Hot and Dense QCD Matter Unraveling the Mysteries of the Strongly Interacting Quark-Gluon-Plasma A data-driven approach to quantifying the A Community White Paper on the Future of Relativistic Heavy-Ion Physics in the US shear viscosity of nature’s most ideal liquid Steffen A. Bass http://www.facebook.com/DukeQCD @Steffen_Bass
Quarks & Gluons: Elementary Building-Blocks of Matter Molecule Atom Nucleus Proton/Neutron Quark Elementary Particles: • 12 elementary building blocks of nature (plus anti-particles) • only need three for creation of ordinary matter (u, d, e) • strong force mediates the interaction between quarks via exchange of gluons: Quantum-Chromo-Dynamics (QCD)
Phases of Matter by adding/removing heat, phase of matter can be changed between solid, liquid and gaseous gaseous liquid Pressure plays an important role for the value of the transition temperature between the phases boiling temperature: solid • sea level: 100 ℃ • Mt. Everest: 71 ℃
Phase Diagram of QCD Matter Phases of QCD matter: Equation of State for an ideal QGP: Ordinary Matter: •heat & compress QCD matter: • phases determined by (electro- ! LFT predicts a phase-transition ‣ collide heavy atomic nuclei magnetic) interaction between to a state of deconfined nearly molecules •numerical simulations: massless quarks and gluons ‣ solve partition function (Lattice • apply heat & pressure to study ! QCD becomes simple at high Field Theory) phase-diagram temperature and/or density • calculate via derivatives of partition function e.g. for a gas of ultra-relativistic massless bosons, steep rise would indicate a change in DOFs:
The Early Universe: Quark-Gluon-Plasma • a few microseconds after the Big Bang the entire Universe was in a QGP state • compressing & heating nuclear matter allows to investigate the history of the Universe • the only means of recreating temperatures and densities of the early Universe is by colliding beams of ultra- relativistic heavy-ions
Properties of QCD: Transport Coefficients shear and bulk viscosity are defined as the coefficients in the expansion of the stress tensor in terms of the velocity fields: � ⇥ ⇤ i u k + ⇤ k u i � 2 T ik = ε u i u k + P ( δ ik + u i u k ) � η + ς δ ik ⇤ · u 3 δ ik ⇤ · u η /s from Lattice QCD: The confines of the Euklidian Formulation: •preliminary estimates: •extracting η /s formally requires taking the T 1.58 T C 2.32 T C zero momentum limit in an infinite spatial volume, which is numerically not η /s 0.2-0.25 0.25-0.5 possible… A. Nakamura & S. Sakai: Phys. Rev. Lett. 94 (2005) 072305 Harvey B. Meyer: Phys. Rev. D79 (2009) 011502 Harvey B. Meyer: arXiv:0809.5202 [hep-lat] The determination of the QCD transport coefficients is one of the key goals of the global relativistic heavy-ion effort!
Quark-gluon plasma 1 2 P c P c P c /2 Water P c η / s 10 0.1 P c /2 T / T c 2.5 2.0 1.5 1.0 0.5 0.0 2 P c Helium QGP Shear-Viscosity: 2006 vs. today Jonah E. Bernhard, J. Scott Moreland & Steffen A. Bass, Nature Physics 15 (2019) 11, 1113-1117 He • more than a decade of hard work by multiple research groups H 2 O • cooperation between theory & experiment • significant investment by the funding agencies
Telescopes for the Early Universe: Heavy-Ion Collider Facilities
Heating & Compressing QCD Matter The only way to heat & compress QCD matter under controlled laboratory conditions is by colliding two heavy atomic nuclei!
Probes of the Early Universe ALICE experiment at CERN: •1000+ scientists from 105+ institutions •dimensions: 26m long, 16m high, 16m wide •weight: 10.000 tons two other experiments: CMS, ATLAS
Typical Particle Physics Event
Typical Heavy-Ion Event Pb+Pb Collision at the LHC: • thousands of particle tracks • challenge: reconstruction of final state to characterize matter created in collision
Transport Theory: Connecting Data to Knowledge
Transport Theory microscopic transport models based on the (viscous) relativistic fluid dynamics: Boltzmann Equation : •transport of macroscopic degrees of freedom • transport of a system of microscopic particles •based on conservation laws: • all interactions are based on binary scattering � � � � t + � E × � p � f 1 ( � r, t ) = C ( � r, t ) p, � p, � = ε u i u k + P ( δ ik + u i u k ) �� r T ik processes � � � i u k + � k u i � 2 η 3 δ ik � · u � diffusive transport models based + ς δ ik � · u on the Langevin Equation : (plus an additional 9 eqns. for dissipative flows) • transport of a system of microscopic particles in a thermal medium • interactions contain a drag term related to the properties of the hybrid transport models: medium and a noise term representing random collisions •combine microscopic & macroscopic degrees of freedom p ( t ) − � v · ∆ t + � p ( t + ∆ t ) = � � ( t ) ∆ t � 2 T � •current state of the art for RHIC modeling Each transport model relies on roughly a dozen physics parameters to describe the time-evolution of the collision and its final state. These physics parameters act as a representation of the information we wish to extract from RHIC & LHC.
