MIXED HARMONIC FLOW CORRELATIONS

Transcription

1 MIXED HARMONIC FLOW CORRELATIONS RECENT RESULTS ON SYMMETRIC CUMULANTS Matthew Luzum F. Gardim, F. Grassi, ML, J. Noronha-Hostler; arxiv: Universidade de São Paulo NBI Mini Workshop 19 September, 216 MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 1 / 22

2 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

3 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

4 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

5 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

6 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution 2π dn N dφ 1 + 2v n cos n(φ ψ n ) n p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

7 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution 2π dn N dφ 1 + 2v n cos n(φ ψ n ) n dn pairs d 3 p a d 3 p b = dn d 3 p a dn d 3 p b + C(pa, p b ) p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

8 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution 2π dn N dφ 1 + 2v n cos n(φ ψ n ) n dn pairs d 3 p a d 3 p b = dn quad. d 3 p a d 3 p b d 3 p c d 3 p d = dn d 3 p a dn dn d 3 p a d 3 p b + C(pa, p b ) dn dn d 3 p b d 3 p c dn d 3 p d +... p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

9 INTRODUCTION EVOLUTION OF HEAVY-ION COLLISION Hydro picture: system thermalizes and expands as fluid Particles emitted independently at end of evolution 2π dn N dφ 1 + 2v n cos n(φ ψ n ) n dn pairs d 3 p a d 3 p b = dn quad. d 3 p a d 3 p b d 3 p c d 3 p d = dn d 3 p a dn d 3 p b dn d 3 p a dn d 3 p b dn d 3 p c dn d 3 p d p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

10 INTRODUCTION FLUCTUATIONS; A HISTORY 2π N dn dφ = 1 + 2v 2 cos 2φ +... If no fluctuations: only v 2 at midrapidity (+ small v 4 ) Fluctuations are important! No symmetry = more harmonics, flow coefficients are vectors Flow vectors fluctuate from event-to-event p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 3 / 22

11 INTRODUCTION FLUCTUATIONS; A HISTORY 2π N dn dφ = 1 + 2v 2 cos 2φ +... If no fluctuations: only v 2 at midrapidity (+ small v 4 ) Fluctuations are important! No symmetry = more harmonics, flow coefficients are vectors Flow vectors fluctuate from event-to-event p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 3 / 22

12 INTRODUCTION FLUCTUATIONS; A HISTORY 2π N dn dφ = (v n e inψn )e inφ n=1 If no fluctuations: only v 2 at midrapidity (+ small v 4 ) Fluctuations are important! No symmetry = more harmonics, flow coefficients are vectors Flow vectors fluctuate from event-to-event p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 3 / 22

13 INTRODUCTION FLUCTUATIONS; A HISTORY 2π N dn dφ = (V n )e inφ n=1 If no fluctuations: only v 2 at midrapidity (+ small v 4 ) Fluctuations are important! No symmetry = more harmonics, flow coefficients are vectors Flow vectors fluctuate from event-to-event p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 3 / 22

14 INTRODUCTION FLUCTUATIONS; A HISTORY 2π N dn dφ = (V n )e inφ n=1 If no fluctuations: only v 2 at midrapidity (+ small v 4 ) Fluctuations are important! No symmetry = more harmonics, flow coefficients are vectors Flow vectors fluctuate from event-to-event p t φ ψ RP MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 3 / 22

15 INTRODUCTION 1 p >.5 GeV, η <2.5 T ATLAS Pb+Pb s NN =2.76 TeV 1 L int = 7 µb 1 p >.5 GeV, η <2.5 T ATLAS Pb+Pb s NN =2.76 TeV 1 L int = 7 µb 2 1 p >.5 GeV, η <2.5 T ATLAS Pb+Pb s NN =2.76 TeV 1 L int = 7 µb 1 ) 2 p(v ) 3 p(v ) 4 p(v centrality: 1% 5 1% 2 25% 3 35% 4 45% 6 65%.1.2 v centrality: 1% 5 1% 2 25% 3 35% 4 45%.5.1 v 3 centrality: 1% 5 1% 2 25% 3 35% 4 45% v 4.5 Fluctuations imply a set of statistical properties: Magnitude of flow coefficients have event-by-event distribution Flow vectors at different momenta can have non-trivial correlation Different harmonics can also have non-trivial correlations MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 4 / 22

