Unraveling the Mysteries of the Strongly Interacting Quark-Gluon-Plasma. Steffen A. Bass

Transcription

1 Hot andhep101: Dense Heavy-Ion QCD Matter Collisions Unraveling the Mysteries of the Strongly Interacting Quark-Gluon-Plasma A Community White Paper on the Future of Relativistic Heavy-Ion Physics in the US Steffen A. Bass

2 Introduction: Phase diagram of matter Quark-Gluon-Plasma

3 Phases of Matter by adding/removing heat, phase of matter can be changed between solid, liquid and gaseous gaseous solid liquid Pressure plays an important role for the value of the transition temperature between the phases boiling temperature: sea level: 100 Mt. Everest: 71

4 Phase Diagram Ordinary Matter: phases determined by (electromagnetic) interaction apply heat & pressure to study phase-diagram 4

5 Phase Diagram Ordinary Matter: phases determined by (electromagnetic) interaction apply heat & pressure to study phase-diagram Phases of QCD matter: heat & compress QCD matter: collide heavy atomic nuclei numerical simulations: solve partition function (Lattice) 4

6 Calculating the QCD Phase Diagram

7 Calculating the QCD Phase Diagram how to calculate the QCD Phase Diagram: evaluate the QCD Partition Function: path integral with n time steps in imaginary time evidence for new phase at high T and density: Quark-Gluon-Plasma

8 Calculating the QCD Phase Diagram how to calculate the QCD Phase Diagram: evaluate the QCD Partition Function: path integral with n time steps in imaginary time evidence for new phase at high T and density: Quark-Gluon-Plasma Equation of State for an ideal QGP: (ultra-relativistic gas of massless bosons) F. Ø LGT predicts a phase-transition to a state of deconfined nearly massless quarks and gluons Ø QCD becomes simple at high temperature and/or density

9 QGP and the Early Universe 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 heavyions

10 Telescopes for the Early Universe: Heavy-Ion Collider Facilities

11 Heating & Compressing QCD Matter The only way to heat & compress QCD matter under controlled laboratory conditions is by colliding two heavy atomic nuclei!

12 Probes of the Early Universe ALICE experiment at CERN: scientists from 105+ institutions dimensions: 26m long, 16m high, 16m wide weight: tons two other experiments: CMS, ATLAS

13 Heavy-Ion Collision Data typical Pb+Pb Collision at the LHC: thousands of particle tracks challenge: reconstruction of final state to characterize matter created in collision

14 Connecting Data to Knowledge Transport Theory

15 Visualizing a Transport Calculation 3+1D Hydro + Boltzmann Hybrid

16 Visualizing a Transport Calculation 3+1D Hydro + Boltzmann Hybrid

17 Time-Evolution of a Heavy-Ion Collision

18 Time-Evolution of a Heavy-Ion Collision 1x s 10 x s 30 x s

19 Time-Evolution of a Heavy-Ion Collision nuclei at 99.99% speed of light 1x s 10 x s 30 x s

20 Time-Evolution of a Heavy-Ion Collision nuclei at 99.99% speed of light Quark-Gluon-Plasma 1x s 10 x s 30 x s

21 Time-Evolution of a Heavy-Ion Collision nuclei at 99.99% speed of light Quark-Gluon-Plasma hadronic final state interactions 1x s 10 x s 30 x s

22 Time-Evolution of a Heavy-Ion Collision nuclei at 99.99% speed of light Quark-Gluon-Plasma hadronic final state interactions measurable (stable) particles in detector 1x s 10 x s 30 x s

23 Time-Evolution of a Heavy-Ion Collision nuclei at 99.99% speed of light Quark-Gluon-Plasma hadronic final state interactions measurable (stable) particles in detector 1x s 10 x s 30 x s non-equilibrium early time dynamics viscous fluid dynamics hadronic transport Principal Challenges of Probing the QGP with Heavy-Ion Collisions: time-scale of the collision process: seconds! [too short to resolve] characteristic length scale: 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!

