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Systematic Study of Elliptic Flow at RHIC

Systematic Study of Elliptic Flow at RHIC. Maya SHIMOMURA University of Tsukuba. ATHIC 2008 University of Tsukuba, Japan October 13-15, 2008. Contents. Introduction RHIC-PHENIX Elliptic Flow (v 2 ) Motivation Results Energy dependence System size dependence Universal v 2

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Systematic Study of Elliptic Flow at RHIC

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  1. Systematic Study of Elliptic Flow at RHIC Maya SHIMOMURA University of Tsukuba ATHIC 2008 University of Tsukuba, Japan October 13-15, 2008

  2. Contents • Introduction • RHIC-PHENIX • Elliptic Flow (v2) • Motivation • Results • Energy dependence • System size dependence • Universal v2 • Comparison with theory • Summary ATHIC2008

  3. Relativistic Heavy Ion Collider (RHIC) • Brookhaven National Laboratory • First relativistic heavy ion collider in the world • Circumference 3.83 km、2 rings • Collision species (Au+Au, Cu+Cu, d+Au, p+p) • Energy (A+A); up to 100 GeV/nucleon • PHENIX is the one of the main experiment group Time-evolution after collision Thermal freezeout Chemical freezeout PHENIX Experiment v2 can increase hadronization QGP thermal equilibrium collision ATHIC2008

  4. non central collision z φ Ｙ beam axis Reaction plane Ｙ x x (Reaction Plane) Elliptic Flow (v2) v2 is the strength of the elliptic anisotropy of produced particles. A sensitive probe for studying properties of the hot dense matter made by heavy ion collisions. Fourier expansion of the distribution of produced particle angle, Φ, to RP v2is the coefficient of the second term  indicates ellipticity If yield is (x direction)>(y direction), v2 >0. The initial geometrical anisotropy is transferred by the pressure gradients into a momentum space anisotropy  the measured v2 reflects the dense matter produced in the collisions. ATHIC2008

  5. PRL 98, 162301 Motivation From the results at 200GeV in Au+Au collision ｖ２at low pT (< ~2 GeV/c)→ can be explained by a hydro-dynamical model ｖ２at mid pT (<4~6 GeV/c)　→ is consistent with recombination model The results are consistent with Quark number +KET scaling. PRL 91, 182301 How about other systems and energies !? KET = mT-m0 ATHIC2008

  6. Results • Energy dependence • System size dependence • Eccentricity scaling • Universal v2 • Quark number + KET scaling • Universal scaling ATHIC2008

  7. <words> Npart --- Number of nucleons participating the collision eccentricity() --- geometirical eccentricity of participant nucleons • -Nucleus formed by wood-Saxon shape • Monte-Carlo simulation with Glauber model • Participant eccentricity which is calculated with long and short axis determined by distribution of participants at each collision.  vs. Npart ATHIC2008

  8. Comparison Table Size Particle species System (CuCu, AuAu) Centrality Energy nq+KET scaling AuAu 200 AuAu 62 CuCu 200 CuCu 62 Already known Is going to check next ATHIC2008

  9. Comparison Table Size Particle species System (CuCu, AuAu) Centrality Energy nq+KET scaling AuAu 200 AuAu 62 CuCu 200 CuCu 62 Already known Is going to check next ATHIC2008

  10. 2.0-4.0 GeV/c 1.0-2.0 GeV/c 0.2-1.0 GeV/c 1.0-2.0 GeV/c 0.2-1.0 GeV/c Energy dependence - dependence of centrality (Npart) • - compare the results in Cu + Cu which is smaller collision size than Au+Au • comparison of PID hadrons. pi/K/p next page Comparison of s = 62.4 and 200 GeV Cu+Cu Au+Au black 200GeV red 62.4GeV black 200GeV red 62.4GeV PHENIX PRELIMINARY PHENIX PRELIMINARY v2 of 200GeV and 62GeV are consistent ATHIC2008

  11. Energy dependence Mean pT • identified hadrons (/K/p) • pT dependence open: negative close: positive Produced by p Au+Au v2 vs. pT Higher collision energy has larger v2 up to RHIC energy. Above 62.4 GeV, v2 is saturated. This indicates the matter reached thermal equilibrium state at RHIC PHENIX PRELIMINARY K <pT> of 62.4 GeV and 200 GeV are consistent within errors on pi/K/ｐ. Therefore v2 agree at any pT region in figures. FOPI : Phys. Lett. B612, 713 (2005). E895 : Phys. Rev. Lett. 83, 1295 (1999) CERES : Nucl. Phys. A698, 253c (2002). NA49 : Phys. Rev. C68, 034903 (2003) STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary. PHOBOS : nucl-ex/0610037 (2006) ATHIC2008

  12. System Size Dependence • Eccentricity Scaling • What can change the size of collision system. • Species of collision nucleus (Au+Au ,Cu+Cu) • Centrality ATHIC2008

