Lvy exponent analysis

6A rszecskk Standard ModelljeElektron elemi rszecskeProton, neutron, hadronok nem azok kvarkokHrom klcsnhats, kzvett bozonok

Ers, gyenge, elektromgneses tltsErs tlts: szn QCD: kvantum-szn-dinamikauupccharmttopddownsstrangebbottomneelectron neutrinonmmuon neutrinonttau neutrinoeelectronmmuonttaukvarkokleptonokfermionokggluongphotonZZ bosonWW bosonbozonokklcsnh.erselektro-mgnesesgyenge

The perfect fluid of quarksMire lesz szksgMatematikai ismeretek:Alapmveletek :)Differencils, integrlsDifferencil-egyenletekFizikai ismeretek:KinematikaFolytonos kzegekTermodinamikaRelativitaselmeletKvantumelmeletekDe a fentieket mindet megtanuljuk kzbe2The perfect fluid of quarksMirl lesz sz?RszecskefizikaElemi rszecskk: kvark, lepton, fermion, bozonFolyamatokNagyenergis fizikatkzsek nagy energin (GeV)Rszecskekelts (nem rugalmas tkzs)NehzionfizikaAtommagokat tkztetnkKzeget akarunk ltrehozni3The perfect fluid of quarksKinematikai alapokAlapvet mennyisgek ismerete fontos, llandan hivatkozunk rjuk4

The perfect fluid of quarksKlcsnhatsok5

The perfect fluid of quarks16Kutatsi helysznek: CERNSPS: Pb+Pb @ Ecms = 17 GeV/nukleonh+p, p+p, p+Pb, Pb+Pb tkzsekKsrleti egyttmkdsek: NA44, NA45, NA49, NA50, NA52, NA57, NA60, WA98, NA61KFKI-ELTE rszvtel az NA49 s az NA61 ksrletben LHC: p+p (14 TeV) s Pb+Pb (5,5 TeV/nukleon)2009. okt.: fleg p+p fizika; ALICE, ATLAS, CMS, LHCb, LHCf, MoEDAL, TOTEM2010. nov.: nehzionfizika program is indul; ALICE, CMS

The perfect fluid of quarks7Ismert mezonok s barionok

The perfect fluid of quarksAz ers klcsnhatsKvantumtrelmlet, msodik kvantls, Fut csatols!

8

The perfect fluid of quarks19The RHIC complexTandem (1 MeV, +32)Booster (95 MeV, +77)AGS (9 GeV, +77)RHICProtons: Linac (200 MeV)Booster (95 MeV)AGS (9 GeV)RHIC

The perfect fluid of quarks1920RHIC geometry & numbersTwo rings (blue and yellow) 3.9 km eachSix crossings, four experiments57 bunches of ions at 99.995% of the speed of light1740 superconducting magnets at 4 K15 MW power consumption ~ 300 TJ/run (30 weeks)Luminosity: 2-31026 1/cm2/s

The perfect fluid of quarks2021The four CollaborationsBRAHMS (Broad Range Hadron Magnetic Spectrometer)Two small but distant spectrometers, detect charged hadrons precisely4 countries, 14 institutions, 60 participants, until 2006PHENIX (Pioneering High Energy Nuclear Interactions eXperiment)Many different detector-types, detect electrons, muons, photons, hadrons14 countries, 69 institutions, 600 participantsPHOBOSSmall silicon detectors, broad rapidity range, look for rare events, fluctuations 3 countries, 12 institutions, until 2006STAR (Solenoidal Tracker At RHIC)Time Projection Chamber, detect all hadrons12 countries, 46 institutions, 550 participants, 1200 tonsThe perfect fluid of quarks2123DetectorsTracking (momentum measurement)Drift Chamber (DC), Pad Chamber (PC)Calorimetry (energy measurement)PbSc, PbGl (EMCal)Identification (velocity measurement)Cerenkov-counters RICH, Aerogel, Time Of Flight (TOF), Hadron Blind Detector (HBD)Event characterisationBeam-Beam Counter (BBC), Zero Degree Calorimeter (ZDC), Reaction Plane Detector (RxNP)Muon detectorsMuon Tracker (MuTr), Muon Identifier (MuId)The perfect fluid of quarks2324Current setupPhysicsCharged hadrons ( , K, etc.)Photons, direct or decay ( , 0)Light mesons , and Single leptons heavy flavorDi-leptons heavy flavor, J/