24 Modeling of Heavy-Ion Collisions microscopic transport models based on the Boltzmann Equation: transport of a system of microscopic particles all interactions are based on binary scattering t + p E r f 1(p, r, t) = processes C(p, r, t) diffusive transport models based on the Langevin Equation: transport of a system of microscopic particles in a thermal medium interactions contain a drag term related to the properties of the medium and a noise term representing random collisions p(t + t) =p(t) 2T v t+ (t) t (viscous) relativistic fluid dynamics: transport of macroscopic degrees of freedom based on conservation laws: T ik = u i u k + P ( ik + u i u k ) iu k + k u i 2 3 ik u + ik u (plus an additional 9 eqns. for dissipative flows) hybrid transport models: combine microscopic & macroscopic degrees of freedom current state of the art for RHIC modeling 14

25 Modeling of Heavy-Ion Collisions microscopic transport models based on the Boltzmann Equation: transport of a system of microscopic particles all interactions are based on binary scattering t + p E r f 1(p, r, t) = processes C(p, r, t) diffusive transport models based on the Langevin Equation: transport of a system of microscopic particles in a thermal medium interactions contain a drag term related to the properties of the medium and a noise term representing random collisions p(t + t) =p(t) 2T v t+ (t) t (viscous) relativistic fluid dynamics: transport of macroscopic degrees of freedom based on conservation laws: T ik = u i u k + P ( ik + u i u k ) iu k + k u i 2 3 ik u + ik u (plus an additional 9 eqns. for dissipative flows) hybrid transport models: combine microscopic & macroscopic degrees of freedom 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. 14

26 Key Discoveries: the Case for the QGP

27 1x s 10 x s 30 x s

28 1x s 10 x s 30 x s Jet Energy-Loss

29 Jets in Proton-Proton Collisions What are Jets? hadrons parton parton shower parton shower parton hadrons if two protons collide at high energy, it is the partons within the proton that interact with each other when two partons scatter with a large momentum-transfer, showers of secondary partons are emitted back-toback the parton showers convert into hadron showers that can be measured by the experiments

30 Jets in Proton-Proton Collisions What are Jets? parton parton shower hadrons parton shower parton How to measure Jets parton shower are emitted back-to-back due to conservation of energy and momentum measurement via calorimeters hadrons if two protons collide at high energy, it is the partons within the proton that interact with each other when two partons scatter with a large momentum-transfer, showers of secondary partons are emitted back-toback the parton showers convert into hadron showers that can be measured by the experiments

31 Jet-Quenching: Basic Idea hadrons q q leading particle suppressed suppression can be experimentally quantified in terms of R AA ratio: R AA d 2 N AA /dydp d 2 N pp /dydp Ncoll AA hadrons leading particle suppressed partons lose energy and/or fragment differently than in the vacuum: radiative energy loss q L ˆq = ρ dσ q 2 dq 2 2 ρσ k dq 2 T q g = µ 2 λ f CNM pion gas QGP data q-hat Øtransport coefficient q is sensitive to density of (colored) charges Ø RHIC data shows values for q-hat far larger than expected even for a QGP!

32 Jet Suppression at LHC ATLAS & CMS observe unbalanced jets direct evidence for QGP jet-suppression

33 1x s 10 x s 30 x s

34 1x s 10 x s 30 x s Elliptic Flow and the viscosity of the QGP

35 RHIC in the press: Perfect Liquid on April 18 th, 2005, BNL announced in a press release that RHIC had created a new state of hot and dense matter which behaves like a nearly perfect liquid. how does one measure/ calculate the properties of a near ideal liquid? are there any other near ideal liquid systems found in nature? Steffen A. Bass

36 Relativistic Fluid Dynamics (RFD)

37 Relativistic Fluid Dynamics (RFD) transport of macroscopic degrees of freedom based on conservation laws: μ T μν =0 μ j μ =0 for an ideal fluid: T μν = (ε+p) u μ u ν - p g μν & j i μ = ρ i u μ Equation of state needed to close the system of PDE s: p=p(t,ρ i ) connection to Lattice QCD calculation of EoS initial conditions (i.e. thermalized QGP) required for calculation ideal hydro assumes local thermal equilibrium

38 Relativistic Fluid Dynamics (RFD) transport of macroscopic degrees of freedom based on conservation laws: μ T μν =0 μ j μ =0 for an ideal fluid: T μν = (ε+p) u μ u ν - p g μν & j i μ = ρ i u μ Equation of state needed to close the system of PDE s: p=p(t,ρ i ) connection to Lattice QCD calculation of EoS initial conditions (i.e. thermalized QGP) required for calculation ideal hydro assumes local thermal equilibrium Viscosity: shear and bulk viscosity are defined as the coefficients in the expansion of the stress tensor in terms of the velocity fields: T ik = u i u k + P ( ik + u i u k ) i u k + k u i 2 3 ik u + ik u viscous RFD requires solving an additional 9 eqns. for the dissipative flows Note: for quasi-particulate matter, viscosity decreases with increasing cross section for viscous RFD, the microscopic origin of viscosity is not relevant!