  13. Comparison Table Size Particle species System (CuCu, AuAu) Centrality Energy nq+KET no change scaling AuAu 200 AuAu 62 CuCu 200 CuCu 62 Already known checked Is going to check next ATHIC2008

  14. System size dependence v2 vs. Npart 0.2<pT<1.0 [GeV/c] Compare v2 normalized by eccentricity () in the collisions of different size. PHENIX PRELIMINARY ATHIC2008

  15. System size dependence v2/ vs. Npart v2 vs. Npart 0.2<pT<1.0 [GeV/c] Compare v2 normalized by eccentricity () in the collisions of different size. PHENIX PRELIMINARY v2/ (Au+Au) = v2/ (Cu+Cu) ! Systematic errors from eccentricity is not included here. ATHIC2008

  16. System size dependence v2/ vs. Npart v2 vs. Npart 0.2<pT<1.0 [GeV/c] Compare v2 normalized by eccentricity () in the collisions of different size. PHENIX PRELIMINARY v2/ (Au+Au) = v2/ (Cu+Cu) ! Systematic errors from eccentricity is not included here. but v2/ is not constant and it shades depending on Npart . v2can be normalized by  at same Npart , but  is not enough to determine v2 . ATHIC2008

  17. System size dependence 0.2<pT<1.0 [GeV/c] V2//Npart1/3 vs. Npart Dividing by Npart1/3 v2/ vs. Npart v2 vs. Npart PHENIX PRELIMINARY Systematic errors from eccentricity is not included here. v2/ (Au+Au) = v2/ (Cu+Cu) v2/eccentricity is scaled by Npart1/3 and not dependent on the collision system. ATHIC2008

  18. System size dependence 1.0<pT<2.0 [GeV/c] V2//Npart1/3 vs. Npart Dividing by Npart1/3 v2/ vs. Npart v2 vs. Npart PHENIX PRELIMINARY Systematic errors from eccentricity is not included here. v2/eccentricity is scaled by Npart1/3 and not dependent on the collision system. ATHIC2008

  19. System size dependence 2.0<pT<4.0 [GeV/c] V2//Npart1/3 vs. Npart Dividing by Npart1/3 v2/ vs. Npart v2 vs. Npart PHENIX PRELIMINARY Systematic errors from eccentricity is not included here. v2/eccentricity is scaled by Npart1/3 and not dependent on the collision system. ATHIC2008

  20. Comparison Table Size Particle species System (CuCu, AuAu) Centrality Energy nq+KET eccentricity no change Npart1/3 scaling AuAu 200 AuAu 62 CuCu 200 CuCu 62 Already known checked Is going to check next ATHIC2008

  21. Universal v2 • Quark number + KET scaling • Universal Scaling ATHIC2008

  22. Comparison Table Size Particle species System (CuCu, AuAu) Centrality Energy nq+KET eccentricity no change Npart1/3 scaling AuAu 200 AuAu 62 CuCu 200 CuCu 62 Already known checked Is going to check next ATHIC2008

  23. Quark number + KET scaling (AuAu 62.4GeV) Centrality 10-40 % PHENIX: Error bars include both statistical and systematic errors. STAR: Error bars include statistical errors. Yellow band indicates systematic errors. Star results : Phys. Rev. C 75 quark number + KET scaling is OK at 62.4 GeV, too! v2 vs. pT v2/nq vs. pT/nq v2/nq vs. KET/nq v2(pT) /nquark vs. KET/nquark is the universal curve independent on particle species. ATHIC2008

  24. Cu+Cu s = 200GeV Quark number + KET scaling quark number + KET scaling seems to works out at Cu+Cu 200GeV. At all centrality, (between 0- 50 %) v2 of /K/p is consistent to quark number + KET scaling. ATHIC2008

  25. Summary of Scaling • Collision energy  no change • Eccentricity of participants eccentricity scaling • Particle species  nq +KET scaling • Number of participants  Npart1/3 scaling ATHIC2008

  26. Comparison Table Size Particle species System (CuCu, AuAu) Centrality Energy nq+KET eccentricity no change Npart1/3 scaling AuAu 200 AuAu 62 CuCu 200 CuCu 62 Already known checked Is going to check next ATHIC2008

  27. + eccentricity scaling ex. Au+Au 200GeV  Universal Scaling quark number + KET scaling. ATHIC2008

  28. + eccentricity scaling + Npart1/3 scaling ex. Au+Au 200GeV  Universal Scaling quark number + KET scaling. v2(KET/nq)/nq/par/Npart1/3 is consistent at 0-50% centralities. ATHIC2008

  29. Universal Scaling v2(KET/nq)/nq/epar/Npart1/3 • Different System (Au+Au, Cu+Cu) • Different Energy (200GeV - 62.4GeV) • Different Centrality (0-50%) • Different particles (/ K /p) Universal Curve !! Large symbol - AuAu Small symbol - CuCu χ2/ndf = 8.1 (without systematic errors) χ2/ndf = 3.2 (with systematic errors) ATHIC2008

  30. QGP fluid+hadron gas with Glauber I.C. Comparison with hydro-simulation Hydro calculations done by Prof. Hirano. ref: arXiv:0710.5795 [nucl-th] and Phys. Lett.B 636, 299 (2006)  Hydro should be middle of two data. Au+Au 200GeV Au+Au 62.4GeV Cu+Cu 200GeV The Au+Au results agree well with hydro but Cu+Cu results don’t.

