Correlations and Fluctuations in Nuclear Collisions - Experimental Overview

Correlations and Fluctuations in Nuclear Collisions - Experimental Overview Gunther Roland - MIT Supercomputing RHIC Physics TIFR, Mumbai Dec 5-9 2005

This talk dn/dη/<1/2 N part > Pseudorapidity Hadron Multiplicities Elliptic Flow Event-by-event Fluctuations STAR preliminary Two-particle Correlations

Pre-requisites: Centrality Characterization Participants PHOBOS Glauber Au+Au MC N part /2 ~ A Cu+Cu L~A 1/3 N coll = # of NN collisions: ~A 4/3 Collisions Number of participating nucleons from Glauber MC

Pre-requisites: Hard vs Soft Hadron Production Energy Density Central A+A ε 1 GeV/fm 3 I. Vitev Fast rise of high p T yields from hard collisions Logarithmic rise of particle ( energy) density

Hadron Multiplicities 19.6 GeV 62.4 GeV 130 GeV 200 GeV PHOBOS preliminary Au+Au preliminary preliminary Cu+Cu d+au Au+Au : PRL 91, 052303 (2003) d+au : PRL 93, 082301 (2004) Cu+Cu: QM 2005

PHOBOS PRL 93, 082301 (2004) PHOBOS preliminary Hadron Multiplicities d+au PHOBOS PRL 93, 082301 (2004) <Nch> pp *<0.5Npart> Shape changes dramatically versus centrality PHOBOS Multiplicity per participant is constant

dn/dη/<1/2 N part > central 200 GeV peripheral central Hadron Multiplicities PHOBOS PRL 91, 052303 (2003) PHOBOS PRL 91, 052303 (2003) Au+Au <Nch>e+e-*<0.5Npart> 200 GeV 130 GeV peripheral 19.6 GeV 19.6 GeV Pseudorapidity Au+Au Shape changes dramatically versus centrality Multiplicity per participant is constant

Limiting Fragmentation Hadron Multiplicities Ratio of 0-6% and 35-40% centrality bins, each normalized by N part Au+Au 0-6% PHOBOS 200GeV 130GeV 62.4 GeV (prel) 19.6 GeV Au+Au 35-40% preliminary Au+Au 35-40% 0-6% 200GeV 130GeV 62.4 GeV (prel) 19.6 GeV Shape change of longitudinal distributions is energy independent

Mid-rapidity dn/dη vs s and N part dn/dη/<0.5*n part > 200 GeV 130 GeV 62.4 GeV 19.6 GeV Au+Au : nucl-ex/0509034, submitted to PRC Cu+Cu: QM 2005 PHOBOS PHOBOS Cu+Cu preliminary Au+Au Energy (GeV) Centrality

dn/dη vs s and N part dn/dη/<0.5*n part > Energy (GeV) x2.5 Centrality norm. dn/dη Energy (GeV) = norm. dn/dη x1.95 x1.3 x1.3 Centrality x1.95 Energy (GeV) Centrality

Initial State Parton Saturation Hadron Multiplicities Low Energy norm. dn/dη High Energy Energy (GeV) Centrality Armesto, Salgado, Wiedemann hep-ph/0407018 Also limiting fragmentation, N part scaling (c.f. Kharzeev, McLerran, Venugopalan, Jalilian-Marian, Nardi et al) norm. dn/dη Energy (GeV) Centrality

Hadron Multiplicities Participant scaling of total multiplicities Global constraints over full η range Slow growth of multiplicity with energy Saturation + LPHD? Factorization of energy/centrality dependence Saturation +LPHD? No modification during expansion/hadronization/recscattering?

Transverse Plane Hydrodynamic Evolution Time 2*v 2 Non-central collision: Initial state eccentricity PHOBOSAzimuthal Angle (rad) Momentum space anisotropy

Hydrodynamic Evolution Phys. Rev. Lett. 86 (2001) 402 STAR Au+Au 130 GeV Hydro Calculation Kolb, Heinz Phys Lett B459 Centrality Elliptic Flow signal exhausts hydro limit for mid-central to central collisions Geometrical initial state eccentricity from Glauber model

Elliptic Flow Hydrodynamic Evolution Parton Cascade Hadron Cascade <v 2 > HSD Calculation pt>2 GeV/c Molnar et al p T (GeV/c) Cassing et al Neither partonic nor hadronic cascades reproduce flow

Hydrodynamic Evolution 200 GeV Au+Au Baryons PHENIX (open symbols): Phys. Rev. Lett. 91, 182301 (2003) Mesons Rich structure vs mass (?) and pt M. Oldenburg, STAR, QM2005

