Constraining the bulk viscosity of QCD

Constraining the bulk viscosity of QCD (with heavy ion collisions) Bwidth Bnorm Jean-François Paquet Tpeak July 21, 2017 Triangle Nuclear Theory Colloquium

In collaboration with... Charles Gale Sangyong Jeon Chun Shen Gabriel Denicol Many results presented by Gabriel Denicol in Quark Matter 2017 (proceeding written but not yet published) 2

Heavy ion physics RHIC (STAR & PHENIX) LHC (ATLAS, CMS & ALICE) Figure credits: BNL Figure credits: CERN Collisions of large nuclei at ultra-relativistic energies Hundreds of measurements from the different collaborations 3

Many-body quantum field theory Dominated by strong nuclear force (Quantum ChromoDynamics - QCD) High density of particle/energy >> Many-body QCD << Many-body QFT, as opposed to Few-body QFT : particle decays, cross-sections,... 4

Very Many-body QCD: fluid dynamics Pre-equilibrium phase (~0.1-1 fm) Late hadronic phase Figure credits: J. Bernhard and H. Petersen Fluid ( Thermal ) period (~10 fm) Hot QCD fluid ( quark-gluon plasma ) Simplest model: ideal hydrodynamics Experimental access to QCD Thermodynamics (Equation of State) 5

QCD Thermodynamics QCD EOS: constrained from lattice QCD for T>~100 MeV and small baryon chemical potential (mb/t<~2) Figure credits: The Frontiers of Nuclear Science - A Long Range Plan (2007); Borsanyi et al, Phys.Lett.B 730 (2014) 6

Small deviations from equilibrium Viscosities: Universal properties of a medium characterising its response to deviations from equilibrium Viscosities are functions of the equilibrium properties: temperature, the baryon chemical potential,... Figure credits: The Frontiers of Nuclear Science - A Long Range Plan (2007) 7

Equation of state & viscosities Viscosities difficult to evaluate from lattice QCD Other approaches: Perturbative QCD Holography Effective models of QCD Functional Renormalization Group (FRG) et al... J. Noronha-Hostler [arxiv:1512.06315] 8

QCD viscosities from heavy ion collisions Pre-equilibrium phase (~0.1-1 fm) Late hadronic phase Figure credits: J. Bernhard and H. Petersen Fluid ( Thermal ) period (~10 fm) Hot QCD fluid: relativistic viscous hydrodynamics Combined with: - Initial conditions and pre-eq. dynamics - Transition to hadronic degrees of freedom (Cooper-Frye) & interactions (e.g. UrQMD) 9

2 order viscous hydrodynamics nd Energy density Flow velocity Bulk pressure Shear tensor Conservation of energy-momentum tensor: Complemented by equation of motions for shear and bulk: (2nd order terms) The bulk viscosity z and the shear viscosity h characterise the response of QCD to deviations from equilibrium [ Ref. For EOM: Denicol, Niemi, Molnar and Rischke (2012) PRD ] 10

Standard model of heavy ion collisions? Pre-equilibrium phase (~0.1-1 fm) Late hadronic phase Hydrodynamic expansion (~10 fm) Figure credits: J. Bernhard and H. Petersen Studying QCD viscosities with hadronic (&other) observables Depend on: - Initial conditions and pre-eq. dynamics (e.g. IP-Glasma) - Transport coefficients (h/s, z/s,...) and equation of state - Late stage hadronic interactions (e.g. UrQMD) 11

Constraining bulk viscosity QCD bulk viscosity can have measurable effects on hadronic observables Measurable effect Large suppression [ Ref.: Ryu, Paquet, Shen, Denicol, on hadronic vn of <pt> Schenke, Jeon & Gale (2015) PRL ] Mean transverse Multiplicity of p+, momentum of p+, K+ & p K+ & p v2/3/4 of charged hadrons 12

Temperature dependence of z/s Previous work This work Bnorm Bwidth Tpeak T/Tpeak Inspired from: HRG: Noronha-Hostler, Noronha and Greiner (2009) PRL LQCD: Karsch, Kharzeev and Tuchin (2008) PLB B norm ~ 0.3, B width ~ 0.1 T peak =180 MeV 13

Probabilistic parameter constraints 14

Observable vs parameter Charged hadron v2 vs (effective) shear viscosity: v 2=v 2 (η/ s, fixed ζ / s parametrization, lattice EOS, "IP-Glasma init.", "UrQMD") effective = no temperature dependence 15

