Determining quark-gluon plasma initial condition and transport properties with quantitative uncertainty

DOE Stewardship Science Graduate Fellowship program review, Las Vegas, NV

Transcript

1. Determining quark-gluon plasma initial condition and transport properties with quantitative uncertainty J. Scott Moreland Advisor: Steffen A. Bass SSGF Program Review Las Vegas, NV. May 25, 2016 Funding provided by DOE NNSA Stewardship Science Graduate Fellowship
2. Melting point of the proton Protons and neutrons have substructure: constituent quarks, sea quarks, gluons, etc. When are degrees of freedom liberated? Back of the envelope estimate Thermal energy exceeds rest mass when... proton mass ∼ 1 GeV proton size ∼ (0.5 fm)3 energy density gluon gas: = 64 15 π2 ( c)3 T4 proton = 8 GeV/fm3 ↔ Tc ∼ 200 MeV Proton should melt at ∼2,000,000,000,000 K! J. Scott Moreland (Duke U.) 1 / 27
3. QCD predicts new phase of matter QCD calculations on the lattice find the phase transition at T ≈ 155 MeV, where nucleons ’melt’ to form a plasma of deconfined quarks and gluons dubbed a quark-gluon plasma T ~ 155 MeV Baryon Density μ [GeV] Temperature T [MeV] critical point? quark-gluon plasma early universe hadron gas nuclear collisions J. Scott Moreland (Duke U.) 2 / 27
4. Quark-gluon plasma in nature Conditions to produce QGP occur(ed) naturally in two places Early universe, mere microseconds after big bang where T > 200 MeV Center of neutron stars at extreme baryon density Big bang First stars Quark-gluon plasma Cosmic microwave background Credit: NASA / WMAP Quark-gluon plasma? Fermi liquid Electrons, neutrons, nuclei Ions, electrons Credit: Robert Schultz Neutron Star J. Scott Moreland (Duke U.) 3 / 27
5. Creating quark-gluon plasma in the laboratory General strategy... collide nuclei at ultrarelativistic energies Relativistic Heavy-ion Collider (RHIC): Beam energy 7.7–200 GeV per nucleon pair Large Hadron Collider (LHC): Beam energy 2760–13000 GeV per nucleon pair time: 0 fm/c 20 fm/c Fig. MADAI collaboration J. Scott Moreland (Duke U.) 4 / 27
6. Creating quark-gluon plasma in the laboratory General strategy... collide nuclei at ultrarelativistic energies Relativistic Heavy-ion Collider (RHIC): Beam energy 7.7–200 GeV per nucleon pair Large Hadron Collider (LHC): Beam energy 2760–13000 GeV per nucleon pair Relativistic nuclei highly Lorentz contracted ...pancake-shaped in lab frame J. Scott Moreland (Duke U.) 4 / 27
7. Creating quark-gluon plasma in the laboratory General strategy... collide nuclei at ultrarelativistic energies Relativistic Heavy-ion Collider (RHIC): Beam energy 7.7–200 GeV per nucleon pair Large Hadron Collider (LHC): Beam energy 2760–13000 GeV per nucleon pair Nuclei collide, compress and heat matter beyond QGP critical point J. Scott Moreland (Duke U.) 4 / 27
8. Creating quark-gluon plasma in the laboratory General strategy... collide nuclei at ultrarelativistic energies Relativistic Heavy-ion Collider (RHIC): Beam energy 7.7–200 GeV per nucleon pair Large Hadron Collider (LHC): Beam energy 2760–13000 GeV per nucleon pair QGP thermalizes, starts to expand hydrodynamically J. Scott Moreland (Duke U.) 4 / 27
9. Creating quark-gluon plasma in the laboratory General strategy... collide nuclei at ultrarelativistic energies Relativistic Heavy-ion Collider (RHIC): Beam energy 7.7–200 GeV per nucleon pair Large Hadron Collider (LHC): Beam energy 2760–13000 GeV per nucleon pair Quarks and gluons recombine into colorless hadrons and hit the detector. J. Scott Moreland (Duke U.) 4 / 27
10. Studying bulk properties of the QGP liquid How and under what conditions is it formed in a nuclear collision? How does it recombine to form colorless hadrons? Equation of state? Relations between thermal quantities, e.g. P = P( ) Transport properties? shear/bulk viscosity, probe energy loss, etc J. Scott Moreland (Duke U.) 5 / 27
11. Quark-gluon plasma is not directly detectable What the experiment sees... Quark-gluon plasma Measure extrinsic final-state properties • particle yields • mean particle momenta • angular particle correlations ~ 10-14 m extent ~ 10-23 s lifetime Study intrinsic QGP properties • equation of state • transition temperature • viscosity J. Scott Moreland (Duke U.) 6 / 27
12. Notable example: infer viscosity from flow anisotropy Overlap region, compressed and heated Elliptic flow (v2 ): pressure gradients steeper along short axis of ellipse, drives asymmetric flow quantified by 2nd Fourier coeff. of angular dist: v2 Good agreement for small viscosity η/s Fig. credit: Luzum, Romatschke
13. Notable example: infer viscosity from flow anisotropy A. Adams, et. al. New Journal of Physics 14 (2012) QGP believed to be most ideal fluid in nature!
