Estimating nucleon substructure properties in a unified hydrodynamic model of p-Pb and Pb-Pb collisions

Quark Matter International Conference on Ultra-relativistic
Nucleus-Nucleus Collisions, Venice, Italy

Transcript

1. Estimating nucleon substructure properties in a unified hydrodynamic model of p-Pb and Pb-Pb collisions J. S. Moreland, J. E. Bernhard & S. A. Bass Duke University Quark Matter | Venice, Italy 14 May 2018 1This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
2. Flow in small systems Important questions: Is hydro applicable to small collision systems? If so, can we fit small system collectivity using current hydro models? First question precludes the second, but also more difficult to answer. Let’s tackle the second question assuming hydrodynamic models make sense down to length scales ∆x = .2 fm. Under this assumption, does a unified hydrodynamic description of p+A and A+A data even exist? η ∆ -4 -2 0 2 4 (radians) φ ∆ 0 2 4 φ ∆ d η ∆ d pair N 2 d trig N 1 2.4 2.6 2.8 < 260 offline trk N ≤ = 2.76 TeV, 220 NN s (a) CMS PbPb < 3 GeV/c trig T 1 < p < 3 GeV/c assoc T 1 < p η ∆ -4 -2 0 2 4 (radians) φ ∆ 0 2 4 φ ∆ d η ∆ d pair N 2 d trig N 1 3.1 3.2 3.3 3.4 < 260 offline trk N ≤ = 5.02 TeV, 220 NN s (b) CMS pPb < 3 GeV/c trig T 1 < p < 3 GeV/c assoc T 1 < p J. Scott Moreland (Duke) 1 / 14
3. I. Bayesian parameter estimation of heavy-ion collisions
4. Heavy-ion collision model Figure: H. Petersen, MADAI TrENTo initial conditions parametric entropy deposition PRC.92.011901 freestream pre-flow infinitely weak coupling limit PRC.91.064906, PRC.80.034902 VISH2+1 viscous hydro 14-mom. approx w/ shear & bulk PRC.77.064901, J.CPC.2015.08.039 frzout sampler non-RTA shear & bulk corrections J.E. Bernhard thesis UrQMD Boltzmann cascade hadronic afterburner, simulate scatterings and decays PPNP.98.00058, JPG.25.9.308 Final observables calculated as similar as possible to experiment J. Scott Moreland (Duke) 2 / 14
5. Bayesian parameter estimation Input parameters IC and QGP properties Physics theory initial stages, hydro, and Boltzmann transport Computer model minimum bias event-by- event simulations Gaussian process emulator surrogate model MCMC calibrate model to data Posterior distribution quantitative estimates of each parameter Experimental data yields, mean pT , flows J. Scott Moreland (Duke) 3 / 14 Objective: Explore parameter space of a given model Quantify posterior probability of every parameter region given the model, data and known uncertainties
6. Parameter estimates from lead-lead collisions Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ ƐƏƐ ƐƏƑ ƐƏƒ 71_ ņ7 ķ 7ņ7‹ķ 7 $ ņ7 Œ;(œ rƳ0ƔĺƏƑ$;( Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ +b;Ѵ7v 0Ƴ0ƔĺƏƑ$;( Ɛ Ƒ ƒ Ɠ Ɣ ѵ 1_ ņ 1_ ƏĺƏ ƏĺƔ ƐĺƏ ƐĺƔ r$ Œ;(œ Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ ;-mr$ Ɛ Ƒ ƒ Ɠ Ɣ ѵ o==Ѵbm; |uh ņ o==Ѵbm; |uh ƏĺƏƏ ƏĺƏƔ ƏĺƐƏ ƏĺƐƔ ˆm ŔƑŕ Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ Ѵo‰1†l†Ѵ-m|v N ew ! Combined analysis of 2.76 and 5.02 TeV beam energies Parametric initial conditions and medium parameters See thesis by Jonah Bernhard [99999] 0.15 0.20 0.25 0.30 Temperature [GeV] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 η/s KSS bound 1/4π ? N ew !