Hydrodynamic Evolution 200 GeV Au+Au PHENIX (open symbols): Phys. Rev. Lett. 91, 182301 (2003) Mass scaling Quark-number scaling M. Oldenburg, STAR, QM2005

Hydrodynamic Evolution 200 GeV Au+Au Data: STAR, PHENIX Hydro: P. Huovinen et al., Phys. Lett. B503, 58 (2001) Mass splitting at low p T understood in hydro calculations

Elliptic Flow Hydrodynamic Evolution 19.6 GeV 62.4 GeV 130 GeV 200 GeV PHOBOS Au+Au preliminary preliminary Cu+Cu Au+Au: PHOBOS PRL 94 122303 (2005) Cu+Cu: PHOBOS QM 2005 Strong rapidity dependence of elliptic flow Challenge to hydrodynamic calculations Connection between flow and dn/dη

Elliptic Flow Hydrodynamic Evolution PHENIX nucl-ex/0411040 62 GeV 200GeV 17.2 GeV Saturation of v 2 (p T ) above s 62 GeV

Hydrodynamic Evolution Nucleus 1 y Nucleus 2 PHOBOS Glauber MC Participant Region x Au+Au ε 2 2 σ y σ x = 2 2 σ y + σ x wrt reaction plane Cu+Cu Au+Au vs Cu+Cu Interplay of initial geometry and initial density Test ideas of early thermalization and collectivity

Hydrodynamic Evolution v2 near mid-rapidity PHOBOS 200 GeV Statistical PHOBOS 200 errors GeV only h ± Statistical errors only Au+Au preliminary Cu+Cu preliminary Geometrical initial state eccentricity from Glauber model

Hydrodynamic Evolution v2 near mid-rapidity PHOBOS 200 GeV Statistical PHOBOS 200 errors GeV only h ± Statistical errors only Au+Au preliminary Cu+Cu preliminary Surprisingly large flow signal in Cu+Cu! Geometrical initial state eccentricity from Glauber model

Hydrodynamic Evolution Nucleus A σy 2 Nucleus B Glauber model of AuAu collision: σx 2 b Participant Nucleons Using the impact parameter as the x-axis, we define the standard eccentricity using the widths of the distribution in x and y ε = σ σ 2 y 2 y σ + σ 2 x 2 x

Hydrodynamic Evolution Au+Au Cu+Cu Large fluctuations in eccentricity Many peripheral events with negative eccentricity Even bigger fluctuations in Cu+Cu Glauber MC Calculations

Hydrodynamic Evolution Possibly reasonable method is to realign the coordinate system to maximize the ellipsoidal shape (a principal axis transformation) Nucleus 1 y x b Participant Region Nucleus 2 Participant eccentricity (versus standard eccentricity)

Hydrodynamic Evolution Low Density Limit: STAR, PRC 66 034904 (2002) Voloshin, Poskanzer, PLB 474 27 (2000) Heiselberg, Levy, PRC 59 2716, (1999) using Standard Eccentricity Cu+Cu Au+Au Surprisingly strong elliptic flow in Cu+Cu Challenge to hydrodynamic picture?? Cu+Cu: PHOBOS QM 2005

Hydrodynamic Evolution Low Density Limit: STAR, PRC 66 034904 (2002) Voloshin, Poskanzer, PLB 474 27 (2000) Heiselberg, Levy, PRC 59 2716, (1999) using Participant Eccentricity Cu+Cu Hydro-Limit Au+Au Participant Eccentricity provides universal scaling Approach to equilibrium? Cu+Cu: PHOBOS QM 2005

Hydrodynamic Evolution Low Density Limit: STAR, PRC 66 034904 (2002) Voloshin, Poskanzer, PLB 474 27 (2000) Heiselberg, Levy, PRC 59 2716, (1999) Cu+Cu Au+Au LHC Will flow saturate at LHC as thermalization is achieved? Cu+Cu: PHOBOS QM 2005

Hydrodynamic Evolution Large collective flow signal observed in Au+Au Overall magnitude + mass splitting hydro Additional (geometrical?) azimuthal correlations in Cu+Cu How is thermalization/pressure build-up achieved? What are the (early) degrees of freedom?