14. Transport models connect experiment and theory time kinetic freezeout Boltzmann transport (red glyphs) hydrodynamics (heatmap) initial conditions pre-collision Figure credit Zhi Qiu Initial conditions Describe initial Tµν at the QGP thermalization time Hydrodynamics (QGP) Hydrodynamics imposes energy and momentum conservation, ∂µ Tµν = 0 Requires medium viscosity and equation of state from LQCD Boltzmann Eqn (hadron gas) Fluid discretized into particles at transition temperature. Non-equillibrium Boltz. transport, dfi (x, p) dt = Ci (x, p)
15. Model-to-data comparison: solving the inverse problem Theory • QCD equation of state • relativistic hydrodynamics • hadronic cross sections Measured observables Model Data Simulated observables tune free model parameters Procedure given model with some unknown parameters f(x 1 , x 2 , ..., x n ) optimize the parameters x 1 , x 2 , ..., x n to fit an observed data set y 1 , y 2 , ..., y m extract new physics insight J. Scott Moreland (Duke U.) 9 / 27
16. Current practicum and thesis work ”What are you doing and why are you doing it.” –sponsors 1 Quantify sensitivity of hydrodynamic simulations to different calculations of the QCD equation of state (LLNL) Phys. Rev. C93 (2016) 044913 2 Improve theoretical description of the QGP initial conditions Nucl. Phys. A 904-905, 815c (2013) Phys. Rev. C92 (2015) 011901 3 Rigorously constrain QGP medium properties using Bayesian model-to-data analysis pre-print arXiv:1605.03954 (2016) J. Scott Moreland (Duke U.) 10 / 27
17. Current practicum and thesis work ”What are you doing and why are you doing it.” –sponsors 1 Quantify sensitivity of hydrodynamic simulations to different calculations of the QCD equation of state (LLNL) Phys. Rev. C93 (2016) 044913 2 Improve theoretical description of the QGP initial conditions Nucl. Phys. A 904-905, 815c (2013) Phys. Rev. C92 (2015) 011901 3 Rigorously constrain QGP medium properties using Bayesian model-to-data analysis pre-print arXiv:1605.03954 (2016) J. Scott Moreland (Duke U.) 10 / 27
18. Studying the QGP equation of state Equation of state calculable from QCD Lagrangian L[Aa µ , ¯ Ψ, Ψ] Vaccuum-to-vaccuum transition amplitude Z Z = DAa µ (x)D ¯ Ψ(x)DΨ(x)ei d4xL[Aa µ ,¯ Ψ,Ψ] Partition function Z = tr ˆ ρ, where ˆ ρ = e−βˆ H Z = DAa µ (x, τ)D ¯ Ψ(x, τ)DΨ(x, τ)e− β 0 dτ d3xLE[Aa µ ,¯ Ψ,Ψ] t → iτ Path integral is discretized and solved on a lattice → Partition function yields the QCD equation of state J. Scott Moreland (Duke U.) 11 / 27
19. Lattice QCD equation of state error analysis Quantify effect of different LQCD equation of state calculations on heavy-ion collision observables JSM and RAS, Phys. Rev. C93, 044913 (2016) Three different LQCD EoS calc. Modern Monte Carlo hydro model Large scale simulation on open science grid 0.0 0.1 0.2 0.3 0.4 0.5 0.6 T [GeV] 1 2 3 4 5 6 (e ¡ 3p)=T4 HRG HotQCD Wuppertal-Budapest s95p-v1 0.60 0.61 0.62 pT [GeV] §0: 6% +0: 9% ¡2: 6% S95 WB HQ HQ samples 0.052 0.054 0.056 0.058 v2 © 2 ª §1: 5% +1: 7% ¡6: 9% 0.018 0.020 0.022 v3 © 2 ª §3: 4% +2: 8% ¡12: 6% 0 20 40 60 80 100 H Q W B S95 EoS Number 3.5 4.5 5.5 max I(T) §6: 2% ¡6: 9% +38: 3% 200 GeV Au+Au 20–30% centrality
