recent results of a non-perturbative determination of the static heavy-quark potential in quenched and dynamical lattice QCD at finite temperature. The real and imaginary part of this complex quantity are extracted from the spectral function of Wilson line correlators in Coulomb gauge. To obtain spectral information from Euclidean time numerical data, our study relies on a novel Bayesian prescription that differs from the Maximum Entropy Method. We perform simulations on quenched $32^3\times N_τ$ $(β=7.0,ξ=3.5)$ lattices with $N_τ=24,...,96$, which cover $839{\rm MeV} \geq T\geq 210 {\rm MeV}$. To investigate the potential in a quark-gluon plasma with light u,d and s quarks we utilize $N_f=2+1$ ASQTAD lattices with $m_l=m_s/20$ by the HotQCD collaboration, giving access to temperatures between $286 {\rm MeV} \geq T\geq 148{\rm MeV}$. The real part of the potential exhibits a clean transition from a linear, confining behavior in the hadronic phase to a Debye screened form above deconfinement. Interestingly its values lie close to the color singlet free energies in Coulomb gauge at all temperatures. We estimate the imaginary part on quenched lattices and find that it is of the same order of magnitude as in hard-thermal loop perturbation theory. From among all the systematic checks carried out in our study, we discuss explicitly the dependence of the result on the default model and the number of datapoints.

hep-lat↗

arXiv2014

The in-medium heavy quark potential from quenched and dynamical lattice QCD

We present our latest results for the the complex valued static heavy-quark potential at finite temperature from lattice QCD. The real and imaginary part of the potential are obtained from the position and width of the lowest lying peak in the spectral function of the Wilson line correlator in Coulomb gauge. Spectral information is extracted from Euclidean time data using a novel Bayesian approach different from the Maximum Entropy Method. In order to extract both the real and imaginary part, we generated anisotropic quenched lattices $32^3\times N_τ$ $(β=7.0,ξ=3.5)$ with $N_τ=24,\ldots,96$, corresponding to $839{\rm MeV} \geq T\geq 210 {\rm MeV}$. For the case of a realistic QCD medium with light u, d and s quarks we use isotropic $48^3\times12$ ASQTAD lattices with $m_l=m_s/20$ provided by the HotQCD collaboration, which span $286 {\rm MeV} \geq T\geq 148{\rm MeV}$. We find a clean transition from a confining to a Debye screened real part and observe that its values lie close to the color singlet free energies in Coulomb gauge. The imaginary part, estimated on quenched lattices, is found to be of the same order of magnitude as in hard-thermal loop (HTL) perturbation theory.

hep-lat↗

arXiv2014

Static quark-antiquark potential in the quark-gluon plasma from lattice QCD

We present a state-of-the-art determination of the complex valued static quark-antiquark potential at phenomenologically relevant temperatures around the deconfinement phase transition. Its values are obtained from non-perturbative lattice QCD simulations using spectral functions extracted via a novel Bayesian inference prescription. We find that the real part, both in a gluonic medium as well as in realistic QCD with light $u$, $d$ and $s$ quarks, lies close to the color singlet free energies in Coulomb gauge and shows Debye screening above the (pseudo) critical temperature $T_c$. The imaginary part is estimated in the gluonic medium, where we find that it is of the same order of magnitude as in hard-thermal loop resummed perturbation theory in the deconfined phase.

hep-lat↗

arXiv2014

NRQCD based S- and P-wave bottomonium spectra at finite temperature from $48^3 \times 12$ lattices with $N_f=2+1$ light HISQ flavors

We study S-wave and P-wave bottomonium spectral functions at non-zero temperature in 2+1 flavor QCD using the NRQCD formulation for bottom quarks. We use a novel Bayesian approach to reconstruct the spectral functions and find that $χ_{b1}$ survives up to $T=249 {\rm MeV}$. We also study the effect of different temporal discretizations of the NRQCD formalism on the bottomonium correlation functions

hep-lat↗

arXiv2013

Lattice NRQCD study of in-medium bottomonium states using $N_f = 2+1, 48^3 \times 12$ HotQCD configurations

The behavior of bottomonium state correlators at non-zero temperature, $140.4 (β= 6.664) \le T \le 221 (β= 7.280)$ (MeV), where the transition temperature is $154(9)$ (MeV), is studied, using lattice NRQCD on $48^3 \times 12$ HotQCD HiSQ action configurations with light dynamical $N_f = 2 + 1$ ($m_{u,s}/m_s = 0.05$) staggered quarks. In order to understand finite temperature effects on quarkonium states, zero temperature behavior of bottomonium correlators is compared based on $32^4$ ($β= 6.664, 6.800$ and $6.950$) and $48^3 \times 64$ ($β= 7.280)$ lattices. We find that temperature effects on S-wave bottomonium states are small but P-wave bottomonium states show a noticeable temperature dependence above the transition temperature.

hep-lat↗

arXiv2013

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 $N_ω\gg N_τ$ 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.

hep-lat↗

arXiv2013

Benchmarking the Bayesian reconstruction of the non-perturbative heavy $Q\bar{Q}$ 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 $Q\bar{Q}$ potential.

hep-lat↗

arXiv2013

A novel Bayesian approach to spectral function reconstruction

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 MEM. We present a realistic test of our method in the context of the non-perturbative 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. An improved potential estimation from previously investigated quenched lattice QCD correlators is provided.

hep-lat↗

arXiv2013

A hard thermal loop benchmark for the extraction of the nonperturbative $Q\bar{Q}$ 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 part of this complex potential. Here 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. 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 part are reproduced. Possible venues for improvement of the extraction strategy are discussed.

hep-ph↗

arXiv2013

From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma

The 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 Schroedinger 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.

hep-ph↗

arXiv2013

Improved Maximum Entropy Analysis with an Extended Search Space

The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.

physics.comp-ph↗