Summary of flow and its correlation in ALICE

Transcription

1 Summary of flow and its correlation in ALICE Myunggeun Song Yonsei Univ. November, 6 HIM ibs

2 Based on PRL his Presentation based on one Letter in six is highlighted as a Suggestion due to its particular importance, innovation, and broad appeal Reports from referee he first and only observables for measure correlation between magnitudes of flow harmonics It was demonstrated that this method has a good potential to validate different heavy-ion models and has high chances to be used in new measurements at the LHC energies, in particular in 5 ev PbPb collisions and possibly in small systems like ppb collisions. he results are of significant importance for the field and without doubt worth to be published in PRL. And also contains follow up paper (ongoing, IRC round stage) Flow harmonic correlations November, 6 /

3 Introduction - Heavy ion collision At RHIC(GeV) and LHC(.76eV) energies, lattice calculation of QCD predicts a transition to new state of matter, the so-called quark-gluon Plasma (QGP) hese QCD state are thought to consist of asymptotically free quarks and gluons, and expected to occur around = 5 MeV Hydrodynamics is consider as the most successful approach to describe QGP state Flow harmonic correlations November, 6 /

4 Introduction - Hydrodynamics In spite of its simple-looking Lagrangean of QCD L = ψ i (iγ µd µ ij mδ ij )ψ j FµvαF µvα () It is very difficult to make any predictions directly from QCD (due to its complexity which mainly arises from the interactions of the gluons, the strong coupling...) Need coarse-grained theory If one is only interested in macroscopic properties, degree of freedom and their interactions are not necessary new equation of states(eos) from Hydrodynamics P = P(ɛ, n) with additional parameter the transport coefficient such as η, ζ, λ One of the most important observables supporting to the discovery of the QGP and validation of hydrodynamic is the high values of elliptic flow Quantum Chromodynamics, W. Greiner et al., Springer Flow harmonic correlations November, 6 /

5 Introduction - Flow Large elliptic flow v in Heavy-ion collisions Fourier decomposition is used to quantify the anisotropic distribution of produced particles dn dφ = v π + (v n cos n(ϕ ψ n)) π n= he large elliptic flow discovered at RHIC energies, and continues to increase also at LHC energies. Large elliptic flow(v ) has indicated fluid behavior of matter created Particles are more boosted in higher pressure gradient direction (for High p, energy lose of jet) Share viscosity (η) plays a key role during coordinate space anisotropy momentum space anisotropy Flow harmonic correlations November, 6 5 /

6 Shear viscosity he large share viscosity is related to the large mean free path (λ mfp ) he large mean free path weakly coupled long distance until next collision easy mixing he short mean free path mixing takes long time Share viscosity smears out flow difference (diffusion) Share viscosity reduces non-sphericity Since, η/s α s ln(/α s ) QCD coupling α s decreases as temperature η/s must increase as incresases Low temperature hadron gas is known to have large viscosity P. Kovtun, D.. Son and A. O. Starinets, Phys. Rev. Lett. 9, 6 (5) η/s must have a minimum near c Figure: R. A. Lacey et al., Phys. Rev. Lett. 98, 9 (7) Flow harmonic correlations November, 6 6 /

7 Flow Odd and higher harmonics flow Not only almomd shape geometry but also its fluctuation formed anisotropic distribution of produced particles Currently, anisotropic ditribution is understood as the result of Initial density profile which is fluctuate event-by-event Hydrodynamic response (both linear and non-linear) which is related to transport coefficient Flow harmonic correlations November, 6 7 /

8 Extracting η/s from experimental data: Initial conditions MC-Glauber MC-KLN v /ε MC-KLN (a) hydro (η/s) + UrQMD v {} / ε part / KLN v / ε part KLN (/S) dn ch /dy (fm - ) η/s..8.6 MC-Glauber (b) hydro (η/s) + UrQMD v {} / ε part / Gl v / ε part Gl η/s..8.6 (/S) dn ch /dy (fm - ) IP-Glasma C. Shen, S. A. Bass,. Hirano, P. Huovinen, Z. Qiu, H. Song and U. Heinz J. Phys. G 8, 5 () [arxiv:6.65[nucl-th]] η/s.8 - Large uncertainty from the initial conditions (MC-Glauber vs. MC-KLN) Initial energy density B. Schenke,P. ribedy,r. Venugopalan Phys.Rev.Lett. 8 () 5 MC-KLN :. Hirano, U. W. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys. Lett. B66, 99 (6); A. Adil, H.J. Drescher, A. Dumitru, A. Hayashigaki, Y. Nara Phys. Rev. C, 7 (6), p. 95 MC-Glauber : Z. Qiu and U. W. Heinz, Phys. Rev. C8, 9 ();Z. Qiu, C. Shen, and U. W. Heinz, Phys. Lett. B77,5 ();S. Esumi (PHENIX Collaboration), J.Phys.G G8, (). IP-Glasma : B. Schenke,P. ribedy,r. Venugopalan Phys.Rev.Lett. 8 () 5 need better observable than single flow, more sensitive to initial conditions and η/s Flow harmonic correlations November, 6 8 /

