arXiv subjects
Publications and source records attributed to Ulrich Heinz.
A new formulation of (3+1)-dimensional anisotropic hydrodynamics is presented that accounts nonperturbatively for the large longitudinal-transverse pressure anisotropy and bulk viscous pressure in heavy-ion collisions. The initialization of the anisotropic hydrodynamic stage is discussed, and a comparison to standard viscous hydrodynamics for (0+1)- dimensional Bjorken expansion is presented.
We study the evolution of hydrodynamic and non-hydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e. of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from non-hydrodynamic modes coupling into the entropy evolution which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise macroscopic description for these highly anisotropically expanding systems.
Starting from IP-Glasma initial conditions, we investigate the effects of bulk pressure on low mass dilepton production at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) energies. Though thermal dilepton $v_2$ is affected by the presence of both bulk and shear viscosity, whether or not these effects can be measured depends on the dilepton "cocktail" contribution to the the low mass dilepton $v_2$. Combining the thermal and "cocktail" dileptons, the effects of bulk viscosity on total dilepton $v_2$ is investigated.
The modification of hard jets in an extended static medium held at a fixed temperature is studied using three different Monte-Carlo event generators (LBT, MATTER, MARTINI). Each event generator contains a different set of assumptions regarding the energy and virtuality of the partons within a jet versus the energy scale of the medium, and hence, applies to a different epoch in the space-time history of the jet evolution. For the first time, modeling is developed where a jet may sequentially transition from one generator to the next, on a parton-by-parton level, providing a detailed simulation of the space-time evolution of medium modified jets over a much broader dynamic range than has been attempted previously in a single calculation. Comparisons are carried out for different observables sensitive to jet quenching, including the parton fragmentation function and the azimuthal distribution of jet energy around the jet axis. The effect of varying the boundary between different generators is studied and a theoretically motivated criterion for the location of this boundary is proposed. The importance of such an approach with coupled generators to the modeling of jet quenching is discussed.
Starting from IP-Glasma initial conditions, we investigate the effects of bulk pressure on thermal dilepton production at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) energies. Though results of the thermal dilepton $v_2$ under the influence of both bulk and shear viscosity is presented for top RHIC energy, more emphasis is put on LHC energy where such a calculation is computed for the first time. The effects of the bulk pressure on thermal dilepton $v_2$ at the LHC are explored through bulk-induced modifications on the dilepton yield.
A systematic analysis of correlations between different orders of $p_T$-differential flow is presented, including mode coupling effects in flow vectors, correlations between flow angles (a.k.a. event-plane correlations), and correlations between flow magnitudes, all of which were previously studied with integrated flows. We find that the mode coupling effects among differential flows largely mirror those among the corresponding integrated flows, except at small transverse momenta where mode coupling contributions are small. For the fourth- and fifth-order flow vectors $V_4$ and $V_5$ we argue that the event plane correlations can be understood as the ratio between the mode coupling contributions to these flows and and the flow magnitudes. We also find that for $V_4$ and $V_5$ the linear response contribution scales linearly with the corresponding cumulant-defined eccentricities but not with the standard eccentricities.
We quantitatively estimate properties of the quark-gluon plasma created in ultra-relativistic heavy-ion collisions utilizing Bayesian statistics and a multi-parameter model-to-data comparison. The study is performed using a recently developed parametric initial condition model, TRENTO, which interpolates among a general class of particle production schemes, and a modern hybrid model which couples viscous hydrodynamics to a hadronic cascade. We calibrate the model to multiplicity, transverse momentum, and flow data and report constraints on the parametrized initial conditions and the temperature-dependent transport coefficients of the quark-gluon plasma. We show that initial entropy deposition is consistent with a saturation-based picture, extract a relation between the minimum value and slope of the temperature-dependent specific shear viscosity, and find a clear signal for a nonzero bulk viscosity.