The perfect fluid of quarks242426Event characterisationControl over the event geometry:When (time zero) and where (vertex)Overlap (centrality), number of participants (Npart)Orientation with respect to overlap (reaction plane)Central Au+AuNpart~300Peripheral Au+AuNpart~50d+Aup+pReaction PlaneThe perfect fluid of quarks2627Time zero + vertex: BBC & ZDCBBC & ZDC south and north at high rapidityBBC at h 3-4 particles from vertexZDC at h evaporating neutronsTime zero from Vertex from DTNorthSouthLLTNTSVertex position: (TS-TN) c/2Time zero: (TN+TS)/2 L/c

The perfect fluid of quarks2728Centrality determinationOverlapping region: participants

Evaporated neutrons: toward ZDC (charged wiped out)ZDC measures energy (calorimetry) ~ number of evaporated neutronsParticipants: new particles toward BBCSpectatorsParticipantsToward ZDCToward BBC

The perfect fluid of quarks2830

SimulationCentrality determinationMore central: more charge in BBCVery central or very peripheral: no energy in ZDCEZDC versus QBBC

Real dataGlauber model to simulate centrality vs physical parameters

The perfect fluid of quarks3032Results from a Glauber Monte CarlosNN=200 GeV Au+Au simulation in varios centrality classes

The perfect fluid of quarks3235Particle propertiesParticle = spatial track Set of hits in several detectors measuredMomentum measured via curvatureKnown magnetic fieldParticle type determined via mass & chargeCharge: curvature againMass: momentum & (velocity or energy)Measure all this for hadrons, g, leptons etcQuality assurance: matching of the aboveThe perfect fluid of quarks3536Tracking: DC+PCTrack particles, measure momentumHit Track Curvature MomentumWire chambersTrack reco: DC+PC1Matching: PC2-3

The perfect fluid of quarks3638Tracking processDC + PC1 Track modelInclination momentumPC2 + PC3: matchingReduces background

The perfect fluid of quarks3839Hadron identification by TOFTime Of Flight detectortime measurement120 ps resolutionAcceptance = /4|| 1/ncosq=1/nbe-: 0.02 4.9 GeV/c

e- (b > 1/n)qcL

The perfect fluid of quarks4142Lepton+ photon ID by EMCalEnergy + momentum massLeptons and photons to deposit all their energy in EMCalLead Scintillator and Lead Glass: light ~ energyHadrons: additional recalibration needed

Pb absorbergenerates showerScintillatorgenerates lightOptical fibercollects lightgPMTgPMTScintillatorgenerates -radPbScPbGlThe perfect fluid of quarks4252Nagyimpulzus rszecskk elnyelseNukleris modifikcis faktor: Mrs Au+Au, referencia: p+pNagyimpulzus rszecskk elnyeldnek (1. mrfldk)!Jet QuenchingEllenprba: d+Au Kzeg hatsa (2. mrfldk)2 PRL cmlap

Au+Aud+Au

Zajc, Riordan, Scientific AmericanThe perfect fluid of quarks5254Szisztematikus vizsglatGLV formalizmus: Gyulassy, Lvai, Vitevlers pQCD segtsgvel

SuppressedEnhancedPhys.Rev.C76:034904,2007

Centrlis Au+Au: elnyeldsPerifrikus Au+Au, d+Au: nincs elnyeldsThe perfect fluid of quarks5455Csak a hadronok nyeldnek el!Direkt fotonok tfnylenek az anyagonA pionok elnyeldse vltozatlan 20 GeV-igA kzeg fotonok szmra tltsz, hadronoknak thatolhatatlan

Ngy mrs:Foton- s pion-spektrumAu+Au s p+pSzisztematikus hibk ellenrzse tbb nagysgrenden keresztlThe perfect fluid of quarks5556Szgeloszlsok vizsglata: STARKifel men jet: p+p, d+Au, Au+Au hasonlBefel men jet: elnyelds csak Au+Au esetnNincs elnyelds p+p, d+Au esetnErsen klcsnhat kzeg, az anyag egy j formja2. mrfldk

pedestal and flow subtracted Nagyimpulzus rszecskk (jet) szgeloszlsnak vizsglataThe perfect fluid of quarks57

J/ suppression in Au+AuEven J/ suppressed!beyond extrapolations from cold nuclear matter effectsRAA ~ 0.3 for central collisionsLarger suppression at |y|>1.2Phys. Rev. Lett. 98, 232301 (2007)The perfect fluid of quarks5762A folyadk kp megerstseAzimutlis aszimmetria sokdimenzis fggse:Transzverz impuzlusRapiditstkztets energijaCentralitsRszecsketpus

