Bayesian parameter estimation for heavy-ion collisions: inferring properties of the quark-gluon plasma

XLVII International Symposium on Multiparticle Dynamics, Tlaxcala City, Mexico

Transcript

1. Bayesian parameter estimation for heavy-ion collisions: inferring properties of the quark-gluon plasma J. Scott Moreland—Duke U. XLVII International Symposium on Multiparticle Dynamics September 14, 2017
2. Lattice predicts existence of a quark-gluon plasma Lattice QCD calculations find a pseudo-critical phase transition temperature T ≈ 155 MeV, where hadrons melt to form a deconfined soup of quarks and gluons dubbed a quark-gluon plasma (QGP) T ~ 155 MeV Baryon Density μ [GeV] Temperature T [MeV] critical point? quark-gluon plasma early universe hadron gas nuclear collisions J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 1 / 24
3. What are the quark-gluon plasma bulk properties? 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. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 2 / 24
4. Formulating an inverse problem Model-to-data comparison (in an ideal world) Model A Model B Model C Model D Model E Exp Data J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 3 / 24
5. Formulating an inverse problem Realistic model-to-data comparison Model A Model B Model C Model D Model E ? ? Exp Data J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 3 / 24
6. I) Bayesian parameter estimation
7. Formulating an inverse problem Parametrize Theory landscape Model A Model B Model C Model D Model E Exp Data J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 4 / 24
8. Formulating an inverse problem Bayesian parameter estimation continuous model parameter: x Exp Data P(x |model, data) Bayes’ Theorem: P(x |model, data) posterior ∝ P(model, data|x ) likelihood P(x ) prior J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 4 / 24
9. Formulating an inverse problem Bayesian parameter estimation continuous model parameter: x Exp Data P(x |model, yexp) Bayes’ Theorem: P(x |model, data) posterior ∝ P(model, data|x ) likelihood P(x ) prior J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 4 / 24
10. Formulating an inverse problem Bayesian parameter estimation continuous model parameter: x Exp Data P(x |model, yexp) Bayes’ Theorem: P(x |model, data) posterior ∝ P(model, data|x ) likelihood P(x ) prior J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 4 / 24
11. Formulating an inverse problem Yields posterior distribution on x 4 2 0 2 4 x P(x |model,data) Includes uncertainty in “best-fit value” J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 4 / 24
12. Multiple observables posterior = likelihood × prior More than one observable f : x → (y1, ..., yn)? No problem, calculate likelihood using multivariate Gaussian Log-likelihood ln(L) = − 1 2 (ln(|Σ|) + (y − yexp)T Σ−1(y − yexp) + k ln(2π)) Σ = Σmodel + Σstat exp + Σsys exp J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 5 / 24
13. Multiple model parameters posterior = likelihood × prior Likelihood function L(x) → L(x1, ..., xn) Curse of dimensionality Typically interested in marginalized probabilities L(x1, ..., xn) easy to calculate, hard to integrate. Solution Monte Carlo integration, e.g. importance sampling MCMC importance sampling: 1. large number of walkers in {x1, ..., xn } space 2. update walker positions 3. accept new x with prob P ∼ Lnew/Lold Marginalize by histogramming over flattened dimensions J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 6 / 24
14. MCMC and evaluating the likelihood Number of likelihood samples needed for MCMC varies greatly not enough better better still Several of the published results in this talk use Nsample > 106 If model is slow, e.g. 1 CPU hour per likelihood evaluation ...good luck J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 7 / 24