16 v 2 3 {2} INTRODUCTION (b).1.5 3%--4% LS US.1 (c) CI 3%--4% %--5% Fluctuations imply a set of statistical properties: Magnitude of flow coefficients have event-by-event distribution Flow vectors at different momenta can have non-trivial correlation Different harmonics can also have non-trivial correlations η MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 4 / 22

17 v 2 3 {2} INTRODUCTION (b).1.5 3%--4% LS US.1 (c) CI 3%--4% %--5% Fluctuations imply a set of statistical properties: Magnitude of flow coefficients have event-by-event distribution Flow vectors at different momenta can have non-trivial correlation Different harmonics can also have non-trivial correlations η MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 4 / 22

18 INTRODUCTION ELLIPTIC FLOW ALONE Glauber initial Glauber conditions CGC initial CGC conditions.1 PHOBOS.1 η/s=1-4 PHOBOS v 2.8 η/s= η/s=.8.2 η/s=.16 v 2.8 η/s=.8.6 η/s=.16.4 η/s= N Part N Part (ML & Romatschke, Phys.Rev. C78 (28) 34915) Can fit v 2 with different combinations of initial cond. + viscosity = Neither initial conditions nor viscosity individually constrained MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 5 / 22

19 ADDING CONSTRAINTS ADD v 3 : v 2 v (a) v, p = GeV/c 2 T PHENIX KLN + 4 πη/s = 2 Glauber + 4πη/s = 1 (1).1 (c) v, p = GeV/c 3 T.8 UrQMD + 4πη/s = Glauber + 4πη/s = 1 (2).6 1 (b) v, p = GeV/c T PHENIX, arxiv: N part N part 2 1 (d) v, p = GeV/c 3 T Combining v 2 and v 3 can rule out models of initial conditions... but different combinations of initial conditions and medium properties are still consistent with data: MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 6 / 22

20 ADDING CONSTRAINTS ADD v 3 : v 2 v (a) v, p = GeV/c 2 T PHENIX KLN + 4 πη/s = 2 Glauber + 4πη/s = 1 (1).1 (c) v, p = GeV/c 3 T.8 UrQMD + 4πη/s = Glauber + 4πη/s = 1 (2).6 1 (b) v, p = GeV/c T PHENIX, arxiv: N part N part 2 1 (d) v, p = GeV/c 3 T Combining v 2 and v 3 can rule out models of initial conditions... but different combinations of initial conditions and medium properties are still consistent with data: MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 6 / 22

21 ADDING CONSTRAINTS CALCULATIONS VS RHIC DATA v 2 v 3 v NeXSPheRIO NeXSPheRIO PHENIX NeXSPheRIO NeXSPheRIO PHENIX NeXSPheRIO NeXSPheRIO PHENIX v NeXSPheRIO NeXSPheRIO p T GeVc (F. Gardim, F. Grassi, ML, J.-Y. Ollitrault, Phys.Rev.Lett. 19 (212) 2232 ) NeXus initial conditions + η/s = at RHIC MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 7 / 22

22 ADDING CONSTRAINTS CALCULATIONS VS LHC1 DATA v n 2 1/ v 2 v 3 v 4 v 5 ALICE data v n {2}, p T >.2 GeV η/s = centrality percentile (C. Gale, S. Jeon, B. Schenke, P. Tribedy, R. Venugopalan, Phys.Rev.Lett. 11 (213) 1232 ) IP-Glasma initial conditions + η/s =.2 at LHC run 1 MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 8 / 22

23 ADDING CONSTRAINTS CALCULATIONS VS LHC1 DATA v n { 2 } (a) η/s =.2 η/s =param1 η/s =param2 η/s =param3 η/s =param4 ALICE v n { 2 } LHC 2.76 TeV Pb +Pb p T =[.2 5.] GeV centrality [%] (H. Niemi, K.J. Eskola, R. Paatelainen, Phys.Rev. C93 (216) 2497 ) EKRT initial conditions + various η/s(t ) at LHC run 1 MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 9 / 22

24 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Basic building block is n-particle correlation: m n1,n 2,...,n m cos(n 1 φ + n 2 φ... + n m φ) m particles (flow) = V n1 V n2... V nm ni =... 2 particles 1 M... N pairs i=1 j i events... W... events W Typical weights: W 2 = M(M 1) W 4 = M(M 1)(M 2)(M 3) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 1 / 22

