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event-by-event viscous relativistic hydrodynamics Caio A. G. Prado with Jacquelyn Noronha-Hostler, Mauro R. Cosentino, Marcelo G. Munhoz, Jorge Noronha and Alexandre A. P. Suaide Strangeness in Quark Matter 2016 UC Berkeley June 30, 2016

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SLIDE 1

Heavy flavor 𝑆AA and π‘€π‘œ in event-by-event viscous relativistic hydrodynamics

Caio A. G. Prado

with Jacquelyn Noronha-Hostler, Mauro R. Cosentino, Marcelo G. Munhoz, Jorge Noronha and Alexandre A. P. Suaide

Strangeness in Quark Matter 2016

UC Berkeley β€” June 30, 2016

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SLIDE 2

Introduction

Status quo

5 10 15 π‘žπ‘ˆ (GeV) 0.3 0.6 0.9 1.2 𝑆(electrons)

AA

ALICE (prelim.) BAMPS Rapp et al. POWLANG

  • Coll. + LPM

0–10% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

3 6 9 12 π‘žπ‘ˆ (GeV) 0.25 𝑀2{EP, τΏ—Ξ”πœƒτΏ— > 0.9}

20–40% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

􏿗𝑧􏿗 < 0.7

ALICE, 𝑓± ← HF TAMU MC@HQ+EPOS, Coll+Rad (LPM) POWLANG with frag. BAMPS el. BAMPS el. + rad.

(QM2015) AIP Conference Proceedings 1625, 226–229 (2014) arXiv:1606.00321 Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 1 / 16

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SLIDE 3

Introduction

Open questions

What happens with the higher Fourier

harmonics?

How sensitive are these observables to the

energy loss model?

Is there collectivity in the heavy flavor

sector?

How do fluctuations in an event-by-event

approach affect these observables?

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 2 / 16

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SLIDE 4

Introduction

Observables

Nuclear Modification Factor: 𝑆AA(π‘žπ‘ˆ, πœ’) =

d𝑂AA dπ‘žπ‘ˆ dπœ’

𝑂coll

d𝑂pp dπ‘žπ‘ˆ

;

Collective flow:

𝐹

d3𝑂 dπ‘ž3 = 1 2𝜌 d2𝑂 π‘žπ‘ˆ dπ‘žπ‘ˆ d𝑧 τΏΌ1 + βˆ‘π‘œ 2π‘€π‘œ cos τΏ―π‘œ τΏ΅πœ’ βˆ’ Ξ¨π‘œτΏΈτΏ²τΏΏ ;

π‘œ = 2 π‘œ = 3 π‘œ = 4 π‘œ = 5 π‘œ = 6

Multi-particle Cumulants: 2-, 4-, 6- and 8-particle.

Ξ¨2 Ξ¨3

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 3 / 16

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SLIDE 5

Simulation Development

Details of the modeling

Develop a Monte Carlo simulation; C++ programming language; ROOT and Pythia8. Modular paradigm (QCD factorization): Initial conditions (MCKLN); Event-by-event hydrodynamics (v-USPhydro); Energy loss model; Hadronization; Meson decay; Heavy quarks (bottom and charm) are probes: What happens in the heavy-flavor sector? High multiplicity experiments allow for the heavy-flavor

study.

Sampled at the beginning of the simulation and evolved

with the medium.

We currently neglect any effect of the probes on the

medium.

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 4 / 16

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SLIDE 6

Simulation Development

Energy Loss and Hadronization

Simple energy loss model: d𝐹

d𝑦 (π‘ˆ, 𝑀; 𝛽) = 𝛽Γflow𝑔(π‘ˆ, 𝑀); Ξ“flow = 𝛿 τΏ―1 βˆ’ 𝑀 cos(πœ’quark βˆ’ πœ’flow)τΏ² .

PRC 72 064910 (2005); arXiv:1602.03788 [nucl-th].

Fit the 𝛽 parameter:

1

Fit 𝛽charm using D0 𝑆AA data;

2

With fixed 𝛽charm, fit 𝛽bottom using electron 𝑆AA data;

The energy loss model can be changed at will. Hadronization using Peterson fragmentation function: Occurs after heavy-quarks have crossed π‘ˆfrag isothermal; Currently not implementing coalescence; Decays performed by Pythia8.