7. Parameter estimates from lead-lead collisions 0 20 40 60 80 100 101 102 103 104 105 dNch /dη, dN/dy, dET /dη [GeV] Nch ET π K p Pb+Pb 2.76 TeV 0 20 40 60 80 100 101 102 103 104 105 Nch ET π K p Yields Pb+Pb 5.02 TeV 0 20 40 60 80 0.0 0.5 1.0 1.5 ­ pT ® [GeV] π K p 0 20 40 60 80 0.0 0.5 1.0 1.5 π K p Mean pT 0 20 40 60 80 0.00 0.01 0.02 0.03 0.04 δpT / ­ pT ® 0 20 40 60 80 0.00 0.01 0.02 0.03 0.04 Mean pT fluctuations 0 20 40 60 80 Centrality % 0.00 0.05 0.10 vn {2} v2 v3 v4 0 20 40 60 80 Centrality % 0.00 0.05 0.10 v2 v3 v4 Flow cumulants N ew ! Combined analysis of 2.76 and 5.02 TeV beam energies Parametric initial conditions and medium parameters See thesis by Jonah Bernhard [99999] 0.15 0.20 0.25 0.30 Temperature [GeV] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 η/s KSS bound 1/4π Posterior median 90% credible region N ew !
8. II. Adding nucleon substructure to the model
9. Nuclear structure Pb208 nucleus Original TRENTo model: Sample nucleon radii from spherical or deformed Woods-Saxon distributions Euler angles resampled to preserve minimum nucleon distance dmin [fm] Gaussian nucleons of width w [fm] This work: Trade Gaussian nucleon for lumpy nucleon J. Scott Moreland (Duke) 5 / 14
10. Nucleon substructure Sampling radius 1 fm .8 fm .6 fm .4 fm Parton width Parton number Free parameters: Width of the Gaussian distribution used to sample parton radial coordinates Number of Gaussian partons inside each nucleon Width of the Gaussian partons Absent from this work: Parton spatial correlations, see talk by Alba Soto Ontoso
11. Cross sections MC-Glauber cross sections (proton d.o.f. shown) Original TRENTo model: Pcoll = 1 − exp[−σgg Tpp(b)] σinel nn = 2πb db Pcoll (b) Ə Ɛ Ƒ ƒ Ɠ Ɣ 0Œ=lœ ƏĺƏƏ ƏĺƑƔ ƏĺƔƏ ƏĺƕƔ ƐĺƏƏ 1oѴѴ Ő0ő bm;Ѵ mm ƷѵĺƓ=lƑ 0Ѵ-1h7bvh ‰ƷƏĺƓŒ=lœ ‰ƷƏĺƕŒ=lœ ‰ƷƏĺƖŒ=lœ J. Scott Moreland (Duke) 7 / 14
12. Cross sections MC-Glauber cross sections (proton d.o.f. shown) Original TRENTo model: Pcoll = 1 − exp[−σgg Tpp(b)] σinel nn = 2πb db Pcoll (b) This work: Pcoll → 1 − npart i,j=1 [1 − Pcoll (bij )] Solve for opacity parameter σgg numerically J. Scott Moreland (Duke) 7 / 14
13. Participant thickness functions Original TRENTo model: Tnucleus (x, y) = Npart i=1 γi Tproton(x −xi , y −yi ) Random weight γi sampled from Gamma distribution with unit mean and variance 1/k. This work: γi Tproton → Nparton j=1 γj Tparton J. Scott Moreland (Duke) 8 / 14