20. Lattice QCD equation of state error analysis Quantify effect of different LQCD equation of state calculations on heavy-ion collision observables JSM and RAS, Phys. Rev. C93, 044913 (2016) Three different LQCD EoS calc. Modern Monte Carlo hydro model Large scale simulation on open science grid 0.0 0.1 0.2 0.3 0.4 0.5 0.6 T [GeV] 1 2 3 4 5 6 (e ¡ 3p)=T4 HRG HotQCD Wuppertal-Budapest s95p-v1 0.60 0.61 0.62 pT [GeV] §0: 6% +0: 9% ¡2: 6% S95 WB HQ HQ samples 0.052 0.054 0.056 0.058 v2 © 2 ª §1: 5% +1: 7% ¡6: 9% 0.018 0.020 0.022 v3 © 2 ª §3: 4% +2: 8% ¡12: 6% 0 20 40 60 80 100 H Q W B S95 EoS Number 3.5 4.5 5.5 max I(T) §6: 2% ¡6: 9% +38: 3% 200 GeV Au+Au 20–30% centrality
21. Current practicum and thesis work ”What are you doing and why are you doing it.” –sponsors 1 Quantify sensitivity of hydrodynamic simulations to different calculations of the QCD equation of state (LLNL) Phys. Rev. C93 (2016) 044913 2 Improve theoretical description of the QGP initial conditions Nucl. Phys. A 904-905, 815c (2013) Phys. Rev. C92 (2015) 011901 3 Rigorously constrain QGP medium properties using Bayesian model-to-data analysis pre-print arXiv:1605.03954 (2016) J. Scott Moreland (Duke U.) 13 / 27
22. What are the initial conditions? Initial conditions: energy density and fluid velocity at τ = τ0 . Initial energy density (3D) x η x η x η Figure credit: Schenke, Schlichting Common to project out beam dimension (η-coordinate) Initial energy density (2D) −8 −4 0 4 8 x [fm] −8 −4 0 4 8 y [fm] −8 −4 0 4 8 x [fm] −8 −4 0 4 8 x [fm]
23. The initial condition problem The QGP initial conditions are not well understood. Many models/the- ories proposed in the literature. Participant quark model Glasma graphs Binary collision scaling Minijet saturation Color-glass condensate Pomerons ? ? ? ? ? ? ? ? ? QGP viscosity extracted by tuning simulation viscosity to fit elliptic flow data. Different initial condition models predict different flow behavior and hence prefer different QGP viscosity values! Extracted QGP viscosity depends on theoretical initial conditions! Estimates inherit large theory uncertainty! J. Scott Moreland (Duke U.) 15 / 27
24. The initial condition problem Solution—data driven approach Parametrize QGP initial conditions using flexible ’meta-model’. Apply rigorous statistical methods to simultaneously constrain initial condition and QGP medium parameters. J. Scott Moreland (Duke U.) 15 / 27
25. TRENTo: new parametric initial condition model Sample positions of nucleons within colliding nuclei J. Scott Moreland (Duke U.) 16 / 27
26. TRENTo: new parametric initial condition model Nuclei collide at some random offset (impact parameter) J. Scott Moreland (Duke U.) 16 / 27
27. TRENTo: new parametric initial condition model Determine nucleons which are struck in the collision J. Scott Moreland (Duke U.) 16 / 27
