Status quo 3 1 / 16 5 0.6 0.9 1.2 Coll. + LPM 15 10 - PowerPoint PPT Presentation

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 Heavy flavor 𝑆 AA and 𝑤 𝑜 in

Introduction MC@HQ+EPOS, Coll+Rad (LPM) 6 9 12 0 0.25 TAMU POWLANG with frag. 0 BAMPS el. BAMPS el. + rad. (QM2015) AIP Conference Proceedings 1625 , 226–229 (2014) arXiv:1606.00321 Caio Prado SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 Status quo 3 1 / 16 5 0.6 0.9 1.2 Coll. + LPM 15 10 𝑆 (electrons) 0 AA 0 ALICE (prelim.) BAMPS Rapp et al. POWLANG 0.3 ALICE, 𝑓 ± ← HF 􏿗𝑧􏿗 < 0.7 𝑤 2 { EP , 􏿗Δ𝜃􏿗 > 0.9} 20–40% Pb-Pb, √𝑡 NN = 2.76 TeV 0–10% Pb-Pb, √𝑡 NN = 2.76 TeV 𝑞 𝑈 ( GeV ) 𝑞 𝑈 (GeV)

Introduction Open questions harmonics? energy loss model? sector? approach affect these observables? Caio Prado SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 2 / 16 � What happens with the higher Fourier � How sensitive are these observables to the � Is there collectivity in the heavy flavor � How do fluctuations in an event-by-event

Introduction 2𝜌 June 30, 2016 SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics Caio Prado Ψ 3 Ψ 2 𝑜 = 6 𝑜 = 5 𝑜 = 4 𝑜 = 3 𝑜 = 2 Observables d 2 𝑂 1 d 3 𝑂 𝐹 ; d𝑞𝑈 d𝑂 pp 𝑂 coll d𝑂 AA 3 / 16 � Nuclear Modification Factor: 𝑆 AA (𝑞 𝑈 , 𝜒) = d𝑞𝑈 d𝜒 � Collective flow: 𝑞 𝑈 d𝑞 𝑈 d𝑧 􏿼1 + ∑ 𝑜 2𝑤 𝑜 cos 􏿯𝑜 􏿵𝜒 − Ψ 𝑜 􏿸􏿲􏿿 ; d𝑞 3 = � Multi-particle Cumulants: � 2-, 4-, 6- and 8-particle.

Simulation Development Details of the modeling June 30, 2016 SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics Caio Prado medium. with the medium. study. 4 / 16 � 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 � Sampled at the beginning of the simulation and evolved � We currently neglect any effect of the probes on the

Simulation Development 2 June 30, 2016 SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics Caio Prado Energy Loss and Hadronization 5 / 16 1 PRC 72 064910 (2005); arXiv:1602.03788 [nucl-th]. � Simple energy loss model: d𝐹 d𝑦 (𝑈, 𝑤; 𝛽) = 𝛽Γ flow 𝑔(𝑈, 𝑤) ; Γ flow = 𝛿 􏿯1 − 𝑤 cos(𝜒 quark − 𝜒 flow )􏿲 . � Fit the 𝛽 parameter: Fit 𝛽 charm using D 0 𝑆 AA data; With fixed 𝛽 charm , fit 𝛽 bottom using electron 𝑆 AA data; � The energy loss model can be changed at will. � Hadronization using Peterson fragmentation function: � Occurs after heavy-quarks have crossed 𝑈 frag isothermal; � Currently not implementing coalescence; � Decays performed by Pythia8.

Results Electron 𝑆 AA 20 0 0.3 0.6 0.9 1.2 𝑆 (electron) AA ALICE Nuclear modification factor 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 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 15 10 5 0.6 d𝐹 10 20 30 40 0 Simulation 0.3 0.9 1.2 𝑆 D 0 AA ALICE CMS 6 / 16 � d𝑦 = 𝛽Γ flow 𝑈 frag = 140 MeV. PLB 747 260–264 (2015) D 0 𝑆 AA 0–10% Pb-Pb, √𝑡 NN = 2.76 TeV 0–10% Pb-Pb, √𝑡 NN = 2.76 TeV 𝑞 T (GeV) 𝑞 T (GeV)