Hidrodinamikai elrejelzs: egy sklavltoz, egy sklagrbe

Az elrejelzs helyes!Csrg, Akkelin, Hama, Lukcs, Sinyukov (Phys. Rev. C67, 034904, 2003)Csand, Csrg, Lrstad, Ster (Nucl. Phys. A742:80-94,2004)Csand, Csrg, Lrstad, Ster et al. (Eur.Phys.J.A38:363-368,2008)

The perfect fluid of quarks6263A 3. mrfldkAz Amerikai Fizikai Intzet szerint 2005. legfontosabb esemnye: az ersen klcsnhat folyadk felfedezse a RHIC-nlNgy ksrlet t ves munkja, egybehangzan3350 hivatkozs az sszefoglal cikkekre

The perfect fluid of quarks6364Milyen tkletes folyadk ez?Tkletes idelis, tkletes nem ragads!Tkletes: elhanyagolhat viszkozits s hvezets,nyr erknek nem ll ellenIdelis: sszenyomhatatlanA nyr erknek val ellenlls h:Nyrfeszltsg:

Alacsony viszkozits nagy hatsk.m. ers csatolsKinematikai viszkozits: h/s Maldacena: CFTD AdSD+1A fekete lyuk (brane) felleteh = fellet/16pG, s = fellet/ 4Gh/s=1/4pGyantott als hatrminden relativisztikus kvantumtrelmletre, vges hmrskletre s nulla kmiai potencilra

The perfect fluid of quarks6465Phys. Rev. Lett. 98, 172301 (2007)Even heavy flavour flow!Electrons from heavy flavour measuredEven heavy flavour is suppressedEven heavy flavour flowsStrong coupling of charm+bottom to the mediumSmall charm+bottom relaxation time in medium and small viscosity

The perfect fluid of quarks65Viscosity estimatesAdS/CFT lower bound:hep-th/9711200, gr-qc/0602037, hep-th/0405231MeasurementsR. Lacey et al., nucl-ex/0609025

H.-J. Drescher et al., arx:0704.3553

S. Gavin, M. Abdel-Aziz, nucl-th/0606061

A. Adare et al., nucl-ex/0611018

The perfect fluid of quarks664. mrfldk: szinte tkletes folyadkAdS/CFT als hatr Malcadena et al.: Adv.Theor.Math.Phys.2:231-252,1998Kovtun et al.: Phys.Rev.Lett. 94 (2005) 111601Mrsi eredmnyekR. Lacey et al., Phys.Rev.Lett.98:092301,2007

H.-J. Drescher et al., Phys.Rev.C76:024905,2007

S. Gavin, M. Abdel-Aziz, Phys.Rev.Lett. 97 (2006) 162302

PHENIX: Phys.Rev.Lett.98:172301,2007

The perfect fluid of quarks67685. mrfldk: kvarkok folyadkaRelevns vltoz: transzverz kinetikus energia, KEtAz elliptikus folys a konstituens kvarkok szmval sklz!Szabadsgi fokok: kvarkokPHENIX Collaboration, Phys.Rev.Letters 98:162301, 2007

The perfect fluid of quarks6869

Sklzs igaz d, D s esetre isA ritka s a bjos kvarkok is rszei a folysi kpnekD (bjos) s (ritka) esetn v2 a mezonokkaldeuteron esetn v2 az nq= 6 esetnek megfelelen

nucl-ex/0703024The perfect fluid of quarks6973

A new look at the starsIntensity interferometry in radio astronomyAngular diameter of a main sequence star measured

R. H. BrownThe perfect fluid of quarks74Hanbury Brown and TwissEngineers, worked in radio astronomyIn fact two people: Robert Hanbury Brown and Richard Q. TwissRobert, Hanbury and Richard: all given namesInterference between two different photons can never occur. P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford, 1930In fact to a surprising number of people the idea that the arrival of photons at two separated detectors can ever be correlated was not only heretical but patently absurd, and they told us so in no uncertain terms, in person, by letter, in print, and by publishing the results of laboratory experiments, which claimed to show that we were wrong I was a long way from being able to calculate, whether it would be sensitive enough to measure a star. To do that one has to be familiar with photons and as an engineer my education in physics had stopped far short of the quantum theory. Perhaps just as well, otherwise like most physicists I would have come to the conclusion that the thing would not work ignorance is sometimes a bliss in science The perfect fluid of quarks75Bose-Einstein correlationsTwo plane-waves:

