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Exploring Azimuthal Anisotropy in High-Energy Heavy-Ion Collisions

Investigating the azimuthal anisotropy as a powerful probe of early-stage collisions, particle emission, and parton energy loss in hot, dense mediums. Analysis includes identified hadron v2, electron v2, charm v2, photon v2, and system energy dependence.

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Exploring Azimuthal Anisotropy in High-Energy Heavy-Ion Collisions

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  1. The azimuthal anisotropy in high energy heavy ion collisions at RHIC Shingo Sakai Univ. of Tsukuba

  2. pｙ ｙ pｘ ｘ Azimuthal anisotropy • A powerful probe of the initial state of • the high energy heavy ion collision • Low pT • pressure gradient of early stage of collision • High pT • parton energy loss in hot & • dense medium Initial spatial anisotropy Momentum space anisotropy of particle emission dN/dφ ∝ N0(1+2v2cos(2φ))

  3. Reaction plane method • Reaction plane ; defined beam direction & impact parameter direction • particle’s φ measured with respect to the reaction plane v2 is obtained (1) by fitting dN/dφ (2) <cos(2(-))> Y  wi*sin(2i) tan2 rp =  wi*cos(2i) Reaction Plane X dN/d(-) ∝ N (1 + 2v2obscos(2(-)))

  4. Today’s topics • Identified particles v2 (Au+Au 200 GeV) • pions, kaons, protons • φ • electrons • photons • Energy dependence of v2 • 62.4, 130 and 200 GeV • System size dependence • Au+Au & Cu+Cu These measurement gives us much more information of the collision dynamics and particle productions

  5. Identified particles v2

  6. Identified hadron v2 • pT<1.5 GeV/c • mass dependence v2(π)>v2(K)>v2(p) • consistent with hydro model prediction (τ0 = 0.6 fm/c) System thermalizes very early • pT>2.0 GeV/c • v2(ｂ) > v2(ｍ) • consistent with quark coalescence model (N.Q.S)

  7. v2 already developed in partonic phase ? • identified hadrons v2 after scaling number of quarks • v2 after scaling fall on same curve • partonic level v2 • v2 already formed in the partonic phase for hadrons made of light quarks (u,d,s)

  8. Φ meson v2 • φ v2 is important • mass dependence ? v2(p) ~ v2(φ) • Quark number scale ? => number of quarks = 2 saturate around 2.0 GeV/c like π,K v2 • Current φ v2 has large error =>consistent with hydro model & quark coalescence model

  9. Electron v2 • electron sources ; • photonic --- hadronic decay • (π0,η, etc.) • non-photonic --- heavy flavor • decay (c) • => give us charm flow info. • v2non-γe = {(1+RNP)v2e - v2γe} }/RNP RNP ; phonic / non-photonic v2γe; phonic e v2 converter ; experimentally determined with/without converter cocktail ; simulation Non photonic signal Photonic b.g. Experimentally determined simulation photonic e v2 inclusive e v2

  10. Non-photonic electron v2 • pT dependence non-γ e v2 • low pT ; increasing with pT • high pT ; small energy loss ? B contribution ? • Compared with quark coalescence model prediction. • with/without charm quark flow • (Greco, Ko, Rapp: PLB 595 (2004) 202) • Below 2.0 GeV/c ; • consistent with charm quark • flow model. • indicate charm quark flow 0 1 2 3

  11. Charm v2 estimate from non-γ e v2 • Estimate charm v2 with non-γ e v2 • Assuming several v2 shape for D meson v2 Dv2(pT) = api * pi v2 Dv2(pT) = aK * kaon v2 Dv2(pT) = ap * proton v2 • Calculate D -> e • chi-squared test with • “measured” non-photonic electron v2 • find chi-squared “a” • Calculate charm v2 from the D v2 with N.Q.S D meson v2 Decay electron v2

  12. Charm quark v2 (private analysis) • mass effect for N.Q.S • v2M (pT) = v21 (R1 pT) + v22 (R2pT) • Ri = mi / mM • (mi ; effective mass of quark i) • (Phys.Rev. C68 (2003) 044901 • Zi-wei & Dence Molnar) • v2π(pT) ~ 2*v2q(1/2pT) • v2D(pT) ~ v2u (1/6*pT) + v2c (5/6*pT) u quark v2 • Mass effect in partonic level ?

  13. Photon v2 [Photon production mechanism] thermalization Hadronisation Direct photon thermal photon ; v2>0 Bresmsrahlung ; v2<0 prompt photon v2=0 Hadron decay • direct photon provide very early time information • photon @ high pT • prompt photon dominant • prompt photon ; binary scale (no energy loss) • v2 @ high pT ; expect v2 = 0

  14. Direct photon v2 R*direct photon v2 • Trend ; v2 seems like smaller @ most central => bremsstrahlung main source pT < 4.0 GeV/c ? • direct photon v2 @ high pT < 10 GeV/c coming soon !