Results 0.9 20 30 40 0 0.3 0.6 1.2 B meson 𝑆 AA 𝑆 AA d𝐹 d𝐹 d𝐹 Caio Prado SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 Nuclear modification factor 10 d𝐹 0.9 10 20 30 40 0.3 0.6 0 1.2 d𝐹 7 / 16 d𝐹 𝑆 AA � 𝑆 AA is highly affected by the energy loss model! � 𝑈 frag = 140 MeV. D 0 meson 𝑆 AA d𝑦 = 𝛽𝑈 2 d𝑦 = 𝛽𝑈 2 d𝑦 = 𝛽 d𝑦 = 𝛽 d𝑦 = 𝛽𝑤𝛿 d𝑦 = 𝛽𝑤𝛿 0–10% Pb-Pb, √𝑡 NN = 2.76 TeV 0–10% Pb-Pb, √𝑡 NN = 2.76 TeV 𝑞 𝑈 (GeV) 𝑞 𝑈 (GeV)

Results 𝑒 𝑜 {6} June 30, 2016 SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics Caio Prado PRC 83 044913 (2011); PRC 89 064904 (2014); CMS-PAS-HIN-15-014 (CMS). 􏿯33(−𝑑 𝑜 {8}) 7 􏿲 −𝑒 𝑜 {8} 𝑤 𝑜 {8}(𝑞 𝑈 ) = Multi-particle cumulants 􏿯4(𝑑 𝑜 {6}) 5 􏿲 𝑤 𝑜 {6}(𝑞 𝑈 ) = 􏿵−𝑑 𝑜 {4}􏿸 −𝑒 𝑜 {4} 𝑤 𝑜 {4}(𝑞 𝑈 ) = heavy-quarks!!! First calculation of cumulants event-by-event for 8 / 16 � 𝑑 𝑜 {4} = 􏾊⟨4⟩􏽽 − 2 􏾊⟨2⟩􏽽 2 3/4 ; � 𝑑 𝑜 {6} = 􏾊⟨6⟩􏽽 − 9 􏾊⟨4⟩􏽽 􏾊⟨2⟩􏽽 + 12 􏾊⟨2⟩􏽽 3 1/6 ; � 𝑑 𝑜 {8} = 􏾊⟨8⟩􏽽 − 16 􏾊⟨6⟩􏽽 􏾊⟨2⟩􏽽 − 18 􏾊⟨4⟩􏽽 2 + 144 􏾊⟨4⟩􏽽 􏾊⟨2⟩􏽽 2 − 144 􏾊⟨2⟩􏽽 4 1/8 .

Results 0.15 light 2 −1 −0.5 0 0.5 1 Ψ heavy 2 0.05 0.1 𝑤 1 light 2 0.02 0.04 0.06 0.08 0.1 𝑤 heavy 2 Caio Prado SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 Ψ 0 Elliptic flow 𝑜 𝑤 𝑜 {2}(𝑞 𝑈 ) = 􏾋𝑤 heavy 𝑜 (𝑞 𝑈 )𝑤 light 𝑜 heavy 𝑜 (𝑞 𝑈 ) − Ψ −1 light 􏿸􏿲􏽾 􏽱 􏾋􏿵𝑤 light 𝑜 􏿸 2 􏽾 . Heavy sector inherits geometrical fluctuations of soft sector; PRL 116 252301 (2016). 9 / 16 � Correlation between light quarks in a small 𝑞 𝑈 bin and heavy quarks: cos 􏿯𝑜 􏿵Ψ �

Results 0.08 10 15 20 0 0.02 0.04 0.06 0.1 B meson 𝑤 2 {2} 𝑤 2 {2} d𝐹 d𝐹 d𝐹 Caio Prado SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 𝑤 2 {2} — Energy loss dependence 5 d𝐹 0.08 5 10 15 20 0.02 0.04 0.06 0 0.1 d𝐹 10 / 16 d𝐹 𝑤 2 {2} � 𝑈 frag = 140 MeV; � 𝑤 2 {2} depends heavily on the energy loss model. D 0 meson 𝑤 2 {2} d𝑦 = 𝛽𝑈 2 d𝑦 = 𝛽 d𝑦 = 𝛽𝑈 2 d𝑦 = 𝛽 d𝑦 = 𝛽𝑤𝛿(𝑤) d𝑦 = 𝛽𝑤𝛿(𝑤) 30–50% Pb-Pb, √𝑡 NN = 2.76 TeV 30–50% Pb-Pb, √𝑡 NN = 2.76 TeV 𝑞 𝑈 (GeV) 𝑞 𝑈 (GeV)

