Recently, Jia Liu implemented the second order nonlinear coupling terms between shear and bulk viscosities. The hydrodynamic evolution is cross checked with MUSIC. A systematic investigation of the phenomenological importance of these terms will come soon!

## Photon emission from relativistic heavy-ion collisions

## Probing the properties of event-by-event distributions in Hanbury-Brown–Twiss radii

Christopher Plumberg, Ulrich Heinz, arXiv:1507.04968 [nucl-th]

**Abstract: **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.

## Collision Geometry and Flow in Uranium+Uranium Collisions

A. Goldschmidt, Z. Qiu, C. Shen and U. Heinz, arXiv:1507.03910 [nucl-th]

**Abstract: **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.

## Added link to HBT afterburner package

A link to an HBT afterburner package is now added on the download page

## Thermal photon radiation in high multiplicity p+Pb collisions at the Large Hadron Collider

C. Shen, J.-F. Paquet, G. S. Denicol, S. Jeon, C. Gale, arXiv:1504.07989 [nucl-th]

**Abstract: **The collective behaviour of hadronic particles has been observed in high multiplicity proton-lead collisions at the Large Hadron Collider (LHC), as well as in deuteron-gold collisions at the Relativistic Heavy-Ion Collider (RHIC). In this work we present the first calculation, in the hydrodynamic framework, of thermal photon radiation from such small collision systems. Owing to their compact size, these systems can reach temperatures comparable to those in central nucleus-nucleus collisions. The thermal photons can thus shine over the prompt background, and increase the low p_T direct photon spectrum by a factor of 2-3 in 0-1% p+Pb collisions at 5.02 TeV. This thermal photon enhancement can therefore serve as a clean signature of the existence of a hot quark-gluon plasma during the evolution of these small collision systems, as well as validate hydrodynamic behavior in small systems.

## Pre-equilibrium evolution effects on heavy-ion collision observables

Jia Liu, Chun Shen, Ulrich W. Heinz, arXiv:1504.02160 [nucl-th]

**Abstract:** In order to investigate the importance of pre-equilibrium dynamics on relativistic heavy-ion collision observables, we match a highly non-equilibrium early evolution stage, modeled by free-streaming partons generated from the Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) and Monte Carlo Glauber (MC-Glb) models, to a locally approximately thermalized later evolution stage described by viscous hydrodynamics, and study the dependence of final hadronic transverse momentum distributions, in particular their underlying radial and anisotropic flows, on the switching time between these stages. Performing a 3-parameter fit of the measured values for the average transverse momenta ⟨p⊥⟩ for pions, kaons and protons as well as the elliptic and triangular flows of charged hadrons v^ch_{2,3}, with the switching time τ_s, the specific shear viscosity η/s during the hydrodynamic stage, and the kinetic decoupling temperature Tdec as free parameters, we find that the preferred “thermalization” times τs depend strongly on the model of the initial conditions. MC-KLN initial conditions require an earlier transition to hydrodynamic behavior (at τ_s ≈ 0.13 fm/c) , followed by hydrodynamic evolution with a larger specific shear viscosity η/s≈ 0.2, than MC-Glb initial conditions which prefer switching at a later time (τ_s ≈ 0.6 fm/c) followed by a less viscous hydrodynamic evolution with η/s≈ 0.16. These new results including pre-equilibrium evolution are compared to fits without a pre-equilbrium stage where all dynamic evolution before the onset of hydrodynamic behavior is ignored. In each case, the quality of the dynamical descriptions for the optimized parameter sets, as well as the observables which show the strongest constraining power for the thermalization time, are discussed.

## Interferometric signatures of the temperature dependence of the specific shear viscosity in heavy-ion collisions

Christopher Plumberg, Ulrich Heinz, arXiv:1503.05605 [nucl-th]

**Abstract:** 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.

## Shape and flow fluctuations in ultra-central Pb+Pb collisions at the LHC

Chun Shen, Zhi Qiu, Ulrich Heinz, arXiv:1502.04636 [nucl-th]

**Abstract:** 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.

## Collision Geometry and Flow in Uranium+Uranium Collisions

Andy Goldschmidt, Zhi Qiu, Chun Shen, Ulrich Heinz, arXiv:1502.00603 [nucl-th]

**Abstract:** 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 near 0.5% centrality 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. An enrichment of tip-tip configurations by triggering solely on high-multiplicity in the U+U collisions thus does not work. On the other hand, using the Zero Degree Calorimeters (ZDCs) coupled with event-shape engineering, we identify the selection purity of body-body and tip-tip events in the full-overlap U+U collisions. With additional constraints on the asymmetry of the ZDC signals one can further increases the probability of selecting tip-tip events in U+U collisions.