Nuclear Physics a 1003 (2020) 122016
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Available online at www.sciencedirect.com ScienceDirect Nuclear Physics A 1003 (2020) 122016 www.elsevier.com/locate/nuclphysa Dynamics of critical fluctuations: Theory – phenomenology – heavy-ion collisions ∗ Marcus Bluhm a,b, , Alexander Kalweit c, Marlene Nahrgang a,b, Mesut Arslandok e, Peter Braun-Munzinger b,e,g, Stefan Floerchinger f, Eduardo S. Fraga h, Marek Gazdzicki i,k, Christoph Hartnack a, Christoph Herold l, Romain Holzmann g, Iurii Karpenko a,m, Masakiyo Kitazawa n,o, Volker Koch p, Stefan Leupold q, Aleksas Mazeliauskas d,f, Bedangadas Mohanty c,r, Alice Ohlson e,s, Dmytro Oliinychenko p, Jan M. Pawlowski b,f, Christopher Plumberg t, Gregory W. Ridgway u, Thomas Schäfer v, Ilya Selyuzhenkov g,w, Johanna Stachel e, Mikhail Stephanov x, Derek Teaney y, Nathan Touroux a, Volodymyr Vovchenko j,z, Nicolas Wink f a SUBATECH UMR 6457 (IMT Atlantique, Université de Nantes, IN2P3/CNRS), 4 rue Alfred Kastler, 44307 Nantes, France b ExtreMe Matter Institute EMMI, GSI, Planckstr. 1, 64291 Darmstadt, Germany c Experimental Physics Department, CERN, CH-1211 Geneva 23, Switzerland d Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland e Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, D-69120 Heidelberg, Germany f Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120, Heidelberg, Germany g GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany h Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972, Rio de Janeiro, RJ, Brazil i Institut für Kernphysik, Goethe Universität Frankfurt, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany j Institut für Theoretische Physik, Goethe Universität Frankfurt, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany k Division of Nuclear Physics, Jan Kochanowski University, 25-406 Kielce, Poland l School of Physics and Center of Excellence in High Energy Physics & Astrophysics, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand m Czech Technical University in Prague, FNSPE, Bˇrehová 7, Prague 115 19,Czech Republic n Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan o J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK, 203-1, Shirakata, Tokai, Ibaraki, 319-1106, Japan p Nuclear Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA q Institutionen för fysik och astronomi, Uppsala universitet, Box 516, S-75120 Uppsala, Sweden https://doi.org/10.1016/j.nuclphysa.2020.122016 0375-9474/© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 2 M. Bluhm et al. / Nuclear Physics A 1003 (2020) 122016 r School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni 752050, India s Lund University Department of Physics, Division of Particle Physics, Box 118, S-22100 Lund, Sweden t Theoretical Particle Physics, Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, SE-22362 Lund, Sweden u Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA v Department of Physics, North Carolina State University, Raleigh, NC 27695, USA w National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe highway 31, 115409, Moscow, Russia x Department of Physics, University of Illinois, Chicago, IL 60607, USA y Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA z Frankfurt Institute for Advanced Studies, Giersch Science Center, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, Germany Received 1 June 2020; received in revised form 17 August 2020; accepted 17 August 2020 Available online 20 August 2020 Abstract This report summarizes the presentations and discussions during the Rapid Reaction Task Force “Dy- namics of critical fluctuations: Theory – phenomenology – heavy-ion collisions”, which was organized by the ExtreMe Matter Institute EMMI and held at GSI, Darmstadt, Germany in April 2019. We address the current understanding of the dynamics of critical fluctuations in QCD and their measurement in heavy-ion collision experiments. In addition, we outline what might be learned from studying correlations in other physical systems, such as cold atomic gases. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Keywords: Fluctuations; Dynamics of critical fluctuations; QCD critical point; Heavy-Ion collisions; Cold atomic gases Contents 1. Introduction . 3 2. Theory of dynamical fluctuations........................................... 6 2.1. Implementation of stochastic fluid dynamics . 7 2.2. Implementation of deterministic hydro-kinetics............................. 