Two- and Multi-particle Cumulant Measurements of v n and Isolation - PowerPoint PPT Presentation

Two- and Multi-particle Cumulant Measurements of v n and Isolation of Flow and Nonflow in 200 GeV Au+Au Collisions by STAR = s NN Li Yi (for the STAR collaboration) Purdue University Aug. 15th, 2012

Outline • Physics motivation • Results • 2- and multi-particle anisotropy • 2- and 4-particle η - η cumulants � Isolation of flow and nonflow • Summary 2 Aug. 15th, 2012

Azimuthal Anisotropy Flow and Nonflow Alver, Roland, PRC 81, 054905 (2010) • Hydrodynamic expansion � anisotropic flow; • Flow is sensitive to early stage of heavy ions collisions ∞ ∑ φ ∝ + φ − Ψ dN / d 1 2 v cos( n ( ) ) n nR = n 1 3 Aug. 15th, 2012

Azimuthal Anisotropy Flow and Nonflow Alver, Roland, PRC 81, 054905 (2010) • Hydrodynamic expansion � anisotropic flow; • Flow is sensitive to early stage of heavy ions collisions ∞ ∑ φ ∝ + φ − Ψ dN / d 1 2 v cos( n ( ) ) n nR = n 1 • Event-by-event initial geometry fluctuation � odd harmonics 3 Aug. 15th, 2012

Azimuthal Anisotropy Flow and Nonflow Alver, Roland, PRC 81, 054905 (2010) Correlation Pair (Nonflow) • Hydrodynamic expansion � anisotropic flow; • Flow is sensitive to early stage of heavy ions collisions ∞ ∑ ϕ ∝ + ϕ − Ψ d N / d 1 2 v cos( ( n )) n n R = n 1 • Event-by-event initial geometry fluctuation � odd harmonics • The reaction plane azimuthal angle is unknown � the measured anisotropies = flow(v) + flow fluctuation ( σ ) + nonflow ( δ ) particle correlation unrelated to the reaction plane 3 Aug. 15th, 2012

Constraint on η /s 20% uncertainty in v 2 / ε � 100% uncertainty in η /s The question is how to reduce uncertainty in v 2 / ε : 1. ε from theoretical part 2. v 2 from experimental part Song, Bass, Heinz, etal. PRL 106, 192301 (2011) "The extraction of η/ s from a comparison with hydrodynamics thus requires careful treatment of both fluctuation and nonflow effects" 4 Aug. 15th, 2012

v 3 vs Centrality AuAu@200GeV Q-Cumulant Method Particle 1 Particle 2 −1<η < 1 with η -gap p T < 2 GeV/ c ∆ η statistical error only statistical error only STAR preliminary STAR preliminary v • shows modest centrality dependence (Also see: Pandit, 1A, Tue.) 3 v v • is 3 × smaller than in peripheral to mid-central collisions 3 2 5 Aug. 15th, 2012

v 3 vs p T • v 3 : more sensitive to η /s than v 2 p ref = 0 − 10 GeV / c Q-Cumulant Method T statistical error only STAR preliminary 2 v 3 η /s = 0.08 i.c. : : : : Glauber MC • hydro describes data trend well at p T <2 GeV/c • Data may contain nonflow 6 Aug. 15th, 2012 * Schenke, Jeon, Gale, PRL 106, private commu.

Isolation of Flow and Nonflow using 2-, and 4-Particle η - η Cumulants Xu, LY, arXiv:1204.2815 • 2-particle cumulant: η =0 { η η , } = ( η ) ( η ) + σ η ( ) ( σ η ) + σ (∆ ) + η δ (∆ η ) v v ' V α β α β α β ∆η -dep nonflow ∆η -dep fluct. flow fluct. ‘flow’ ∆ {2} = {− η ,− η } − {− η η , } = ∆ σ + ∆ δ ' V V V α β α β − η = η σ − η = σ η v ( ) v ( ) ( ) ( ) β β β β • 4-particle cumulant: { η , η η η , , } = ( η ) ( η ) − σ η ( ) ( σ η ) − σ (∆ η ) 1/2 v v ' V α α β β α β α β ~ 0 (next slide) ∆ V = −∆ σ 1/2 { 4} ' 7 Aug. 15th, 2012

Isolation of Flow and Nonflow using 2-, and 4-Particle η - η Cumulants 1 Xu, LY, arXiv:1204.2815 • 2-particle cumulant: - η α η =0 { η η , } = ( η ) ( η ) + σ η ( ) ( σ η ) + σ (∆ ) + η δ (∆ η ) v v ' V α β α β α β ∆η -dep nonflow ∆η -dep fluct. flow fluct. ‘flow’ ∆ {2} = {− η ,− η } − {− η η , } = ∆ σ + ∆ δ ' V V V α β α β − η = η σ − η = σ η v ( ) v ( ) ( ) ( ) β β β β • 4-particle cumulant: { η , η η η , , } = ( η ) ( η ) − σ η ( ) ( σ η ) − σ (∆ η ) 1/2 v v ' V α α β β α β α β ~ 0 (next slide) ∆ V = −∆ σ 1/2 { 4} ' 7 Aug. 15th, 2012