39 QCD Transport Coefficients: Shear Viscosity

40 QCD Transport Coefficients: Shear Viscosity shear and bulk viscosity are defined as the coefficients in the expansion of the stress tensor in terms of the velocity fields: 2 T ik = u i u k + P ( ik + u i u k ) i u k + k u i 3 ik u + ik u

41 QCD Transport Coefficients: Shear Viscosity shear and bulk viscosity are defined as the coefficients in the expansion of the stress tensor in terms of the velocity fields: 2 T ik = u i u k + P ( ik + u i u k ) i u k + k u i 3 ik u + ik u assuming matter to be quasi-particulate in nature: microscopic kinetic theory: η is given by the rate of momentum transport 1 3 n p f = p 3 tr unitary limit on cross sections suggests a lower bound for η tr 4 p 2 p3 12 viscosity decreases with increasing cross section (forget molasses!) for viscous RFD, the microscopic origin of viscosity is not relevant!

42 QCD Transport Coefficients: Shear Viscosity shear and bulk viscosity are defined as the coefficients in the expansion of the stress tensor in terms of the velocity fields: 2 T ik = u i u k + P ( ik + u i u k ) i u k + k u i 3 ik u + ik u assuming matter to be quasi-particulate in nature: microscopic kinetic theory: η is given by the rate of momentum transport 1 3 n p f = p 3 tr unitary limit on cross sections suggests a lower bound for η tr 4 p 2 p3 12 viscosity decreases with increasing cross section (forget molasses!) for viscous RFD, the microscopic origin of viscosity is not relevant! The determination of the QCD transport coefficients is one of the key goals of the global relativistic heavy-ion effort!

43 Collision Geometry: Elliptic Flow two nuclei collide rarely head-on, but mostly with an offset: Reaction plane z y only matter in the overlap area gets compressed and heated up x

44 Collision Geometry: Elliptic Flow two nuclei collide rarely head-on, but mostly with an offset: Reaction plane z y only matter in the overlap area gets compressed and heated up x elliptic flow (v 2 ): gradients of almond-shape surface will lead to preferential emission in the reaction plane asymmetry out- vs. in-plane emission is quantified by 2 nd Fourier coefficient of angular distribution: v 2 Ø vrfd: good agreement with data for very small η/s

45 Temperature Dependence of η/s what can ordinary matter, e.g. He or H2O teach us about η/s? He H2O η/s has minimum & discontinuity at TC

46 Temperature Dependence of η/s what can ordinary matter, e.g. He or H2O teach us about η/s? temperature dependence of η/s in QCD can be estimated in low- and high-temperature limit: low temperature: chiral pions high temperature: QGP in HTL approximation He pqcd/htl AdS/CFT vrfd H2O terra incognita η/s has minimum & discontinuity at TC L.P. Csernai, J.I. Kapusta & L. McLerran: Phys. Rev. Lett. 97: (2006) M. Prakash, M. Prakash, R. Venugopalan & G. Welke: Phys. Rept. 227, 321 (1993) P. Arnold, G.D. Moore & L.D. Yaffe: JHEP 05: 051 (2003)

47 How to extract knowledge from a comparison of model with data?

48 Determining the QGP Shear Viscosity via a Model to Data Comparison Model Parameter: eqn. of state shear viscosity initial state pre-equilibrium dynamics thermalization time quark/hadron chemistry particlization/freeze-out experimental data: π/k/p spectra yields vs. centrality & beam elliptic flow HBT charge correlations & BFs density correlations