9 Correlation between flow-vectors Correlations of v m and v n A linear correlation coefficient c(v n,v m) was proposed (H. Niemi et al.,phys. Rev. C 87, 59 ()) to study the correlations between v n and v m c(v m, v n) = (vm vm ev )(vn vn ev ) ev σ vn σ vm c(v, v ) is sensitive to initial conditions and insensitive to η/s, c(v, v ) is sensitive to both However, this observable is not easily accessible in flow measurements which are relying on two- and multi-particle correlations. Flow harmonic correlations November, 6 9 /

10 Correlation between flow-vectors Symmetric -harmonic -particle Cumulants New Observable : Symmetric -harmonic -particle Cumulants (SC) cos(mϕ +nϕ mϕ nϕ ) c = cos(mϕ +nϕ mϕ nϕ ) By construction, not sensitive to non-flow effects inter-correlations of various event-planes = cos[m(ϕ ϕ )] cos[n(ϕ ϕ )] vmv n vm vn It is non-zero if the event-by-event amplitude fluctuations of v n and v m are (anti-)correlated. Also SC(m,n) can be normalizable with vm v n SC(m, n) norm = SC(m, n)/ vm vn Normalized SC(m,n) reflects the degree of the correlation. While SC(m,n) contains both the degree of the correlation and individual v n. Ante Bilandzic et al., Phys. Rev. C 89, 69 () Flow harmonic correlations November, 6 /

11 Correlation between flow-vectors Analysis details Event selection and track selection are just followed as like ALICE SC short paper Dataset : LHCh, HIJING(Hijing PbPb LHCh), AMP Set String Melting Rescattering Denote as AMP LHCfb OFF ON AMP, default AMP LHCfc ON ON AMP, String melting AMP LHCfa ON OFF AMP, String melting w/o hadronic rescattering Event selection : zvtx < cm, cut on outliers rackcut condition : η <.8, < p < 5. GeV/c PC Only tracks SC(m,n) with various model comparison (AMP, Hydro simulation.. ) SC(,), SC(,) + higher harmonics SC(5,), SC(5,), SC(,) ( + normalized ) p dependence SC(,) and SC(,) ( + normalized ) Paper preparation group twiki page 5 PC ( Ante Bilandzic, DongJo Kim(Rep.), Myunggeun Song, You Zhou ) Proposed IRC ( Sergei Voloshin, Sudhir Raniwala, Peter Christiansen, Shinichi Esumi ) list of the PAG presentations and analysis notes arxiv:6.766, submitted to PRL hanks to the production team for x stat., Flow harmonic correlations November, 6 /

12 Results List of works Measure SC(, ) and SC(, ) (and also normalized SC(, ) and SC(, )) Compare with HIJING simulation to check the effect of Non-flow Measure SC(m, n) with higher order flow harmonics (up to 5th order) Evaluate with various Hydrodynamic simulation ( pqcd + viscous, AMP, VISH+(iEbE)...) with various initial conditions and η/s Check the p dependence Cross-check with Scalar Product method oymc simulation (+ PYHIA jet) Systematic uncertainty estimation Contribution on SC(m, n) paper arxiv:6.766 (Phys.Rev.Lett.) Follow up paper (long SC paper) is being preparing (IRC review round ongoing) Flow harmonic correlations November, 6 /