15. Training an emulator Gaussian process: • Stochastic function: maps inputs to normally-distributed outputs • Specified by mean and covariance functions As a model emulator: • Non-parametric interpolation • Predicts probability distributions • Narrow near training points, wide in gaps • Fast surrogate to actual model −2 −1 0 1 2 Output Random functions 0 1 2 3 4 5 Input −2 −1 0 1 2 Output Conditioned on data Mean prediction Uncertainty Training data J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 8 / 24
16. Work ow Physics model Emulated model MCMC update update walkers {x} → {x } Bayesian posterior y = f (x) L(y, yexp) ...after many steps histogram {x} to visualize J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 9 / 24
17. Bayesian parameter estimation in physics LIGO Experiment 10 20 30 40 50 60 m1 (M ) 0 10 20 30 40 m2 (M ) GW150914 LVT151012 GW151226 GW170104 Average Effective Precession Full Precession est. black hole masses PRL 118.221101 • Planck Collaboration 2015: constraints on inflation Astron. Astrophys. 594 (2016) • CKM parameters Eur. Phys. J. C21 (2001) • Galaxy formation Astron. Astrophys. 409 (2003) ...and many more examples not listed here Adapt machinery to relativistic heavy-ion collisions? J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 10 / 24
18. II) Bayesian parameter estimation applied to heavy-ion physics
19. Bayesian methodology for heavy-ion collisions Trusted framework Experimental data Free parameter(s) General relativity gravitational waves black hole masses Relativistic hydro particle yields & corr. transport coefficients Analogue time: 0 fm/c 20 fm/c Hydro framework imposes local energy and momentum conservation. Clearly breaks in dilute limit. Should apply with care. J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 11 / 24
20. Bayesian methodology for heavy-ion collisions Trusted framework Experimental data Free parameter(s) General relativity gravitational waves black hole masses Relativistic hydro particle yields & corr. transport coefficients Analogue Hydro for heavy-ion collisions not trusted on same level as e.g. GR for gravitational waves • Posterior results always subject to framework credibility J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 11 / 24
21. Seminal Bayesian works in heavy-ion physics Rel. Probability 0 2.5 5 Rel. Probability T dep. of η energy norm. σsat (mb) 30 50 σsat (mb) W.N./Sat. frac. 0 1 W.N./Sat. frac. Init. Flow 0.25 1.25 Init. Flow η/s 0.02 0.5 η/s T dep. of η 0.85 1.025 1.2 energy norm. 0 5 30 40 50 σsat (mb) 0 0.5 1 W.N./Sat. frac. 0.25 0.75 1.25 Init. Flow 0.02 0.26 0.5 η/s • Event-averaged hydro • Parametric pre-flow • Parametric initial state • First Bayesian posterior on (η/s)(T) • Omits bulk viscosity • Two centrality bins Determining Fundamental Properties of Matter Created in Ultrarelativistic Heavy-Ion Collisions, Novak, Novak, Pratt, Vredevoogd, Coleman-Smith, Wolpert PRC 89 (2014) 034917 J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 12 / 24
22. Seminal Bayesian works in heavy-ion physics • Equation of state from lattice QCD is very close to parametric equation of state preferred by simulation ��� ��� ��� ��� ��� ��� ��� �� � ������� ������������� ��� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��� ��� ��� ��� ��� ����������� ������� ���������� ��� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ������� BNL Constraining the Eq. of State of Super-Hadronic Matter from Heavy-Ion Collisions, Pratt, Sangaline, Sorensen, Wang, PRL 114 (2015) 202301 J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 13 / 24
23. Seminal Bayesian works in heavy-ion physics 0.0 0.1 0.2 0.3 ´=s Glauber 0.08 KLN 0.20 Theoretical biases affect preferred viscosity • Event-by-event hydro • MC-Glauber & KLN initial conditions • Centrality bins like experiment • Constant η/s • Omits bulk viscosity, pre-flow Constraining the Eq. of State of Super-Hadronic Matter from Heavy-Ion Collisions, Bernhard, Marcy, Coleman-Smith, Huzurbazar, Wolpert, Bass, PRC 91 (2015) 054910 J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 14 / 24
