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

2008/10/14ATHIC20082 Contents Introduction RHIC-PHENIX Elliptic Flow (v 2 ) Motivation Results Energy dependence System size dependence Universal v 2 Comparison with theory Summary

2008/10/14ATHIC20083 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 PHENIX Experiment Time-evolution after collision collision QGP thermal equilibrium Chemical freezeout Thermal freezeout hadronization v 2 can increase

2008/10/14ATHIC20084 Elliptic Flow (v 2 ) A sensitive probe for studying properties of the hot dense matter made by heavy ion collisions. beam axis x z Reaction plane non central collision Ｙ Fourier expansion of the distribution of produced particle angle, Φ, to RP v 2 is the coefficient of the second term  indicates ellipticity x (Reaction Plane) Ｙ φ If yield is (x direction)>(y direction), v 2 >0. The initial geometrical anisotropy is transferred by the pressure gradients into a momentum space anisotropy  the measured v 2 reflects the dense matter produced in the collisions. v 2 is the strength of the elliptic anisotropy of produced particles.

2008/10/14ATHIC20085 Motivation ｖ ２ at low p T (< ~2 GeV/c) → can be explained by a hydro-dynamical model ｖ ２ at mid p T (<4~6 GeV/c) → is consistent with recombination model The results are consistent with Quark number +KE T scaling. From the results at 200GeV in Au+Au collision How about other systems and energies !? PRL 98, PRL 91, KE T = mT-m0

2008/10/14ATHIC20086 Results Energy dependence System size dependence Eccentricity scaling Universal v 2 Quark number + K ET scaling Universal scaling

2008/10/14ATHIC20087 N part --- 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. N part

2008/10/14ATHIC20088 Comparison Table Energy Particle species System (CuCu, AuAu) Centrality Size AuAu 200 AuAu 62 CuCu 200 CuCu 62 scaling n q +K ET Already known Is going to check next

2008/10/14ATHIC20089 Comparison Table Energy Particle species System (CuCu, AuAu) Centrality Size AuAu 200 AuAu 62 CuCu 200 CuCu 62 scaling n q +K ET Already known Is going to check next

2008/10/14ATHIC Energy dependence Comparison of  s = 62.4 and 200 GeV - 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 v 2 of 200GeV and 62GeV are consistent black 200GeV red 62.4GeV Au+Au Cu+Cu GeV/c GeV/c GeV/c GeV/c GeV/c black 200GeV red 62.4GeV PHENIX PRELIMINARY

2008/10/14ATHIC Energy dependence Higher collision energy has larger v2 up to RHIC energy. Above 62.4 GeV, v 2 is saturated.  This indicates the matter reached thermal equilibrium state at RHIC open: negative close: positive p Produced by Mean p T Au+Au v 2 vs. p T - identified hadrons (  /K/p) - p T dependence K of 62.4 GeV and 200 GeV are consistent within errors on pi/K/ ｐ. Therefore v 2 agree at any p T region in figures. PHENIX PRELIMINARY FOPI : Phys. Lett. B612, 713 (2005). E895 : Phys. Rev. Lett. 83, 1295 (1999) CERES : Nucl. Phys. A698, 253c (2002). NA49 : Phys. Rev. C68, (2003) STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary. PHOBOS : nucl-ex/ (2006)

2008/10/14ATHIC System Size Dependence Eccentricity Scaling What can change the size of collision system. Species of collision nucleus (Au+Au,Cu+Cu) Centrality

2008/10/14ATHIC Comparison Table System (CuCu, AuAu) Centrality Size AuAu 200 AuAu 62 CuCu 200 CuCu 62 scaling n q +K ET Energy checked no change Particle species Already known Is going to check next

2008/10/14ATHIC System size dependence 0.2<p T <1.0 [GeV/c] Compare v 2 normalized by eccentricity (  ) in the collisions of different size. v 2 vs. N part PHENIX PRELIMINARY

2008/10/14ATHIC System size dependence 0.2<p T <1.0 [GeV/c] Compare v 2 normalized by eccentricity (  ) in the collisions of different size. v 2 vs. N part v 2 /  vs. N part v 2 /  (Au+Au) = v 2 /  (Cu+Cu) ! PHENIX PRELIMINARY Systematic errors from eccentricity is not included here.

