Partha Pratim Bhaduri Subhasis Chattopadhyay VECC, Kolkata

1. Differential elliptic flow of identified hadrons & number of constituent quark (NCQ) scaling at FAIR Partha Pratim Bhaduri Subhasis Chattopadhyay VECC, Kolkata 1

2. Introduction • Over past two decades, relativistic heavy-ion collision experiments are performed around the world; ultimate aim is to map the QCD phase diagram & to discover the new state of QCD matter the Quark Gluon Plasma (QGP). • The Compressed Baryonic Matter (CBM) experiment at FAIR : exploration of the QCD phase diagram at high net baryon densities and moderate temperatures. EL = 10 – 40 GeV/n. • Main challenge is to predict unambiguous & experimentally viable probes to indicate the formation of dense partonic medium. • Collective flow of the produced particles in the transverse plane of the collision signature of the creation of thermalized matter nuclear collisions. • Of particular interest is the elliptic flow parameter (v2) ; signals a strong evidence for the creation of a hot & dense system at a very early stage in the non-central collisions.

3. Elliptic flow v2 y py px x y z x • non-central collisions: azimuthal anisotropy in coordinate-space • interactions asymmetry in momentum-space • sensitive to early time in the system’s evolution • Measurement: Fourier expansion of the azimuth particle distribution M. Oldenburg 3 v2 (pT) : Differential elliptic flow

4. Elliptic Flow at RHIC • A large elliptic flow is found for identified hadrons • Data is well described by hydrodynamics in low pT region. • Hydrodynamic mass ordering at low pT (pT<= 1.5 GeV/c) • Baryon-Meson crossing at intermediate pT (1.5 < pT < 5 GeV/c) • NCQ scaling 4

5. Number of constituent quark (NCQ) scaling Recombination Extended to Elliptic Flow

6. Excellent KET/n scaling for the full measured range • Contrast to pT scaling NCQ scaling in KET /n KET = mT – m0 mT2 = pT2 + m02 6

7. What we have done: 1. To study the differential elliptic flow of identified hadrons in the FAIR energy regime. 2. To test the NCQ scaling of v2 of identified hadrons . Models used for the study : UrQMD (hadronic transport model) AMPT - string melting (partonic transport model) AMPT- default (hadronic transport model) System : Au + Au Energy : EL = 25 GeV/n & 40 GeV/n Impact parameter : b = 5 - 9 fm.

8. Differential elliptic flow at top (40A GeV) & intermediate (25A GeV) FAIR energies Hydrodynamic mass ordering at low pT Baryon-Meson crossing at high pT

9. Partonic scatterings enhance the flow Elliptic Flow : comparison of different models Accepted for publication in PRC

10. Constituent Quark Number Scaling No reasonable NCQ scaling in pT over the investigated pT range Ruling out of recombination picture ? Accepted for publication in PRC

11. Transverse Kinetic Energy (KET = mT – m0) scaling Remarkable scaling behaviour by UrQMD (hadronic) & AMPT with string melting (partonic) Accepted for publication in PRC

12. Summary • Observations at FAIR are quite in-line with the elliptic flow measurements at RHIC. Hadron mass ordering at low pT ; switch over at high pT. • Partonic scattering enhances the flow. • No, reasonable NCQ scaling is found in pT , over the investigated pT range • Remarkable scaling is found with respect to KET by both UrQMD & string • melting version of AMPT. • Insensitive to distinguish between hadronic & partonic phase. • Relative values of v2 might serve as a better observable at FAIR to indicate the • formation of a partonic medium .

13. Thank you 13

14. Back Ups

15. Observations • However a remarkable scaling behavior is indeed found with respect to KET by both UrQMD & string melting version of AMPT. • This can be attributed to hydrodynamic mass scaling • The degree of scaling seems to be better for UrQMD than AMPT. • Observation of NCQ scaling w.r.t KET by both hadronic & partonic model makes this observable rather insensitive to indicate the formation of partonic matter at FAIR. • If at all, a universal scaling behavior of elliptic flow is observed at RHIC, whether it should be interpreted as a signature of color de-confinement is still a debated issue. • Relative values of v2 might serve as a better observable.

16. AMPT with string-melting slightly over estimates the flow UrQMD & default AMPT under estimates the flow at high pT Large error bar in the data !! No conclusive picture Comparison with existing data (NA49)

17. Why Elliptic Flow ? Z • The probe for early time • The dense nuclear overlap is ellipsoid at the beginning of heavy ion collisions • Pressure gradient is largest in the shortest direction of the ellipsoid • The initial spatial anisotropy evolves (via interactions and density gradients )  Momentum-space anisotropy • Signal is self-quenching with time Reaction plane Y X Pz Py Px 17

18. Elliptic flow v2 Coordinate-Space Anisotropy Momentum-Space Anisotropy 18

19. Why Elliptic Flow ? Z • The probe for early time • The dense nuclear overlap is ellipsoid at the beginning of heavy ion collisions • Pressure gradient is largest in the shortest direction of the ellipsoid • The initial spatial anisotropy evolves (via interactions and density gradients )  Momentum-space anisotropy • Signal is self-quenching with time Reaction plane Y X Pz Py Px 19