Temperature (MeV) 200 Event-by-Event Physics (last century) Quark-Gluon Plasma Critical Point N event Normal events Stock Special events 0 0 Hadron Gas Phase Boundary Atomic Nuclei 1 Matter Density µb (GeV) <(X - <X>) 2 > X E-by-E Enhanced Fluctuations near Critical Point Event-by-event Physics : Search for critical phenomena induced near phase transition/critical point Rajagopal, Shuryak, Stephanov, Wilczek s

Temperature (MeV) 200 0 0 Fluctuations and the QCD Phase Diagram Hadron Gas Quark-Gluon Plasma Critical Point Phase Boundary Atomic Nuclei 1 Matter Density µb (GeV) Phase transition/latent heat - Supercooling - Droplet Formation - <pt>, Multiplicity Fluctuations Location of critical point - <pt> Fluctuations Deconfinement - Charge/DoF - Charge Fluctuations Chiral Symmetry Restoration - DCC formation - Charge/neutral fluctuations Mishustin Rajagopal, Shuryak, Stephanov, Wilczek Jeon, Koch Asakawa, Heinz,Mueller Rajagopal, Wilczek Bjorken

Net Charge N + - NṈet Charge Fluctuations Net Charge/Δy Fluctuations <-> Charge/DoF Jeon, Koch hep-ph/0003168 Asakawa, Heinz, Mueller hep/ph/0003169 Change from 1-2 (QGP) to 4 (Pion Gas) Fluctuations frozen b/c charge conservation Diffusion vs Expansion timescale Ratio N + /N - Fluctuations of N + /N - or N + - N - vs statistical reference

Net Charge Fluctuations STAR PRC 68 (2003) η < 0.7, 0.1 GeV/c < p T P130 GeV Au+Au Charge Conservation HIJING Quark- Coalescence Bialas, 2003 Resonance Gas

? Net Charge Fluctuations vs s QGP

? Is this a Problem? Basic argument still appears valid Possible Explanations - Diffusion in long-lived hadronic phase? - Resonances? - A feature of hadronization? - Quark Coalescence? - Bound states? Need connection to other data and QCD

<p T > Fluctuations p T - simple observable (supposedly...) High statistical precision: σ pt /<pt> inc < 0.1% NA49, Phys Lett B459 (1999) 679 Central Pb+Pb s = 17.2 GeV Sensitive to many interesting scenarios Critical Point DCC production Droplet formation Any non-statistical, momentum-localized process Event-by-event <p T > compared to stochastic reference (mixed events)

<p T > Fluctuations p T - simple observable (supposedly...) High statistical precision: σ pt /<pt> inc < 0.1% Sensitive to many interesting scenarios Critical Point DCC production Droplet formation Any non-statistical, momentum-localized process PHENIX: Au+Au 200GeV

Energy Dependence? STAR No evidence for non-monotonic energy dependence But: Interpretation choice of variables Non-monotonic system-size dependence

STAR preliminary STAR centrality STAR STAR CERES Normalization to <pt> Normalization per particle Linear or quadratic measures

Fluctuations for small systems [NA49, PRC 70, 034902 (2004)] all negatives, acceptance: 4 < yπ < 5.5 and 0.005 < pt < 1.5 GeV/ c NA49 preliminary Text - Fluctuations and Percolation (Clustering) in small systems - Connection to elliptic flow in Cu+Cu? - Connection to strangeness enhancement vs N part?

Search for unusual events in Au+Au Frequency of events Total Multiplicity Fluctuations Shape Fluctuations 2M Events 200 Events Multiplicity distribution and χ 2 (shape) distribution shows distinct tails - O(10-4 )

Total Multiplicity Fluctuations Shape Fluctuations Rate of unusual events correlates with luminosity - Consistent with collision-pileup as source of rare events

E-by-E fluctuations in the K/π ratio Is strangeness enhanced in every event? Can we see signs of super-cooling below T crit? NA49 Measurement - Use de/dx to identify π,k,p event-by-event K/π T - Do Max Likelihood fit to extract K/π ratio eventby-event - Required 2 years of detector calibation to eliminate de/dx multiplicity correlation

E-by-E fluctuations in the K/π ratio Pb+Pb, 17.2 GeV NA49, PRL 86 (2001) 1965 Dynamical fluctuations are small ( < ~5%) Compatible with resonance gas (Jeon, Koch; nuclth/9906074) Strangeness enhancement in every event Chemical freeze-out at same T in every event

NA49 Horn Strangeness Fluctuations vs s NA49 (QM 04) NA49 preliminary Fluctuations in K/pi ratio Rajagopal, Stephanov: Compatible with constant correlation strength

Event-by-Event fluctuations p T fluctuations show smooth s dependence no 20, 30 GeV data yet Fluctuations small in central events at top SPS energy + above Energy dependence of k/pi fluctuations? Multiplicity + p T fluctuations for peripheral events?

