Event-by-event Fluctuation & Phase Transition OUTLINE Motivation Fluctuation measures: <pT> fluctuation Multiplicity fluctuation Particle ratio, strangeness Balance functions Net charge fluctuation Moments of net charge DCC Long range correlations Near term activities at RHIC at LHC Summary critical point Tapan K. Nayak CERN & VECC Strangeness in Quark Matter UCLA March 28, 2006 Event-by-event fluctuation and phase transition

QCD phase diagram critical point ? Tc hadron gas nucleon gas nuclei r0 Stephanov, Rajagopal & Shuryak PRL 81 (1998) Phase transition/Latent heat Supercooling QGP droplet formation <pT>, Multiplicity fluctuations Baryon-strangeness correlations Moments of strangeness, baryon number and net charge distributions - (recent calculations by Ejiri-Karsch-Redlich, Gavai-Gupta and Koch-Majumdar-Randrup) Location of the critical point detailed study of particle ratio and fluctuations Chiral symmetry restoration formation of DCC charge-neutral fluctuations Tc r0 baryon density Temperature Neutron stars Early universe nuclei nucleon gas hadron gas colour superconductor quark-gluon plasma critical point ? vacuum CFL At the CRITICAL POINT: singularities in thermodynamical observables => LARGE EbyE FLUCTUATIONS Event-by-event fluctuation and phase transition

Event-by-event fluctuation and phase transition Lattice predictions Karsch et al. Gavai, Gupta hep-lat/0412035 Fodor, Katz JHEP 0404 (2004) 050 Lattice calculations have not yet converged on the location of Critical Point. The best guess so far: around c.m. energy of 5-20 GeV/nucleon. CRITICAL END POINT From lattice: TC ~ 170 15 MeV eC ~ 0.7-1.5 GeV/fm3 Location of the Critical point Theoretical expectations Fluctuation measures Fluctuation sources (statistical+dynamic) geometrical: impact parameter number of participants detector Acceptance (y, pT) energy, momentum, charge conservation anisotropic flow Bose-Einstein correlation resonance decays jets and mini-jets formation of DCC color collective phenomena …. Role of strangeness Dedicated measurements? Points for discussion: Event-by-event fluctuation and phase transition

<pT> fluctuations NA49, Phys Lett B459 (1999) 679 Central Pb+Pb √s = 17.2 GeV data mixed events charged hadrons y>4.0 <pT> fluctuations <pT> of emitted particles is related to the temperature of the system. EbyE fluctuations of <pT> is sensitive to temperature fluctuations predicted for QCD phase transition. non-statistical (dynamical) part of the <pT> fluctuation provides valuable information regarding: critical point of phase transition droplet formation Formation of DCC Can be measured experimentally with high precision. Event-by-event <pT> compared to stochastic reference (mixed events) STAR: Phys. Rev. C 72 (2005) 044902 The following are used to construct various fluctuation measures: pT of particle Mean pT of the event (<pT>) Mean of the <pT> distribution Event-by-event fluctuation and phase transition

<pT> fluctuations: centrality dependence CERES K. Perl PRC 70 (2004) 034902 H. Sako QM04 NA49 M. Tannenbaum J. Mitchell nucl-ex/0403037 Different observables are sensitive to different processes. STAR sees a smooth dependence on collision centrality whereas NA49 and PHENIX see larger fluctuations in mid-central collisions. STAR attributes this difference due to effects of acceptance and elliptic flow (Pruneau QM05, Voloshin Bergen05) Phys. Rev. C 72 (2005) 044902 PHENIX STAR PRL 93 (04) 092301 Event-by-event fluctuation and phase transition

<pT> fluctuations: energy dependence C. Pruneau QM05 Adamova et al., Nucl. Phys. A727, 97 (2003) <pT> fluctuations in (h-f) bins STAR: nucl-ex/0509030 fluctuations correlations 200 GeV No Energy dependence of <pT> fluctuations is seen from CERES & STAR data. This study is also useful for studying contributions from (mini)jets to fluctuations. Event-by-event fluctuation and phase transition

Multiplicity fluctuations NA49: M. Rybczynski, QM2004 PRC 65 (2002) 054912 Charged particles Photons Gaussians for narrow bins in centrality WA98: Fine bins in centrality so that fluctuation from Npart is minimal. Centrality dependence of multiplicity fluctuations do not show evidence of non-statistical contribution. However recent NA49 analysis of scaled variance show non-statistical fluctuations at mid-central collisions. Charged Particles Photons Photons w = s2/ < N > Fine bins in centrality Event-by-event fluctuation and phase transition