24. Initial stages and onset of hydrodynamic ow Strong coupling limit → hydrodynamics Weak coupling limit → freestreaming �me momentum anisotropy free streaming hydrodynamics free streaming + hydro τs Pre-equilibrium dynamics and heavy-ion observables, Heinz, Liu, Nucl. Phys. A956 (2016) 549-552 J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 15 / 24
25. Towards precision extraction of QGP properties Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and QGP medium, Bernhard, Moreland, Bass, Liu, Heinz PRC 94 (2016) 024907 Generational improvements • New TRENTo initial condition model: absorbs initial state uncertainties into several free parameters • Full event-by-event hydro with hadronic afterburner • Calculate observables exactly as experiment • Bulk and shear viscous corrections • More experimental observables Physics insights η/s min = 0.07 ± 0.05 non-zero bulk viscosity 0.15 0.20 0.25 0.30 Temperature [GeV] 0.0 0.2 0.4 0.6 /s KSS bound 1/4 Prior range Posterior median 90% CI J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 16 / 24
26. Towards precision extraction of QGP properties Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and QGP medium, Bernhard, Moreland, Bass, Liu, Heinz PRC 94 (2016) 024907 Model calculations with high-likelihood parameters from Bayesian posterior provide excellent description of bulk observables 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. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 17 / 24
27. Leveraging data from RHIC beam energy scan 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.0 0.1 0.2 0.3 η/s 0.15 0.30 0.45 0.60 0.75 SW [GeV/fm3] 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.15 0.30 0.45 0.60 SW [GeV/fm3] √ sNN = 19 GeV Left: Bayesian posterior for hydrodynamic model param- eters calibrated at different beam energies √ sNN Revealing the collision energy dependence of η/s in RHIC-BES Au+Au collisions using Bayesian statistics, Auvinen, Karpenko, Bernhard, Bass, QM17 proceedings J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 18 / 24
28. Leveraging data from RHIC beam energy scan 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.0 0.1 0.2 0.3 η/s 0.15 0.30 0.45 0.60 0.75 SW [GeV/fm3] 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.15 0.30 0.45 0.60 SW [GeV/fm3] √ sNN = 39 GeV Left: Bayesian posterior for hydrodynamic model param- eters calibrated at different beam energies √ sNN Revealing the collision energy dependence of η/s in RHIC-BES Au+Au collisions using Bayesian statistics, Auvinen, Karpenko, Bernhard, Bass, QM17 proceedings J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 18 / 24
29. Leveraging data from RHIC beam energy scan 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.0 0.1 0.2 0.3 η/s 0.15 0.30 0.45 0.60 0.75 SW [GeV/fm3] 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.15 0.30 0.45 0.60 SW [GeV/fm3] √ sNN = 62 GeV Left: Bayesian posterior for hydrodynamic model param- eters calibrated at different beam energies √ sNN Revealing the collision energy dependence of η/s in RHIC-BES Au+Au collisions using Bayesian statistics, Auvinen, Karpenko, Bernhard, Bass, QM17 proceedings J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 18 / 24
30. Leveraging data from RHIC beam energy scan 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.0 0.1 0.2 0.3 η/s 0.15 0.30 0.45 0.60 0.75 SW [GeV/fm3] 0.8 1.6 2.4 τ0 [fm/c] 0.6 1.2 1.8 Wtrans [fm] 0.6 1.2 1.8 Wlong [fm] 0.15 0.30 0.45 0.60 SW [GeV/fm3] Beam-energy dependence of η/s 19.6 39 62.4 √ sNN [GeV] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 η/s Revealing the collision energy dependence of η/s in RHIC-BES Au+Au collisions using Bayesian statistics, Auvinen, Karpenko, Bernhard, Bass, QM17 proceedings J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 18 / 24