Isolation of Flow and Nonflow using 2-, and 4-Particle η - η Cumulants 1 2 Xu, LY, arXiv:1204.2815 ∆η 1 • 2-particle cumulant: - η α - η β η =0 { η η , } = ( η ) ( η ) + σ η ( ) ( σ η ) + σ (∆ ) + η δ (∆ η ) v v ' V α β α β α β ∆η -dep nonflow ∆η -dep fluct. flow fluct. ‘flow’ ∆ {2} = {− η ,− η } − {− η η , } = ∆ σ + ∆ δ ' V V V α β α β − η = η σ − η = σ η v ( ) v ( ) ( ) ( ) β β β β • 4-particle cumulant: { η , η η η , , } = ( η ) ( η ) − σ η ( ) ( σ η ) − σ (∆ η ) 1/2 v v ' V α α β β α β α β ~ 0 (next slide) ∆ V = −∆ σ 1/2 { 4} ' 7 Aug. 15th, 2012

Isolation of Flow and Nonflow using 2-, and 4-Particle η - η Cumulants 1 2 2' Xu, LY, arXiv:1204.2815 ∆η 1 • 2-particle cumulant: ∆η 2 - η α - η β η =0 η β { η η , } = ( η ) ( η ) + σ η ( ) ( σ η ) + σ (∆ ) + η δ (∆ η ) v v ' V α β α β α β ∆η -dep nonflow ∆η -dep fluct. flow fluct. ‘flow’ ∆ {2} = {− η ,− η } − {− η η , } = ∆ σ + ∆ δ ' V V V α β α β − η = η σ − η = σ η v ( ) v ( ) ( ) ( ) β β β β • 4-particle cumulant: { η , η η η , , } = ( η ) ( η ) − σ η ( ) ( σ η ) − σ (∆ η ) 1/2 v v ' V α α β β α β α β ~ 0 (next slide) ∆ V = −∆ σ 1/2 { 4} ' 7 Aug. 15th, 2012

∆η -dependence σ '( ∆η ) AuAu@200GeV 20-30% V 2 {4} 1/2 STAR preliminary statistical error only (η (η (η (η α α ,η ,η ,η ,η β β ) ) ) ) α α β β → ∆η → → ∆η → ∆η ∆η 2 (η ,−η ) (η (η (η α α ,−η ,−η ,−η β β ) ) ) 2 2 2 α α β β → → ∆η ∆η → → ∆η ∆η 1 1 1 1 Flow fluctuation appears independent of ∆η . 8 Aug. 15th, 2012

∆η -dependent δ ( ∆η ) V 2 {2} AuAu@200GeV 20-30% δ(∆η 2 )- δ(∆η 1 ) linear in ∆η 2 - ∆η 1 at a given • ∆η 1 with similar slopes (η (η ,η ,η ) ) (η (η α α ,η ,η β β ) ) Intercept changes with ∆η 1 exponentially • α α β β (η ,−η ) (η (η α (η α ,−η ,−η β ,−η β ) ) ) α α β β ∆ V 2 {2} STAR preliminary STAR preliminary statistics error only 2 2 2 2 −∆ η −∆ η −∆ η σ −∆ η σ ∆ δ ∆ η ∆ η = − + − / b / b /2 /2 ( , ) a e ( e ) A e ( e ) 1 2 1 2 1 2 2 2 δ ∆ η = −∆ η + −∆ η σ / b / 2 ( ) ae Ae 9 STAR preliminary Aug. 15th, 2012

Cumulant V {2}, Nonflow δ , 'Flow' v n2 AuAu@200GeV 20-30% 2 > δ n parameterized decomposed <v n V n {2} v 2 η α η β v 3 STAR preliminary No Assumption about flow η dependence in our analysis The decomposed 'flow' appears to be independent of η . 10 Aug. 15th, 2012

∆η -dep Near-side Nonflow AuAu@200GeV 20-30% Calculate <nonflow> of all ( η α , η β ) bins with x < η -gap < 2. • (x = horizontal axis). STAR preliminary � < δ 2 >/<v 2 2 > � < δ 2 > STAR preliminary � < δ 3 > � < δ 3 >/<v 3 2 > bands are fitting errors bands are fitting errors 2δ 2 STAR preliminary |∆η| > 0.7 2δ 2 δ 2 : replace Gaus by e (-(x/ σ )4) • With | ∆η | > 0.7, significant nonflow still exits. 11 Aug. 15th, 2012

'Flow' and Nonflow vs Centrality Au+Au@200GeV fitting error only STAR preliminary STAR preliminary • √ δ 2 / v 2 ~ 20% for | ∆η |>0.7 δ 2 / v 22 ~ 4% 12 Aug. 15th, 2012

'Flow' vs η AuAu@200GeV 20-30% raw 2-particle cumulant × 10 10 10 10 -4 -4 -4 -4 = δ + 2 {2} v V STAR preliminary 2 2 2 nonflow 2 v 2 − 2 1/2 v {4} σ 2 V decomposed flow 2 2 2 ~ ~13% 2 2 + 1/2 v {4 } v V 2 2 2 + − ~12.6% 0.7% 4.0% = − σ 1/2 2 2 { 4} v 2 V 2 2 2 raw 4-particle cumulant • Flow seems independent of η . Note no assumption of η dependence in our approach. • (Fluctuation / flow) 2 ~ 13% 13 Aug. 15th, 2012

4- and 6-Particle Cumulant Assuming the flow fluctuations are Gaussian, we have two options: 1. v x , v y are Gaussian: v{6} = v{4} Voloshin, Poskanzer, Tang, Wang, PLB 2. v is Gaussian: LY, Wang, Tang, arXiv: 1101.4646 6 2 ≈ − σ σ << 6 2 v { 6 } v { 4 } 1 3 v , if v 1 n n n n STAR preliminary * No-weight applied, non-uniform acceptance corrected. Systematic errors estimated by applying weight and no acceptance correction 14 Aug. 15th, 2012