The unreasonable effectiveness of hydrodynamics in heavy ion collisions

Transcription

1 The unreasonable effectiveness of hydrodynamics in heavy ion collisions Jacquelyn Noronha-Hostler Columbia University Yale University Sept. 10th, 2015

2 Outline 1 Heavy Ion Collisons 2 Initial conditions 3 Hydro Modeling 4 Known Observables 5 Novel Developments v 2 /v 3 Large scale structure vs small scale fluctuations Solving the v 2 vs. R AA puzzle 6 Conclusions and Outlook

3 Extremely Hot, Extremely Small, and Extremely Fluid Every day matter is made up of hadrons with confined quarks and gluons The Quark Gluon Plasma has deconfined quarks and gluons as its degrees of freedom Recipe for Quark Gluon Plasma (QGP) in the lab Extremely high temperatures (Brookhaven National Lab- RHIC and CERN- LHC) T 400 MeV K 10 6 sun Accelerate heavy ions (gold nucleus 7.5 fm = cm) to ultrarelativistic speeds Observe the final particle yields and position to work back to QGP signals Can t observe the QGP directly!

4 In the Press... Smallest liquid measured Alice CMS Atlas

5 Evolution of a Heavy-Ion Collision Heavy ion collisions are modeled through Initial Condition: Pre-equilibrium state using gluon saturation models/glauber-like models Viscous hydrodynamical evolution/lattice Equation of State Hadronization mechanism: Cooper Frye including viscous corrections Hadronic afterburner

6 Relevant Experimental Observables Experimentalists measure the particle species (π s, K s, p s etc), position, and momentum Looking for signs of collective behavior i.e. "flow", observables sensitive to initial conditions, sensitivity to viscosity, effects from the Equation of State etc. Everything affects everything else! How can we disentangle such a complicated system? Christy Georg- Giant Monkey s Fist

7 Relevant Experimental Observables The distribution of particles can be written as a Fourier series (event plane method) [ E d 3 N d 3 p = 1 d 2 N 1 + ] 2v n cos [n (φ ψ n )] 2π p T dp T dy n Flow Harmonics at mid-rapidity where Ψ n = 1 n v n (p T ) = 2π 0 dφ dn arctan sin[(nφ)] cos[(nφ)] p T dp T dφ cos [n (φ Ψ n)] 2π 0 dφ dn p T dp T dφ

8 Initial state eccentricities predict flow harmonics Initial eccentricities converted to large momentum anisotropies via hydrodynamical evolution Initial eccentricity ε 2 nearly perfectly predictor for elliptical flow v Q2 ε2 ideal 0.9 bulk f shearbulk f shear f NeXSPheRIO centrality Head on collisions=small centrality, circular (zero ε 2 ) Peripheral collisions=large Gardim, JNH, Luzum, Grassi, Phys.Rev. C91 (2015) 3, Goes to 1 for a perfect mapping from initial eccentricity to final elliptical flow

9 The success of relativistic hydrodynamics Describes experimental data (1/2π) dn/dy p T dp T v n 2 1/ ALICE 0-5% IP-Glasma+MUSIC π + + π - K + + K - p + p p T [GeV] v 2 v 3 v 4 v 5 η/s =0.2 ATLAS 10-20%, EP For relativistic hydrodynamics to work: An extremely small shear viscosity to entropy density is needed η/s All components of the modeling needs to be understood i.e. effects of initial states, hadronic decays, etc Flow harmonics, v n s, are used to demonstrate collective behavior p T [GeV] Gale et al, Phys.Rev.Lett. 110 (2013) 1,

10 Probing the scales JNH, Noronha, Gyulassy, arxiv:

11 Types of Initial Conditions Energy Density profile Schenke, Tribedy, Venugopalan,Phys.Rev.Lett. 108 (2012) Two extremes- super spiky vs. smooth Hard to compare because the eccentricities are different! Glauber MCKLN NEXUS IPGlasma 2030 ε 2 ε 3 ε 1,3 ε 2 ε 4 Also- MCKLN, Glauber, URQMD, AMPT, etc. Drescher,Hladik,Ostapchenko,Pierog, Werner, Phys.Rept. 350, 93 (2001)