28. TRENTo: new parametric initial condition model J. Scott Moreland (Duke U.) 16 / 27
29. TRENTo: new parametric initial condition model Construct participant density—superposition of struck nucleons J. Scott Moreland (Duke U.) 16 / 27
30. TRENTo: new parametric initial condition model Convert local overlap density → entropy deposition Mapping represents some scalar function of two arguments J. Scott Moreland (Duke U.) 16 / 27
31. Parametrizing local entropy deposition Generalized mean ansatz: dS d2r dy ∝ Tp A + Tp B 2 1/p −8 −6 −4 −2 0 2 4 6 8 x [fm] 0 2 4 Thickness [fm−2] Pb+Pb 2.76 TeV Tmin < T < Tmax −1 < p < 1 p = ∞ maximum 1 arithmetic: TA + TB 2 0 geometric: TATB −1 harmonic: 2TATB TA + TB −∞ minimum J. Scott Moreland (Duke U.) 17 / 27
32. Parametrizing local entropy deposition Generalized mean ansatz: dS d2r dy ∝ Tp A + Tp B 2 1/p −8 −6 −4 −2 0 2 4 6 8 x [fm] 0 2 4 Thickness [fm−2] Pb+Pb 2.76 TeV Tmin < T < Tmax −1 < p < 1 p = 1 p = ∞ maximum 1 arithmetic: TA + TB 2 0 geometric: TATB −1 harmonic: 2TATB TA + TB −∞ minimum J. Scott Moreland (Duke U.) 17 / 27
33. Parametrizing local entropy deposition Generalized mean ansatz: dS d2r dy ∝ Tp A + Tp B 2 1/p −8 −6 −4 −2 0 2 4 6 8 x [fm] 0 2 4 Thickness [fm−2] Pb+Pb 2.76 TeV Tmin < T < Tmax −1 < p < 1 p = 0 p = ∞ maximum 1 arithmetic: TA + TB 2 0 geometric: TATB −1 harmonic: 2TATB TA + TB −∞ minimum J. Scott Moreland (Duke U.) 17 / 27
34. Parametrizing local entropy deposition Generalized mean ansatz: dS d2r dy ∝ Tp A + Tp B 2 1/p −8 −6 −4 −2 0 2 4 6 8 x [fm] 0 2 4 Thickness [fm−2] Pb+Pb 2.76 TeV Tmin < T < Tmax −1 < p < 1 p = − 1 p = ∞ maximum 1 arithmetic: TA + TB 2 0 geometric: TATB −1 harmonic: 2TATB TA + TB −∞ minimum J. Scott Moreland (Duke U.) 17 / 27
35. Compare parametrization to existing IC models 0 1 2 3 Entropy density [fm−3] 1 fm−2 2 fm−2 TB = 3 fm−2 Gen. mean, p = 1 WN 0 1 2 3 Entropy density [fm−3] Gen. mean, p = 0 EKRT 0 1 2 3 4 Participant thickness TA [fm−2] 0 1 2 3 Entropy density [fm−3] Gen. mean, p = − 0. 67 KLN Wounded nucleon model dS dy d2r⊥ ∝ TA + TB ∗T denotes participant thickness EKRT model PRC 93, 024907 (2016) after brief free streaming phase dET dy d2r⊥ ∼ Ksat π p3 sat (Ksat, β; TA, TB) KLN model PRC 75, 034905 (2007) dNg dy d2r⊥ ∼ Q2 s,min 2 + log Q2 s,max Q2 s,min J. Scott Moreland (Duke U.) 18 / 27
36. Modern event-by-event hybrid model TRENTo initial conditions Moreland, Bernhard, Bass, PRC 92, no. 1, 011901 (2015) norm entropy normalization p entropy deposition parameter k proton-proton multiplicity fluctuations w Gaussian nucleon width HotQCD equation of state Bazavov, et. al. PRD 90, 094503 (2014) iEBE-VISHNU hydrodynamics Shen, Qiu, Song, Bernhard, Bass, Heinz, Comp. Phys. Comm. 199, 61 (2016) η/s min shear viscosity minimum η/s slope shear viscosity slope ζ/s norm bulk viscosity normalization Tsw hydro-to-urqmd switching temp UrQMD hadronic afterburner Bass et. al, Prog. Part. Nucl. Phys. 41, 255 (1998) J. Scott Moreland (Duke U.) 19 / 27