  15. Summary for identified v2 • Identified hadrons (π,K,p,Λ,φ ---) • v2 @ low pT consistent with hydro model => early timethermalization • v2 scale number of quarks (quark coalescence) => partonic level flow • non-photonic electron • consistent with charm flow model => charm quark flow • direct photon • Trend ; v2 seems like smaller @ most central • => bremsstrahlung main source pT < 4.0 GeV/c ?

  16. Energy &System size dependence

  17. v2 (Au+Au) @ 62.4 , 130 & 200 GeV Phys. Rev. Lett. 94, 232302 • very similar v2 @ 62.4, 130 & 130 GeV at same Npart • same v2 @ 62.4 GeV & 200 GeV

  18. Energy dependence ; Softening EOS @ RHIC 130 62.4 200 AGS SPS RHIC Phys. Rev. Lett. 94, 232302 • v2saturate @ √sNN = 62.4 ~ 200 GeV => indicate “softening” of EOS

  19. Cu+Cu results Hirano et al., nucl-th/0506058 • Hydrodynamical behavior @ Cu+Cu collisions ? • What’s the scaling laws of v2 between Au+Au & Cu+Cu ?

  20. v2 is scaled by system size (A) linearly ? • AMPT : v2 scale system size ; v2 (Cu+Cu) ~ 0.3 * v2(Au+Au) • v2 (Cu+Cu) ~ 0.8 * v2(Au+Au) • v2 doesn’t scale system size (A) linearly

  21. Eccentricity scaling • Hydro ; v2 scales with eccentricity Y Eccentricity ; relate to geometry of overlap region x (1) v2(cent,pT) divide by v2(cent) ; v2(pT,cent)/v2(cent) v2(cent) = ∫v2(pT,cent)dpT ~ ε (2) v2 divide by eccentricity (ε) ; v2/<ε>

  22. Eccentricity scailing v2 @ Au+Au & Cu+Cu Au+Au Cu+Cu • v2 Au+Au @ Cu+Cu fall on same curve after eccentricity scailing • Eccentricity works well

  23. dN/dη& RAA @ Au+Au & Cu+Cu 200 GeV PHOBOS Cu+Cu Preliminary (PHOBOS) Cu+Cu Preliminary 15-25%, Npart = 61 Au+Au Au+Au 45-55%, Npart = 56 • dN/dη & RAA @ Au+Au & Cu+Cu --- very similar at same Npart

  24. v2 scales with Npart ? PHOBOS PHOBOS • v2 @ Au+Au & Cu+Cu ; very different same at Npart • v2/<εpart> @ is very similar at same Npart < εpart >; taking into account fluctuation in <ε> Cu+Cu Au+Au Image ; same Npart Au+Au & Cu+Cu

  25. Summary for energy & system size dependence • Energy dependence same v2 @ 62.4 GeV, 130 GeV and 200 GeV => indicate “softening” of EOS • System size dependence (Au+Au v.s. Cu+Cu) • v2 doesn’t scale with system size (A) • Eccentricity scailing well works • Npart scaling between Au+Au & Cu+Cu

  26. Outlook • Detector update @ PHENIX • new reaction plane detector => good reaction plane resolution (reduce error bar) • silicon vertex detector => direct measurement of D meson • Future v2 result @ PHENIX • High pT v2 with smaller error (non-γ e & direct photon, etc・・・) • J/ψ v2 • D meson v2, etc ・・・

  27. Back Up

  28. Converter method Separate non-photonic & photonic e v2 by using Non-converter run & converter run Non-converter ; Nnc = Nγ+Nnon-γ Converter ; Nc = R *Nγ+Nnon-γ (1+RNP)v2nc = v2γ + RNPv2non-γ (R+RNP) v2c = Rv2γ + RNPv2non-γ v2non-γ(non-photonic) & v2γ(photonic) is “experimentally” determined ! RNP；non-photonic/photonic R --- ratio of electrons with & without converter (measured) RNP --- non-photonic/photonic ratio (measured) v2nc --- inclusive e v2 measured with non-converter run (measured) v2c --- inclusive e v2 measured with converter run (measured)

  29. Cocktail method Determined photonic electron v2 with simulation Then subtract it from electron v2 measured with non-converter run dNe/d = dNpho.e /d + dNnon-pho.e /d v2non-γ = {(1+RNP) v2 - v2γ} } / RNP measured RNP；non-photonic/photonic measured calculate Clear non-photonic signal ! S/B > 1 in pT>1.5 GeV/c RNP --- non-photonic/photonic ratio experimentally determined v2 --- inclusive electron v2 (without converter) v2γ --- photonic electron v2 calculated from pi0 (pion) v2 From F. Kajihara

  30. Chi2 map & D meson v2 v2 D = a * pi v2 v2 D = a * kaon v2 v2 D = a * proton v2 v2 D = a * D v2 (y_T scailing)

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