The Core Corona Model

The Core Corona Model or Is the Centrality Dependence of Observables more than a Core-Corona Effect? inspired by the first multiplicity results in CuCu then used to extract the physics of EPOS simulations finally compared to all available observables Multiplicities <p i t>, elliptic flow v 2 (v 2i ) spectra of identified particles in collaboration with C. Schreiber and K. Werner 1

Geometry of a Heavy-Ion Collision Non-central collision z The Model Number of participants (Npart): number of incoming nucleons (participants) in the overlap region In equilibrium: y 2 x Plasma to be studied Reaction plane Multipl /Npart =const, independent of b and hadrons species Experimentally not seen

Centrality Dependence of Hadron Multiplicities In reality more complicated (EPOS) -shape fluctuations, finite particle number -some of the participants scatter only once (cannot equilibrate) separation of core and corona The Model 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 AuAu 0.1 CuCu 0.0 0 50 100 150 200 250 300 350 400 Core corona model Assumption: Nucleons with 1 initial coll: corona Nucleons with more: core Calculated in Glauber Model 3

The Model M i (Npart) follows a very simple law Phys.Rev.C79:064907 Calculation for Cu+Cu without any further input 4

Multiplicities works for non strange and for strange hadrons at 200 (and 62 and 17.3) AGeV 200 AGeV Au+Au Cu+Cu Theory=lines Cu+Cu: completely predicted from Au+Au and pp 5

Further confirmation of the core-corona effect strong correlation between multiplicity ratios peripheral/central and pp/central for all hadrons (strange and non-strange) Multiplicities Such a correlation is neither expected in statistical nor in hydro models M periph /M central Ω 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 DATA STAR eq.1 Ω Ξ 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 π reproduces quantitatively this correlation M pp /M central AA 6

This model explains STRANGENESS ENHANCEMENT in particular that the enhancement at SPS is larger than at RHIC 25 Multiplicities Fraction of strings with E<m fraction 0.8 0.6 0.4 0.2 10 2 5 10 2 2 7 1 10 10 2 2 20 15 10 PRD 65, 057501 (2002) 1.2 pp at s=17.3 GeV pp at s=200 GeV 1 90% too low E 5 a a +a 5 10 2 2 Strangeness enhancement in HI is in reality strangeness suppression in pp 30% too low E to produce Ω mass m (GeV/c )

- Central M i /N part same in Cu+Cu and Au+Au (pure core) - very peripheral same in Cu+Cu and Au+Au (pp) increase with N part stronger in Cu+Cu - all particle species follow the same law Multiplicities Φ is nothing special (the strangeness content is not considered in this model) Strangeness enhancement is in reality strangeness suppression in pp (core follows stat model predictions) - works for very peripheral reactions (N core =25). The formation of a possible new state is not size dependent Consequence: Light hadrons insensitive to properties of matter prior to freeze out 8

Dynamical Variables Dynamical variables Can we go further and investigate also kinematical variables like <p T (N part )>, v 2 (N part ) or even single particle spectra? Yes, if we make an additional (strong) assumption: <p T > is different for different corona hadrons. Therefore interactions among corona hadrons change their momentum <p T > is different for corona and core hadrons Therefore interactions between core and corona hadrons change their momentum If the core corona model works: improbable that core hadrons interact with corona hadrons EPOS gives evidence that this is indeed the scenario. 9

v 2 as a function of centrality has a long history Dynamical Variables: v 2 In ideal hydrodynamics: a) v 2 /ε (ε= eccentricity in coordinate space) is independent of the geometry if v 2 is caused by ε b) All RHIC and SPS data(for heavy systems) fall on a common line if plotted as: v 2 /ε as a fct of 1/SdN/dy 1/S dn/dy = measures the particle density c) Experiments and ideal hydro results do not agree Hydrodynamics describes many features in central collisions 10 Snellings QM09 therefore Centrality dependence points toward the need of viscous hydro (which in the limit of large dn/dy agrees with ideal hydrodynamics)

Centrality dependence of v 2 allows for the determination of the viscosity Dynamical Variables: v 2 v 2 assuming that visocus hydrodynamics describes the expansion There are no other observables which require a viscous hydro approach Drescher et al. PRC76,024905 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 hydro fixed coupling hydro running coupling σ=5.5 mb fixed coupling σ=3.3 mb running coupling Phobos 50 100 150 200 250 300 350 400 0.08 0.06 0.04 0.02 11 N part v 2 Luzum et al. PRC78,034915 0.1 0 η/s=10-4 η/s=0.08 η/s=0.16 Glauber PHOBOS 0 100 200 300 400 N Part

But the situation is not that simple Dynamical Variables: v 2 v2 / ecc_part 0.35 0.3 0.25 0.2 0.15 0.1 EPOS: Ideal hydro describes the data if core- corona is taken into account EPOS 2 with hadron cascade w/o hadron cascade 0.05 data: phobos 0 0 50 100 150 200 250 300 350 400 Npart viscosity and core-corona give about the same effect 12

Core-corona model: Only core particles develop elliptic flow (corona part. fragment like pp) Dynamical Variables: v 2 v 2 /ε(n part ) = (v 2 /ε) ideal hydro f core (N part ) All data compatible with a straight line and hence with the core-corona assumption No free parameter 13 40 35 30 25 20 15 10 5 0 Pb+Pb 49 AGeV (NA49) 0 100 200 300 400

Possibility to distinguish between viscosity and core-corona? Dynamical Variables: v 2 v 2 of identified particles: core corona fraction is dependent on the species Less corona particles -> v 2 larger Good agreement for Λ less good for K 0 Deviation at central collision not understood Relative core fraction for Λ larger than for charge part more data needed 14