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 5 / 16

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SLIDE 7

Results

Nuclear modification factor

  • d𝐹

d𝑦 = 𝛽Γflow

π‘ˆfrag = 140 MeV. PLB 747 260–264 (2015)

10 20 30 40 π‘žT (GeV) 0.3 0.6 0.9 1.2 𝑆D0

AA

D0 𝑆AA

0–10% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV ALICE CMS Simulation

5 10 15 20 π‘žT (GeV) 0.3 0.6 0.9 1.2 𝑆(electron)

AA

Electron 𝑆AA

0–10% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV ALICE Charm Bottom Total

*Gray area: where coalescence should be important.

QM2015 (ALICE); CMS-PAS-HIN-15-005 (CMS) (QM2015) AIP Conference Proceedings 1625, 226–229 (2014) Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 6 / 16

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SLIDE 8

Results

Nuclear modification factor

𝑆AA is highly affected by the energy loss model! π‘ˆfrag = 140 MeV.

10 20 30 40 π‘žπ‘ˆ (GeV) 0.3 0.6 0.9 1.2 𝑆AA

d𝐹 d𝑦 = π›½π‘ˆ2 d𝐹 d𝑦 = 𝛽 d𝐹 d𝑦 = 𝛽𝑀𝛿

B meson 𝑆AA

0–10% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

10 20 30 40 π‘žπ‘ˆ (GeV) 0.3 0.6 0.9 1.2 𝑆AA

d𝐹 d𝑦 = π›½π‘ˆ2 d𝐹 d𝑦 = 𝛽 d𝐹 d𝑦 = 𝛽𝑀𝛿

D0 meson 𝑆AA

0–10% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 7 / 16

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SLIDE 9

Results

Multi-particle cumulants

First calculation of cumulants event-by-event for heavy-quarks!!! π‘‘π‘œ{4} = τΎŠβŸ¨4⟩τ½½ βˆ’ 2 τΎŠβŸ¨2⟩τ½½2

π‘€π‘œ{4}(π‘žπ‘ˆ) = βˆ’π‘’π‘œ{4} τΏ΅βˆ’π‘‘π‘œ{4}τΏΈ

3/4 ;

π‘‘π‘œ{6} = τΎŠβŸ¨6⟩τ½½ βˆ’ 9 τΎŠβŸ¨4⟩τ½½ τΎŠβŸ¨2⟩τ½½ + 12 τΎŠβŸ¨2⟩τ½½3

π‘€π‘œ{6}(π‘žπ‘ˆ) = π‘’π‘œ{6} τΏ―4(π‘‘π‘œ{6})5τΏ²

1/6 ;

π‘‘π‘œ{8} = τΎŠβŸ¨8⟩τ½½ βˆ’ 16 τΎŠβŸ¨6⟩τ½½ τΎŠβŸ¨2⟩τ½½ βˆ’ 18 τΎŠβŸ¨4⟩τ½½2 + 144 τΎŠβŸ¨4⟩τ½½ τΎŠβŸ¨2⟩τ½½2 βˆ’ 144 τΎŠβŸ¨2⟩τ½½4

π‘€π‘œ{8}(π‘žπ‘ˆ) = βˆ’π‘’π‘œ{8} τΏ―33(βˆ’π‘‘π‘œ{8})7τΏ²

1/8 .

PRC 83 044913 (2011); PRC 89 064904 (2014); CMS-PAS-HIN-15-014 (CMS). Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 8 / 16

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SLIDE 10

Results

Elliptic flow

  • Correlation between light quarks in a small π‘žπ‘ˆ bin and heavy quarks:

π‘€π‘œ{2}(π‘žπ‘ˆ) = τΎ‹π‘€

heavy

π‘œ

(π‘žπ‘ˆ)𝑀

light

π‘œ

cos τΏ―π‘œ τΏ΅Ξ¨

heavy

π‘œ

(π‘žπ‘ˆ) βˆ’ Ξ¨

light

π‘œ

􏿸􏿲􏽾 􏽱 􏾋􏿡𝑀

light

π‘œ

􏿸

2

􏽾 .

  • Heavy sector inherits geometrical fluctuations of soft sector;

PRL 116 252301 (2016).

βˆ’1 1 Ξ¨

light

2

βˆ’1 βˆ’0.5 0.5 1 Ξ¨

heavy

2

0.05 0.1 0.15 𝑀

light

2

0.02 0.04 0.06 0.08 0.1 𝑀

heavy

2

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 9 / 16

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SLIDE 11

Results

𝑀2{2} β€” Energy loss dependence

π‘ˆfrag = 140 MeV; 𝑀2{2} depends heavily on the energy loss model.