25 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Basic building block is n-particle correlation: m n1,n 2,...,n m cos(n 1 φ + n 2 φ... + n m φ) m particles (flow) = V n1 V n2... V nm ni =... 2 particles 1 M... N pairs i=1 j i events... W... events W Typical weights: W 2 = M(M 1) W 4 = M(M 1)(M 2)(M 3) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 1 / 22

26 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Basic building block is n-particle correlation: m n1,n 2,...,n m cos(n 1 φ + n 2 φ... + n m φ) m particles (flow) = V n1 V n2... V nm ni =... 2 particles 1 M... N pairs i=1 j i events... W... events W Typical weights: W 2 = M(M 1) W 4 = M(M 1)(M 2)(M 3) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 1 / 22

27 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Basic building block is n-particle correlation: m n1,n 2,...,n m cos(n 1 φ + n 2 φ... + n m φ) m particles (flow) = V n1 V n2... V nm ni =... 2 particles 1 M... N pairs i=1 j i events... W... events W Typical weights: W 2 = M(M 1) W 4 = M(M 1)(M 2)(M 3) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 1 / 22

28 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Basic building block is n-particle correlation: m n1,n 2,...,n m cos(n 1 φ + n 2 φ... + n m φ) m particles (flow) = V n1 V n2... V nm ni =... 2 particles 1 M... N pairs i=1 j i events... W... events W Typical weights: W 2 = M(M 1) W 4 = M(M 1)(M 2)(M 3) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 1 / 22

29 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Basic building block is n-particle correlation: m n1,n 2,...,n m cos(n 1 φ + n 2 φ... + n m φ) m particles (flow) = V n1 V n2... V nm ni =... 2 particles 1 M... N pairs i=1 j i events... W... events W Typical weights: W 2 = M(M 1) W 4 = M(M 1)(M 2)(M 3) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 1 / 22

30 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Examples: v n {2} = (flow) = 2 n, n v 2 n, Enforce gap in rapidity between pair = suppressed non-flow v n {4} 4 4 n,n, n, n n, n (flow) = v 2 n 2 v 2 n 2 Suppresses non-flow without rapidity gaps MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

31 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Examples: v n {2} = (flow) = 2 n, n v 2 n, Enforce gap in rapidity between pair = suppressed non-flow v n {4} 4 4 n,n, n, n n, n (flow) = v 2 n 2 v 2 n 2 Suppresses non-flow without rapidity gaps MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

32 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Examples: v n {2} = (flow) = 2 n, n v 2 n, Enforce gap in rapidity between pair = suppressed non-flow v n {4} 4 4 n,n, n, n n, n (flow) = v 2 n 2 v 2 n 2 Suppresses non-flow without rapidity gaps MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

33 MIXED HARMONIC CORRELATIONS FLOW MEASUREMENTS Examples: v n {2} = (flow) = 2 n, n v 2 n, Enforce gap in rapidity between pair = suppressed non-flow v n {4} 4 4 n,n, n, n n, n (flow) = v 2 n 2 v 2 n 2 Suppresses non-flow without rapidity gaps MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

34 MIXED HARMONIC CORRELATIONS SYMMETRIC CUMULANTS Can also define a mixed-harmonic cumulant: SC(n, m) 4 n,m, n, m 2 n, n 2 m, m (flow) = v 2 n v 2 m v 2 n v 2 m. Independent information better encoded in normalized quantity: SC(n, m) NSC(n, m) 2 n, n 2 m, m (flow) = v 2 n v 2 m v 2 n v 2 m v 2 n v 2 m. (Bilandzic, Christensen, Gulbrandsen, Hansen, Zhou, Phys. Rev. C 89, no. 6, 6494 (214)) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

35 MIXED HARMONIC CORRELATIONS SYMMETRIC CUMULANTS Can also define a mixed-harmonic cumulant: SC(n, m) 4 n,m, n, m 2 n, n 2 m, m (flow) = v 2 n v 2 m v 2 n v 2 m. Independent information better encoded in normalized quantity: SC(n, m) NSC(n, m) 2 n, n 2 m, m (flow) = v 2 n v 2 m v 2 n v 2 m v 2 n v 2 m. (Bilandzic, Christensen, Gulbrandsen, Hansen, Zhou, Phys. Rev. C 89, no. 6, 6494 (214)) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

36 MIXED HARMONIC CORRELATIONS CENTRALITY BINNING v n 2 1/ v 2 v 3 v 4 v 5 ALICE data v n {2}, p T >.2 GeV η/s = centrality percentile The magnitude of all v n increase from central peripheral = impact parameter fluctuations increase NSC(n, m) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

