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From Heavy-Ion Collisions to Quark Matter

From Heavy-Ion Collisions to Quark Matter. Lecture 2. Constantin Loizides (LBNL). CERN summer student programme 2014. Study QCD bulk matter at high temperature. >10 GeV/c. Bulk QCD matter at high temperature. Momentum transfer. Nebula M1-67 (see hubblesite.org). 0.2 GeV/c. ~1fm.

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From Heavy-Ion Collisions to Quark Matter

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  1. From Heavy-Ion Collisions to Quark Matter Lecture 2 Constantin Loizides (LBNL) CERN summer student programme 2014

  2. Study QCD bulk matter at high temperature >10 GeV/c Bulk QCD matter at high temperature Momentum transfer Nebula M1-67 (see hubblesite.org) 0.2 GeV/c ~1fm ~10fm Transverse size of collision region

  3. Drees, QM 01 External parameters: Collision energy Ratio of “soft” to “hard” processes Initial conditions and freeze-out paths Collision energy μB (MeV)

  4. y x b Participants Impact parameter External parameters: Collision centrality Nuclear cross-section classes(by slicing in bins of multiplicity) • Centrality classes • Cross section percentile • Impact parameter (<b>) • #Participants (<Npart>~A) • Nucleons struck at least once • #NN-collisions (<Ncoll>~A4/3) • Total number of collisions • Relate to data via Glauber MC based detector simulations Collision energy Cross-section percentile (in %) Collision centrality

  5. y x b Participants Impact parameter External parameters: Collision centrality Nuclear cross-section classes(by slicing in bins of multiplicity) Glauber model • Centrality classes • Cross section percentile • Impact parameter (<b>) • #Participants (<Npart>~A) • Nucleons struck at least once • #NN-collisions (<Ncoll>~A4/3) • Total number of collisions • Relate to data via Glauber MC based detector simulations Collision energy Via model Cross-section percentile (in %) Number of participants (collisions) Collision centrality

  6. Nucleus 1 y Nucleus 2 φ Eccentricity x PHOBOS Glauber MC Overlap (participant) region is asymmetric in azimuthal angle Number of participants External parameters: Transverse geometry Initial state eccentricity Center of mass energy Collision centrality

  7. Time evolution in heavy-ion collisions The “fireball” evolution: • Starts with a “pre-equilibrium state” • Forms a QGP phase (if T is larger than Tc) • At chemical freeze-out, Tch, hadrons stop being produced • At kinetic freeze-out, Tfo, hadrons stop scattering

  8. Time evolution in heavy-ion collisions Observables Multiplicity Thermal photons HBT Particle yields Particle spectra Transverse flow Hard probes(jets, heavy flavor) Experimental approach is to study various observables with different sensitivity to the different stages of the collision

  9. Energy dependence of dN/dη and dET/dη PRL 109 (2012) 152303 Central collisions CMS Central collisions arXiv:1202.3233 Use these measurements to get an estimate of the energy density

  10. Estimate of energy density • Consider two nuclei contracted with Lorentz factor γ. In the moment of total overlap one gets • For RHIC 200 AGeV collisions Huge!

  11. Estimate of energy density • Consider two nuclei contracted with Lorentz factor γ. In the moment of total overlap one gets • For RHIC 200 AGeV collisions • Need to account for the formation time needed to produce particles • Imagine colliding nuclei as thin pancakes (Lorentz-contraction) which, after crossing, leave an initial volume with a limited longitudinal extension, where the particles are produced Huge! Bjorken, PRD 27 (1983) 140

  12. Energy dependence of dN/dη and dET/dη PRL 109 (2012) 152303 Central collisions CMS Central collisions arXiv:1202.3233 • Take into account that the system undergoes a rapid evolution • Using 1 fm/c as an upper limit for the time needed to thermalization • Leads to densities far above the transition region (except for AGS)

  13. Initial temperature at RHIC Direct photons: No charge, no color, ie. they do not interact after Use (at low pT) to extract temperature of the system.