12 Changes to the energy density profile Smoothing out a spiky (mckln) initial condition up to a scale λ... Small λ indicates quarks and gluons as degrees of freedom

13 Robustness of Eccentricities Eccentricities measure large scale structure so there is almost no effect smoothing from the microscale up to the mesocale ε2,n n b. mckln Λfm JNH, Noronha, Gyulassy, arxiv: ε2,n 10 n PbPb s NN 2.76 TeV 6 mckln Λfm

14 Setup- v-usphydro JNH et al, Phys.Rev. C90 (2014) 3, , Phys.Rev. C88 (2013) v-usphydro, a 2+1 event-by-event relativistic hydrodynamical model, can run ideal/shear/bulk viscosity, simulates particle decays Lagrangian method to solve hydrodynamics known as Smoothed Particle Hydrodynamics (SPH) i.e. fluid SPH particles SPH is applied in many other fields such astrophysics (originally invented by Gingold and Monaghan 1977 and Lucy 1977), video games, volcanology, viscoplastic fluids etc

15 Setup- v-usphydro Smoothed Particle Hydrodynamics Motivation SPH discretizes the fluid into a number of SPH particles whose trajectories (r and u) you observe over time Imagine observing a lake SPH (Lagrangian)- you are in a boat on the lake and move over the coarse of time watching your trajectory. Grid (Euler)- you are seated at a dock and observe the rise and fall of water at a set spot 2m away from you.

16 v-usphydro and Jets v-usphydro can observe diffusion wakes with the hydro evolution in heavy ions Used for jets in astrophysics THE ASTROPHYSICAL JOURNAL, ,1997 IP-Glasma from B. Schenke in v-usphydro (JNH)

17 Equations of Motion Conservation of Energy and Momentum µ T µν = 0 (1) The energy-moment tensor contains a bulk dissipative term Π and the shear stress tensor π µν is T µν = εu ν u ν (p + Π) µν + π µν (2) Coordinate System: x µ = (τ, x, y, η) where τ = ( ) t 2 z 2 and η = 0.5 ln t+z t z

18 Equations of Motion SPH conserves reference density current: J µ = σu µ where σ is the local density of a fluid element in its rest frame Density obeys µ (τσu µ ) = 0 in hyperbolic coordinates (in Cartesian Dσ + σθ = 0) where D = u µ µ and θ = τ 1 µ (τu µ ) We use this set of IS equations, which provides the simplest equations for viscous hydrodynamics. τ Π (DΠ + Πθ) + Π + ζθ = 0, τ π ( µναβ Dπ αβ + 4 ) 3 π µνθ + π µν = 2ησ µν PRC75(2007) Four transport coefficients: η/s, ζ/s, τ π, and τ Π

19 Shear Viscosity in Heavy-Ion Collisions Ηs Resistance against the deformation of a fluid Π µν Navier Stokes η µ u ν UrQMD PHSD kubo PHSD kin. AdSCFT HRGHSQGP semiqgp YangMills TMeV Minimum at T c : HRG+HS+QGP(JNH et al PRL103(2009)172302, Niemi et al PRL106(2011) ) PHSD (PRC87(2013)064903) AdS/CFT -KSS limit (Kovtun,Son,Stairnets PRL94(2005)111601) UrQMD (Demir, Bass PRL(2009)102 ) semi-qgp- κ = 32 ( Hidaka,Pisarski PRD81(2010) ) Also, Csernai,Kapusta,McLerran PRL 97, (2006) (minimum suggestednot shown)