Results B meson 𝑤 2 {2} June 30, 2016 SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics Caio Prado 𝑤 2 {2} 0.1 0.08 0.06 0.04 0.02 0 20 15 10 5 11 / 16 𝑤 2 {2} 0.04 d𝐹 5 10 15 0 0.02 20 0.06 0.1 0.08 𝑤 2 {2} — 𝑈 frag dependence � d𝑦 = 𝛽Γ flow ; � The increase of 𝑈 frag decreases the flow. D 0 meson 𝑤 2 {2} 𝑈 frag = 120 MeV 𝑈 frag = 120 MeV 𝑈 frag = 130 MeV 𝑈 frag = 130 MeV 𝑈 frag = 140 MeV 𝑈 frag = 140 MeV 𝑈 frag = 150 MeV 𝑈 frag = 150 MeV 𝑈 frag = 160 MeV 𝑈 frag = 160 MeV 30–50% Pb-Pb, √𝑡 NN = 2.76 30–50% Pb-Pb, √𝑡 NN = 2.76 𝑞 T (GeV) 𝑞 T (GeV)

Results 0.05 5 10 15 20 0.02 0.03 0.04 0.06 𝑤 2 {6} 𝑤 2 𝑤 2 {2} 𝑤 2 {4} 𝑤 2 {6} 𝑤 2 {8} Caio Prado SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 Convergence of cumulants! 𝑤 2 {8} 𝑤 2 {4} 0.02 d𝐹 B meson; sector. 5 10 15 𝑤 2 {2} 20 0.03 0.04 0.05 0.06 𝑤 2 12 / 16 � d𝑦 = 𝛽Γ flow � Convergence may indicate collectivity in the heavy 𝑈 frag = 120 MeV 𝑈 frag = 160 MeV 30–50% Pb-Pb, √𝑡 NN = 2.76 TeV 30–50% Pb-Pb, √𝑡 NN = 2.76 TeV 𝑞 𝑈 (GeV) 𝑞 𝑈 (GeV)

Results 0.08 5 10 15 20 0.02 0.04 0.06 𝑤 2 𝑤 2 {6} 𝑤 2 {2} 𝑤 2 {4} 𝑤 2 {6} 𝑤 2 {8} Caio Prado SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics June 30, 2016 Convergence of cumulants! 𝑤 2 {8} 𝑤 2 {4} 0.02 d𝐹 sector. 5 10 𝑤 2 {2} 20 15 0.04 0.06 0.08 𝑤 2 13 / 16 � D 0 meson. d𝑦 = 𝛽Γ flow � Convergence may indicate collectivity in the heavy 𝑈 frag = 120 MeV 𝑈 frag = 160 MeV 30–50% Pb-Pb, √𝑡 NN = 2.76 TeV 30–50% Pb-Pb, √𝑡 NN = 2.76 TeV 𝑞 𝑈 (GeV) 𝑞 𝑈 (GeV)

Results 𝑤 3 {2} June 30, 2016 SQM2016 — Heavy flavor event-by-event relativistic hydrodynamics Caio Prado 𝑤 3 {2} 0.02 0.01 0 20 15 10 5 B meson 𝑤 3 {2} 0.02 0 d𝐹 5 0.01 15 20 10 14 / 16 𝑤 3 for heavy flavor! � d𝑦 = 𝛽Γ flow ; � First calculation of 𝑤 3 {2} ≠ 0 for heavy-quark!!! � 𝑤 3 {2} also decreases with the increase of 𝑈 frag . D 0 meson 𝑤 3 {2} 𝑈 frag = 120 MeV 𝑈 frag = 120 MeV 𝑈 frag = 130 MeV 𝑈 frag = 130 MeV 𝑈 frag = 140 MeV 𝑈 frag = 140 MeV 𝑈 frag = 150 MeV 𝑈 frag = 150 MeV 𝑈 frag = 160 MeV 𝑈 frag = 160 MeV 30–50% Pb-Pb, √𝑡 NN = 2.76 30–50% Pb-Pb, √𝑡 NN = 2.76 𝑞 T (GeV) 𝑞 T (GeV)