Flow in small and large QGP droplets: role of nucleon substructure J. S. Moreland, J. E. Bernhard, W. Ke, S. A. Bass (Duke University) Quark Matter, Chicago, USA 8 February 2017 Funding provided by DOE NNSA Stewardship Science Graduate Fellowship Computing resources provided by the Open Science Grid, supported by the NSF and DOE Office of Science 

Success of saturation models + hydro Hydro models with saturation IC, e.g. TRENTo, IP-Glasma and EKRT, provide excellent description of bulk observables in A+A collisions 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 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 20 40 60 80 100 〈v n 〉 centrality percentile 0.5 GeV < pT < 1GeV η/s=0.18 filled - ATLAS open - IP-Glasma+MUSIC 〈v2 〉 〈v3 〉 〈v4 〉 PRL 113, 102301 [1405.3605] 0 10 20 30 40 50 60 70 80 centrality [%] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 vn 2 (a) pT =[0.2 5.0] GeV LHC 2.76 TeV Pb+Pb η/s=0.20 η/s=param1 η/s=param2 η/s=param3 η/s=param4 ALICE vn 2 PRC 93, 024907 [1505.02677] PRC 94, 024907 [1605.03954] 

Not so good in small systems... PHENIX submitted to PRC [1609.02894] (GeV/c) T p 0.5 1 1.5 2 2.5 3 2 v 0 0.05 0.1 0.15 0.2 0.25 0-5% p+Au 200 GeV 2 PHENIX v AMPT SONIC superSONIC IPGlasma+Hydro (a) PHENIX (GeV/c) T p 0.5 1 1.5 2 2.5 3 2 v 0 0.05 0.1 0.15 0.2 0.25 0-5% d+Au 200 GeV (b) (GeV/c) T p 0.5 1 1.5 2 2.5 3 2 v 0 0.05 0.1 0.15 0.2 0.25 He+Au 200 GeV 3 0-5% (c) IP-Glasma + hydro could not reproduce experimental multiparticle correlations in small systems... what’s wrong? Perhaps hydro isn’t valid, incorporate initial CGC correlations SONIC model works quite well, revisit the MC-Glauber model? Saturation IC + hydro correct picture, small systems require additional nucleon substructure J. Scott Moreland (Duke U.) 2 / 17 

"Eccentric protons?" Schenke, Venugopalan PRL 113 102301 Data highly constrains functional form of initial entropy deposition (talk by J. Bernhard). Cannot modify the mapping without spoiling bulk A+A observables, but we can add fine structure to the inputs (thickness functions) Optical nucleus Nucleus w/ nucleons Historical analogue: nucleon position hot spots necessary for v3 J. Scott Moreland (Duke U.) 3 / 17 

"Eccentric protons?" Schenke, Venugopalan PRL 113 102301 Data highly constrains functional form of initial entropy deposition (talk by J. Bernhard). Cannot modify the mapping without spoiling bulk A+A observables, but we can add fine structure to the inputs (thickness functions) Optical proton Proton w/ partons Possibly similar picture for partons inside the nucleon? J. Scott Moreland (Duke U.) 3 / 17 

Objective: Extend TRENTo initial conditions to include nucleon substructure Estimate new substructure parameters using Bayesian methodology J. Scott Moreland (Duke U.) 4 / 17 

TRENTo: parametric initial condition model Sample nucleon positions J. Scott Moreland (Duke U.) 5 / 17 

TRENTo: parametric initial condition model Nuclei collide at random impact parameter b dP(b) = 2πb db J. Scott Moreland (Duke U.) 5 / 17 

TRENTo: parametric initial condition model Determine participants by pairwise collision probability Pcoll(b) = 1 − exp −σpartonic Tpp(b) J. Scott Moreland (Duke U.) 5 / 17 

TRENTo: parametric initial condition model Construct participant thickness functions ˜ TA,B = Npart i=1 wi Tp(x − xi) using Gamma random weights wi J. Scott Moreland (Duke U.) 5 / 17 

TRENTo: parametric initial condition model Construct participant thickness functions ˜ TA,B = Npart i=1 wi Tp(x − xi) using Gamma random weights wi J. Scott Moreland (Duke U.) 5 / 17 

TRENTo: parametric initial condition model Deposit entropy according to eikonal parametrization: dS dy τ=τ0 ∝ ˜ Tp A + ˜ Tp B 2 1/p generalized mean of participant nuclear density J. Scott Moreland (Duke U.) 5 / 17 

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.) 6 / 17 

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.) 6 / 17 

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.) 6 / 17 

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.) 6 / 17 

Sampling partons inside the proton Variable parameters: Nucleon width Parton width Number of partons Necessary constraints: Fit inelastic p+p cross section Preserve avg proton radial distribution Procedure 1 Sample parton radius v from deconvolved proton radius w rsample = √ w2 − v2 2 Given a nucleon pair, take all possible parton pairs. Parton pair collision prob given by: Pcoll = 1 − exp(−σppTpp) 3 Nucleon pair collides if one or more parton pairs collide. All partons in participant nucleon added to nucleon thickness function. 4 Partonic cross section parameter σpp is numerically tuned to fit σinel nn σinel nn = ∫ d2b 1 − i,j Pij miss J. Scott Moreland (Duke U.) 7 / 17 