20. Momentum anisotropy Spatial anisotropy Interactions among the produced particles lead to pressure gradients which generate an azimuthal anisotropy in particle emission or elliptic flow, measured by v2, from which can be obtained valuable information about the early dynamics after the collision Why Elliptic Flow ? 20

21. Resent PHENIX Elliptic Flow Data Detailed differential measurements now available for π, K, p, φ, d, D 21

22. Substantial elliptic flow signals are observed for a variety of particle species at RHIC. Indication of rapid thermalization? RHIC Elliptic Flow Data 22

23. Substantial elliptic flow signals are observed for a variety of particle species at RHIC. Indication of rapid thermalization? RHIC Elliptic Flow Data 23

24. Identified particle v2 at 200 GeV PRL 92(04) 052302 • v2 appears to saturate at ~0.13 for KS and ~0.20 for  with the saturation setting in at different pT. Quark Matter 2006, Shanghai China 24

25. Elliptic flow at RHIC and perfect fluid hydrodynamics The v2 measurements at RHIC are in a good agreement with the predictions of ideal relativistic hydrodynamics 25

26. Scaling breaks = mT – m ( WHY ? ) P • Elliptic flow scales with KET up to KET ~1 GeV • Indicates hydrodynamic behavior • Possible hint of quark degrees of freedom become apparent at higher KET Transverse kinetic energy scaling Baryons scale together Mesons scale together PHENIX preliminary PHENIX article submitted to PRL: nucl-ex/0608033 26

27. NCQ-scaling: Partonic flow In this scenario we can infer the value of the parton v2 in the relevant pT region (~7%). Quark Matter 2006, Shanghai China 27

28. Partonic Collectivity (ii) PHENIX PRELIMINARY WWND 2006, M. Issah SQM2006, S. Esumi Data :QM2005, PHENIX K0S,  (STAR) : PR 92, 052302 (2004)  (STAR) : PRL 95, 122301 (2005)  (STAR) : preliminary STAR preliminary 0-80% Au+Au 200GeV Yan Lu SQM05 P. Sorensen SQM05 M. Oldenburg QM05 K0S • Hydro + NCQ scaling describes v2 for a variety of particles measured at RHIC • Scaling breaks for higher pT Hiroshi Masui / University of Tsukuba 28

29. KET/n scaling works for the full measured range with deviation less than 10% from the universal scaling curve • NCQ- scaling works only at 20% level for pt>2 GeV/c and breakes below with clear systematic dependence on the mass NCQ (pT/n) scaling compared to KET /n NCQ- Scaling PHENIX Preliminary 29

30. Elliptic flow of multistrange hadrons (φ, Ξ and ) with their large masses and small hadronic  behave like other particles → consistentwith the creation of elliptic flow on partonic level before hadron formation Multi-strange baryon elliptic flow at RHIC (STAR) From M. Oldenburg SQM2006 talk (STAR) J. Phys G 32, S563 (2006) Scaling test STAR preliminary 200 GeV Au+Au 30

31. Elliptic flow at FAIR D J/  AMPT calculations: C.M. Ko at CPOD 2007 31 Measure flow for all particles over CBM energy range

32. What does theory expect? → mainly predictions from lattice QCD: • crossover transition from partonic to hadronic matter at small B and high T • critical endpoint in intermediate range of the phase diagram • first order deconfinement phase transition at high B but moderate T The Compressed Baryonic Matter (CBM) experiment : Exploration of the phase diagram at very high baryon densities and moderate temperatures to look for : • De-confinement phase transition at high temperature & baryon density • In-medium modification of hadrons – signal of the onset of chiral symmetry restoration. • Location of the critical end point QCD Phase Diagram 32

33. Thank you 33

34. Discontinuity in strangeness production: signature for phase transition ? C. Blume et al. (NA49 at CERN-SPS), nucl-ex/0409008 Decrease of baryon-chemical potential: transition from baryon-dominated to meson-dominated matter ? 34

35. Extra Slides 35

36. Net-baryon densities in central Au+Au collisions at FAIR: consistent picture from transport models Compilation by J. Randrup, CBM Physics Book, in preparation see also I.C. Arsene et al., Phys. Rev. C 75 (2007) 034902 36

37. high baryon and energy densities created in central Au+Au collisions • remarkable agreement between different models • maximum net baryon densities from 5 - 40 AGeV ~ 1 - 2 fm-3 ~ (6 – 12) 0 (net baryon density  = 1 fm-3 ~60) • max. excitation energy densities from 5 - 40 AGeV ~ (0.8 – 6) GeV/fm3 (* =  – mN,  total energy density) CBM physics book (to be published) High density matter at CBM net baryon density 37