Bosons: need for symmetrization

Spectrum:

Two-particle spectrum (momentum-distribution):

x1x2k1k2Y1,2S(x,k)sourceobserverApproximations: Plane-wave, no multiparticle symmetrization, thermalization

The perfect fluid of quarks76Bose-Einstein correlationsNow the invariant correlation functionDepends on relative and average momenta

Uses Fourier-transformed of the source, if momenta nearly identical

We can figure out something about the source!The ONLY tool for geometrical shape/size informationDrop the average momentum dependence

The perfect fluid of quarks77What brings us all this?If the source is approximated with Gaussian:

Then the correlation function is also Gaussian

These are the so-called HBT radiiTransformed to the out-side-long system:Out: mean pt of the pairLong: beam directionSide: orthogonal to bothNot reflecting the geometrical sizeHydro model of an expanding ellipsoid:

The perfect fluid of quarks81Msodrend fzistalakuls?Msodrend fzistalakulsok esetn: kritikus exponensekA kritikus pont krnyknFajh ~ ((T-Tc)/Tc)-aSzuszepcibilits ~ ((T-Tc)/Tc)-gKorrelcis hossz ~ ((T-Tc)/Tc)-nA kritikus pontbanTrbeli korrelcis fggvny ~ r-d+2-h Ginzburg-Landau: a=0, g=1, n=0.5, h=0QCD 3D Ising modell, h=0.05Random tr hozzadsa esetn: h=0.5Ez az exponens mrhet!The perfect fluid of quarks8182A kritikus pont keresseKtrszecske korrelci (trbeli)jraszrs anomlis diffzi, szles eloszlsltalnostott hatreloszls-ttelNem Gauss hanem Lvy eloszls!Lvy(R,a): az exp(-|Rq|a) Fourier-transzformltjaKorrelcis exponens: Megegyezik a ktrszecske-eloszlsok a Lvy-stabilitsi indexvel h=a, Csrg et. al., Eur. Phys. J. C36 (2004) 67-78 A 200 GeV/n Au+Au adatok elemzsbl: a1.4Msodrend fzistalakulsFodor s Katz: cross-over!Kritikus hmrsklet feletti hadronok is ezt jelzikThe perfect fluid of quarks8286Signal of chiral dynamics

Study electron pair distribution versus invariant mass

If hadron e + e: minv=mhadron

Significant excess central Au+AuNot in p+p or Au+AuRegion: 0.2-0.9 GeVIn-medium enhancement of , , ?

The perfect fluid of quarks8690How analytic hydro worksTake hydro equations and EoSFind a solutionWill contain parameters (like Friedmann, Schwarzschild etc.)Will use a possible set of initial conditionsUse a freeze-out conditionEg fixed proper time or fixed temperatureGenerally a hyper-surfaceCalculate the hadron source functionCalculate observablesE.g. spectra, flow, correlationsStraightforward calculationHydrodynamics: Initial conditions dynamical equations freeze-out conditions

The perfect fluid of quarks92How analytic hydro works

Hydro equations + EoSPhase-space distribution Boltzmann-equationFreeze-out conditionSourceS(x,p)PRC67:034904,2003 hep-ph/0108067 Self-similar solution:PLB505:64-70,2001 hep-ph/0012127

ObservablesN1(p), C2(p1,p2), v2(p)PRC54:1390-1403,1996 hep-ph/9509213

The perfect fluid of quarks96Equations of relativistic hydroBasic equations:Assuming local thermal equilibriumFor a perfect fluid:Equations in four-vector form and nonrelativistic notationEuler equation:

Energy conservation:

Charge conservation:

comoving proper-time derivative

comoving derivative

The perfect fluid of quarks97Famous solutionsLandaus solution (1D, developed for p+p):Accelerating, implicit, complicated, 1DL.D. Landau, Izv. Acad. Nauk SSSR 81 (1953) 51I.M. Khalatnikov, Zhur. Eksp.Teor.Fiz. 27 (1954) 529L.D.Landau and S.Z.Belenkij, Usp. Fiz. Nauk 56 (1955) 309Hwa-Bjorken solution:Non-accelerating, explicit, simple, 1D, boost-invariantR.C. Hwa, Phys. Rev. D10, 2260 (1974)J.D. Bjorken, Phys. Rev. D27, 40(1983)OthersChiu, Sudarshan and WangBaym, Friman, Blaizot, Soyeur and CzyzSrivastava, Alam, Chakrabarty, Raha and SinhaThe perfect fluid of quarksMag-mdosulsi tnyezProton+protonNucleus+nucleusEgyszeren csak tbb?A+A = sok p+p?Particle yield in A+AParticle yield in p+pRAA=Number of p+p collisionsThe perfect fluid of quarks51