Particle ratio & fluctuations <K+>/<p+> Particle Ratio: <K/p> has an increasing trend with energy, whereas a horn structure seen in <K+/ p+>. <K->/<p-> s2data - s2mix = s2dynamic Fluctuation in Ratio: K/p fluctuations are large at low beam energy & decrease with increasing energy. p/p fluctuations are negative, indicating a strong contribution from resonance decays. J. Phys. G30 (2004) S1381 M. Gazdzicki QM04 C. Roland (NA49) SQM2004 sdyn Event-by-event fluctuation and phase transition

K/p fluctuation in STAR Supriya Das: SQM’06 Symposium s = rms/mean sdyn = sqrt(sdata2 – smixed2) Fluctuation in K/p decreases with increasing energy till the top SPS energy and remains flat above it. The amount of fluctuation decreases with increasing centrality and is similar for 62 GeV as well as 200GeV AuAu collisions. Event-by-event fluctuation and phase transition

Event-by-event fluctuation and phase transition Balance functions Z=0 Bass-Danielewicz-Pratt, PRL 85, 2000 D. Drijard et al, NP B(155), 1979 Early Hadronization  Large  Opposite charged particles are created at the same location of space–time. Charge–anticharge particles created earlier (early stage hadronization) get further separated in rapidity. Particle pairs that were created later (late stage hadronization) are correlated at small Δy. The Balance Function quantifies the degree of this separation and relates it with the time of hadronization. Late Hadronization  Small  Event-by-event fluctuation and phase transition

Balance functions: centrality & energy dependence Gary Westfall: STAR Panos Christakoglou: NA49 Panos Christakoglou STAR: Au+Au@ √sNN = 130 GeV PRL 90 (2003) NA49: Pb+Pb@ √sNN = 17.2 GeV PRC 71 (2005) STAR data NA49 data NA49 shuffling STAR shuffling simulation NA49 data STAR data W is a normalized measure of the time of hadronization with respect to uncorrelated data sample. This is consistent with delayed hadronization at RHIC compared to SPS energies. peripheral central DATA show a strong centrality dependence of balance function width. Event-by-event fluctuation and phase transition

Balance functions for identified particles Bass-Danielewicz-Pratt, PRL 85, 2000 and Gary Westfall, J.Phys.G30, S345-S349 (2004) Heavier particles are characterized by narrower bf distributions: The balance function width for pions get narrower with increasing centrality, remains constant for kaons. HIJING reproduces results for kaons, but not for pions. The ratio of widths of pions to kaons is consistent with delayed hadronization picture. STAR Preliminary pions 1.3-1.4 Panos Christakoglou in ALICE PPR p kaons K ALICE simulation showing BF widths of p,K,p p Mass (GeV) Event-by-event fluctuation and phase transition

Net charge fluctuations confined: few d.o.f. deconfined: many d.o.f. Charged multiplicity: nch = n+ + n– Net charge: Q = n+ - n– Charge ratio: R = n+ / n- (1) v(Q)  Var(Q)/<nch> (for stochastic emission, v(Q) = 1) (2) v(R)  Var(R) * <nch> (for stochastic emission, v(R) = 4) (3) F(Q) ndynamic Moments of Net charge distributions Prediction: A drastic decrease in the EbyE fluctuations of net charge in local phase space regions in the deconfined QGP phase compared to that of the confined case hadronic gas. QGP:4 and pion gas: 1-2 Jeon, Koch: PRL (2000) 2076 Asakawa, Heinz & Muller: PRL (2000) 2072 Evolution of fluctuation Shuryak & Stephanov: PR C63 (2001) 064903 Heiselberg & Jackson: PR C63 (2001) 064904 Mohanty, Alam & TN: PR C67 (2003) 024904 Event-by-event fluctuation and phase transition

Event-by-event fluctuation and phase transition Net charge fluctuation: energy dependence J. Mitchell, QM’04 STAR: Au+Au Preliminary nucl-ex/0401016 peripheral central PHENIX ||<0.35, =/2 CERES 2.0<  <2.9 STAR: 5% Central Au+Au C. Pruneau QM05 Net charge fluctuations measured by PHENIX & NA49 are consistent with independent emission. Net charge fluctuations measured by STAR are close to the quark coalescence model of Bialas. Fluctuations are larger at SPS compared to RHIC, but remain constant over a large range of energy. Event-by-event fluctuation and phase transition