Effect on nuclear thickness functions Parton width [fm] Lead nucleus 5 0 5 3 partons 20 partons width 0.2 fm 5 0 5 5 0 5 5 0 5 width 0.3 fm x [fm] y [fm] Parton number Proton 1 0 1 3 partons 20 partons width 0.2 fm 1 0 1 1 0 1 1 0 1 width 0.3 fm x [fm] y [fm] Parton number nucleon width fixed, w = 0.5 fm J. Scott Moreland (Duke U.) 8 / 17 

Exploring the parameter space Model Parameters ▪ e.g. nucleon width, parton width, etc Physics Model ▪ TRENTo initial conditions with partonic substructure ▪ iEBE VISHNU hybrid model CPC 199, 61-85 [1409.8164] Experimental Data ▪ ALICE p+Pb 5.02 TeV yields and correlations Gaussian Process Emulator ▪ nonparametric interpolation ▪ fast surrogate full model Markov chain Monte Carlo ▪ random walk through param space, weighted by posterior Bayes' Theorem ▪ posterior ∝ likelihood × prior Posterior Distribution ▪ prob distribution for true values of model parameters calc events on la�n hypercube a�er many steps, MCMC equilibriates to J. Scott Moreland (Duke U.) 9 / 17 

Creating the design space parton number npartons = 2k, k ∈ 1–4.5 nucleon width w ∈ 0.4–1 fm parton width: vmin = Amin nparton vmax = w v = vmin + x (vmax − vmin) x ∈ [0, 1], Amin = 0.1 fm2 0.4 0.6 0.8 1.0 nucleon width [fm] 0.0 0.2 0.4 0.6 0.8 1.0 parton width [fm] 1 parton 22 partons J. Scott Moreland (Duke U.) 10 / 17 

Measuring hydrodynamic response 0 100 200 dS/dy [fm−2] 0 100 200 Nch(|´| < 1) p+Pb, p sNN = 5. 02 TeV 0 2 4 6 8 Nch (|´| < 1)/Area [fm−2] 0.0 0.2 0.4 q­ v2 n ® / q­ "2 n ® v2 v3 0. 2 < pT < 3 GeV, ¢´ > 1 1 Sample IC parameters from design, fix hydro parameters using Bayesian constraints determined from Pb+Pb collisions (talk by J. Bernhard) (η/s)min = 0.06, (η/s)slope = 2.0 GeV−1, τfs = 0.6 fm/c (ζ/s)max = 0.015, (ζ/s)width = 0.02 GeV J. Scott Moreland (Duke U.) 11 / 17 

Measuring hydrodynamic response 0 100 200 dS/dy [fm−2] 0 100 200 Nch(|´| < 1) p+Pb, p sNN = 5. 02 TeV 0 2 4 6 8 Nch (|´| < 1)/Area [fm−2] 0.0 0.2 0.4 q­ v2 n ® / q­ "2 n ® v2 v3 0. 2 < pT < 3 GeV, ¢´ > 1 1 Sample IC parameters from design, fix hydro parameters using Bayesian constraints determined from Pb+Pb collisions (talk by J. Bernhard) 2 Run O(104) min bias hydro + UrQMD events 3 Fit functions for yield, elliptic and triangular flows J. Scott Moreland (Duke U.) 11 / 17 

Training data Lines: model calculations at each design point, calculated by applying response functions to dS/dy and εn Symbols: ALICE 5.02 p+Pb data; central bins combined, and v3 data interpolated to match v2 centrality bins 0 10 20 30 40 50 60 70 80 Centrality % 101 102 Nch(|´| < 1) ALICE p+Pb, 5.02 TeV 0 5 10 15 20 25 30 35 40 Centrality % 0.00 0.05 0.10 0.15 0.20 vn {2} v2 v3 0. 2 < pT < 3 GeV, ¢´ > 1 Data: ALICE, PRC 90, 054901 [1406.2474] J. Scott Moreland (Duke U.) 12 / 17 

Posterior samples One-hundred samples drawn from the calibrated model Spread encapsulates uncertainty in the optimal values of the model parameters 0 10 20 30 40 50 60 70 80 Centrality % 101 102 Nch(|´| < 1) ALICE p+Pb, 5.02 TeV 0 5 10 15 20 25 30 35 40 Centrality % 0.00 0.05 0.10 0.15 0.20 vn {2} v2 v3 0. 2 < pT < 3 GeV, ¢´ > 1 Data: ALICE, PRC 90, 054901 [1406.2474] J. Scott Moreland (Duke U.) 13 / 17 