Suppression of high pt particlesPeripheral Au+Au and d+Au: no suppressionCentral Au+Au: large suppression

Phys.Rev.C76, 034904 (2007)The perfect fluid of quarks5358Az els kt mrfldkKt Phys. Rev. Letter cmlap, tudomnyos konszenzusRszvtel komoly anyagi rfordts nlkl (sok munkval)Lehetsg az jabb felfedezsekre

1. mrfldk2. mrfldkThe perfect fluid of quarks59A kollektv dinamika jeleiA hidrodinamika sklaviselkedst jelez Mit jelent a sklzs?Plda: Reynolds szm, rvr/hA paramterek egy kombincija szmtKollektv, termlis viselkeds Informci-vesztesgSpektrumok: Boltzmann-eloszls + folysspektrum ~ exp[-pt /Teff], Teff = T0 + mu2

The perfect fluid of quarks60Hydrodynamic predictionsHydro predicts scaling (even viscous) What does a scaling mean? See Hubbles law or Newtonian gravity:Cannot predict acceleration or heightCollective, thermal behavior Loss of informationSpectra slopes:Elliptic flow:HBT radii:

The perfect fluid of quarks61

Folyadk kp: a 3. mrfldkImpulzuseloszls: tengelyszimmetria?sszenyomds s tguls kapcsolataElliptikus folys, v2: azimut aszimmetriaMsodik Fourier-komponensKollektv viselkeds mrszmaRitka gz: v2 = 0Hidrodinamika: v2 > 0M. Cs. et al., Eur.Phys.J.A38:363-368,2008

f(j)0 p 2pjThe perfect fluid of quarks6170

Mekkora a kezdeti hmrskletHadronok csak a vgllapotban, g vgig keletkeznek!

llapotegyenlet a direkt foton spektrumbl: k=7.70.8Kezdeti hmrsklet (t=1 fm/c)Ti 440 MeV

M. Cs., M. Vargyas.Eur. Phys. J. A 44, 473 (2010)M. Cs., I. MjerWorkshop on Particle Correlationsand Femtoscopy 2010The perfect fluid of quarks6. mrfldk: magas kezdeti hmrskletModell-szmtsok: Tini = 300 - 600 MeV Rcs QCD: Tc ~ 170 MeV

PHENIX direkt foton adatokPhys.Rev.C81, 034911 (2010)Phys.Rev.Lett.104,132301(2010)

The perfect fluid of quarks717172Rszecskeelnyels, Au+Au: j jelensgNincs elnyels, d+Au: ersen klcsnhat anyagEgybehangz kvetkeztets: folyadkSklzsi viselkeds: kvark szabadsgi fokokNehz kvarkok viselkedse: tkletes folyadkFotonspektrum: magas kezdeti hmrskletKvetkeztets: kvarkok tkletes folyadka, sQGP!Fzistalakuls, kritikus pont, kirlis tmenet?RHIC mrfldkvek mgegyszerThe perfect fluid of quarks78Elsrend fzistalakuls?Csillagok szgtmrje intenzits-korrelcikkal R. H. Brown, s R. Q. Twiss, Nature 178, 1046 (1956)Mret-megfigyels impulzus-korrelcivalG. Goldhaber, S. Goldhaber, W. Y. Lee, A. Pais, Phys. Rev. 120, 300 (1960)Korrelcis sugr ~ (forrsmret)-1Pr-koordintarendszerben:Out: pr tlagos impuzlusaLongitudinal: nyalbirnySide: elz kettre merlegesElsrend fzistalakuls ltens h, lass talakuls out sideoutside

The perfect fluid of quarks79Elsrend fzistalakuls kizrva!Elsrend fzistalakuls: Out SideHidrodinamikai jslat: Out Side~50 modell rossz: HBT rejtlySok hidrodinamikai model mkdikKsrlet: Out SideHol a kritikus pont?