37 MIXED HARMONIC CORRELATIONS CENTRALITY BINNING εsc3, centrality binning MCKLN centrality Large centrality bins produce a bias Biggest effect in central collisions, where v n vs. centrality steepest MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

38 MIXED HARMONIC CORRELATIONS EVENT WEIGHTING NSC(n, m) (flow) = v 2 n v 2 m v 2 n v 2 m v 2 n v 2 m Typically, 4-particle correlations have M 4 event weights, while 2-particle correlations have M 2 weighting = first term and second term are sensitive to different events = negative bias with large centrality bins MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

39 MIXED HARMONIC CORRELATIONS EVENT WEIGHTING NSC(n, m) (flow) = v 2 n v 2 m v 2 n v 2 m v 2 n v 2 m Typically, 4-particle correlations have M 4 event weights, while 2-particle correlations have M 2 weighting = first term and second term are sensitive to different events = negative bias with large centrality bins MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

40 MIXED HARMONIC CORRELATIONS EVENT WEIGHTING NSC(n, m) (flow) = v 2 n v 2 m v 2 n v 2 m v 2 n v 2 m Typically, 4-particle correlations have M 4 event weights, while 2-particle correlations have M 2 weighting = first term and second term are sensitive to different events = negative bias with large centrality bins MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

41 MIXED HARMONIC CORRELATIONS EVENT WEIGHTING εsc3, rcbknbd 5 binsm 5 bins avg 1 binsm avg 1 bins centrality = negative bias with large centrality bins No bias with small centrality bins MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

42 MIXED HARMONIC CORRELATIONS FIRST CALCULATION η/s η/s =.2 η/s =param1 η/s =param2 η/s =param3 η/s =param T [MeV] v n { 2 } (a) η/s =.2 η/s =param1 η/s =param2 η/s =param3 η/s =param4 LHC 2.76 TeV Pb +Pb p T =[.2 ALICE v n { 2 } 5.] GeV centrality [%] (H. Niemi, K.J. Eskola, R. Paatelainen, Phys.Rev. C93 (216) 2497 ) Various η/s(t ) fit single harmonic data at RHIC + LHC. Other mixed harmonic measurements ruled out some MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

43 MIXED HARMONIC CORRELATIONS FIRST CALCULATION cos(4(ψ2 Ψ 4 )) SP cos(6(ψ2 Ψ 3 )) SP LHC 2.76 TeV Pb +Pb cos(8(ψ2 Ψ 4 )) SP centrality [%].8.7 η/s =.2 η/s =param1.6 η/s =param2.5 η/s =param3.4 η/s =param4.3 ATLAS.2 p.1 T =[.5 5.] GeV centrality [%] cos(6(ψ2 Ψ 6 )) SP centrality [%] cos(12(ψ2 Ψ 4 )) SP centrality [%] (H. Niemi, K.J. Eskola, R. Paatelainen, Phys.Rev. C93 (216) 2497 ) cos(6(ψ3 Ψ 6 )) SP centrality [%] centrality [%] Various η/s(t ) fit single harmonic data at RHIC + LHC. Other mixed harmonic measurements ruled out some MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

44 Hydrodynamics MIXED HARMONIC 1 CORRELATIONS SC(4,2), η/s=.2 2 SC(4,2), η/s(t) param4 FIRST CALCULATION / SC(3,2), FIRST η/s=.2 DATA 3 SC(4,2), η/s(t) param1 AMPT: String Melting SC(3,2), η/s(t) param1 SC(3,2) SC(3,2), η/s(t) param4 SC(4,2) SC(m,n)/ v v 2 n 2 m SC(4,2)/ v v SC(3,2)/ v 2 v Hydrodynamics SC(4,2)/ v v, η/s= SC(4,2)/ v v, η/s(t) param1,2,3,4 4 2 SC(3,2)/ v v, η/s= SC(3,2)/ v v, η/s(t) param1,2,3,4 3 2 AMPT: String Melting SC(3,2)/ v v 3 2 SC(4,2)/ v v 4 2 ε 2 m / ε ε SC(m,n) 2 n MC-Glauber 1 SC(4,2) / ε ε, WN ALICE, arxiv: ; Niemi, Eskola, Paatelainen, ε SC(4,2) / ε ε, BC ε 4 2 / ε ε, WN 3 2 Doesn t seem to fit NSC(3,2) and NSC(4,2).6 ε SC(3,2) / ε ε, BC ε 3 2 SC(4,2)/ v v 4 2 (may be affected by centrality binning effects).4.2 SC(3,2)/ v v 3 2 NSC(3,2) insensitive to η/s(t ), NSC(4,2) is sensitive MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