  14. PHENIX Excess PRL 104 (2010) 132301 PRL 94 (2005) 232301 PRC 87 (2013) 054907 QGP dominated Initial temperature at RHIC Direct photons: No charge, no color, ie. they do not interact after Use (at low pT) to extract temperature of the system. • Different measurements performed using real and virtual photons • Exponential (thermal) shape with inverse slope of T~200 MeV in excess region • No excess seen in d+Au (or pp)

  15. Initial temperature at RHIC Direct photons: No charge, no color, ie. they do not interact after Use (at low pT) to extract temperature of the system. • Different measurements performed using real and virtual photons • Exponential (thermal) shape with inverse slope ofT~220 MeV in excess region • No excess seen in d+Au (or pp) • Emission rate and shape consistent with that from equilibrated matter • From models: Tinit = 300 - 600 MeV (> 2 Tc) Models First experimental observation of T>Tc PRC 81 (2010) 034911

  16. 1 2 Intensity interferometry (HBT) • Two particles whose production or propagation are correlated in any way exhibit wave properties in their relative momentum difference • First used with photons by Hanbury Brown and Twiss to measure size of star Sirius • Quantum statistics effect: Enhancement of correlation for identical bosons • From uncertainty principle • Δq Δx ~ 1 • Use to extract source size from correlation function • Need Δq ~ 200 MeV to be sensitive to fm scale HBT, Nature 178 (1956) 1046

  17. Intensity interferometry (HBT) • In LCMS (pL,1+pL,2=0), can decompose correlation function in three directions • Longitudinal direction • Outward (along kT direction) • Sideward (orthogonal) direction • Assuming Gaussian • Three components of C(q)for pairs of identical pions in 8 intervals of the pair transverse momentum Side: geometrical, Long=extract total evolution time, Out=emission duration

  18. PLB 696 (2011) 328 Intensity interferometry (HBT) From RHIC to LHC • Increase of radii in all directions • Out, side and long

  19. PLB 696 (2011) 328 Intensity interferometry (HBT) From RHIC to LHC • Increase of radii in all directions • Out, side and long • “Homogeneity” volume: 2x RHIC • Substantial expansion • For comparison: R(Pb) ~ 7fm →V~1500fm3 • Lifetime (extr. from Rlong) ~ 10fm/c

  20. Thermal equilibrium • In HI usually two aspects of thermal equilibrium are considered • Kinetic Equilibrium • Are the pT distributions of particle species at low pTdescribed by a thermal distribution? • Chemical Equilibrium • Are all particle species produced at the right relative abundances?

  21. Statistical models • Statistical models of hadronization • Hadron and resonances gas with masses < 2 GeV/c • Well known hadronic spectrum • Well known decay chains • The formula for the yield per species • Here, Ei is the energy and gi is the degeneracy of the species i, and μB, μS, μ3 are baryon, strangeness and isospin chemical potentials, respectively • In principle, 5 unknowns but also have information from initial state about Ns neutron and Zs stopped protons • Only two parameters remain: μB and T • Typically use ratio of particle yields between various species to determine μB and T

  22. Particle ratios at the AGS Au+Au: Ebeam = 10.7 GeV/nucleon ↔ √sNN=4.85 GeV Minimum χ2 for : Tch = 124±3 MeV and μB = 537±10 MeV c2 contour lines NPA 772 (2006) 167

  23. Particle ratios at the SPS Pb+Pb: Ebeam = 40 GeV/nucleon ↔ √sNN=8.77 GeV Minimum χ2 for : Tch = 156±3 MeV and μB = 403±18 MeV c2 contour lines NPA 772 (2006) 167

  24. Particle ratios at RHIC Au+Au: √sNN=130 GeV Minimum χ2 for : Tch = 166±5 MeV and μB = 38±11 MeV c2 contour lines NPA 772 (2006) 167

  25. Particle ratios at the LHC Pb+Pb: √sNN=2.76 TeV Minimum χ2 for : Tch = 156±2 MeV and μB = 0 MeV (fixed) • Ratios except p/π well described • Disagreement for p/π may point to the relevance of other effects at LHC like • Rescattering in hadronic phase • Non-equilibrium effects • Flavor-dependent freeze-out arXiv:1407.5003 χ2/dof = 17.4/9

  26. Statistical model parameters vs √sNN NPA 772 (2006) 167 arXiv:1407.5003 • Tch quickly increases with √sNN up to about 160 MeV 7-8 GeV and then stays roughly constant • 160 MeV is well within the range of the (cross-over) phase transition • Also in the range where εBJ exceeds 2 GeV/fm3 • The chemical potential μB decreases with √sNN from AGS to RHIC energies as expected Chemical freeze-out points