20 Bulk Viscosity in Heavy-Ion Collisions Resistance against the radial expansion or compression of a fluid Π Navier Stokes ζ( µ u µ ) Evolution with a non-zero ζ/s slows down the expansion of the fluid. Ζs HRGHS PHSD T c 160 MeV nonconf. AdS QCD est TMeV From: HRG+HS(Kadam and Mishra arxiv: ) PHSD (PRC 87, (2013) ) non-conformal holographic model (Finazzo, Rougemont, Noronha, JHEP 1502 (2015) 051) pqcd (Arnold, Dogan, Moore Phys.Rev. D74 (2006) ) Peak also seen in: JNH, PRL 103 (2009) , Kharzeev JHEP 0809 (2008) 093

21 Viscosity in Heavy-Ion Collisions JNH et al, Phys.Rev. C90 (2014) 3, , Phys.Rev. C88 (2013) Given the Glauber Initial Condition τ = 1fm

22 Viscosity in Heavy-Ion Collisions JNH et al, Phys.Rev. C90 (2014) 3, , Phys.Rev. C88 (2013)

23 Applicability of hydrodynamics vs. Smoothing λ JNH, Noronha, Gyulassy, arxiv: Separation of microscale vs. macroscale needed for hydrodynamics Knudsen number K nθ = l micro /L macro τ π θ for radius of r < 5.5

24 Applicability of hydrodynamics vs. Smoothing λ JNH, Noronha, Gyulassy, arxiv: τ π = 5η Ts is the relevant microscopic scale for the shear stress tensor At LHC T max 400 MeV and η/s 0.1 so τ π 0.25 fm Sets a lower bound on the applicability of hydrodynamics (and λ!) When λ < τ π the Knudsen number is clearly invalid. Other theories (Holography) have a smaller τ π so may be required for small systems

25 Effects in the spectra JNH, Noronha, Gyulassy, arxiv: Momentum distribution of charge particles produces slightly more high p T particles for small scales Large shear viscosity is needed for larger scaled structures "bad" Knudsen number produces reasonable spectra dn 2Π pt dp T dy best fitting η/s mckln 05 BestfittingΗs CMS all Λ 0.1 Λ 0.3 Λ ptgev

26 Differential v n (p T ) s JNH, Noronha, Gyulassy, arxiv: Almost no effect on differential flow harmonics from the micro- to meso-scales v2pt v3pt CMS all Ηs 0.11 idealλ 0.3fm mckln CMS all Ηs 0.11 idealλ 0.3fm p T GeV mckln p T GeV v2pt v3pt CMS all Ηs idealλ 1.0fm mckln CMS all Ηs idealλ 1.0fm p T GeV mckln p T GeV

27 Integrated v n s JNH, Noronha, Gyulassy, arxiv: Only elliptical flow is slightly affected by the scale Reasonable fit to experimental data found "bad" Knudsen number is below data λ = 0.1 η/s = 0 λ = 0.3 η/s = 0.11 λ = 1.0 η/s = vn best fitting η/s mckln 2030 Λ 0.1 fm Λ 0.3 fm Λ 1.0 fm v 2 v 3 v 4 v 5 Error bars represent T FO = 120 MeV n

28 ppb 0 1% vs PbPb 65 70% Comparing the same multiplicities for PbPb and ppb ppb collisions are on the cusp of hydrodynamics ε2,n ε2,n n ppb trento Λfm n ppb trento Λfm JNH, Noronha, Gyulassy, arxiv: ε2,n ε2,n n mckln Λfm 10 n PbPb s NN 2.76 TeV 6 mckln Λfm

29 Outline 1 Heavy Ion Collisons 2 Initial conditions 3 Hydro Modeling 4 Known Observables 5 Novel Developments v 2 /v 3 Large scale structure vs small scale fluctuations Solving the v 2 vs. R AA puzzle 6 Conclusions and Outlook

30 v 2 /v 3 with ε n scaling/averaged initial conditions Qiu, Shen, Heinz, Phys.Lett. B707 (2012) (above) Retinskaya, Luzum, Ollitrault Phys.Rev. C89 (2014) 1, (right) Averaged initial conditions too small v 3 compared to v 2 η/s is much larger than η/s = 0.11 for λ = 0.3 fm