The effects of event-by-event fluctuations in the initial geometry of the colliding nuclei are important in the analysis of final flow observables in relativistic heavy-ion collisions. We use hydrodynamic simulations to study the amplitude correlations between different orders of event-by-event fluctuating anisotropic flow harmonics. While the general trends seen in the experimental data are qualitatively reproduced by the model, deviations in detail, in particular for peripheral collisions, point to the need for more elaborate future calculations with a hybrid approach that describes the late hadronic stage of the evolution microscopically. It is demonstrated explicitly that the observed anti-correlation between $v_2$ and $v_3$ is the consequence of approximately linear hydrodynamic response to a similar anti-correlation of the corresponding initial eccentricities $ε_2$ and $ε_3$. For $n{\,>\,}3$, the hydrodynamic correlations between $v_{2,3}$ and $v_n$ deviate from the rescaled correlations among the corresponding initial eccentricities, demonstrating nonlinear mode coupling effect in higher order flows.
This document summarizes thoughts on opportunities in the soft-QCD sector from high-energy nuclear collisions at high luminosities.
We explore the effects of event-by-event fluctuations of Hanbury Brown-Twiss (HBT) radii and show how they can be observed experimentally. The relation of measured HBT radii extracted from ensemble-averaged correlation functions to the mean of their event-by-event probability distribution is clarified. We propose a method to experimentally determine the mean and variance of this distribution and test it on an ensemble of fluctuating events generated with the viscous hydrodynamic code VISH2+1. Using the same code, the sensitivity of the mean and variance of the HBT radii to the specific QGP shear viscosity $η/s$ is studied. We report sensitivity of the mean pion HBT radii and their variances to the temperature dependence of $η/s$ near the quark-hadron transition at a level similar (10-20%) to that which was previously observed for elliptic and quadrangular flow of charged hadrons [1].
The iEBE-VISHNU code package performs event-by-event simulations for relativistic heavy-ion collisions using a hybrid approach based on (2+1)-dimensional viscous hydrodynamics coupled to a hadronic cascade model. We present the detailed model implementation, accompanied by some numerical code tests for the package. iEBE-VISHNU forms the core of a general theoretical framework for model-data comparisons through large scale Monte-Carlo simulations. A numerical interface between the hydrodynamically evolving medium and thermal photon radiation is also discussed. This interface is more generally designed for calculations of all kinds of rare probes that are coupled to the temperature and flow velocity evolution of the bulk medium, such as jet energy loss and heavy quark diffusion.
We give a pedagogical review of relativistic hydrodynamics relevant to relativistic heavy ion collisions. Topics discussed include linear response theory derivation of 2nd order viscous hydrodynamics including the Kubo formulas, kinetic theory derivation of 2nd order viscous hydrodynamics, anisotropic hydrodynamics and a brief review of numerical algorithms. Emphasis is given to the theory of hydrodynamics rather than phenomenology.
Hanbury-Brown--Twiss interferometry is a technique which yields effective widths (i.e., "HBT radii") of homogeneity regions in the fireballs produced in heavy ion collisions. Because the initial conditions of these collisions are stochastically fluctuating, the measured HBT radii also exhibit variation on an event-by-event basis. However, HBT measurements have, to date, been performed only on an ensemble-averaged basis, due to inherent limitations of finite particle statistics. In this paper, we show that experimental measurements to date are best characterized theoretically as weighted averages of the event-by-event HBT radii, and we propose a new method for extracting experimentally both the arithmetic mean and the variance of the event-by-event distribution of HBT radii. We demonstrate the extraction of the mean and variance of this distribution for a particular ensemble of numerically generated events, and offer some ideas to extend and generalize the method to enable measurement of higher moments of the HBT distribution as well.