49 Determining the QGP Shear Viscosity via a Model to Data Comparison Model Parameter: eqn. of state shear viscosity initial state pre-equilibrium dynamics thermalization time quark/hadron chemistry particlization/freeze-out experimental data: π/k/p spectra yields vs. centrality & beam elliptic flow HBT charge correlations & BFs density correlations

50 Determining the QGP Shear Viscosity via a Model to Data Comparison Model Parameter: eqn. of state shear viscosity initial state pre-equilibrium dynamics thermalization time quark/hadron chemistry particlization/freeze-out experimental data: π/k/p spectra yields vs. centrality & beam elliptic flow HBT charge correlations & BFs density correlations 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 general problem, not restricted to RHIC Physics collaboration with Statistical Sciences

51 Setup of a Bayesian Statistical Analysis Model Parameters - System Properties initial state temperature-dependent viscosities hydro to micro switching temperature calculate events on Latin hypercube Physics Model: Trento iebe-vishnu Experimental Data ALICE flow & spectra Gaussian Process Emulator non-parametric interpolation fast surrogate to full Physics Model MCMC (Markov-Chain Monte-Carlo) random walk through parameter space weighted by posterior probability Bayes Theorem posterior likelihood prior prior: initial knowledge of parameters likelihood: probability of observing exp. data, given proposed parameters after many steps, MCMC equilibrates to Posterior Distribution diagonals: probability distribution of each parameter, integrating out all others off-diagonals: pairwise distributions showing dependence between parameters

52 Prior vs. Posterior Prior: model calculations evenlyfor distributed over full design space Posterior: emulator predictions highest likelihood parameter values 7 m 7r u 1 mu 7 7 m 7r u 1 mu l m o 1 l mu m

53 Prior vs. Posterior Posterior: emulator predictions for highest likelihood parameter values I7emtifie7 rauti1le yiel7s 1.8 I7emtifie7 rauti1le leam p T 0.12 Flow 1ululamts dn/dy π ± K ± pp pt [GeV] pp K ± π ± vn {2} v 3 v 4 v Cemtuality % Cemtuality % Cemtuality %

54 Prior vs. Posterior Prior: model calculations evenlyfor distributed over full design space Posterior: emulator predictions highest likelihood parameter values 7 m 7r u m mu 7r u 1 l m o mu 1 l m mu Posterior: emulator predictions for highest likelihood parameter values 7 m 7r u 1 mu 7 7 m 7r u 1 mu l m o 1 l mu m

55 Analysis Outcome temperature dependent shear viscosity: analysis favors small value and shallow rise results do not fully constrain temperature dependence: inverse correlation between (η/s)slope slope and intercept (η/s)min insufficient data to obtain sharply peaked likelihood distributions for (η/s)slope and curvature β independently current analysis most sensitive to T< 0.23 GeV RHIC data may disambiguate further η/s Pubou uam]e Posteubou medbam 90% CR!/s(T) = (!/s)min + (!/s)slope (T-TC) (T/TC) β Temreuatuue [GeV] KSS 0oumd 1/4π aside from the specific shear viscosity, many other model parameters and QGP properties have been constrained in the same analysis: temperature dependence of the specific bulk viscosity shape and eccentricity scaling properties of the hydrodynamic initial condition thermalization time of the QGP particlization temperature for conversion from fluid to particles

56 Summary & Outlook

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58 the QGP is the most extreme liquid in nature, with a large opacity and the smallest specific shear viscosity ever observed computational models and statistical analysis tools have reached a level of sophistication that allows for the determination of the temperature dependent transport coefficients of the QGP in the future this analysis will be refined with data on asymmetric collision systems and additional beam energies frontier science entering the precision era!

59 Resources Trento: J. Scott Moreland, Jonah E. Bernhard & Steffen A. Bass: Phys. Rev. C 92, (R) iebe-vishnu: Chun Shen, Zhi Qiu, Huichao Song, Jonah Bernhard, Steffen A. Bass & Ulrich Heinz: Computer Physics Communications in print, arxiv: UrQMD: Steffen A. Bass et al. Prog. Part. Nucl. Phys. 41 (1998) , arxiv:nucl-th/ Marcus Bleicher et al. J.Phys. G25 (1999) , arxiv:hep-ph/ MADAI Collaboration: Visualization and Bayesian Analysis packages Duke Bayesian Analysis Package: this work has been made possible through support from

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