45 Hydrodynamics MIXED HARMONIC 1 CORRELATIONS SC(4,2), η/s=.2 2 SC(4,2), η/s(t) param4 FIRST CALCULATION / SC(3,2), FIRST η/s=.2 DATA 3 SC(4,2), η/s(t) param1 AMPT: String Melting SC(3,2), η/s(t) param1 SC(3,2) SC(3,2), η/s(t) param4 SC(4,2) SC(m,n)/ v v 2 n 2 m SC(4,2)/ v v SC(3,2)/ v 2 v Hydrodynamics SC(4,2)/ v v, η/s= SC(4,2)/ v v, η/s(t) param1,2,3,4 4 2 SC(3,2)/ v v, η/s= SC(3,2)/ v v, η/s(t) param1,2,3,4 3 2 AMPT: String Melting SC(3,2)/ v v 3 2 SC(4,2)/ v v 4 2 ε 2 m / ε ε SC(m,n) 2 n MC-Glauber 1 SC(4,2) / ε ε, WN ALICE, arxiv: ; Niemi, Eskola, Paatelainen, ε SC(4,2) / ε ε, BC ε 4 2 / ε ε, WN 3 2 Doesn t seem to fit NSC(3,2) and NSC(4,2).6 ε SC(3,2) / ε ε, BC ε 3 2 SC(4,2)/ v v 4 2 (may be affected by centrality binning effects).4.2 SC(3,2)/ v v 3 2 NSC(3,2) insensitive to η/s(t ), NSC(4,2) is sensitive MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

46 Hydrodynamics MIXED HARMONIC 1 CORRELATIONS SC(4,2), η/s=.2 2 SC(4,2), η/s(t) param4 FIRST CALCULATION / SC(3,2), FIRST η/s=.2 DATA 3 SC(4,2), η/s(t) param1 AMPT: String Melting SC(3,2), η/s(t) param1 SC(3,2) SC(3,2), η/s(t) param4 SC(4,2) SC(m,n)/ v v 2 n 2 m SC(4,2)/ v v SC(3,2)/ v 2 v Hydrodynamics SC(4,2)/ v v, η/s= SC(4,2)/ v v, η/s(t) param1,2,3,4 4 2 SC(3,2)/ v v, η/s= SC(3,2)/ v v, η/s(t) param1,2,3,4 3 2 AMPT: String Melting SC(3,2)/ v v 3 2 SC(4,2)/ v v 4 2 ε 2 m / ε ε SC(m,n) 2 n MC-Glauber 1 SC(4,2) / ε ε, WN ALICE, arxiv: ; Niemi, Eskola, Paatelainen, ε SC(4,2) / ε ε, BC ε 4 2 / ε ε, WN 3 2 Doesn t seem to fit NSC(3,2) and NSC(4,2).6 ε SC(3,2) / ε ε, BC ε 3 2 SC(4,2)/ v v 4 2 (may be affected by centrality binning effects).4.2 SC(3,2)/ v v 3 2 NSC(3,2) insensitive to η/s(t ), NSC(4,2) is sensitive MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

47 MIXED HARMONIC CORRELATIONS (m, n) v NSC.8 (a).6.4 (b) NSC(m, n) points: ALICE data curves: VISH (c).2.2 v NSC (4, 2) v NSC (5, 2) v NSC (5, 3) (m, n) ε.4 (d) ε NSC (4, 2) (e) ε NSC (5, 2) NSC(m, n).4 (f) ε NSC (5, 3) NSC.2.2 (m, n) v NSC.2 (g) NSC(m, n).2 (h) NSC(m, n).2 ε NSC (m, n) MC-Glb ε NSC (m, n) MC-KLN ε NSC (m, n) AMPT Centrality Percentile (m, n) ε NSC.2 v NSC (3, 2) ε 4 5 ε.2 (i) NSC (3, 2).2 (j) NSC (4, 3) Centrality Percentile NSC(m, n).2 v NSC (4, 3) Centrality Percentile.2 v NSC (m,n) MC-Glb v NSC (m,n) MC-KLN v NSC (m,n) AMPT solid: η/s=.8 dashed: η/s=.2 (MC-Glb/KLN) dashed: η/s=.16 (AMPT) Centrality Percentile Centrality Percentile Centrality Percentile Zhu, Zhou, Xu, Song; arxiv: NSC(3,2) also insensitive to magnitude of η/s (NSC(4,2) sensitive) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