31 ε 2 /ε 3 increases with smoothing Centrality (ε 2 /ε 3 ) % 0 5% 21% 20 30% 13% 65 70% 6% For smooth initial conditions ε 2 so v 2 For larger v 2 must η/s to compensate v 3 is more strongly affected by η/s so this in turn v 2 /v 3 further v 2 /v for averaged mckln and η/s = 2 at 20 30%

32 v 2 /v 3 vs. centrality JNH, Schenke, Noronha, Gyulassy in writing v2v CMSALICE mcklnε n glbε n mcklnε n Λ centrality v 2 /v 3 depends on the energy density scale λ v 2 /v 3 increases significantly with η/s Small energy fluctuations are needed for v 2 vs. v 3! v2v3 v2v glb ideal glbηs 0.08 glbηs PbPb 2.76 TeV CMSALICE centrality mckln Λ 0.3 mckln Λ centrality

33 Outline 1 Heavy Ion Collisons 2 Initial conditions 3 Hydro Modeling 4 Known Observables 5 Novel Developments v 2 /v 3 Large scale structure vs small scale fluctuations Solving the v 2 vs. R AA puzzle 6 Conclusions and Outlook

34 What can we learn from soft physics? Wide v n distributions Event-by-event calculations are necessary to describe the v n distributions From [Atlas] JHEP 1311, 183 (2013) [arxiv: [hep-ex]] v n distributions place a new constraint on initial conditions

35 What can we learn from soft physics? cumulants v n {2} v 2 n > v n v n {4} ( 2 v 2 n 2 v 4 n ) 0.25 Higher order cumulants converge sign of collective behavior! Higher order cumulants eliminate non-flow effects [ALICE] Phys. Rev. C 90 (2014)

36 SHEE=Soft Hard Event Engineering Picking events out of the low p T v 2 distribution ( v 2 v 2 ) Pv glbηs ε 2 v For the centrality 20 30% ebe random ε 2 : 150 events ebe top 1% ε 2 : 150 events with the top 1% of ε 2 event averaged: smoothed, single shot profile with rotated angles JNH in preparation Temperature profiles ran on an event-by-event basis in v-usphydro and energy loss from Betz and Gyulassy PRC86(2012)024903,JHEP1408(2014)090

37 High p T physics and event-by-event hydrodynamics Betz, JNH, Noronha, Gyulassy in writing Almost no differences between event by event and smoothed initial conditions- same as low p T 1 (a) de/dτ = κ(e 2,T) E 0 τ 1 T 3 ζ 0 v f v USPhydro, η/s = 0.08, π 0 central (b) de/dτ = κ(e 2,T) E 0 τ 1 T 3 ζ 0 v f mid central 0.8 ebe top 1% e 2 ebe random e 2 averaged event R AA (p T ) ALICE, 0 5% CMS, 0 5% p T [GeV] Betz, JNH, Noronha, Gyulassy in writing ALICE, 20 30% CMS, 10 30% p T [GeV]

38 High p T physics and event-by-event hydrodynamics Betz, JNH, Noronha, Gyulassy in writing Event-by-event calculations fit both R AA and v 2. Fluctuations matter at high p T too. 0.2 (a) de/dτ = κ(e 2,T) E 0 τ 1 T 3 ζ 0 v f 0.1 (b) mid central 20 30% v 2 high (pt ) CMS, v 2 {EP} ALICE, v 2 {EP} ATLAS, v 2 {EP} v 3 high (pt ) 0.05 ALICE, v 3 {EP} ebe top 1% e 2 ebe random e 2 averaged event p T [GeV] p T [GeV] Betz, JNH, Noronha, Gyulassy in writing

39 Correlations between soft and hard physics Low p T : Large ε 2 large v 2 ran. EbE top 1% ε 2 v 2 (0 5%) v 2 (20 30%) Same goes for higher v n s Phys.Rev. C91 (2015) 3, , Phys.Rev. C85 (2012) High p T sees the same effect (see right from ATLAS)!