13 Results Result :SC(m,n) and Comparison to Hydrodynamics prediction SC(m,n) ALICE Pb Pb SC(,) SC(,) s NN =.76 ev (a) SC(m,n)/ v v m n.8.6. ALICE Pb Pb s NN =.76 ev SC(,)/ v v SC(,)/ v v (b) parm (η/s = ) parm (η/s()) parm (η/s()) parm (η/s()) parm (η/s()). parm (η/s = ) parm (η/s()) parm (η/s()) parm (η/s()) parm (η/s()) 5 Centrality Percentile.6 5 Centrality Percentile SC(m,n) results shows that the correlation between v and v is positive, and v and v is negative indicates finding v > v in an event enhances the probability of finding v > v and finding v < v in that event. hese trends are also shown in hydro prediction 6 too But, none of η/s parametrization can reproduce exactly same result as data for both of SC(,) and SC(,) at the same time he differences between data and hydrodynamic predictions become worse in normalized SC 6 Phys. Rev. C 9, 97 (6), H.Niemi et al Flow harmonic correlations November, 6 /

14 Results SC(m, n) results with HIJING: is Non-flow contribution? SC(m,n) Pb-Pb s NN =.76 ev SC(,) SC(,) ALICE Preliminary HIJING SC(,) SC(,) ALI-PREL = = cos(mϕ +nϕ mϕ nϕ ) c cos(mϕ +nϕ mϕ nϕ ) cos[m(ϕ ϕ )] cos[n(ϕ ϕ )] vm v n vm vn It is found that both v mv n and v m v n are non-zero in HIJING, but calculation of SC(m,n) from HIJING are compatible with zero Moreover, the results from like-sign method which is another approach to estimate non-flow effects, show only few % differences (See Backup) suggests SC measurements are not coming from non-flow constirbution Flow harmonic correlations November, 6 /

15 Results Result : SC with higher order harmonics SC(m,n).. ALICE Pb Pb s NN =.76 ev SC(,) ( x.) SC(,) ( x.) SC(5,) SC(5,) SC(,) (a) n v m SC(m,n)/ v.5 ALICE Pb Pb s NN =.76 ev SC(,)/ v v SC(,)/ v v SC(5,)/ v v 5 SC(5,)/ v v 5 SC(,)/ v v (b) SC(,) is negative(anti-correlated), while SC(5,) and SC(5,) are positive(correlated). he strength of correlation between v 5 and v is stronger than v 5 and v in SC(m,n) however in NSC(m,n), the strength of correlation become weaker than v 5 and v the strength of higher order SC(m, n) is weaker than lower order correlations not because correlation is weak, but because its single flow is weak. Flow harmonic correlations November, 6 5 /

16 Results Results : Comparison with the Correlation from the Eccentricity If there is only linear response (v n ɛ n), then NSC(m, n) in coordinate space are able to capture NSC(m, n) in the momentum space SC(m, n) ɛ/ ɛ n ɛ m ( ɛ nɛ m ɛ n ɛ m )/ ɛ n ɛ m () Where the ɛ n is the nth order coordinate space anisotropy 7 /<ε m ><ε n > ε SC(m,n) /<ε m ><ε n > ε SC(m,n) ALICE Pb Pb s NN NSC(,) NSC(,) (WN) ε NSC(,) (BC) ε =.76 ev. ALICE Pb Pb s NN NSC(,) NSC(,) (WN) ε NSC(,) (BC) ε =.76 ev A large deviation of NSC(, ) indicates the contribution of the non-linear response of initial condition though hydrodynamic evolution NSC(, ) describes the data better than NSC(, ), because the NSC(, ) appears to be sensitive only to initial conditions and not sensitive to hydrodynamic properties. 7 defined in Phys. Rev. C 8 () 99 Flow harmonic correlations November, 6 6 /

17 Results Lower order SC : Comparison with Hydrodynamic calculation SC(,) SC(,).5 ALICE Pb Pb s NN =.76 ev.5 SC(,) VISH+ (AMP, η/s=.8).5 VISH+ (AMP, η/s=.6) VISH+ (MC KLN, η/s=.8).5 VISH+ (MC KLN, η/s=).5.5 ALICE Pb Pb s =.76 ev NN SC(,) VISH+ (AMP, η/s=.8) VISH+ (AMP, η/s=.6) VISH+ (MC KLN, η/s=.8) VISH+ (MC KLN, η/s=) VISH+ (MC Glauber, η/s=.8) VISH+ (MC Glauber, η/s=).5.5 VISH+ (MC Glauber, η/s=.8) VISH+ (MC Glauber, η/s=) ><v > SC(,)/<v..5 SC(,)/<v ><v > SC(,)/(<v ><v >) SC(,)/(<v ><v >) 5 5 Hydro calculation with VISH+ with two different share viscosity (large η/s : dashed line, small η/s : solid line), and three initial conditions Prediction with large share viscosity all failed to capture the SC(m,n). he sign of the NSC(,) is opposite to the data in most central range(where the fluctuation dominant region) NSC(,) does not show sensitivity to initial conditions or η/s parametrizations, while NSC(,) is sensitive to both Flow harmonic correlations November, 6 7 /