Computational Modeling 3+1D Hydro + Boltzmann Hybrid
Probing the QGP in Relativistic Heavy-Ion Collisions measurable (stable) hadronic final state nuclei at 99.99% Quark-Gluon-Plasma particles in detector interactions speed of light 10 x 10 -23 s 30 x 10 -23 s 1x 10 -23 s non-equilibrium viscous fluid hadronic transport early time dynamics dynamics Principal Challenges of Probing the QGP with Heavy-Ion Collisions: • time-scale of the collision process: 10 -24 seconds! [too short to resolve] • characteristic length scale: 10 -15 meters! [too small to resolve] • confinement: quarks & gluons form bound states, experiments don’t observe them directly ‣ computational models are need to connect the experiments to QGP properties!
Knowledge Extraction from Relativistic Heavy-Ion Collisions
Probing QCD in Heavy-Ion Collisions Data: Model: initial conditions, τ 0 , η /s, ζ /s, …. Glauber 20-25% .L1 20-25% 2 10 p >0.5 GeV, | |<2.5 p >0.5 GeV, | |<2.5 p >0.5 GeV, | |<2.5 η η η T T T ATLAS Pb+Pb ATLAS Pb+Pb ATLAS Pb+Pb 0odel 10 ATLAS s =2.76 TeV s =2.76 TeV s =2.76 TeV NN NN NN 10 -1 -1 -1 L = 7 b L = 7 b L = 7 b µ µ µ int int int P ( v 2 ) 1 ) ) ) 2 3 4 p(v p(v p(v 10 1 -1 10 centrality: centrality: centrality: 0-1% 0-1% 0-1% 5-10% 5-10% 5-10% extracted QGP properties: η /s, … 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 20-25% 20-25% 20-25% 30-35% 30-35% 30-35% v 2 v 2 -2 10 40-45% 40-45% 40-45% -1 10 60-65% 1 0 0.1 0.2 0 0.05 0.1 0 0.01 0.02 0.03 0.04 0.05 v v v 2 3 4
Determining the QGP Properties via a Model to Data Comparison Model Parameter: experimental data: eqn. of state π /K/P spectra shear viscosity yields vs. centrality & beam initial state elliptic flow pre-equilibrium dynamics HBT thermalization time charge correlations & BFs quark/hadron chemistry density correlations particlization/freeze-out • large number of interconnected parameters w/ non-factorizable data dependencies • data have correlated uncertainties • develop novel optimization techniques: Bayesian Statistics and MCMC methods • transport models require too much CPU: need new techniques based on emulators → collaboration with Statistical Sciences • general problem, not restricted to RHIC Physics
Bayesian Analysis Each computational model relies on a set of physics parameters to describe the dynamics and properties of the system. These physics parameters act as a representation of the information we wish to extract from comparison to data. Model Parameters - System Properties • initial state estimate or calculate parameters • temperature-dependent viscosities • hydro to micro switching temperature Physics Model: • Trento • iEbE-VISHNU a t a d o t e r a p m o c & s e l b a v r e s b o e t a l u c l Experimental Data a c • ALICE flow & spectra
Bayesian Analysis Each computational model relies on a set of physics parameters to describe the dynamics and properties of the system. These physics parameters act as a representation of the information we wish to extract from comparison to data. Model Parameters - System Properties • initial state • temperature-dependent viscosities • hydro to micro switching temperature Physics Model: Bayesian analysis • Trento • iEbE-VISHNU Experimental Data • ALICE flow & spectra • Bayesian analysis allows us to simultaneously calibrate all model parameters via a model-to-data comparison • determine parameter values such that the model best describes experimental observables • extract the probability distributions of all parameters
Example: Gravitational Waves LIGO gravitational wave signal: Bayesian analysis of GR model of merging black holes of masses m 1 and m 2 that is capable of reproducing LIGO data:
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