  27. Raimond.Snellings@nikhef.nl Transverse momentum distributions To address the question of kinetic equilibrium, inspect pT distributions • Low pT (<~1 GeV/c) • “Soft” (ie. non-perturbative) production mechanisms • 1/pT dN/pT ~ exponential i.e. Boltzmann-like • Almost independent of √s • High pT (>>1 GeV/c) • “Hard” (ie. perturbative) production mechanisms • Deviation from exponential towards power-law

  28. Raimond.Snellings@nikhef.nl Transverse mass (mT) scaling in pp collisions • Exponential behaviorat low pT, in pp collisions • Identical for all hadrons • Transverse mass (mT) scaling • Tslope ~ 170 MeV for all particles • These distributions look like thermal spectra • Tslope can be interpreted as the temperature at the timewhen kinetic interactions between particles ended • Kinetic freeze-out temperature (Tfo)

  29. Raimond.Snellings@nikhef.nl Breaking of mT scaling in A+A collisions • Harder spectra (i.e. larger Tslope) for larger masses • Consistent with a shift towards larger pT for heavier particles • Remember pT = m0vT

  30. Flow: collective motion of particles superimposed to thermal motion • Due to the high pressures generated when nuclear matter is heated and compressed • Flux velocity of an element of the system is given by the sum of the velocities of the particles in that element • Collective flow is a correlation between the velocity v of a volume element and its space-time position y v x v Flow in A+A collisions • Interpretation in the flow picture:Collective motion of particles superimposed to thermal motion • For any interacting system of particles expanding into vacuum, radial flow is a natural consequence • During the cascade process, one naturally develops an ordering of particles with the highest common underlying velocity at the outer edge • This motion complicates the interpretation of the momentum of particles at kinetic freeze-out and should be subtracted Radial flow first mentioned:Shuryak, PLB 89 (1980) 253

  31. Raimond.Snellings@nikhef.nl • Boost source radially with a velocity β and evaluate at y=0with • Simple assumption: Consider uniform sphere of radius R and parametrize surface velocity as Three parameters: T,βs and n (sometimes n=2 is fixed) Decoupling motion: Blast wave description • Consider a thermal Boltzman source Schnedermann et al., PRC 48 (1993) 2462

  32. Radial flow and kinetic freeze-out PRL 109 (2012) 252301 LHC RHIC • Strong radial flow up toβLHC,central = 0.65c • βLHC,central=1.1βRHIC,central • Similar kinetic freeze-out Tkin≈100 MeV

  33. Thermal equilibrium vs √sNN arXiv:1407.5003

  34. How do we prove that we make “matter”? Non-interacting particles Collective expansion What happens to the shape (eccentricity) information during the expansion?

  35. dN/dφ dN/dφ 1 3 1 2 4 Flat azimuthal distribution cos 2φ modulation How do we prove that we make “matter”? Non-interacting particles Non-interacting particles Collective expansion Collective 2 1 3 4 Eccentricity information does get transferred to momentum space Eccentricity information is not transferred to momentum space

  36. Time Illustration with liquid 6Li, Science 298 5601 (2002) 2179-2182 (Process is self quenching) Raimond.Snellings@nikhef.nl dN/dφ Nucleus 1 y Nucleus 2 φ x Initial and final state anisotropy cos 2φ modulation Momentum space anisotropy:Elliptic flow Initial spatial anisotropy: Eccentricity Interactions present early

  37. Raimond.Snellings@nikhef.nl Illustration with liquid 6Li,Science 298 5601 (2002) 2179 Elliptic flow: Self quenching • The geometrical anisotropy, which gives rise to the elliptic flow becomes weaker with the evolution of the system • Pressure gradients are stronger in the first stages of the collision • Elliptic flow is therefore an observable particularly sensitive to the early stages of the system

  38. Raimond.Snellings@nikhef.nl Elliptic flow: Self quenching Kolb, Heinz, nucl-th/0305084 • The picture is supported by a hydrodynamical calculation using two different equations of state • The momentum anisotropy is dominantly built up in the QGP (τ<2-3fm/c) phase and stays constant in the (first-order) phase transition, and only slightly rises in the hadronic phase

  39. Raimond.Snellings@nikhef.nl Measuring the v2 coefficient Needs to deal with the reaction plane angle: Either use differences or reconstruct it Two-particle correlations Estimate reaction plane angle using two sub-events. Then correlateparticles of interest, and correct for event plane resolution. Can suppress “non-flow” by employing cuts in |Δη| Poskanzer, Voloshin, nucl-ex/9805001