Csrg, Csernai (Phys.Lett.B333:494-499,1994)Csrg, Lrstad (Phys.Rev.C54:1390-1403,1996)

The perfect fluid of quarks80Core-Halo modelHydrodynamically expanding corePions correlated here, R~5-10 fmHalo of long-lived resonancesK0S, h, h, w, R > 50 fmHalo particles not correlatedHalo not resolvable, q ~ R-1Due to finite momentum resolutionIntroduce fc=Nc / (Nc+Nh)Introduce S=SC+SH, at q > 4 MeV, S=SCCore: , K, , , Halo: , , , KS

The perfect fluid of quarks83Ksrleti eredmnyek

Nucl.Phys. A774 (2006) 611-614

0-20%, 0.48-0.6GeVR5.69fm 0.16fma1.57 0.06l1.00 0.04Chi2/NDF68.1/78Braz.J.Phys.37:949-962,2007The perfect fluid of quarks84A szimmetrik helyrellsaz szimmetria: U(3)U(3), U(3)=U(1)SU(3)SUR(3)SUL(3)SUV(3)Spontn srlsGoldstone bozonokEzek a knny mezonokMezon-oktett: 8 dbUA(1)UV(1)UV(1) (barionszm)Explicit szimmetriasrtsUA(1) srl: 9. tmeges mezon h (958 MeV)Szimmetria helyrellsa: tmegcskkensJ. I. Kapusta, D. Kharzeev, L. D. McLerran Phys.Rev.D53:5028-5033,1996.Keletkezsi valsznsg: s ~ ma e-m/T (Hagedorn)

K0

+

K+

K

K0

0The perfect fluid of quarks848485Channels of ObservationLifetime: 1000 fm/cDirect leptonic decay h'+ Increased h'/p proportion in the low-pT rangeExcess in the + spectrum under the r mass h meson (BR=46%) h'hp+p Including decay through rDecay of h meson 23% hp+ pp0 5% hp+ pg 39% h2g 33% h3p0 Enhanced production of uncorrelated pionsBEC of charged pionsSensitive to the sources of the pionsDirect measurement h'ggWould be convincing, however, poor S/B ratio (0)

The perfect fluid of quarks858587A tmegcskkens jeleiA kifagys, a hadronok ltrejtteHagedorn-modell: s ~ m3/2 e-m/T, ahol m a hadron tmegeA cskkent tmeg h mezon nagyobb szmban jn ltreBomls eltt tmeghjra kerl, hossz lettartammalKapusta, Kharzeev, McLerran Phys.Rev.D53:5028,1996.Z. Huang, X-N. Wang, Phys.Rev.D53:5034,1996p+hhp-p+p-p0h150000 fm/c1000 fm/cKorrellatlan pionok ltrejttehtlagos pion-impulzus: 138 MeVtlet: korrellt pionok arnynak mrseVance, Csrg Kharzeev Phys.Rev.Lett.81:2205,1998 T. Hatsuda, T. Kunihiro Phys. Rept. 247:221,1994The perfect fluid of quarks88A korrelcis fggvny erssgeForr, sr kzegh tmegcskkensMegnvekedett h tartalomHossz lettartam, vgn a tmeg visszallhh+p+ +p- (p0+p++p)+p++ptlagos pion-impulzus alacsonyTbb korrellatlan pion-pr keletkezsel lecskken alacsony impulzusnlA korrellt (Bose-Einstein) pionon szmnak arnya a korrelcis fggvny erssge, l(mt): Core: , K, , , Halo: , , , KS150000 fm/c1000 fm/c

+

+

0

helyettThe perfect fluid of quarks8889Tmegcskkens szimulciCsrg, Vrtesi, Sziklai: arXiv:0912.0258, .5526 (PRL)Maximlis tmeg 5.4s kontrral (99,9%): 730 MeVLegjobb illeszkeds 340-530 MeVEllenrzs: h-bl szrmaz pionok eldobsaKinematikai vgs lehetsges ksrleti analzisben!M. Cs. s Kfarag M., Workshop on Particle Correlations and Femtoscopy 2010PHENIX mrs vglegestshez fontos elem

The perfect fluid of quarksHow analytic hydro works

Quark (gluon?) medium evolves hydrodynamicallyTemperature dropsAt the freeze-out: quark-hadron transitionKinetic freeze-out even later maybe?91The perfect fluid of quarks93A nonrelativistic solutionTake the following nonrel. solutionCsrg, Akkelin, Hama, Lukcs, Sinyukov, Phys.Rev.C67:034904,2003