Observable vs parameter vs data v 2=v 2 (η/ s, fixed ζ / s parametrization, lattice EOS, "IP-Glasma init.", "UrQMD") Data ( v2{2}=0.0642 ) Hydro calculation effective = no temperature dependence 16

Observable vs parameter vs data v 2=v 2 (η/ s, fixed ζ / s parametrization, lattice EOS, "IP-Glasma init.", "UrQMD") Data ( v2{2}=0.0642 ) Hydro calculation Data-driven extraction of h/s? 17

Including experimental uncertainties v 2=v 2 (η/ s, fixed ζ / s parametrization, lattice EOS, "IP-Glasma init.", "UrQMD") Data Hydro calculation Data-driven extraction of h/s (including exp. uncertainty) 18

Uncertainties and probability distrib. v 2=v 2 (η/ s, fixed ζ / s parametrization, lattice EOS, "IP-Glasma init.", "UrQMD") ch v Data: 2 {2 }="probability distribution" with average ~ 0.0642 and σ ~ exp. uncertainty Hydro calculation If data is a probability distribution, constraint on h/s is one too 20

Theoretical uncertainties v 2=v 2 (η/ s, fixed ζ / s parametrization, lattice EOS, "IP-Glasma init.", "UrQMD") ch v Data: 2 {2 }="probability distribution" Theory prediction: probability distribution e.g. Gaussian with average= hydro calculation and s= theoretical uncert. 21

Bottom line v 2=v 2 (η/ s, fixed ζ / s parametrization, lattice EOS, "IP-Glasma init.", "UrQMD") Data and theory summarized as probability distribution Constraints are probabilistic Note: what if parameter is a distribution? 22

Probabilistic parameter constraints in equations 23

Mathematical formulation My favourite reference: Tarantola, A. (2005). Inverse problem theory and methods for model parameter estimation. SIAM. [the] inverse problem theory is about the quantitative rules to be used for [the] comparison between predictions and observations. (Available for free on the author s website) 24

Theoretical uncertainties (Gaussian) Probability distribution for observables A given parameters p : ch 2 ch 3 A={dN /dy, pt, v, v } p={η/ s(t ), ζ / s(t ), EOS,... } (Assuming Gaussian uncertainties) 25

Theoretical uncertainties (Gaussian) Probability distribution for observables A given parameters p : ch 2 ch 3 A={dN /dy, pt, v, v } p={η/ s(t ), ζ / s(t ), EOS,... } Covariance matrix with theoretical uncertainties e.g. Result g(p) from hydro model given parameters p : g( p)={hydro prediction for dn /dy given p, prediction for pt,...} 26

Theoretical uncertainties: summary Assuming Gaussian and uncorrelated uncertainties Probability distribution for observables A given a choice of parameters p : What if theoretical uncertainties are very small? How to get hydro results for every parameter set p? Use emulator [ See Novak, Novak, Pratt, Vredevoodg, (from MADAI collaboration) Coleman-Smith, Wolpert (2014) ] 27

Experimental uncertainties Again assuming Gaussian uncertainties Probability distribution for observables A to have a certain experimental value: ch 2 ch 3 A={dN /dy, pt, v, v } d ={135, 0.411 GeV, 0.0642, 0.0183 } Covariance matrix encoding experimental uncertainties 28

Probabilistic constraints The probability distribution describing the constraints on the model parameters is: C=C +C E T Ω( p) χ 2 ( p) 29

Probabilistic constraints The probability density describing the constraints on the model parameters is: C=C +C E T Ω( p) χ 2 ( p) Integrating W(p) over all but one parameter Integrating W(p) over all but two parameters (Results by Steffen A. Bass, Jonah E. Bernhard, J. Scott Moreland) 30

More subtleties Non-Gaussian uncertainties? Systematic, and theoretical uncertainties (non symmetrical) Outliers in data (Tarantola suggests e.g. long-tailed distributions) Priors 31

Constraining bulk viscosity 32

Other model parameters Bwidth Shear viscosity: η/ s eff No temperature dependence (effective) Bnorm ν ν T μhydro ( τ 0 )=ϵnorm T μip-glasma ( τ0) Tpeak 35