18 5 Results NN 5 Higher order SC : Comparison with Hydrodynamic calculation SC(5,). 5 ALICE Pb Pb s =.76 ev NN SC(5,) VISH+ (AMP, η/s=.8) VISH+ (AMP, η/s=.6) VISH+ (MC KLN, η/s=.8) VISH+ (MC KLN, η/s=) VISH+ (MC Glauber, η/s=.8) VISH+ (MC Glauber, η/s=) SC(5,).6.. ALICE Pb Pb s =.76 ev SC(5,) VISH+ (AMP, η/s=.8) VISH+ (AMP, η/s=.6) VISH+ (MC KLN, η/s=.8) VISH+ (MC KLN, η/s=) VISH+ (MC Glauber, η/s=.8) VISH+ (MC Glauber, η/s=) SC(,) ALICE Pb Pb s =.76 ev NN SC(,)..6.8 VISH+ (AMP, η/s=.8) VISH+ (AMP, η/s=.6). VISH+ (MC KLN, η/s=.8) ><v > 5 SC(5,)/<v SC(5,)/(<v ><v >) ><v > 5 SC(5,)/<v..6.. SC(5,)/(<v ><v >) > SC(,)/<v ><v VISH+ (MC KLN, η/s=) VISH+ (MC Glauber, η/s=.8) VISH+ (MC Glauber, η/s=) SC(,)/(<v ><v >) Prediction with large share viscosity all failed to capture the SC(m,n). Among the models with small η/s, data was well described by one from AMP initial condition. But still cannot capture the data quantitively for most of centrality ranges Flow harmonic correlations November, 6 8 /

19 Results Comparison with various AMP simulations SC(,) SC(,).5 ALICE Pb Pb s NN =.76 ev.5 SC(,) AMP, default AMP, string melting AMP, string melting w/o hadronic rescattering ALICE Pb Pb s NN =.76 ev SC(,) AMP, default AMP, string melting.5 AMP, string melting w/o hadronic rescattering.5 ><v > SC(,)/<v. SC(,)/(<v ><v >) SC(,)/<v ><v >..8 SC(,)/(<v ><v >) AMP default (without string melting) describes better than other configurations For NSC(, )(left, bottom), the AMP default settings(red, open circle) describe the data up to 5% centralities in good agreements However, for the original SC(, )(top), AMP does not described data well. It might come from the difference of single v n of AMP and data, not comes from correlation Flow harmonic correlations November, 6 9 /

20 Results Single v n measurment with data, and AMP v.6 ALICE(PRL.6.) η > (ref) AMP, string melting w/o hadronic AMP, default AMP, string melting v ALICE(PRL.6.) η > (ref) AMP, string melting w/o hadronic AMP, default AMP, string melting Data/Pub..9 Data/Pub Centrality[%] Centrality[%] indeed the signel v n from AMP, default (gray triangle) are relatively smaller than v n from data ( p cumulants method with η >. ) Flow harmonic correlations November, 6 /

21 Results Data AMP Correction AMP s SC(, ) with single v n from Data ALICE Pb Pb 8 s NN =.76eV SC(m,n) <v ><v >, Data 6 <v ><v >, AMP default.5 ALICE Pb Pb s =.76eV NN.5 SC(,) AMP, default AMP x (<v ><v >) / (<v ><v >) ) Ratio. Ratio As the results, the normalize factor v v of AMP is always smaller than Data s When we correction single v n differences of AMP and Data, the original SC(, ) with AMP, default come close to data Flow harmonic correlations November, 6 /