5 10 15 20 π‘žπ‘ˆ (GeV) 0.02 0.04 0.06 0.08 0.1 𝑀2{2}

d𝐹 d𝑦 = π›½π‘ˆ2 d𝐹 d𝑦 = 𝛽 d𝐹 d𝑦 = 𝛽𝑀𝛿(𝑀)

B meson 𝑀2{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

5 10 15 20 π‘žπ‘ˆ (GeV) 0.02 0.04 0.06 0.08 0.1 𝑀2{2}

d𝐹 d𝑦 = π›½π‘ˆ2 d𝐹 d𝑦 = 𝛽 d𝐹 d𝑦 = 𝛽𝑀𝛿(𝑀)

D0 meson 𝑀2{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 10 / 16

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SLIDE 12

Results

𝑀2{2} β€” π‘ˆfrag dependence

  • d𝐹

d𝑦 = 𝛽Γflow; The increase of π‘ˆfrag decreases the flow.

5 10 15 20 π‘žT (GeV) 0.02 0.04 0.06 0.08 0.1 𝑀2{2}

π‘ˆfrag = 120 MeV π‘ˆfrag = 130 MeV π‘ˆfrag = 140 MeV π‘ˆfrag = 150 MeV π‘ˆfrag = 160 MeV

B meson 𝑀2{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76

5 10 15 20 π‘žT (GeV) 0.02 0.04 0.06 0.08 0.1 𝑀2{2}

π‘ˆfrag = 120 MeV π‘ˆfrag = 130 MeV π‘ˆfrag = 140 MeV π‘ˆfrag = 150 MeV π‘ˆfrag = 160 MeV

D0 meson 𝑀2{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 11 / 16

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SLIDE 13

Results

Convergence of cumulants!

  • d𝐹

d𝑦 = 𝛽Γflow B meson; Convergence may indicate collectivity in the heavy sector.

5 10 15 20 π‘žπ‘ˆ (GeV) 0.02 0.03 0.04 0.05 0.06 𝑀2 π‘ˆfrag = 120 MeV

𝑀2{2} 𝑀2{4} 𝑀2{6} 𝑀2{8}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

5 10 15 20 π‘žπ‘ˆ (GeV) 0.02 0.03 0.04 0.05 0.06 𝑀2 π‘ˆfrag = 160 MeV

𝑀2{2} 𝑀2{4} 𝑀2{6} 𝑀2{8}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 12 / 16

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SLIDE 14

Results

Convergence of cumulants!

  • d𝐹

d𝑦 = 𝛽Γflow D0 meson. Convergence may indicate collectivity in the heavy sector.

5 10 15 20 π‘žπ‘ˆ (GeV) 0.02 0.04 0.06 0.08 𝑀2 π‘ˆfrag = 120 MeV

𝑀2{2} 𝑀2{4} 𝑀2{6} 𝑀2{8}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

5 10 15 20 π‘žπ‘ˆ (GeV) 0.02 0.04 0.06 0.08 𝑀2 π‘ˆfrag = 160 MeV

𝑀2{2} 𝑀2{4} 𝑀2{6} 𝑀2{8}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 13 / 16

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SLIDE 15

Results

𝑀3 for heavy flavor!

  • d𝐹

d𝑦 = 𝛽Γflow; First calculation of 𝑀3{2} β‰  0 for heavy-quark!!! 𝑀3{2} also decreases with the increase of π‘ˆfrag.

5 10 15 20 π‘žT (GeV) 0.01 0.02 𝑀3{2}

π‘ˆfrag = 120 MeV π‘ˆfrag = 130 MeV π‘ˆfrag = 140 MeV π‘ˆfrag = 150 MeV π‘ˆfrag = 160 MeV

B meson 𝑀3{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76

5 10 15 20 π‘žT (GeV) 0.01 0.02 𝑀3{2}

π‘ˆfrag = 120 MeV π‘ˆfrag = 130 MeV π‘ˆfrag = 140 MeV π‘ˆfrag = 150 MeV π‘ˆfrag = 160 MeV

D0 meson 𝑀3{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 14 / 16

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SLIDE 16

Results

𝑀3 for heavy flavor!