2008/10/14ATHIC System size dependence 0.2<p T <1.0 [GeV/c] Compare v 2 normalized by eccentricity (  ) in the collisions of different size. v 2 vs. N part v 2 /  vs. N part v 2 /  (Au+Au) = v 2 /  (Cu+Cu) ! PHENIX PRELIMINARY Systematic errors from eccentricity is not included here. but v 2 /  is not constant and it shades depending on N part.  v 2 can be normalized by  at same N part, but  is not enough to determine v 2.

2008/10/14ATHIC System size dependence 0.2<p T <1.0 [GeV/c] Dividing by N part 1/3 v 2 vs. N part v 2 /  vs. N part v 2 /  (Au+Au) = v 2 /  (Cu+Cu) v 2 /eccentricity is scaled by N part 1/3 and not dependent on the collision system. V 2 /  / N part 1/3 vs. N part PHENIX PRELIMINARY Systematic errors from eccentricity is not included here.

2008/10/14ATHIC System size dependence Dividing by N part 1/3 v 2 vs. N part v 2 /  vs. N part v 2 /eccentricity is scaled by N part 1/3 and not dependent on the collision system. V 2 /  / N part 1/3 vs. N part PHENIX PRELIMINARY 1.0<p T <2.0 [GeV/c] Systematic errors from eccentricity is not included here.

2008/10/14ATHIC System size dependence Dividing by N part 1/3 v 2 vs. N part v 2 /  vs. N part v 2 /eccentricity is scaled by N part 1/3 and not dependent on the collision system. V 2 /  / N part 1/3 vs. N part PHENIX PRELIMINARY 2.0<p T <4.0 [GeV/c] Systematic errors from eccentricity is not included here.

2008/10/14ATHIC Comparison Table System (CuCu, AuAu) Centrality Size AuAu 200 AuAu 62 CuCu 200 CuCu 62 scaling n q +K ET eccentricity N part 1/3 Energy checked no change Particle species Already known Is going to check next

2008/10/14ATHIC Universal v 2 Quark number + K ET scaling Universal Scaling

2008/10/14ATHIC System (CuCu, AuAu) Centrality Size AuAu 200 AuAu 62 CuCu 200 CuCu 62 scaling n q +K ET eccentricity N part 1/3 Comparison Table Energy checked no change Particle species Already known Is going to check next

2008/10/14ATHIC Quark number + K ET scaling (AuAu 62.4GeV) 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 Centrality % v 2 (p T ) /n quark vs. K ET /n quark is the universal curve independent on particle species. quark number + K ET scaling is OK at 62.4 GeV, too! v 2 vs. p T v 2 /n q vs. p T /n q v 2 /n q vs. K ET /n q

2008/10/14ATHIC Quark number + K ET scaling Cu+Cu  s = 200GeV quark number + K ET scaling seems to works out at Cu+Cu 200GeV. At all centrality, (between %) v 2 of  /K/p is consistent to quark number + K ET scaling.

2008/10/14ATHIC Summary of Scaling Collision energy  no change Eccentricity of participants  eccentricity scaling Particle species  n q +K ET scaling Number of participants  N part 1/3 scaling

2008/10/14ATHIC System (CuCu, AuAu) Centrality Size AuAu 200 AuAu 62 CuCu 200 CuCu 62 scaling n q +K ET eccentricity N part 1/3 Comparison Table Energy checked no change Particle species Already known Is going to check next

2008/10/14ATHIC Universal Scaling quark number + K ET scaling. ex. Au+Au 200GeV  + eccentricity scaling

2008/10/14ATHIC Universal Scaling v 2 (K ET /n q )/n q /  par /N part 1/3 is consistent at 0-50% centralities. quark number + K ET scaling. ex. Au+Au 200GeV  + eccentricity scaling + Npart 1/3 scaling

2008/10/14ATHIC v2(KET/nq)/nq/epar/Npart1/3 Universal Scaling  Different System (Au+Au, Cu+Cu)  Different Energy (200GeV GeV)  Different Centrality (0-50%)  Different particles (  / K /p) Universal Curve !! χ2/ndf = 8.1 (without systematic errors) χ2/ndf = 3.2 (with systematic errors) Large symbol - AuAu Small symbol - CuCu

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

31 Comparison of v 2(data) /  participant to v 2(hydro) /  standard The Au+Au and Cu+Cu results agree well with hydro. Au+Au 200GeVAu+Au 62.4GeVCu+Cu 200GeV  Hydro should be middle of two data.