9 2.3. Implementation of stochastic diffusion...................................10 2.4. Implementation of nonequilibrium chiral fluid dynamics (NχFD)................13 2.5. Implementation of Hydro+...........................................15 2.6. Relevant scales for transits of the critical point.............................17 2.7. Implementation of fluid to particle conversion..............................19 3. Experimental challenges.................................................22 3.1. Matching between experimental observables and theoretical quantities . 22 3.1.1. Light nuclei production . 24 3.1.2. Additional experimental observables..............................24 B Q 3.1.3. A new observable: χ2 /χ2 ? ...................................27 3.2. Isospin and strangeness randomisation across collision energies .................28 * Corresponding author. E-mail address: [email protected] (M. Bluhm). M. Bluhm et al. / Nuclear Physics A 1003 (2020) 122016 3 3.3. Volume fluctuations...............................................29 3.4. The rapidity window dependence......................................29 3.5. Influence of resonance decays on fluctuation observables......................31 3.6. Overview of the current experimental techniques............................33 3.6.1. Fluctuation measurements in ALICE..............................33 3.6.2. Fluctuation measurements in STAR ..............................35 3.6.3. Fluctuation measurements in HADES . 36 3.6.4. Fluctuation measurements in NA61/SHINE.........................37 3.6.5. Future common standards to be followed by experiments................38 4. Fluctuations in atomic gases and other related systems.............................38 4.1. Equilibrium fluctuations and correlations.................................39 4.2. Fluctuations and transport phenomena in critical systems......................40 4.3. Dynamical evolution in critical systems..................................41 4.4. Other physical systems.............................................42 5. Summary and outlook...................................................42 CRediT authorship contribution statement..........................................44 Declaration of competing interest................................................44 Acknowledgements.........................................................44 Appendix A. Approaches to the theoretical description of the dynamics of fluctuations..........44 A.1. Effective kinetic theory of hydrodynamic fluctuations........................44 A.2. Stochastic diffusion of critical net-baryon density fluctuations...................46 A.3. Nonequilibrium chiral fluid dynamics (NχFD).............................47 A.3.1. Quark-meson model.........................................47 A.3.2. Nonequilibrium chiral fluid dynamics . 48 A.3.3. Expanding medium.........................................49 A.4. QCD assisted transport.............................................49 A.5. Critical dynamics from small, noisy, fluctuating systems.......................51 A.5.1. Including spurious effects near criticality . 51 A.5.2. Finite-size effects...........................................53 A.6. Modeling of time correlations with hydrodynamic fluctuations..................53 A.7. Summary of approaches to critical dynamics . 56 References...............................................................56 1. Introduction Ultra-relativistic heavy-ion collisions create small droplets of deconfined QCD matter – the Quark Gluon Plasma (QGP). As the system expands, it cools and eventually hadronizes. As a function of beam energy, system size, and rapidity the collision explores different regions of temperature T and baryo-chemical potential μB in the QCD phase diagram [1–4], possibly in- cluding a conjectured QCD critical point [5]. This critical point is the endpoint of a line of first order QCD phase transitions, analogous to the critical endpoint in the phase diagram of water. The main tool that connects the evolution of the matter produced in a relativistic heavy-ion collision to bulk properties of QCD is viscous relativistic fluid dynamics [6–9]. Fluid dynamics can be understood as the effective theory of the long-time and long-wavelength behavior of a classical or quantum many-body system. In this limit the system approaches approximate local thermal equilibrium, and the dynamics is governed by the evolution of conserved charges. The system produced in relativistic heavy-ion collisions is not truly macroscopic – the number of 4 M. Bluhm et al. / Nuclear Physics A 1003 (2020) 122016 produced hadrons ranges from about a hundred