Investigation of hadronic matter properties with heavy ion collisions Particle production and flow from SIS to FAIR. Yvonne Leifels GSI

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1 Investigation of hadronic matter properties with heavy ion collisions Particle production and flow from SIS to FAIR Yvonne Leifels GSI

2 Investigation of compressed baryonic matter with heavy ion collisions Probing dense baryonic matter (1 3 0) nuclear equation of state in medium properties of baryons and mesons Towards highest baryon densities (3 10 0) exploring the QCD phase diagram

3 Probing dense baryonic matter (1 3 0) PART II The quest for the EOS Stopping Collective Flow Reconstruction of reaction planes Directed flow Elliptic flow

4 Heavy ion collisions at SIS energies Main features Hydrodynamics not valid in SIS energy range Large fraction of nucleons bound in clusters Energy is removed by particle production EOS is accessible only indirectly via microscopic transport models Production of primary fragments (and subsequent decays) is a complex process which is not incorporated rigorously in most of the models clusterisation in coordinate and momentum space Ab initio calculations of in medium cross sections are complicated Physics of the (lifetime and decay) has to be incorporated properly into the models (see part III)

5 Which observables are constraining the EOS? At a given incident energy different densities are reached for the different parametrization of the EOS p= E =ρ 2 E/N s/ρ=const V ρ pressure p depends on curvature of EOS measure pressure density flow density pile up (stopping) Kaons

6 Stopping and the EOS C. Hartnack Calculations IQMD Stopping depends on the EOS but also on cross sections Data FOPI W. Reisdorf et al.

7 Stopping does not only depend on EOS C. Hartnack, thesis 1993 Qzz = 3p2 pz2 = 2pz2 pt2 > 0 longitudinal dominant < 0 transversal dominant but much more on the cross sections

8 Isospin asymmetric system 400 AMeV RZ = 2 MZ=1 ( MZ=1ZrZr + MZ=1 RuRu) MZ=1ZrZr MZ=1RuRu Rz essentially independent on EOS But depending on NN used in the model Consistent with rapidity distributions Alternatively mass asymmetric systems FOPI measured 25 symmetric system/energy combinations, analysed 5 particle species at 6 different centrality bins

9 Summary Stopping decreases with energy And system size Depending on EOS and cross sections Need for fixing the cross sections independently Mixing in isospin asymmetric systems Investigation of mass asymmetric systems

10 Directed flow Reaction plane reconstruction Resolution Collective flow Directed flow Elliptic flow

11 Collective flow reaction plane Au + Au!AGeV b = 6fm P. Danielewicz et al. Science 298, 1592 (2002)

12 Reaction plane reconstruction Projection of momenta on xy plane Q py = ν p t ν, Q n i forward { 1 ν = 1 y ν y CM y ν y CM φr px backward Generalisation: n = ω n Q p t cos n ϕ, sin n ϕ i n=1,2,3,... ω (n) has different sign in forward/backward hemisphere for odd values of n. n n n Reaction plane angle: R =arctan Q y,q x /n

13 Azimuthal distributions with respect to reaction plane Au+Au Incident energy (AGeV) target rapidity rapidity mid rapidity side flow elliptic flow (squeeze out) side flow projectile rapidity C.Pinkenburg et al., (E895), Phys.Rev.Lett. 83 (1999) 1295 nucl ex/

14 Observables Projection onto the reaction plane 0.4AGeV, Li-fragments P.Crochet et al., (FOPI), NPA624, 755 (1997) v1= cos R v 2= cos 2 R Integral sideflow / Q t ν Q p dir = ω p x ν Classical Sideflow (slope of mean px at midrapidity) F y= d p x / A dy

15 Resolution of the reaction plane determination Ni AGeV (S325e) Reconstructed reaction plane is fluctuating around true reaction plane => measured vi are smaller than true vi. Subevent method: divide one event into two independent sub events calculate for each sub-event the reaction plane n cos n An Bn = cos n n A R cos n B R Estimate for correction factors of Fourier expansion coefficients: n n vm=v obs / cos n m A B or Ollitraut method J.Y. Ollitrault, arxiv:nucl-ex/

16 Ollitraut formalism for reaction plane correction Determination of Fourier coefficients vi: 1) Fit of azimuthal distributions 2) vi=<cos n φ > J.Y. Ollitrault, arxiv:nucl-ex/ Fourier coefficients vi can be corrected consistently by evaluating dimensionless parameter χ!

17 Ollitraut formalism Determination of correction factors From sub events: cos R Determination of χ correction for vn Inverse correction factors

18 Excitation function of side flow p Aint b Fy Fdt peff A int t pass 2R 1 t pass = CM CM A b A int = CM 2 Fy CM CM peff = F y A t pass A b 2R int

19 Scaling of side - flow N. Herrmann, J. Wessels, T. Wienold, Ann. Rev. Nucl. Part. Sci. 49 (1999) 581

20 Excitation function of elliptic flow A.Andronic et al., PLB 612, 173 (2005)

21 Constraining the EOS with flow F= d p x /A d y / y cm P. Danielewicz et al. Science 298, 1592 (2002) side flow elliptic flow Preference for a soft equation of state at low energies Lacking data points between 1 10 AGeV

22 Constraining the EOS with flow P. Danielewicz et al. Science 298, 1592 (2002)

23 Deuteron flow in Au+Au 400 AMeV W. Reisdorf et al. (2009) side flow elliptic flow IQMD IQMD IQMD describes deuteron data with soft EOS much more data available

24 Really? d p x /A F= d y / y cm P. Danielewicz et al. nucl-th/ (2001) Mean field effects clearly visible by difference to cascade calculations. None of the model calculations describes all the available data.

25 Side flow and cluster production Difference diminishing Soft EOS makes more clusters but they are less flowing

26 Differential side flow A.Andronic et al. (FOPI), PRC 67, (2003) Au + Au 0.4 AGeV Tends to hard EOS Not described by any

27 Elliptic flow in comparison to models Au+Au elliptic flow vs BUU Models Influence of the EOS In medium effects with soft EOS A.Andronic et al. (FOPI), PRC 67, (2003) Differences between models larger than the effect of EOS Difficult to get a consistent description for all data Influence of NN cross sections Other parameters (initialization...)

28 Instead of absolute values concentrate on differences or ratios UrQMD predictions Au+Au 400 AMeV for different EOS for asymmetric nuclear matter Q. Li, P. Russotto (2008) size of neutron and proton flow interchanged Proposal submitted by the ASY EOS collaboration to the GSI PAC to measure n/p/h elliptic flow

29 The LAND-FOPI experiment Results on elliptic flow published Y. Leifels et al., PRL 71: (1993) not corrected for reaction plane resolution hydrogen isotopes show slightly larger flow than neutrons (mass difference!) elliptic flow mass separated flow

30 FOPI systematics on stopping and side flow W. Reisdorf et al., PRL 92 (2004) 72203

31 Correlation between stopping and side flow W. Reisdorf et al., PRL 92 (2004) Side flow (here maximum directed momentum ) and stopping are correlated Central semi central collisions Stringent test of models

32 Summary Collective flow is prominent observable Correlated with stopping Flow is depending on the pressure build up, the passage time of the reaction and the size of the colliding system Size of directed and elliptic flow is depending on the EOS Constraining the EOS ( soft at low energies) Consistent description of all flow data by models lacking NN cross sections, azimuthal distributions, initializations