π‘ˆfrag = 140 MeV. 𝑀3{2} very sensitive to energy loss models;

5 10 15 20 π‘žπ‘ˆ (GeV) 0.01 0.02 𝑀3{2}

d𝐹 d𝑦 = π›½π‘ˆ2 d𝐹 d𝑦 = 𝛽 d𝐹 d𝑦 = 𝛽𝑀𝛿(𝑀)

B meson 𝑀3{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

5 10 15 20 π‘žπ‘ˆ (GeV) 0.01 0.02 𝑀3{2}

d𝐹 d𝑦 = π›½π‘ˆ2 d𝐹 d𝑦 = 𝛽 d𝐹 d𝑦 = 𝛽𝑀𝛿(𝑀)

D0 meson 𝑀3{2}

30–50% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 15 / 16

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SLIDE 17

Conclusions and outlook

New framework to study hard probes in an event-by-event hydrodynamics expanding QGP; First prediction of heavy-quark cumulants: Convergence of cumulants: collectivity in the

heavy-flavor sector?

First prediction of 𝑀3{2} for heavy-flavor; Future work: Improvement in the low-π‘žπ‘ˆ sector; Correlations between π‘€π‘œ in the heavy-flavor sector; Soft hard event engineering in the heavy-flavor sector; Check the influence of a π‘ˆ dependent shear and bulk

viscosities;

Check different beam energies; Symmetric cumulants SC(π‘œ, 𝑛).

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 16 / 16

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SLIDE 18

Backup

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SLIDE 19

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Initial Conditions

Actual input of the program; 2D profiles for the hydro: Energy density; Temperature; Transverse

velocity; 0–10% Pb-Pb, βˆšπ‘‘NN = 2.76 TeV

βˆ’7.5 7.5 𝑦 (fm) βˆ’10 βˆ’5 5 10 𝑧 (fm) 30 60 90 120 𝜁 (fmβˆ’4)

MCKLN initial conditions; Quarks position given by number of binary collisions; Initial momentum distribution given by pQCD (FONLL).

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016

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SLIDE 20

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Hydrodynamics

Viscous event-by-event 2D+1 hydrodynamics: v-USPhydro [1]: πœƒ/𝑑 = 0.11;

π‘ˆπœˆπœ‰ = πœπ‘£πœ‰π‘£πœ‰ βˆ’ π‘žΞ”πœˆπœ‰ + πœŒπœˆπœ‰, πœ–πœˆπ‘ˆπœˆπœ‰ = 0

Equations of motion solved using Smoothed Particle Hydrodynamics (SPH) algorithm: SPH-particles: Lagrangian method; Fast computational time; Well tested algorithm. Freeze-out: Cooper-Frye prescription including viscous corrections. π‘ˆFO = 120 MeV.

[1] arXiv:1602.03788 (2016), PRC 90, 034907 (2014); PRC 88 044916 (2013) Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016

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SLIDE 21

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Heavy-flavor production

Quark initial momentum: pQCD (FONLL). Quark initial direction (πœ’): random;

10 20 π‘žπ‘ˆ (GeV) 102 104 106 108 𝐹

d3𝜏 dπ‘ž3 pb/GeV2 FONLL Simulation Charm quark

βˆšπ‘‘NN = 2.76 TeV

JHEP 1210, 137 (2012)

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016

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SLIDE 22

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Heavy-flavor production

Check consistency of the code: Turn off energy loss: get the same as FONLL predictions.

10 20 π‘žπ‘ˆ (GeV) 102 104 106 108 𝐹

d3𝜏 dπ‘ž3 pb/GeV2 FONLL Simulation D0 meson

βˆšπ‘‘NN = 2.76 TeV 10 20 π‘žπ‘ˆ (GeV) 10βˆ’1 101 103 105 107 109 𝐹

d3𝜏 dπ‘ž3 pb/GeV2 FONLL Simulation Electron

βˆšπ‘‘NN = 2.76 TeV

JHEP 1210, 137 (2012)

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016

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SLIDE 23

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Hadronization and Decays

Hadronization: Heavy quarks hadronize after crossing the π‘ˆfrag

isothermal.

We use Peterson fragmentation function:

𝐸(𝑨) ∝ 1 𝑨 τΏΆ1 βˆ’

1 𝑨 βˆ’ 𝜁 1βˆ’π‘¨τΏΉ 2 ;

Currently we’re not implementing coalescence (future

work);

Decays: Performed using Pythia8; Only semi-leptonic channels selected;

Caio Prado SQM2016 β€” Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016