37. The challenge of rigorous model-to-data comparison Parameter Observable shear viscosity bulk viscosity pre-equilibrium flow nucleon width hadronization temp p+p fluctuations identified yields identified mean pT flow cumulants mode mixing observables event plane decorrelations HBT interferometry Testing a single set of parameters requires O(104) hydro events ...and evaluating eight different parameters five times each requires 58 × 104 ≈ 109 hydro events. That’s roughly 105 computer years! J. Scott Moreland (Duke U.) 20 / 27
38. Current practicum and thesis work ”What are you doing and why are you doing it.” –sponsors 1 Quantify sensitivity of hydrodynamic simulations to different calculations of the QCD equation of state (LLNL) Phys. Rev. C93 (2016) 044913 2 Improve theoretical description of the QGP initial conditions Nucl. Phys. A 904-905, 815c (2013) Phys. Rev. C92 (2015) 011901 3 Rigorously constrain QGP medium properties using Bayesian model-to-data analysis pre-print arXiv:1605.03954 (2016) J. Scott Moreland (Duke U.) 21 / 27
39. Solution: Bayesian methodology Model Parameters - System Properties • initial conditions (e.g. nucleon width) • QGP & HRG medium (e.g. η/s) Physics Model • TRENTo IC • iEBE-VISHNU Experimental Data • ALICE flow and spectra Gaussian Process Emulator • non-parameteric interpolation • fast surrogate for full model Markov chain Monte Carlo (MCMC) • random walk through param. space weighted by posterior probability Bayes' Theorem: posterior ∝ likelihood × posterior Posterior Distribution • probability distribution for true values of model parameters after many steps, MCMC equilibriates to calc events on Latin hypercube J. Scott Moreland (Duke U.) 22 / 27
40. Calibrating the model: before and after 100 101 102 103 Training data π± K± p¹ p Yields dN/dy 0.0 0.5 1.0 1.5 π± K± p¹ p Mean pT [GeV] 0.00 0.03 0.06 0.09 v2 v3 v4 Flow cumulants vn {2} 0 10 20 30 40 50 60 70 Centrality % 100 101 102 103 Posterior samples π± K± p¹ p 0 10 20 30 40 50 60 70 Centrality % 0.0 0.5 1.0 1.5 π± K± p¹ p 0 10 20 30 40 50 60 70 Centrality % 0.00 0.03 0.06 0.09 v2 v3 v4 Top: run model (×104 events) at each design point (×300 evals) Bottom: emulator predictions for 100 samples from the posterior J. Scott Moreland (Duke U.) 23 / 27
41. Calibrated to identified particles 100 130 160 norm -1.0 0.0 1.0 p 0.8 1.5 2.2 k 0.4 0.7 1.0 w [fm] 0.0 0.15 0.3 η/s min 0.0 1.0 2.0 η/s slope† 0.0 1.0 2.0 ζ/s norm 100 130 160 norm 0.14 0.15 0.16 Tsw [GeV] -1.0 0.0 1.0 p 0.8 1.5 2.2 k 0.4 0.7 1.0 w [fm] 0.0 0.15 0.3 η/s min 0.0 1.0 2.0 η/s slope† 0.0 1.0 2.0 ζ/s norm 0.14 0.15 0.16 Tsw [GeV] Calibrated to charged particles
42. Calibrated to identified particles 100 130 160 norm -1.0 0.0 1.0 p 0.8 1.5 2.2 k 0.4 0.7 1.0 w [fm] 0.0 0.15 0.3 η/s min 0.0 1.0 2.0 η/s slope† 0.0 1.0 2.0 ζ/s norm 100 130 160 norm 0.14 0.15 0.16 Tsw [GeV] -1.0 0.0 1.0 p 0.8 1.5 2.2 k 0.4 0.7 1.0 w [fm] 0.0 0.15 0.3 η/s min 0.0 1.0 2.0 η/s slope† 0.0 1.0 2.0 ζ/s norm 0.14 0.15 0.16 Tsw [GeV] Calibrated to charged particles -1.0 -0.5 0.0 0.5 1.0 p KLN EKRT WN Entropy deposition parameter Generalized mean parametrization: dS/dy ∝ Tp A +Tp B 2 1/p