48 MIXED HARMONIC CORRELATIONS NSC(m,n) Glauber 2GeV 1% bins NSC(m,n) ideal 3,2 ideal 4,2 1%avg bins+m η/s(t) 3,2 η/s(t) 4, centrality % Even that observation can depend on centrality binning! MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/216 2 / 22

49 MIXED HARMONIC CORRELATIONS NSC(3,2) VS. INITIAL CONDITIONS εsc3, rcbk MCKLN MCGlauber rcbknbd NeXus IPGlasma centrality NSC(3,2) also insensitive to initial conditions Points to universal feature of hydrodynamic paradigm? MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

50 MIXED HARMONIC CORRELATIONS NSC(3,2) VS. INITIAL CONDITIONS εsc3, rcbk MCKLN MCGlauber rcbknbd NeXus IPGlasma centrality NSC(3,2) also insensitive to initial conditions Points to universal feature of hydrodynamic paradigm? MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

51 MIXED HARMONIC CORRELATIONS SUMMARY/CONCLUSIONS Mixed harmonic correlation measurements shed new light on heavy-ion collisions Symmetric cumulants measure correlation between magnitudes of flow vectors of different harmonics, with suppression of non-flow correlations Different sensitivity to initial conditions and viscosity than previous observables. MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

52 EXTRA SLIDES EXTRA SLIDES MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

53 EXTRA SLIDES CUMULANT EXPANSION Idea: (Teaney, Yan; Phys.Rev. C83 (211) 6494) Characterize density by moments (or cumulants) of 2-D Fourier transform ρ(k) = d 2 xρ(x)e ik x (Small m = small power of k in Taylor series) Can write complete hydro response as set of functions v n e inψn = f (W m,n ) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

54 EXTRA SLIDES CUMULANT EXPANSION Idea: (Teaney, Yan; Phys.Rev. C83 (211) 6494) Characterize density by moments (or cumulants) of 2-D Fourier transform ρ(k) = d 2 xρ(x)e ik x = ρ m,n k m e inφ k n,m ρ m,n r m e inφ (Small m = small power of k in Taylor series) Can write complete hydro response as set of functions v n e inψn = f (W m,n ) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

55 EXTRA SLIDES CUMULANT EXPANSION Idea: (Teaney, Yan; Phys.Rev. C83 (211) 6494) Characterize density by moments (or cumulants) of 2-D Fourier transform ρ(k) = d 2 xρ(x)e ik x = ρ m,n k m e inφ k n,m ρ m,n r m e inφ W (k) = log(ρ(k)) = n,m W m,n k m e inφ k (Small m = small power of k in Taylor series) Can write complete hydro response as set of functions v n e inψn = f (W m,n ) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

56 EXTRA SLIDES CUMULANT EXPANSION Idea: (Teaney, Yan; Phys.Rev. C83 (211) 6494) Characterize density by moments (or cumulants) of 2-D Fourier transform ρ(k) = d 2 xρ(x)e ik x = ρ m,n k m e inφ k n,m W m,n r m e inφ W (k) = log(ρ(k)) = n,m W m,n k m e inφ k (Small m = small power of k in Taylor series) Can write complete hydro response as set of functions v n e inψn = f (W m,n ) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

57 EXTRA SLIDES CUMULANT EXPANSION Idea: (Teaney, Yan; Phys.Rev. C83 (211) 6494) Characterize density by moments (or cumulants) of 2-D Fourier transform ρ(k) = d 2 xρ(x)e ik x = ρ m,n k m e inφ k n,m W m,n r m e inφ W (k) = log(ρ(k)) = n,m W m,n k m e inφ k (Small m = small power of k in Taylor series) Can write complete hydro response as set of functions v n e inψn = f (W m,n ) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

58 EXTRA SLIDES CUMULANT EXPANSION Idea: (Teaney, Yan; Phys.Rev. C83 (211) 6494) Characterize density by moments (or cumulants) of 2-D Fourier transform ρ(k) = d 2 xρ(x)e ik x = ρ m,n k m e inφ k n,m W m,n r m e inφ W (k) = log(ρ(k)) = n,m W m,n k m e inφ k (Small m = small power of k in Taylor series) Can write complete hydro response as set of functions v n e inψn = f (W m,n ) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