14. Entropy deposition Generalized Mean Ansatz: dS dη ∝ TR(TA, TB) ≡ Tp A + Tp B 2 1/p TR =                max(TA, TB ) p → +∞, (TA + TB )/2 p = +1, √ TA TB p = 0, 2 TA TB /(TA + TB ) p = −1, min(TA, TB ) p → −∞. T denotes participant thickness function J. Scott Moreland (Duke) 9 / 14
15. Free streaming arrows: fluid velocity weighted by energy density Pre-equillibrium phase: Massless non-interacting parton gas matched to viscous hydrodynamics PRC.91.064906, PRC.80.034902. Must reinterpret initial entropy density as initial gluon density, dNg /y ∼ dS/dy Initialize hydro with non-zero uµ and πµν $bl; Ə bm= o†rѴbm] =u;;v|u;-l _‹7uo =v J. Scott Moreland (Duke) 10 / 14
16. III. Simultaneous calibration to p-Pb and Pb-Pb collisions at √ sNN = 5.02 TeV
17. Computer experiment design Parameter Description Range Norm Overall normalization 12–28 p Entropy deposition parameter −1 to +1 σfluct Relative parton fluct. std. 0–2 w Parton sampling radius 0.4–1.2 fm χstruct Parton structure parameter 0–1 npartons Number of partons 1–10 d3 min Nucleon exclusion volume 0–4.9 fm3 τfs Free streaming time 0.1–1.5 fm/c η/s min Shear viscosity at Tc 0–0.2 η/s slope Slope above Tc 0–8 GeV−1 η/s crv Curvature above Tc −1 to 1 ζ/s norm Bulk viscosity peak height 0–0.1 ζ/s width Bulk viscosity peak width 0–0.1 GeV ζ/s temp Bulk viscosity peak location 150–200 MeV Tswitch Particlization temperature 135–165 MeV Important details: Parton width is reparametrized: v = vmin + χstruct(vmax − vmin ) vmin = 0.2 fm, vmax = w Parton sampling radius is not equivalent to the proton radius in the proton c.o.m. frame, e.g. see PRC.94.024919 Other parameters same as Pb+Pb analysis at 2.76 and 5.02 TeV 500 design points per collision system, O(104) events per design point! J. Scott Moreland (Duke) 11 / 14
18. Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ ƐƏƐ ƐƏƑ ƐƏƒ 71_ ņ7 ķ 7ņ7‹ķ 7 $ ņ7 Œ;(œ rƳ0ƔĺƏƑ$;( Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ +b;Ѵ7v 0Ƴ0ƔĺƏƑ$;( Ɛ Ƒ ƒ Ɠ Ɣ ѵ 1_ ņ 1_ ƏĺƏ ƏĺƔ ƐĺƏ ƐĺƔ r$ Œ;(œ Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ ;-mr$ Ɛ Ƒ ƒ Ɠ Ɣ ѵ o==Ѵbm; |uh ņ o==Ѵbm; |uh ƏĺƏƏ ƏĺƏƔ ƏĺƐƏ ƏĺƐƔ ˆm ŔƑŕ Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ Ѵo‰1†l†Ѵ-m|v Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ ƐƏƐ ƐƏƑ ƐƏƒ 71_ ņ7 ķ 7ņ7‹ķ 7 $ ņ7 Œ;(œ rƳ0ƔĺƏƑ$;( Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ +b;Ѵ7v 0Ƴ0ƔĺƏƑ$;( Ɛ Ƒ ƒ Ɠ Ɣ ѵ 1_ ņ 1_ ƏĺƏ ƏĺƔ ƐĺƏ ƐĺƔ r$ Œ;(œ Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ ;-mr$ Ɛ Ƒ ƒ Ɠ Ɣ ѵ o==Ѵbm; |uh ņ o==Ѵbm; |uh ƏĺƏƏ ƏĺƏƔ ƏĺƐƏ ƏĺƐƔ ˆm ŔƑŕ Ə ƑƏ ƓƏ ѵƏ ѶƏ ;m|u-Ѵb|‹ѷ Ѵo‰1†l†Ѵ-m|v Prior (training data) Posterior (samples)