43. Calibrated to identified particles 100 130 160 norm -1.0 0.0 1.0 p 0.8 1.5 2.2 k 0.4 0.7 1.0 w [fm] 0.0 0.15 0.3 η/s min 0.0 1.0 2.0 η/s slope† 0.0 1.0 2.0 ζ/s norm 100 130 160 norm 0.14 0.15 0.16 Tsw [GeV] -1.0 0.0 1.0 p 0.8 1.5 2.2 k 0.4 0.7 1.0 w [fm] 0.0 0.15 0.3 η/s min 0.0 1.0 2.0 η/s slope† 0.0 1.0 2.0 ζ/s norm 0.14 0.15 0.16 Tsw [GeV] Calibrated to charged particles 0.15 0.20 0.25 0.30 Temperature [GeV] 0.0 0.2 0.4 0.6 η/s KSS bound 1/4π Prior range Posterior median 90% CI Shear viscosity parametrization: (η/s)(T) = (η/s)min+(T−Tc)(η/s)slope
44. Running the model with high probability parameters Choose high probability model parameters from Bayesian posterior (right) Run full hybrid model using high probability parameters (bottom) Initial condition QGP medium norm 120. η/s min 0.08 p 0.0 η/s slope 0.85 GeV−1 k 1.5 ζ/s norm 1.25 w 0.43 fm Tsw 0.148 GeV 100 101 102 103 104 π± K± p¹ p Nch × 5 solid: identified dashed: charged Yields dN/dy, dNch /dη 0 10 20 30 40 50 60 70 Centrality % 0.8 1.0 1.2 Model/Exp 0.0 0.4 0.8 1.2 π± K± p¹ p Mean pT [GeV] 0 10 20 30 40 50 60 70 Centrality % 0.8 1.0 1.2 0.00 0.03 0.06 0.09 v2 v3 v4 Flow cumulants vn {2} 0 10 20 30 40 50 60 70 Centrality % 0.8 1.0 1.2 J. Scott Moreland (Duke U.) 25 / 27
45. Running the model with high probability parameters Choose high probability model parameters from Bayesian posterior (right) Run full hybrid model using high probability parameters (bottom) Initial condition QGP medium norm 120. η/s min 0.08 p 0.0 η/s slope 0.85 GeV−1 k 1.5 ζ/s norm 1.25 w 0.43 fm Tsw 0.148 GeV 0 100 200 300 400 Npart 0 2 4 6 8 10 12 (dNch /dη)/(Npart /2) p+Pb 5.02 TeV 2.76 TeV 200 GeV 130 GeV Pb+Pb 2.76, 5.02 TeV p+Pb 5.02 TeV Au+Au 130, 200 GeV TRENTO Also describes particle production for different collision systems at multiple beam energies. J. Scott Moreland (Duke U.) 25 / 27
46. Conclusions Lattice QCD equation of state (LLNL summer project) Modern LQCD equations of state in good agreement. Negligible differences for experimental observables. Initial condition properties Yields, mean pT and flows impose strong constraints on IC. Entropy deposition mimicked by dS/dy ∼ √ TA TB Preferred initial conditions agree with two theory calc. Hydrodynamic transport properties First quantitative credibility interval on (η/s)(T)!
47. Special thanks to the Krell institute for the exceptional support!
48. Backup: computer experiment design Maximin Latin hypercube Random, space-filling points Maximizes the minimum distance between points → avoids gaps and clusters Uniform projections into lower dimensions This work: 300 points across 8 dimensions 8 centrality bins O(107) events total 0.0 0.1 0.2 0.3 η/s min 0.0 0.5 1.0 1.5 2.0 η/s slope J. Scott Moreland (Duke U.) 1 / 1