59 EXTRA SLIDES CUMULANT EXPANSION: TAYLOR SERIES IN ε m,n Must make quantities with correct symmetries out of W m,n r m e inφ If anisotropies are small, can arrange in Taylor series. E.g., to first order: V n v n e inψn = C n+2p,n W n+2,p p= If hydro is sensitive to large scale structure, first terms are most important (smaller powers of k in Fourier transform). If single term sufficient: v n e inψn = C r n e inφ r n C ε n e inφn (ε n = lowest k mode of initial density) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

60 EXTRA SLIDES CUMULANT EXPANSION: TAYLOR SERIES IN ε m,n Must make quantities with correct symmetries out of W m,n r m e inφ If anisotropies are small, can arrange in Taylor series. E.g., to first order: V n v n e inψn = C n+2p,n W n+2,p p= If hydro is sensitive to large scale structure, first terms are most important (smaller powers of k in Fourier transform). If single term sufficient: v n e inψn = C r n e inφ r n C ε n e inφn (ε n = lowest k mode of initial density) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

61 EXTRA SLIDES CUMULANT EXPANSION: TAYLOR SERIES IN ε m,n Must make quantities with correct symmetries out of W m,n r m e inφ If anisotropies are small, can arrange in Taylor series. E.g., to first order: V n v n e inψn = C n+2p,n W n+2,p p= If hydro is sensitive to large scale structure, first terms are most important (smaller powers of k in Fourier transform). If single term sufficient: v n e inψn = C r n e inφ r n C ε n e inφn (ε n = lowest k mode of initial density) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

62 EXTRA SLIDES CUMULANT EXPANSION: TAYLOR SERIES IN ε m,n Must make quantities with correct symmetries out of W m,n r m e inφ If anisotropies are small, can arrange in Taylor series. E.g., to first order: V n v n e inψn = C n+2p,n W n+2,p p= If hydro is sensitive to large scale structure, first terms are most important (smaller powers of k in Fourier transform). If single term sufficient: v n e inψn = C r n e inφ r n C ε n e inφn (ε n = lowest k mode of initial density) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

63 EXTRA SLIDES CUMULANT EXPANSION: TAYLOR SERIES IN ε m,n Must make quantities with correct symmetries out of W m,n r m e inφ If anisotropies are small, can arrange in Taylor series. E.g., to first order: V n v n e inψn = C n+2p,n W n+2,p p= If hydro is sensitive to large scale structure, first terms are most important (smaller powers of k in Fourier transform). If single term sufficient: v n e inψn = C r n e inφ r n C ε n e inφn (ε n = lowest k mode of initial density) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

64 EXTRA SLIDES FINAL PREDICTION % change in <p t > centrality percentile MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

65 EXTRA SLIDES FINAL PREDICTION % change in v Initial condition Hydro response centrality percentile MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

66 EXTRA SLIDES FINAL PREDICTION 25 2 Initial condition Hydro response % change in v centrality percentile MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

67 EXTRA SLIDES PREDICTION PREVIEW: ABSOLUTE v 2 {2} AND v 3 {2}.12.1 Prediction ALICE 2.76 TeV centrality percentile MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

68 EXTRA SLIDES FIRST DATA FROM RUN 2 v n TeV v 2 {2, η >1} v 3 {2, η >1} v 4 {2, η >1} v 2 {4}.1 ALICE Pb-Pb v 2 {6} v 2 {8} 2.76 TeV v 2 {2, η >1} v 3 {2, η >1} v 4 {2, η >1} v 2 {4} Hydrodynamics 5.2 TeV, Ref.[27] v 2 {2, η >1} v 3 {2, η >1}.5 (a) Ratio Ratio v 2 v 3 v 4 Hydrodynamics, Ref.[25] η /s(t), param1 η/s = (c) Centrality percentile (b) (ALICE Collaboration, Phys.Rev.Lett. 116 (216) 13232) MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

69 EXTRA SLIDES COMPARISON WITH DATA % change in v Prediction ALICE % centrality MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22

70 EXTRA SLIDES COMPARISON WITH DATA 2 Prediction ALICE % change in v % centrality MATT LUZUM (USP) MIXED HARMONIC CORRELATIONS 19/9/ / 22