38. Introduction • States of matter, their defining features and transition between them always been one of the fundamental issues of physics. Strongly interacting matter opens up a new chapter for such studies. • Statistical QCD predicts at high temperature and/or densities, strongly interacting matter will undergo a transition from color neutral hadronic phase to a state of de-confined color charged quarks & gluons – quark gluon plasma (QGP) baryons hadrons partons Compression heating quark-gluon matter (pion production) Neutron stars Early universe In laboratory Relativistic heavy-ion collisions (RHIC) are the only tool to produce such exotic states of QCD matter 38

39. What does theory expect? → mainly predictions from lattice QCD: • crossover transition from partonic to hadronic matter at small B and high T • critical endpoint in intermediate range of the phase diagram • first order deconfinement phase transition at high B but moderate T However ... • deconfinement = chiral phase transition ? • hadrons and quarks at high ? • signatures (measurable!) for these structures/ phases? • how to characterize the medium? • physics program complementary to RHIC, LHC • rare probes CBM Physics : keywords 39

40. Exploring the QCD Phase diagram RHIC result: • new state of matter = perfect liquid? • Tf = 160 – 165 MeV L-QCD Predictions:  TC = 151 ± 7 ± 4 MeV ( μB=0 ) (Z. Fodor, arXiv:0712.2930 hep-lat)  TC = 192 ± 7 ± 4 MeV ( μB=0 ) (F. Karsch, arXiv:0711.0661 hep-lat)  crossover transition at μB=0 (Z. Fodor, arXiv:0712.2930 hep-lat)  1. order phase transition with critical endpoint at μB > 0 High-energy heavy-ion collision experiments: RHIC, LHC: cross over transition, QGP at high T and low ρ Low-energy RHIC:search for QCD-CP with bulk observables NA61@SPS: search for QCD-CP with bulk observables CBM@FAIR: scan of the phase diagram with bulk and rare observables 40

41. The future Facility for Antiproton an Ion Research (FAIR) SIS 100 Tm SIS 300 Tm cooled antiproton beam: Hadron Spectroscopy Ion and Laser Induced Plasmas: High Energy Density in Matter Structure of Nuclei far from Stability low-energy antiproton beam: antihydrogen Compressed Baryonic Matter Primary beams: 1012 /s 238U28+ 1-2 AGeV 4·1013/s Protons 90 GeV 1010/s U 35 AGeV (Ni 45 AGeV) Secondary beams: rare isotopes 1-2 AGeV antiprotons up to 30 GeV 41

42. best way to measure? e+e-↔ +- In medium effects: Dileptons • dileptons are penetrating probes! • modifications in hot and dense matter expected – see CERES, NA50, NA60, HADES [Rapp, Wambach, Adv. Nucl. Phys. 25 (2000) 1, hep-ph/9909229] 42

43. Probing the quark-pluon plasma with charmonium rescaled to 158 GeV Quarkonium dissociation temperatures: (Digal, Karsch, Satz) Measure excitation functions of J/ψ and ψ' in p+p, p+A and A+A collisions ! J/ψ ψ' sequential dissociation? 43

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47. High density matter at CBM CBM physics book (to be published) • high baryon and energy densities created in central Au+Au collisions • remarkable agreement between different models • maximum net baryon densities from 5 - 40 AGeV ~ 1 - 2 fm-3 ~ (6 – 12) 0 (net baryon density  = 1 fm-3 ~60) • max. excitation energy densities from 5 - 40 AGeV ~ (0.8 – 6) GeV/fm3 (* =  – mN,  total energy density) net baryon density 47

48. central midcentral peripheral Collapse of proton flow : order of transition?? • collapse elliptic flow of protons at lower energies signal for first order phase transition?! [e.g. Stoecker, NPA 750 (2005) 121, E. Shuryak, hep-ph/0504048] • full energy dependence needed! [NA49, PRC68, 034903 (2003)] 48

49. Summary: CBM physics topics andobservables CBM Physics Book in preparation The equation-of-state at high B  collective flow of hadrons  particle production at threshold energies (open charm?) Deconfinement phase transition at high B  excitation function and flow of strangeness (K, , , , )  excitation function and flow of charm (J/ψ, ψ', D0, D, c) (e.g. melting of J/ψ and ψ')  exitation function of low-mass lepton pairs QCD critical endpoint excitation function of event-by-event fluctuations (K/π,...) Onset of chiral symmetry restoration at high B in-medium modifications of hadrons (,,e+e-(μ+μ-), D) 50

50. observables detector requirements & challenges tracking in high track density environment (~ 1000) hadron ID lepton ID myons, photons secondary vertex reconstruction (resolution  50 m) large statistics: large integrated luminosity: high beam intensity (109 ions/sec.) and duty cycle beam available for several months per year high interaction rates (10 MHz) fast, radiation hard detector efficient trigger strangeness production: K,  charm production: J/, D flow excitation function rare signals!  e+e- open charm event-by-event fluctuations Detector requirements Systematic investigations: A+A collisions from 8 to 45 (35) AGeV, Z/A=0.5 (0.4) (up to 8 AGeV: HADES) p+A and p+p collisions from 8 to 90 GeV 51