19. 8 14 20 Norm 2.76 TeV 13.9+1.2 −1.1 10.0 17.5 25.0 Norm 5.02 TeV 18.5+1.8 −1.7 −0.5 0.0 0.5 p 0.01+0.08 −0.08 0 1 2 σ fluct 0.90+0.24 −0.27 0.4 0.7 1.0 w [fm] 0.96+0.04 −0.05 0.0 1.2 1.5 1.7 d min [fm] 1.3+0.4 −0.5 0.00 0.75 1.50 τ fs [fm/c] 1.2+0.3 −0.3 0.0 0.1 0.2 η/s min 0.09+0.03 −0.02 0 4 8 η/s slope [GeV−1] 0.83+0.82 −0.83 −1 0 1 η/s crv −0.37+0.79 −0.63 0.00 0.05 0.10 ζ/s max 0.04+0.04 −0.02 0.00 0.05 0.10 ζ/s width [GeV] 0.03+0.04 −0.03 0.150 0.175 0.200 ζ/s T0 [GeV] 0.18+0.02 −0.02 0.135 0.150 0.165 T switch [GeV] 0.152+0.003 −0.003 8 14 20 Norm 2.76 TeV 0.0 0.2 0.4 σ model sys 10.0 17.5 25.0 Norm 5.02 TeV −0.5 0.0 0.5 p 0 1 2 σ fluct 0.4 0.7 1.0 w [fm] 0.0 1.2 1.5 1.7 d min [fm] 0.00 0.75 1.50 τ fs [fm/c] 0.0 0.1 0.2 η/s min 0 4 8 η/s slope [GeV−1] −1 0 1 η/s crv 0.00 0.05 0.10 ζ/s max 0.00 0.05 0.10 ζ/s width [GeV] 0.150 0.175 0.200 ζ/s T0 [GeV] 0.135 0.150 0.165 T switch [GeV] 0.0 0.2 0.4 σ model sys 0.10+0.09 −0.08 Bayesian posterior One row (column) for each parameter Diagonal panels: marginal distribution of a single model parameter Off-diagonal panels: joint distribution between a pair of model parameters
20. 8 14 20 Norm 2.76 TeV 13.9+1.2 −1.1 10.0 17.5 25.0 Norm 5.02 TeV 18.5+1.8 −1.7 −0.5 0.0 0.5 p 0.01+0.08 −0.08 0 1 2 σ fluct 0.90+0.24 −0.27 0.4 0.7 1.0 w [fm] 0.96+0.04 −0.05 0.0 1.2 1.5 1.7 d min [fm] 1.3+0.4 −0.5 0.00 0.75 1.50 τ fs [fm/c] 1.2+0.3 −0.3 0.0 0.1 0.2 η/s min 0.09+0.03 −0.02 0 4 8 η/s slope [GeV−1] 0.83+0.82 −0.83 −1 0 1 η/s crv −0.37+0.79 −0.63 0.00 0.05 0.10 ζ/s max 0.04+0.04 −0.02 0.00 0.05 0.10 ζ/s width [GeV] 0.03+0.04 −0.03 0.150 0.175 0.200 ζ/s T0 [GeV] 0.18+0.02 −0.02 0.135 0.150 0.165 T switch [GeV] 0.152+0.003 −0.003 8 14 20 Norm 2.76 TeV 0.0 0.2 0.4 σ model sys 10.0 17.5 25.0 Norm 5.02 TeV −0.5 0.0 0.5 p 0 1 2 σ fluct 0.4 0.7 1.0 w [fm] 0.0 1.2 1.5 1.7 d min [fm] 0.00 0.75 1.50 τ fs [fm/c] 0.0 0.1 0.2 η/s min 0 4 8 η/s slope [GeV−1] −1 0 1 η/s crv 0.00 0.05 0.10 ζ/s max 0.00 0.05 0.10 ζ/s width [GeV] 0.150 0.175 0.200 ζ/s T0 [GeV] 0.135 0.150 0.165 T switch [GeV] 0.0 0.2 0.4 σ model sys 0.10+0.09 −0.08 Bayesian posterior One row (column) for each parameter Diagonal panels: marginal distribution of a single model parameter Off-diagonal panels: joint distribution between a pair of model parameters Let’s zoom in on some specific regions...