  31. Comparison of v2(data)/participant to v2(hydro)/standard  Hydro should be middle of two data. Au+Au 200GeV Au+Au 62.4GeV Cu+Cu 200GeV The Au+Au and Cu+Cu results agree well with hydro.

  32. Comparison with hydro-simulation p Hydro should be middle of two data. ●・・・hydro ●・・・0-10　％ ●・・・10-20％ ●・・・hydro ●・・・0-10　％ ●・・・10-20％ Cu+Cu 200GeV Normalized by eccentricities ●・・・hydro ●・・・20-30％ ●・・・hydro ●・・・20-30％ v2(data)/participant for proton doesn’t agree with v2(hydro)/standard ATHIC2008

  33. Summary • Systematic study for charged hadron v2 is done for 4 systems. • (Au+Au, Cu+Cu) x (62.4GeV, 200GeV) • Same v2(pT) are obtained in different collision energies at RHIC(s = 62.4 - 200GeV) • v2(pT) of various hadron species are scaled by quark number + KET scaling. • v2(Npart) scaled by participant Eccentricity are consistent between Au+Au and Cu+Cu collisions • v2(pT) /par are scaled by Npart1/3 . • v2(KET/nq)/nq/par/Npart1/3 has Universal Curve. This indicates v2 are determined by the initial geometrical anisotropy and its evolution time depending on the initial size. • With normalization of proper eccentricities, hydro-calculation agree with data for , but not for proton. ATHIC2008

  34. Back Up ATHIC2008

  35. Assumption Calculation of simple expansion model Calculation is done by Dr.Konno Time until chemical freeze-out is proportional to Npart1/3. ATHIC2008

  36. Summary of v2 production and development Time t collision Determine initial geometrical eccentricity, , with the participant. Low to mid pT thermal equilibrium Determine pressure gradient from . v2 is expanding during finite time. Not depending on the kind of quarks. expanding This finite time becomes longer with larger collision system, and the v2 increases proportionally. hadronization radial flow depending on each mass expands. freeze out No change Measurement ATHIC2008

  37. Summary (1) When the systems have same Npart, v2 is scaled by  of paricipant geometry. result v2B result v2A same Npart If v2 only depends on eccentricity of initial participant geometry, v2/ should be constant at any Npart, but it is not. B A v2A/A = v2B/B eccentricity A eccentricity B Therefore, to explain v2, in addition to the initial geometrical eccentricity, there are something related to Npart. result v2C same eccentricity result v2D C D v2C v2D ATHIC2008

  38. Summary (2) result v2C v2 becomes consistent after scaled by not only  but also Npart1/3 . same eccentricity result v2D With same eccentricity, v2 is scaled by (number of participants)1/3. v2C v2D Is it because of thickness increasing along beam axis then energy per unit area increasing ? C D v2C /NpartC1/3= v2D/NpartD1/3 v2(200GeV) = v2(62.4GeV) #of participant NpartC #of participant NpartD This concludes that increasing dN/dy doesn’t change v2 at RHIC energy. result v2F same Npart result v2E It might be because that number of participant to 1/3 (like length) is proportional to the time period taken to freeze out v2 , and v2 expands proportional to that period. F E Ｘ Ｘ v2E = v2F = 200GeV = 62GeV ATHIC2008

  39. Scaling (others) QM2006, S. A. Voloshin QM2006, R. Nouicer • Straight line from SPS to RHIC energy. • v2 is reaching the hydro limit at central collision. ATHIC2008

  40. 3 systemes comparison Various scalings. Eccentricity of Npart and Npart1/3 looks best. ATHIC2008

  41. Quark number + KET scaling (AuAu 200GeV) • Quark number + KET scaling exists. ATHIC2008

  42. v2 vs. pT at Cu+Cu in 200GeV collision Centrality dependence of PID v2 vs. pT for Cu+Cu 200GeV is measured. ATHIC2008

  43. Quark number + KET scaling doesn’t seem to work out at SPS. No flow at partonic level due to nonexistence of QGP ? Errors are to big to conclude it. Additional quark number + KET scaling(PbPb 17.2GeV) v2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/0606026 submitted to PRL v2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003) Pb+Pb at 158A GeV, NA49 Taken from A. Tranenko’s talk at QM 2006 ATHIC2008

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