31. Bulk viscosity: a work in progress... Challenges • Different methods for bulk viscous corrections at freezeout • Less obvious parametric form for (ζ/s)(T) • Hydro cavitates if bulk is too large T/Tpeak band = 1 sigma 0.4 0.8 1.2 1.6 0 0.1 0.2 0.3 0.4 0.5 LHC RHIC z/s(T) 0.08 0.12 0.16 0.20 Temperature [GeV] 0.00 0.04 0.08 ζ/s Prior range Denicol, Paquet, Gale, Jeon, Shen Bernhard, Moreland, Bass J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 19 / 24
32. Studying the QGP reball in D 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] Initial energy density (3D) x η x η x η Figure credit: Schenke, Schlichting J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 20 / 24
33. Studying the QGP reball in D Constraints on rapidity-dependent initial conditions from charged particle pseudorapidity densities and two-particle correlations, Ke, Moreland, Bernhard, Bass (in prep) Optimization problem Find initial energy density that evolves into final single particle distribution • Parametrize initial longitudinal energy profile with moment-generating function • Constrain form using charged particle rapidity distributions −8 −4 0 4 8 η 0 50 100 150 dNch /dη (arb. units) Unregulated −8 −4 0 4 8 η Regulated γ = 0.0 γ = 3.0 γ = 6.0 γ = 9.0 −8 −4 0 4 8 y [fm] Pb+Pb Pb+Pb −8 −4 0 4 8 x [fm] −3 0 3 y [fm] p+Pb −8 −4 0 4 8 ηs p+Pb J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 21 / 24
34. Studying the QGP reball in D Bayesian analysis Initial entropy profile TB = 0.2 rel-skew abs-skew TB = 1.0 TB = 1.8 TA = 0.2 TB = 2.6 TA = 1.0 TA = 1.8 −5 0 5 −5 0 5 −5 0 5 −5 0 5 TA = 2.6 η ds/dη (arb. units) Final particle distribution −5.0 −2.5 0.0 2.5 5.0 η 0 250 500 750 1000 1250 1500 1750 2000 dN/dη ALICE, 2.76 TeV −2 0 2 η 0 10 20 30 40 50 60 70 80 dN/dη ATLAS, 5.02 TeV • Trust in hydro and Bayesian statistical machinery lets us deconvolve complex system evolution J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 22 / 24
35. QGP hard probes: open heavy- avour Analogue Theory framework Free parameter(s) Hydrodynamics QGP viscosity: η/s, ζ/s Langevin transport charm diffusion coefficient: Ds,p QGP shear viscosity 0.15 0.20 0.25 0.30 Temperature [GeV] 0.0 0.2 0.4 0.6 /s KSS bound 1/4 Prior range Posterior median 90% CI Charm diffusion coefficient 0.1 0.2 0.3 0.4 0.5 0.6 T [Ge V] 0 5 10 15 20 Ds 2πT p=0Ge V/c median value prior 90% C.R A data driven analysis for the temperature and momentum dependence of the heavy quark diffusion coefficient in relativistic heavy-ion collisions Xu, Bernhard, Bass, Nahrgang, Cao (in preparation) J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 23 / 24
36. Summary Virtues of Bayesian parameter estimation • Works for models with multiple correlated parameters • Rigorous accounting of errors and effect on quantities of interest • Global analysis can promote and kill models J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 24 / 24
37. Backup slides
38. Seminal Bayesian works in heavy-ion physics dNπ /dy (RHIC, 0-5\%) <pt >π (RHIC, 0-5\%) <pt >K (RHIC, 0-5\%) <pt >p (RHIC, 0-5\%) Rout (RHIC, 0-5\%) Rside (RHIC, 0-5\%) Rlong (RHIC, 0-5\%) dNπ /dy (RHIC, 20-30\%) <pt >π (RHIC, 20-30\%) <pt >K (RHIC, 20-30\%) <pt >p (RHIC, 20-30\%) Rout (RHIC, 20-30\%) Rside (RHIC, 20-30\%) Rlong (RHIC, 20-30\%) v2 (RHIC, 20-30\%) dNπ /dy (LHC, 0-5\%) <pt >π (LHC, 0-5\%) <pt >K (LHC, 0-5\%) <pt >p (LHC, 0-5\%) Rout (LHC, 0-5\%) Rside (LHC, 0-5\%) Rlong (LHC, 0-5\%) dNπ /dy (LHC, 20-30\%) <pt >π (LHC, 20-30\%) <pt >K (LHC, 20-30\%) <pt >p (LHC, 20-30\%) Rout (LHC, 20-30\%) Rside (LHC, 20-30\%) Rlong (LHC, 20-30\%) v2 (LHC, 20-30\%) 0.0 0.1 Z (RHIC) 0.0 0.1 Z (LHC) 0.0 0.1 σsat (RHIC) 0.0 0.1 σsat (LHC) 0.0 0.1 fwn (RHIC) 0.0 0.1 fwn (LHC) 0.0 0.1 τxx (RHIC) 0.0 0.1 τxx (LHC) 0.0 0.1 F0 (RHIC) 0.0 0.1 F0 (LHC) 0.0 0.1 (η/s)0 0.0 0.1 η 0.0 0.1 EoSX 0.0 0.1 EoS R Sensitivity of experimental observables to model parameters Towards a Deeper Understanding of How Experiments Constrain the Underlying Physics of Heavy-Ion Collisions, Sangaline, Pratt, PRC 93 (2016) 024908 J. S. Moreland (Duke U.) Bayesian parameter estimation for HIC 1 / 1