Using event-by-event viscous fluid dynamics to evolve fluctuating initial density profiles from the Monte-Carlo Glauber model for U+U collisions, we report a "knee"-like structure in the elliptic flow as a function of collision centrality, located around the 0.5% most central collisions as measured by the final charged multiplicity. This knee is due to the preferential selection of tip-on-tip collision geometries by a high-multiplicity trigger. Such a knee structure is not seen in the STAR data. This rules out the two-component MC-Glauber model for initial energy and entropy production. Hence an enrichment of tip-tip configurations by triggering solely on high-multiplicity in the U+U collisions does not work. On the other hand, by using the Zero Degree Calorimeters (ZDCs) coupled with event-shape engineering such a selection is possible. We identify the selection purity of body-body and tip-tip events in full-overlap U+U collisions. By additionally constraining the asymmetry of the ZDC signals we can further increase the probability of selecting tip-tip events in U+U collisions.
Recent progress in extracting the specific shear viscosity of the Quark-Gluon Plasma from phenomenological studies is highlighted.
In ultra-central heavy-ion collisions, anisotropic hydrodynamic flow is generated by density fluctuations in the initial state rather than by geometric overlap effects. For a given centrality class, the initial fluctuation spectrum is sensitive to the method chosen for binning the events into centrality classes. We show that sorting events by total initial entropy or by total final multiplicity yields event classes with equivalent statistical fluctuation properties, in spite of viscous entropy production during the fireball evolution. With this initial entropy-based centrality definition we generate several classes of ultra-central Pb+Pb collisions at LHC energies and evolve the events using viscous hydrodynamics with non-zero shear but vanishing bulk viscosity. Comparing the predicted anisotropic flow coefficients for charged hadrons with CMS data we find that both the Monte Carlo Glauber (MC-Glb) and Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) models produce initial fluctuation spectra that are incompatible with the measured final anisotropic flow power spectrum, for any choice of the specific shear viscosity. In spite of this failure, we show that the hydrodynamic model can qualitatively explain, in terms of event-by-event fluctuations of the anisotropic flow coefficients and flow angles, the breaking of flow factorization for elliptic, triangular and quadrangular flow measured by the CMS experiment. For elliptic flow, this factorization breaking is large in ultra-central collisions. We conclude that the bulk of the experimentally observed flow factorization breaking effects are qualitatively explained by hydrodynamic evolution of initial-state fluctuations, but that their quantitative description requires a better understanding of the initial fluctuation spectrum.
We use leading-order anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma. We impose a realistic lattice-based equation of state and perform self-consistent anisotropic freeze-out to hadronic degrees of freedom. We then compare our results for the full spatiotemporal evolution of the quark-gluon plasma and its subsequent freeze-out to results obtained using 1+1d Israel-Stewart second-order viscous hydrodynamics. We find that for small shear viscosities, 4 pi eta/s ~ 1, the two methods agree well for nucleus-nucleus collisions, however, for large shear viscosity to entropy density ratios or proton-nucleus collisions we find important corrections to the Israel-Stewart results for the final particle spectra and the total number of charged particles. Finally, we demonstrate that the total number of charged particles produced is a monotonically increasing function of 4 pi eta/s in Israel-Stewart viscous hydrodynamics whereas in anisotropic hydrodynamics it has a maximum at 4 pi eta/s ~ 10. For all 4 pi eta/s > 0, we find that for Pb-Pb collisions Israel-Stewart viscous hydrodynamics predicts more dissipative particle production than anisotropic hydrodynamics.
Recent work has shown that a temperature dependence of the shear viscosity to entropy ratio, $η/s$, influences the collective flow pattern in heavy-ion collisions in characteristic ways that can be measured by studying hadron transverse momentum spectra and their anisotropies. Here we point out that it also affects the pair momentum dependence of the Hanbury-Brown$-$Twiss (HBT) radii (the source size parameters extracted from two-particle intensity interferometry) and the variance of their event-by-event fluctuations. This observation establishes interferometric signatures as useful observables to complement the constraining power of single-particle spectra on the temperature dependence of $η/s$.