21. 8 14 20 Norm 2.76 TeV 13.9+1.2 −1.1 10.0 17.5 25.0 Norm 5.02 TeV 18.5+1.8 −1.7 −0.5 0.0 0.5 p 0.01+0.08 −0.08 0 1 2 σ fluct 0.90+0.24 −0.27 0.4 0.7 1.0 w [fm] 0.96+0.04 −0.05 0.0 1.2 1.5 1.7 d min [fm] 1.3+0.4 −0.5 0.00 0.75 1.50 τ fs [fm/c] 1.2+0.3 −0.3 0.0 0.1 0.2 η/s min 0.09+0.03 −0.02 0 4 8 η/s slope [GeV−1] 0.83+0.82 −0.83 −1 0 1 η/s crv −0.37+0.79 −0.63 0.00 0.05 0.10 ζ/s max 0.04+0.04 −0.02 0.00 0.05 0.10 ζ/s width [GeV] 0.03+0.04 −0.03 0.150 0.175 0.200 ζ/s T0 [GeV] 0.18+0.02 −0.02 0.135 0.150 0.165 T switch [GeV] 0.152+0.003 −0.003 8 14 20 Norm 2.76 TeV 0.0 0.2 0.4 σ model sys 10.0 17.5 25.0 Norm 5.02 TeV −0.5 0.0 0.5 p 0 1 2 σ fluct 0.4 0.7 1.0 w [fm] 0.0 1.2 1.5 1.7 d min [fm] 0.00 0.75 1.50 τ fs [fm/c] 0.0 0.1 0.2 η/s min 0 4 8 η/s slope [GeV−1] −1 0 1 η/s crv 0.00 0.05 0.10 ζ/s max 0.00 0.05 0.10 ζ/s width [GeV] 0.150 0.175 0.200 ζ/s T0 [GeV] 0.135 0.150 0.165 T switch [GeV] 0.0 0.2 0.4 σ model sys 0.10+0.09 −0.08 Bayesian posterior
22. 8 14 20 Norm 2.76 TeV 13.9+1.2 −1.1 10.0 17.5 25.0 Norm 5.02 TeV 18.5+1.8 −1.7 −0.5 0.0 0.5 p 0.01+0.08 −0.08 0 1 2 σ fluct 0.90+0.24 −0.27 0.4 0.7 1.0 w [fm] 0.96+0.04 −0.05 0.0 1.2 1.5 1.7 d min [fm] 1.3+0.4 −0.5 0.00 0.75 1.50 τ fs [fm/c] 1.2+0.3 −0.3 0.0 0.1 0.2 η/s min 0.09+0.03 −0.02 0 4 8 η/s slope [GeV−1] 0.83+0.82 −0.83 −1 0 1 η/s crv −0.37+0.79 −0.63 0.00 0.05 0.10 ζ/s max 0.04+0.04 −0.02 0.00 0.05 0.10 ζ/s width [GeV] 0.03+0.04 −0.03 0.150 0.175 0.200 ζ/s T0 [GeV] 0.18+0.02 −0.02 0.135 0.150 0.165 T switch [GeV] 0.152+0.003 −0.003 8 14 20 Norm 2.76 TeV 0.0 0.2 0.4 σ model sys 10.0 17.5 25.0 Norm 5.02 TeV −0.5 0.0 0.5 p 0 1 2 σ fluct 0.4 0.7 1.0 w [fm] 0.0 1.2 1.5 1.7 d min [fm] 0.00 0.75 1.50 τ fs [fm/c] 0.0 0.1 0.2 η/s min 0 4 8 η/s slope [GeV−1] −1 0 1 η/s crv 0.00 0.05 0.10 ζ/s max 0.00 0.05 0.10 ζ/s width [GeV] 0.150 0.175 0.200 ζ/s T0 [GeV] 0.135 0.150 0.165 T switch [GeV] 0.0 0.2 0.4 σ model sys 0.10+0.09 −0.08 Bayesian posterior
23. Maximum a posteriori parameters J. Scott Moreland (Duke) 14 / 14