−1 0 1 gen mean p 0 1 2 p+p fluct std 0.00 2.25 4.50 log2(npartons) 0.4 0.7 1.0 proton width [fm] −1 0 1 gen mean p 0.0 0.5 1.0 parton struct 0 1 2 p+p fluct std 0.00 2.25 4.50 log2(npartons) 0.4 0.7 1.0 proton width [fm] 0.0 0.5 1.0 parton struct Posterior distribution flat 15% error on data Diagonal: marginalized posterior dist. for individual model parameters Lower diagonal: joint dist’s for pairs of parameters 

−1 0 1 gen mean p 0 1 2 p+p fluct std 0.00 2.25 4.50 log2(npartons) 0.4 0.7 1.0 proton width [fm] −1 0 1 gen mean p 0.0 0.5 1.0 parton struct 0 1 2 p+p fluct std 0.00 2.25 4.50 log2(npartons) 0.4 0.7 1.0 proton width [fm] 0.0 0.5 1.0 parton struct Posterior distribution flat 15% error on data Diagonal: marginalized posterior dist. for individual model parameters Lower diagonal: joint dist’s for pairs of parameters Red: prior information from Pb+Pb analysis PRC 94, 024907 

Posterior nucleon realizations Nucleon width w = 0.88 fm Parton number m = 22 Parton width v = 0.45 fm Proton thickness functions [fm−2] 

Summary and Outlook Presented Added variable parton number, width to nuclear thickness func’s Proton–lead collisions appear to prefer many partons (>10) No clear tension in A+A and p+A parameters using substructure Current estimates slightly overshoot gap between v2 and v3 To do Replace response function with e-by-e hydro+micro Calibrate to Pb+Pb and p+Pb simultaneously Increase max partons to ∼100 Add observables, e.g. mean pT , and additional collision systems J. Scott Moreland (Duke U.) 17 / 17 

QGP initial conditions in the Eikonal approximation Simplifying postulates Initial energy (entropy) deposition is local Sees only transverse nuclear densities TA,B Hence d2S dx2τ0 dη η=0 ≈ f(TA , TB) The mapping f : TA , TB → s(x, η) should be universal at a given beam energy! ...should not change across p+p, p+Pb, Pb+Pb systems at √ sNN = const. J. Scott Moreland (Duke U.) 1 / 6 

TRENTo: comparing to specific 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 dyd2r⊥ ∝ TA + TB ∗T denotes participant thickness EKRT model PRC 93, 024907 dET dyd2r⊥ ∼ Ksat π p3 sat (Ksat , β; TA , TB) after brief free streaming phase KLN model PRC 75, 034905 dNg dyd2r⊥ ∼ Q2 s,min 2 + log Q2 s,max Q2 s,min J. Scott Moreland (Duke U.) 2 / 6 

Establishing priorities in model-to-data comparison Model-to-data hierarchy find the IC mapping f which describes, ↓ Yields in large, then small systems ↓ Correlations in large systems ↓ Correlations in p+p, p+A? ∗hydrodynamic danger zone Prioritize observables logically simple to complex macroscopic to microscopic −3 −2 −1 0 1 2 3 Á 0.00 0.05 0.10 0.15 0.20 dN/dÁ −3 −2 −1 0 1 2 3 ΔÁ −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20 C(ΔÁ) J. Scott Moreland (Duke U.) 3 / 6 

Nucleon substructure—a new degree of freedom PRC 87 064906 [1304.3403v3] Schematic (a) (b) (c) TRENTo p=1 p=0 p= 1 

Nucleon substructure—a new degree of freedom PRC 87 064906 [1304.3403v3] Schematic (a) (b) (c) TRENTo p=1 p=0 p= 1 

Constraining initial conditions in A+A collisions Identified yields, mean pT and flows 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 Charged particle yields 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 Flow correlations 0 2 4 6 8 10 Centrality % −0.8 −0.4 0.0 0.4 0.8 SC(m, n) 1e−7 0 10 20 30 40 50 60 70 Centrality % −2 −1 0 1 2 1e−6 SC(4, 2) SC(3, 2) ...all provide strong constraints on IC −1.0 −0.5 0.0 0.5 1.0 p KLN EKRT / IP-Glasma Wounded nucleon 0. 03+0. 08 −0. 08 See talk by J. Bernhard for latest results with multiple beam energies, Tuesday, 11:20 AM, parallel session 2.1 J. Scott Moreland (Duke U.) 5 / 6 

Many models, many approaches First principle calculations, e.g. IP-Glasma PRL 108, 252301 [1202.6646] EKRT Nucl. Phys. B 570, 379–389 [9909456] KLN PRC 74, 044905 [0605012] EPOS PRC 92, 034906 [1306.0121] Parametric models MC Glauber Ann. Rev. Nucl. Part. Sci. 57, 205–243 [0701025] TRENTo PRC 92, 011901 [1412.4708] All models effectively implement f : TA , TB → e(x, η) Can compare different model calculations though mapping f J. Scott Moreland (Duke U.) 6 / 6