Self similarly expanding ellipsoid, Gaussian ICFlow profile: directional HubbleEquation of motion for principal axes:Freeze-out at constant temperature assumed

The perfect fluid of quarks94A non-relativistic solutionHydro equations:Solution

Observables

The perfect fluid of quarks95Nonrelativistic solutionsSolutionSymmetryDensity prof.EoSObservablesCsizmadia et al.Phys. Lett. B443:21-25, 1998SphereGaussianCalculatedCsrgCentral Eur.J.Phys.2: 556-565,2004SphereArbitraryNot calculatedAkkelin et al.Phys.Rev. C67,2003EllipsoidGaussian (T=T(t))CalculatedCsrgActa Phys.Polon. B37:483-494,2006EllipsoidArbitrary(T=T(r,t))Not calculatedCsrg, ZimnyiHeavy Ion Phys.17:281-293,2003 EllipsoidGaussianCalculated

The perfect fluid of quarks98Relativistic solutionsSolutionBasic propsEoSObservablesCsrg, Nagy, CsandPhys.Lett.B 663:306-311, 2008 Phys.Rev.C77:024908,2008 Ellipsoidal, 1D acceleratingdn/dy, eLandauIzv. Acad. Nauk SSSR 81 (1953) 51Cylindr., 1D, acceleratingnoneHwa-BjrkenR.C. Hwa, PRD10, 2260,1974J.D. Bjorken, PRD27, 40(1983)Cylindr., 1D,non-acceleratingdn/dy, eBialas et al.A. Bialas, R. A. Janik, and R. B. Peschanski, Phys. Rev. C76, 054901 (2007).1D, betweend Landau and Hwa-Bjrkendn/dyCsrg, Csernai, Hama, KodamaHeavy Ion Phys. A 21, 73 (2004))Ellipsoidal, 3D, non-acceleratingThis work does the calculation

The perfect fluid of quarks99An 1+1D relativistic solution

The perfect fluid of quarks100A relativistic solutionThe hydro fields are these: n(s) arbitrary, but realistic to choose Gaussian bRHBT, mt>T0

The perfect fluid of quarks102Single particle spectrumSource function: spatial origin and momentumMomentum distribution integrate on spatial coordinates:Second order Gaussian approximation around emission maximumAfter integration:

Directional slope parameter:

The perfect fluid of quarks103Transverse momentum spectrumGo to mid-rapidity (y=0)Integrate on transverse angle f

The effective temperature is from the slopes:

The perfect fluid of quarks104The elliptic flowThe elliptic flow can be calculated as:

Result (similar to other models):

In(w): modified Bessel functions

Where w is:

The perfect fluid of quarks105Two-particle correlation radiiDefinition:

From the source function:Changing coordinates

Result:The usual scaling (same for kaons!):Bertsch-Pratt coordinates:Freeze-out: t = const. t = 0 Rout = Rside

The perfect fluid of quarks106Single pion spectum with HBT radii0-30% centrality, Au+Au, PHENIX

T0197 2 MeVcentral freeze-out temp. e0.85 0.01momentum space ecc. ut2/b-0.95 0.07 (b14 GeVIsospin, shadowing and energy loss, see F. Arleo, hep-ph/0601075Suppression of 0 stays nearly constant up to 20 GeV/cDirect photons are not inhibited by hot/dense medium

The perfect fluid of quarks117118A sign of collective dynamicsSpectra: Boltzmann-type distributions + flow

More precise description by exact hydro models

The perfect fluid of quarks119

Confirmation of the hydro pictureMomentum distribution axially symmetric?Bigger compression bigger expansion!Elliptic flow v2: azimuthal asymmetrySecond Fourier coefficient p spectrumMeasures collective behaviorZero v2 for a rare gasHydrodynamic behavior: v2 > 0nucl-th/0512078

f(j)0 p 2pjThe perfect fluid of quarks119120Hydrodynamical scalingBuda-Lund hydro: prediction of scale function (2003)

PHENIX (2005), PHOBOS (2006) and STAR (2005) data do collapse

Prediction based on perfect hydro is VALIDCsrg, Akkelin, Hama, Lukcs, Sinyukov (Phys. Rev. C67, 034904, 2003)Csand, Csrg, Lrstad, Ster (Nucl. Phys. A742:80-94,2004)Csand, Csrg, Lrstad, Ster et al. nucl-th/0512078