  40. Raimond.Snellings@nikhef.nl Measuring the v2 coefficient STAR, PRL 86 (2001) 402 Minbias Au+Au, √sNN=130 GeV Huge elliptic flow coefficients! At 1 GeV: 20% modulation

  41. v2 Hydrodynamic limit STAR PHOBOS √sNN=130 GeV RQMD Nch/Nmax Results on integrated elliptic flow (RHIC) • Elliptic flow depends on • Eccentricity of overlap region, which decreaseswith increasing centrality • Number of interactions, which increases with increasing centrality • At RHIC • Models based on hadronic cascades, such as RQMD, fail. Hence, v2 is likely to be built up in the partonic (deconfined) phase

  42. v2 Hydrodynamic limit STAR PHOBOS √sNN=130 GeV RQMD Nch/Nmax Results on integrated elliptic flow (RHIC) • Elliptic flow depends on • Eccentricity of overlap region, which decreaseswith increasing centrality • Number of interactions, which increases with increasing centrality • At RHIC • Models based on hadronic cascades, such as RQMD, fail. Hence, v2 is likely to be built up in the partonic (deconfined) phase • Measured v2 found for the first time in agreement with ideal hydrodynamical calculations (for central and mid-central collisions) • Fast (<1fm/c) thermalization with matter (close to) an ideal fluid • In more peripheral collisions thermalization is incomplete or slower • Hydro limit is done for perfect fluid, the effect of viscosity would reduce the elliptic flow

  43. Raimond.Snellings@nikhef.nl Hydrodynamical model calculations Heinz, arXiv:0901.4355 + freeze-out conditions Today even second order calculations (full Israel-Stewart) calculations done.

  44. Raimond.Snellings@nikhef.nl Effect of viscosity Heinz, arXiv:0901.4355 Early calculations at RHIC used η/s=0. Today small values between (1-3)/4π used.

  45. Results on elliptic flow vs pT (RHIC) • At low pT the data is described by hydrodynamics • At high pT, significant deviations are observed. Natural explanation: • High-pT particles are produced early and quickly escape the fireball without (enough) rescattering and no thermalization • Hydrodynamics not expected to be applicable

  46. v2 Transverse momentum [GeV] What's needed partonically to get v2? Parton transport model: Bolzmann equation with 2-to-2 gluon processes http://arxiv.org/abs/nucl-th/0602009 D.Molnar, M.Gyulassy NPA 697 (2002) HUGE (almost hadronic!!!) cross sections needed to describe v2 Need large opacity to describe elliptic flow, ie elastic parton cross sections as large as inelastic the proton cross-section

  47. Change of paradigm The quark-gluon liquid “... the fireball made in these [heavy-ion] collisions ... was not a gas of weakly interacting quarks and gluons as earlier expected, but something more like a liquid of strongly interacting quarks and gluons” • Manifestation of strongly coupled QGP • Nota gas of free quarks and gluons • Instead, strongly coupled nearly perfect liquid reaching almost the minimum value of shear viscosity to entropy density ratio (η/s) RHIC whitepapers: NPA 757 1-283 (2005) (see http://www.aip.org/pnu/2005/split/757-1.html) Already conjectured in 2005 for RHIC energies. Picture further substantiated by LHC.

  48. Raimond.Snellings@nikhef.nl ALICE 10-20% 20-30% 30-40% Elliptic flow coefficient, v2{4} Lines/bands are STAR 200 GeV data Elliptic flow vs pT (LHC vs RHIC) PRL 105 (2010) 252302 Observe v2(pT)LHC≈ v2(pT)RHIC above 1 GeV to about 5% despite factor 14 increase in energy, but consistent with hydro predictions! (Int.v2 30% larger due to radial flow)

  49. Raimond.Snellings@nikhef.nl Eccentricity Elliptic flow Identified particle v2 versus pT (LHC) arXiv:1202.3233 Hydro Calculation: M.Luzum, arXiv:1011.5173 Observed mass ordering in v2 due to radial flow can be described by hydrodynamical models

  50. Summary Observables Multiplicity Thermal photons HBT Particle yields Particle spectra Transverse flow Hard probes(jets, heavy flavor) Tomorrow Bulk observables lead to results which are consistent with the interpretation that we create thermalized matter with liquid properties. If you have questions about today's lecture please send them to “cloizides at lbl dot gov”

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