2008/10/14ATHIC Comparison with hydro-simulation ● ・・・ hydro ● ・・・ ％ ● ・・・ ％ ● ・・・ hydro ● ・・・ ％ p Cu+Cu 200GeV Normalized by eccentricities v 2 (data)/  participant for proton doesn’t agree with v 2 (hydro)/  standard ● ・・・ hydro ● ・・・ ％ ● ・・・ hydro ● ・・・ ％ ● ・・・ ％ Hydro should be middle of two data.

2008/10/14ATHIC Summary Systematic study for charged hadron v 2 is done for 4 systems. (Au+Au, Cu+Cu) x (62.4GeV, 200GeV) Same v 2 (p T ) are obtained in different collision energies at RHIC(  s = GeV) v 2 (p T ) of various hadron species are scaled by quark number + K ET scaling. v 2 (N part ) scaled by participant Eccentricity are consistent between Au+Au and Cu+Cu collisions v 2 (p T ) /  par are scaled by N part 1/3. v 2 (K ET /n q )/n q /  par /N part 1/3 has Universal Curve.  This indicates v 2 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.

2008/10/14ATHIC Back Up

2008/10/14ATHIC Calculation of simple expansion model Time until chemical freeze-out is proportional to N part 1/3. Assumption Calculation is done by Dr.Konno

2008/10/14ATHIC Summary of v 2 production and development Low to mid p T collision thermal equilibrium expanding hadronization freeze out Measurement Time tDetermine initial geometrical eccentricity, , with the participant. Determine pressure gradient from . This finite time becomes longer with larger collision system, and the v 2 increases proportionally. v 2 is expanding during finite time. Not depending on the kind of quarks. radial flow depending on each mass expands. No change

2008/10/14ATHIC Summary (1) When the systems have same N part, v 2 is scaled by  of paricipant geometry. same N part A result v 2B v 2A /  A = v 2B /  B B result v 2A eccentricity  A eccentricity  B If v 2 only depends on eccentricity of initial participant geometry, v 2 /  should be constant at any N part, but it is not. same eccentricity CD v 2C v 2D result v 2C result v 2D Therefore, to explain v 2, in addition to the initial geometrical eccentricity, there are something related to N part.

2008/10/14ATHIC Summary (2) With same eccentricity, v 2 is scaled by (number of participants) 1/3. v 2 becomes consistent after scaled by not only  but also N part 1/3. same eccentricity CD v 2C v 2D result v 2C result v 2D #of participant N partC #of participant N partD v 2C /N partC 1/3 = v 2D /N partD 1/3 Is it because of thickness increasing along beam axis then energy per unit area increasing ? v 2 (200GeV) = v 2 (62.4GeV) This concludes that increasing dN/dy doesn’t change v 2 at RHIC energy. Ｘ = 62GeV result v 2E Ｘ = 200GeV result v 2F same N part v 2E = v 2F E F It might be because that number of participant to 1/3 (like length) is proportional to the time period taken to freeze out v 2, and v 2 expands proportional to that period.

2008/10/14ATHIC Scaling (others) Straight line from SPS to RHIC energy. v 2 is reaching the hydro limit at central collision. QM2006, R. NouicerQM2006, S. A. Voloshin

2008/10/14ATHIC systemes comparison Various scalings. Eccentricity of N part and N part 1/3 looks best.

2008/10/14ATHIC Quark number + K ET scaling (AuAu 200GeV) Quark number + K ET scaling exists.

2008/10/14ATHIC v2 vs. pT at Cu+Cu in 200GeV collision Centrality dependence of PID v2 vs. pT for Cu+Cu 200GeV is measured.

2008/10/14ATHIC Additional quark number + K ET scaling (PbPb 17.2GeV) Taken from A. Tranenko’s talk at QM 2006 v 2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/ submitted to PRL Pb+Pb at 158A GeV, NA49 v 2 of K 0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/ ) -Quark number + K ET 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.