The perfect fluid of quarks120121Bose-Einstein correlationsAngular diameter of stars with intensity-correlations R. H. Brown, s R. Q. Twiss, Nature 178, 1046 (1956)Momentum-correlations in our caseG. Goldhaber, S. Goldhaber, W. Y. Lee, s A. Pais, Phys. Rev. 120, 300 (1960)Bose-Einstein effect: Common pair-coordinate system:Out: average momentum of the pairLongitudinal: beam directionSide: perpendicular to the other twoStrong first order phase transition long transition time out sideoutside

The perfect fluid of quarks122Success of hydro again Phase transition prediction:Out SideOut SideNo first order phase transition~50 models failSeveral hydro models work

Csrg, Csernai (Phys.Lett.B333:494-499,1994)Csrg, Lrstad (Phys.Rev.C54:1390-1403,1996)The perfect fluid of quarks123Is there a phase transiton then?Basic observables in second order phase transitions: critical exponentsBelow/above the critical pointSpecific heat ~ ((T-Tc)/Tc)-aSusceptibility ~ ((T-Tc)/Tc)-gCorrelation length ~ ((T-Tc)/Tc)-nAt the critical pointSpatial correlation function ~ r-d+d-h Ginzburg-Landau: a=0, g=1, n=0.5, h=0Universality classes exist (c.f. renormalization group)QCD 3D random field Ising modelCorrelation exponent h=0.5Can this be measured? Yes!The perfect fluid of quarks123124Search for the critical pontTwo-particle spatial correlationsrescattering, anomalous diffusion, long tailgeneralized central limit theoremnot Gaussian but Lvy distribution!Lvy(R,a) Fourier transformed of exp(-|Rq|a)Correlation exponent: Equals to the Lvy-stability index of two-particle correlations a h=a, Csrg et. al., nucl-th/0512060Analysis of 200 GeV Au+Au data: a1.4Second order phase transition closed outFodor&Katz: cross-over!The perfect fluid of quarks124125Experimental results

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0-20%, 0.48-0.6GeVR5.69fm 0.16fma1.57 0.06l1.00 0.04Chi2/NDF68.1/78The perfect fluid of quarks126If its a fluid, how perfect?Perfect ideal, not sticky!Dont equate viscous with sticky (jet suppression)Perfect: negligible viscosity and heat conduction, does not supports a shear stressIdeal: incompressibleMeasure of resistance to shear stress h:Approximately:Low viscosity Large cross-section Strong couplingKinematic viscosity h/s Maldacena: CFTD AdSD+1use Area of the black braneh = Area/16pG, s = Area / 4Gh/s=1/4pConjectured to be a lower bound for all relativistic quantum field theories at finite temperature and zero chemical potential

The perfect fluid of quarks126127Top Story 2005According to the American Institut of Physics the top physics story in 2005 was the discovery of the perfect liquid

The perfect fluid of quarks127128Perfect fluid of quarksRelevant variable: not pt, but transverse kinetic energ KEtElliptic flow scales with number of constituent quarks!Degrees of freedom: quarks?PHENIX Collaboration, Phys.Rev.Letters 98:162301, 2007

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True even for d, D and Strange and even charm quarks participate in the flowv2 for D and flows as mesonsv2 for d flows as barions

nucl-ex/0703024The perfect fluid of quarks129130p+Chiral symmetry restoration?Prediction: h mass reduction in hot and dense matter due to UA(1) symmetry restorationProdigal Goldstone-boson h (mass: 960 MeV)hhp-p+p-p0hvery long lifetimelong lifetimesame sign pairs not correlatedhAverage pion momentum: 138 MeVIdea: measure fraction of correlated p pairs at low pt Kapusta, Kharzeev, McLerranZ. Huang, X-N. WangPhys.Rev.D53:5028-5033,1996Phys.Rev.D53:5034,1996

Vance, Csrg KharzeevT. Hatsuda, T. KunihiroPhys.Rev.Lett.81:2205-2208,1998 Phys. Rept. 247:221,1994The perfect fluid of quarks130131

The l(pt) functionHot and dense matterh mass reductionEnhanced h contentDecay:hh+p+ +p- (p0+p++p)+p++pLong lifetimeAverage pt of ps 138 MeVMore non-interacting ps at 138 MeVl(mt) measures fraction of interacting psA hole in l(mt) PHENIX FINAL DATAAu+Au 200 GeV S. S. Adler et al., PRL93,152302(2004)l(pt): fraction of strongly coupled same sign ps at given pair pt

nucl-ex/0509042PHENIX PRELIMINARYThe perfect fluid of quarks131