Fluctuations at RHIC Temperature (MeV) 200 Quark-Gluon Plasma Critical Point RHIC Close to μ B ~ 0 axis Cross-over? Far from critical point? 0 0 Hadron Gas Phase Boundary Atomic Nuclei 1 Matter Density µb (GeV) =>Fluctuations not induced by phase-change itself?

An Evolving Paradigm Event-by-Event Physics - Critical phenomena (1990s) - Fluctuations of conserved quantities (2000) Fluctuations and Correlations - Connection between correlations and fluctuations (Koch, Bialas 98) Study transport properties of the medium Approach to thermalization Properties of Hadronization

Forward/backward multiplicity correlations N P N (Impact parameter) P+N P-N Use variance σ 2 C (Partitioning) P

Clusters and σ 2 C N P Forward/backward correlations give access to cluster structure of particle production

Cluster-size from F/B fluctuations 40-60% peripheral 0-20% central PHOBOS 200 GeV Au+Au preliminary PHOBOS 200 GeV Au+Au preliminary Forward/backward correlations suggest effective cluster size 2-2.5 for 200 GeV Au+Au

UA5: Phys.Lett.B123:361,1983 Clusters in p+p Keff 546 GeV P+N Clusters in Au+Au reminiscent of results from p+p

Time Correlation Probes of the Medium Probe

Time Correlation Probes of the Medium Armesto et al, nucl-ex/0405301

Correlations at high p T η < 0.7, 4 GeV/c < p Ttrig < 6 GeV/c, 2 < p TAsso < p Ttrig Hadrons q q Hadrons Leading Particle Relative to trigger particle: - Jet-like near-side correlations visible in Au+Au - Away-side correlations disappear for central Au+Au STAR PRL (2003)

PHENIX, ICPAQGP 05 Correlations at not-so-high pt Cone- Structure? Near side Sonic shock waves Stoecker, nucl-th0406018 Casalderrey,Shuryak,Teaney, hep-ph/0411315 Away side cos(θ)=c s

Dainese, Loizides and Paic STAR QM 05 D. Magestro 8 < p T (trig) < 15 GeV/c p T (assoc) > 8 GeV/c Back-to-back jets re-appear at sufficiently high pt Fragmentation of observed jets similar in A+A, p+p Surface emission?

Seeing partons at high pt STAR

Soft Look at Partons p-p 200 GeV STAR preliminary Tom Trainor, STAR Two-particle angular correlations show rich structure at low to moderate p T (~GeV/c)

From p+p to Au+Au Central All Charges Evolution of Structure from p+p to central Au+Au J. Adams et al. (STAR), nucl-ex/0411003. Peripheral p-p 200 GeV STAR preliminary

Correlation Probes of the Medium Time

Momentum Correlations at RHIC 70-80% Subtract fragmentation peak to look at medium φδ 20-30% ηδ parton fragments centrality 0-5% bulk medium STAR preliminary Minijets: velocity/temperature correlation structures on (η,φ) Tom Trainor, STAR, Bad Liebenzell, Oct 05

Correlations in Transport Models STAR Data Denes Molnar, BNL workshop June 05

Summary Evolving experimental + theoretical program - Global scaling rules - Collective flow - Search for critical phenomena - Connection of correlations + fluctuations - Interaction of perturbations with medium Initial entropy production Fluctuations in small systems? Thermalization: How and what? What is the role of hadronization?

r 12 = n 1 n 2 Net Charge, and K/π Fluctuations Instead of measuring the variance of a yield ratio, Study the dynamical fluctuations : (Δr 12 ) 2 (Δn 1) 2 + (Δn 2 ) 2 2 Δn 1Δn 2 r 12 2 n 1 2 n 2 2 n 1 n 2 ν 12,dyn = n 1 n 1 n 2 n 2 2 1 n 1 1 n 2 = % R 11 + % R 22 2 % R 12 Side Note: D n 1 + n 2 (Δr 12 ) 2 <p t > Fluctuations Δp t,1 Δp t,2 = where N k 1 N event N event k=1 C k = p t,i p t i=1 N k j=1,i j N k C k ( N k 1) ( )( p t, j p t ) ~ ~ ~ D ( R+ + + R 2R + ) n+ + n 1+ 4 4 N event p t = p t k / N event k=1 N p = k p t k t,i / N k i=1

v2 vs pt PHENIX nucl-ex/0411040 62 GeV 200GeV <pt> vs s + RHIC SPS 17.2 GeV PHOBOS dn/dη vs s v2(η ) vs s