Event-by-event fluctuation and phase transition Moments of net charge distributions Lattice calculations Ejiri, Karsch and Redlich: hep-ph/0510126 Gavai, Gupta: hep-lat/0510044 Calculation of Non-linear susceptibilities (higher order derivatives of pressure with respect to chemical potentials): 4th moment Net charge Isospin Strangeness 2nd moment 6th moment (similar to kurtosis) => Interesting structure close to T=TC Is it possible to make precise measurement of higher moments of net charge? bins in centrality bins in pT Event-by-event fluctuation and phase transition

MEAN of Q distributions Q(net charge) distributions Q distributions for AuAu 200GeV at 4 different centralities and 6 bins in pT MEAN of Q distributions <Q> low pT high pT <Q>/Npart Q (net charge) <Q>/Npart is independent of centrality. Moments of Q distributions have been analyzed. Event-by-event fluctuation and phase transition

Variance and kurtosis of net charge distributions n(Q) with pT binned AuAu 200GeV Kurtosis (4th moment) Centrality & pT n(Q) is low at low pT ad increases with increase of pT. Could be an effect of more resonance production at low pT. First analysis of the 4th moment of net charge distribution is performed. Detailed comparison in terms of lattice calculations is expected soon. Event-by-event fluctuation and phase transition

Event-by-event fluctuation and phase transition Formation of DCC Bjorken, Kowalski & Taylor SLAC-pub-6109 (1993) Review: Mohanty & Serreau Phy Rep 414 (2005) Methods of Analysis: Gamma-Charge correlation Discrete Wavelet analysis Power spectrum analysis ‘Robust’ variables Event shape analysis Sliding window method (SWM) => WA98 and NA49 have put upper limit on DCC production at 3x10-3 level. => DCC production also shows up in other forms including strangeness correlations. Large fluctuations in number of photons and charged particles Aggarwal, Sood, Viyogi nucl-ex/0602019 Recent simulation for RHIC show better sensitivity for DCC by using SWM with photon and charged multiplicity: WA98 PMD & SPMD PRC 67 (2003) 044901 Event-by-event fluctuation and phase transition

Long-range multiplicity correlations Correlation strength: => Study of correlations among particles produced in different rapidity regions. => The long-range correlations are expected to be much stronger in p-A and A-A, compared to p-p at the same energy. Terence J Tarnowsky Nuclear Dynamics, San Diego March 2006 STAR Preliminary STAR: forward region of 0.8<h<1.0 & backward of -1.0<h<-0.8. Increase in correlation strength observed for central collisions compared to peripheral for AuAu collisions at 200GeV.

RHIC Search for critical point at RHIC Physics measure Energy Density The QCD phase boundary is worthy of study, including that of the tri-critical point. STAR experiment with the inclusion of TOF will be the ideal place for this study. PHENIX will be able to carry out an extensive program for the search of critical point. RHIC has an unique capability to scan the full range from the top AGS to top RHIC energy. The idea is to have an energy scan from c.m. energy of 4.6GeV to 30GeV in suitable steps corresponding to baryon chemical potentials of 150MeV to 550MeV. Fluctuation study especially with strangeness plays a major role in the search for critical point. Physics measure AGS SPS RHIC RHIC QCD Critical Point Energy Density Event-by-event fluctuation and phase transition

EbyE fluctuation in ALICE EbyE measures in ALICE: simulation for Pb+Pb at 5.5TeV Slope parameter <pT> pions <pT> kaons <pT> protons With the large multiplicity of several tens of thousands expected in each collision at LHC energies, EbyE analyses of several quantities become possible. This allows for a statistically significant global as well as detailed microscopic measures of various quantities. http://aliceinfo.cern.ch/ ALICE-PPR Event#1 Event#2 Event#3 EbyE HBT radii K/p p/p Event-by-event fluctuation and phase transition

Event-by-event fluctuation and phase transition Thermodynamic quantity / fluctuation in the quantity Energy Density Fluctuation behavior??? Critical point??? Summary What’s done so far : Fluctuations of thermodynamic quantities are fundamental to the study of phase transition – including quark-hadron phase transition. Lattice calculations suggest fluctuation patterns in strangeness, baryon number & net charge even at small chemical potentials - increasing towards the critical point. Exploratory study using many fluctuation measures continues - interpretation of results become complex because of several competing processes which contribute. Indication of large fluctuation patterns around SPS energies. What’s coming up: Fluctuation study will play a major role in the search for the critical point at RHIC. ALICE: detailed EbyE physics and fluctuation to understand the physics of bulk matter as well as high-pT particles and jets. Future GSI facilities: CBM Event-by-event fluctuation and phase transition