Additional information Emulator 500-600 random parameter samples (per collision energy and centrality) ~100 hydro events per parameter sample Theoretical uncertainty? 5% Gaussian theoretical uncertainty (we ve played with 2.5-10%) 36

Data: collision energy What we used: RHIC Au+Au 200 GeV LHC Pb+Pb 2760 GeV What we didn t use: RHIC beam energy scan; p+a collision data (hydro model may need modifications) LHC 5020 GeV (data not out yet when we started) 37

Data: centrality Used single mid-peripheral centrality (20-30%) at both RHIC and LHC Why only one? We used fixed initial conditions (IP-Glasma): No initial condition parameters needing fixing Also, faster! 38

Data: Observables What we used: pion multiplicity (dn/dy y=0) & mean pt (<pt>) pt integrated charged hadrons v2/3 Why? sensitive to bulk viscosity & some control over theoretical uncertainties (df,...) What we didn t use: hadronic chemistry, jets, heavy quarks, electromagnetic observables, pt & rapidity-differential hadronic observables,... 39

(Preliminary) Results for z/s Example: integrate W(p) over all parameters except z/s(t) peak and width Bwidth Bnorm Ω( p) Tpeak Bnorm 40

(Preliminary) Results for z/s Bnorm Bwidth Constraining bulk viscosity with hadron multiplicity, mean pt and vn? Tpeak Preliminary (5% Gaussian theoretical uncertainty) 41

Posteriors - LHC Np v2 <pt> v3 42

Summary 43

Summary Earlier work: hydro model with bulk viscosity can describe hadronic data well [ Ref.: Ryu, Paquet, Shen, Denicol, Schenke, Jeon & Gale (2015) PRC ] This work: what is the z/s(t) favoured by data (within flexibility of parametrization) 44

Summary Earlier work: hydro model with bulk viscosity can describe hadronic data well [ Ref.: Ryu, Paquet, Shen, Denicol, Schenke, Jeon & Gale (2015) PRL ] This work: what is the z/s(t) favoured by data (within flexibility of parametrization)? Within our model, sizable bulk viscosity favoured by data... but little constrain on peak position 45

Many thanks to: Scott Pratt, Evan Sangaline, Bjoern Schenke, Clint Young and the Duke QCD theory group and the TNT collaboration for the invitation and discussions Triangle Nuclear Theory Colloquium 46

Questions? 47

Backup 48

Emulator 49

G. Denicol QM2017 slide 10 50

Tpeak 51

Isn t the middle plot a little funny? Well... Preliminary 52

Isn t the middle plot a little funny? Well... <h/s>eff 0.25 0.20 0.15 0.10 0.05 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 Tpeak Preliminary 53

(Preliminary) Results for z/s Bnorm Bwidth Constraining bulk viscosity with hadron multiplicity, mean pt and vn? Tpeak Preliminary 54

Hydro model 55

Shear and bulk viscosities Temperature dependence of QCD shear viscosity? QCD bulk viscosity? (Estimate using FRG) [ Ref.: Christiansen, Haas, Pawlowski, Strodthoff (2015) PRL] Minimum of shear viscosity around deconfinement region Ref.: Noronha-Hostler [ arxiv:1512.06315 ] Peak of bulk viscosity around deconfinement? 57

Parametrising the viscosities Shear well-studied: concentrate on bulk viscosity Shear viscosity Bulk viscosity η/ s eff T/Tpeak In this work: constant (effective) η/ s ( η/ s eff 0.1 ) Parametrisation peaks at T=180 MeV Inspired from: HRG: Noronha-Hostler, Noronha and Greiner (2009) PRL LQCD: Karsch, Kharzeev and Tuchin (2008) PLB 58

Completing the model Equation of state: hadron resonance gas+lattice [Ref.: Huovinen and Petreczky (2010) NPA] Initial conditions: IP-Glasma (gluon-saturation based with Yang-Mills evolution) [Ref.: Schenke, Tribedy, Venugopalan (2014) PRC] From hydro to hadrons: (quasi-)thermal production (Cooper-Frye) followed by hadronic transport model (UrQMD) 59

Viscous corrections to momentum distribution (df) 60

df 61

Shear df 62

Bulk df Cooper Frye 63

Bulk df w/ resonance decays 64

Bulk df: vn No significant effect on charged hadron vn 65

Emulator 66

The origin story 2011 MUSIC Then emulators poormanstune.nb 67