What is the difference between Dynamical Variables: v 2 viscous Viscous hydro hydro Core-corona Core-Corona? no surface effects Time evolution of all particles identical with finite viscosity v 2 /ε depends on centrality via (Drescher & Ollitrault PRC76, 024905) Distinction between surface and core core = ideal hydro (visc = 0) corona = pp Parameters: (v 2 /ε) hydro K 0 c S (E beam ) Parameters: (v 2 /ε) hydro (f core same as for multiplicities or <p t >) 15

Average p T <p T > = f i core (Npart)<p T > core + (1-fi core (Npart))<p T > corona 1.2 1.2 1.0 0.8 0.6 0.4 1.1 1.0 0.9 0.8 0.2 0.0 0%-5% 5% - 10% 10% - 20% 20% - 30% 30% - 40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% pt average pt + K + p p, K, π 0.7 p p, Λ, Φ Centrality dep. Of <p T > due to core-corona and not necessarily due to collective flow 16 0.6 0%-5% 5% - 10% 10% - 20% 20% - 30% 30% - 40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% Average pt Particles with similar mass have widely different p T

Single particle spectra (protons) Spectra d 2 N/(2.p T.dp T.dy) [(c/gev) 2 ] 5 2 1 5 2 10-1 5 STAR STAR p spectra Core-Corona Data 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 p T [GeV/c] [0,5%] [70-80%] d 2 N/(2.p T.dp T.dy) [(c/gev) 2 ] 2 1 5 2 10-1 5 2 10-2 5 PHENIX PHENIX p spectra (low p T ) Core-Corona Data 0.7 0.8 0.9 1.0 1.1 p T [GeV/c] 17

Core-corona agrees almost within errorbars with exp spectra Spectra Core - Corona / Data 1.3 1.2 1.1 1.0 0.9 0.8 0.7 STAR 0.5 0.6 0.7 0.8 0.9 1.0 1.1 p T [GeV/c] p inverse slope parameter 0% - 5% 5% - 10% 10% - 20% 20%-30% 30%-40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% Core - Corona / Data 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 PHENIX 0.7 0.8 0.9 1.0 p T [GeV/c] p inverse slope parameter 0% - 5% 5% - 10% 10% - 20% 20%-30% 30%-40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% 80% - 92% 0.4 0.35 0.45 0.4 Core - Corona Data T [GeV] 0.3 0.25 0.2 0.15 0.1 0%-5% 5% - 10% 10% - 20% Core - Corona Data 20% - 30% 30% - 40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% 80% - 92% pp T [GeV] 0.35 0.3 0.25 0.2 0.15 0%-5% 5% - 10% 10% - 20% 20% - 30% 30% - 40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% pp 18 Not at all trivial: slope chance by a factor of 2 from central -> peripheral

Is this compatible with event generator results? no final state int Spectra K + p Final state int K - ap Yes, there is final state interaction but only at low p T where no data exist 19

3.0 2.5 2.0 1.5 1.0 0.5 0.0 spectra ratio STAR/PHENIX 0%-5% 5% - 10% 10% - 20% 20% - 30% 30% - 40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% 5 π +,pt =0.65GeV 2 10 5 2 1 5 π 20 STAR and PHENIX data do not agree Therefore the core and corona parameters are different p, p T =1.15GeV pbar, p T =1.15GeV K +,p T =0.65GeV 0%-5% 5% - 10% 10% - 20% 20% - 30% 30% - 40% 40% - 50% 50% - 60% 60% - 70% 70% - 80% 80% - 92% Spectra d 2 N/(2.pT.dpT.dy) [(c/gev) 2 ] STAR PHENIX

Conclusions Core corona model inspired by first CuCu results, checked against EPOS and developed to make this physics more transparent. V 2, M i,<p i T > and spectrum in central collisions and pp is the only input Conclusions Predicts quantitatively all experimental results on centrality dependence at midrapidity: -M i (Npart) of all hadrons i from SPS to RHIC (strangeness enhancement) -v 2 /ε (Npart) of charged particles from SPS to RHIC -<p i T> (Npart) of hadrons i from SPS to RHIC -single particle spectra -the experimental observation of correlations between peri/central and pp/central for multiplicities and <p T > In short: central and pp collisions is all what we need This is much more than we expected in view of its simplicity (improvement difficult due to large experimental error bars) 21

Conclusion on the Physics Conclusions The fact that the centrality dependence of all observables is described by this simple model may suggest that it describes the essential features of the reaction. If this were the case: What we see in the detector is a superposition of two independent contributions: A corona contribution with properties identical to pp A core contribution whose properties are independent of N part even for very small N part ( 20) The observed centrality dependence is due to the N part dependence of the ratio of both contributions During the expansion the average <p T > of each hadron species does not change The spectra remain a superposition -> very little final state int. after hadron formation above p T >.4 GeV When we have understood central AA and pp, we have understood all 22

Conclusion with respect to other models Conclusions The core-corona models shows (as experiment) correlations between pp and peripheral heavy ion reactions for multiplicities and <p T > which is alien to hydrodynamics. It reproduces the centrality dependence of v 2 without using viscosity In the core-corona model the centrality dependence of <p T > is given by the difference of <p T > in pp and central heavy ion reactions. Particles with similar masses (as p,φ,λ) show a quite different centrality dependence of <p T >. This questions whether collective flow, derived from blast wave fits, is really the origin of the mass dependence of <p T >(N part ). 23

RESULTS Thank you! 24