40 Lots to check... Jets! If they probe the small scale fluctuations, can smoothing in the hydro background make a difference? ppb - the v 2 vs. v 3 problem may very well be fixed by including the correct small scale fluctuations (smaller fluctuations smaller η/s larger v 3 ) Effects from other transport coefficients such as bulk viscosity v-usphydro with all the bells and whistles (3+1, UrQMD etc)- public code eventually

41 Conclusions PbPb and to a lesser extend ppb are surprisingly robust compared to the smoothing of the energy density fluctuations λ New observables needed to probe energy density scale (v 2 /v 3 ) High p T is already sensitive to event by event fluctuationswhat about sub nucleonic fluctuations? Averaged/single shot initial conditions miss the relationships between v n s ppb is on the very edge of applicability of Israel-Stewart hydrodynamics. What about pp collisions???

42 High v n calculation v high n (p T ) = v low all+ n v high n ( (p T )cos v ψ low all+ n 2 low all+ n ) ψn high (p T ) events (3)

43 Mapping of the Initial State onto the Flow Harmonics Gardim et al, PRC85(2012)024908, Gardim,JNH,Luzum,Grassi PRC91(2015)3, How do the eccentricities relate to the flow harmonics? ε n,m e iφn,m = {r m e inφ } {r m } Define Quality of Estimator: Re V n Vest,n Q n = Vn 2 V est,n 2 Estimator as a perturbative series in powers of azimuthally asymmetric cumulants: m max + l=1 m max m max m=l m = n l V est,n = m max m=n k n,mw n,m K l,m,m W l,m W n l,m +O(W 3 ) As Q n 1, the ε n,m s predict the corresponding v n s

44 Smoothing out energy fluctuations Gaussians change the eccentricities Rather, use a cubic spline with a finite size dependent on λ! Bzdak et al, Phys.Rev. C87 (2013) 6, JNH, Noronha, Gyulassy, arxiv:

45 Smoothing of energy fluctuations JNH, Noronha, Gyulassy, arxiv: v-usphydro, a 2+1 event-by-event relativistic hydrodynamical model, can run ideal/shear/bulk viscosity Lagrangian method to solve hydrodynamics known as Smoothed Particle Hydrodynamics (SPH) i.e. fluid SPH particles ε fluctuations smoothed out with a cubic spline W : N ( ) r rα ɛ(τ 0, r; λ) = ɛ α (τ 0 ) W ; λ λ α=1 ( ) ( ) where W r λ ; λ = 10 f r 7π 2 λ 2 λ f (ξ) = if 0 ξ < 1 : ξ ξ3, 1 else if 1 ξ 2 : 4 (2 ξ)3, else 0. (4)

46 Ideal Differential v n (p T ) s JNH, Noronha, Gyulassy, arxiv: v2pt CMS all h 0.1 h 0.3 h 0.5 h 0.7 h 1.0 mckln p T GeV v2pt CMS all h 0.1 h 0.3 h 0.5 h 0.7 h 1.0 mckln p T GeV v3pt CMS all h 0.1 h 0.3 h 0.5 h 0.7 h 1.0 mckln p T GeV v3pt CMS all h 0.1 h 0.3 h 0.5 h 0.7 h 1.0 mckln p T GeV

47 Shear Differential v n (p T ) s JNH, Noronha, Gyulassy, arxiv: v2pt CMS all Ηs 0.11 idealλ 0.3fm mckln p T GeV v2pt CMS all Ηs idealλ 1.0fm mckln p T GeV v3pt CMS all Ηs 0.11 idealλ 0.3fm mckln p T GeV v3pt CMS all Ηs idealλ 1.0fm mckln p T GeV

48 Ideal integrated v n s and spectra JNH, Noronha, Gyulassy, arxiv: vn vn ideal n mckln Λfm n mckln Λfm dn 2Π pt dp T dy mckln 05 ideal CMS all Λ 0.1 Λ 0.3 Λ 0.5 Λ 0.7 Λ p T GeV

49 Equation of State Huovinen&Petreczky, NPA837, 26(2010)