22 Results Higher order SC : Comparison with various AMP simulations SC(5,). 5 ALICE Pb Pb s NN SC(5,) =.76 ev AMP, default SC(5,). ALICE Pb Pb s NN =.76 ev SC(5,).8 AMP, default AMP, string melting SC(,).. AMP, string melting AMP, string melting w/o hadronic rescattering AMP, string melting w/o hadronic rescattering ALICE Pb Pb s NN =.76 ev SC(,).5..8 AMP, default AMP, string melting. AMP, string melting w/o hadronic rescattering ><v > 5 SC(5,)/<v.8.6 SC(5,)/(<v ><v >) 5 ><v > 5 SC(5,)/<v.5 SC(5,)/(<v ><v >) 5 SC(,)/<v ><v > SC(,)/(<v ><v >) Normalized SC(m,n) were well described by AMP default. Other settings are failed to reproduce the data, and even fail to predict negative correlation of SC(, ) Flow harmonic correlations November, 6 /

23 Results ransvers momentum dependence of normalized SC(m,n) as function of p,min (p,min < p < 5), and comparison to model 5% 5 % % ALICE Pb+Pb S NN =.76 ev SC(,) / (<v ><v >) > <v >) AMP, default AMP, string melting AMP, string melting w/o hadronic rescattering SC(,) / (<v % % 5% p ( p < p < 5 ),min,min No clear trends of p dependence for normalized SC(,) AMP default (String melting OFF, Rescattering ON) describes better Flow harmonic correlations November, 6 /

24 Results ransvers momentum dependence of normalized SC(m,n) as function of p,min (p,min < p < 5), and comparison to model.. 5% 5 % % ALICE Pb+Pb S =.76 ev NN SC(,) / (<v ><v >) >) > <v SC(,) / (<v. %.5 AMP, default AMP, string melting AMP, string melting w/o hadronic rescattering % 5% p ( p < p < 5 ),min,min No clear trends of p dependence for normalized SC(,) AMP default (String melting OFF, Rescattering ON) describes better Flow harmonic correlations November, 6 /

25 Results ransvers momentum dependence of SC(m,n) < p,min <.7GeV /c SC(m,n) ALICE Pb Pb s NN =.76 ev SC(,) SC(,) ><v n > m SC(m, n)/<v.8.6. ALICE Pb Pb s NN =.76 ev SC(,)/<v ><v > SC(,)/<v ><v > 5 < p. < p. < p.5 < p.7 < p < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c..6 < p. < p. < p.5 < p.7 < p < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c 5 5 SC results with various min p cuts (left) shows clear p dependence of SC. No significant difference in NSC (right) might indicate that p dependence of SC(m,n) mainly results from p dependence of v n rather than p dependent correlation between flow harmonics Flow harmonic correlations November, 6 5 /

26 Results ransvers momentum dependence of SC(m,n).7 < p,min <.5GeV /c SC(m,n)..5 ALICE Pb Pb s NN SC(,) SC(,) =.76 ev ><v n > m SC(m, n)/<v.8.6. ALICE Pb Pb s NN =.76 ev SC(,)/<v ><v > SC(,)/<v ><v >.5. < p.8 < p.9 < p. < p. < p.5 < p < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c 5..6 < p.8 < p.9 < p. < p. < p.5 < p < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c < 5. GeV/c 5 When expand minimum p cut from.8 to.5 GeV/c SC results with various min p cuts shows clear p dependence of SC (as like previous page) NSC tends to decrease as the minimum p or the centrality increase. But it s not clearly seen in errors Hints of possible viscous correction for the equilbrium distribution at hadronic freeze-out? Flow harmonic correlations November, 6 6 /

27 Results Optional pages Flow harmonic correlations November, 6 7 /

28 Results Measuring SC(m,n) with Scalar Product method Moments can be obtained with normalized Q-vector with sub event groups which seperated η gap range 8 hen SC(m, n) can be expressed as M (V n) kn (Vn ) ln = (Q na ) kn (QnB) ln n (Q An Q BnQ Am Q Bm) (Q An Q Bn) (Q Am Q Bm) where Q n = M M i= einφ i, η gap between A, B subgroups n () but In red part there are auto(self) correlation term between Q An Q Am and Q Bn Q Bm, theses could be corrected by following terms M B Re(Q Bm+n Q AmQ An ) M A Re(Q Am+n Q Bn Q Bm ) + M A M B Re(Q Am+n Q Bm+n ))) 8 Rajeev S. Bhalerao et al, Flow harmonic correlations November, 6 8 /

29 Results Method comparison, QC vs SP SC(m,n) ALICE Pb Pb s NN =.76 ev SC(,) : SP method ( η>.8) SC(,) : Cumulant method SC(,) : SP method ( η>.8) SC(,) : Cumulant method HIJING SC(,) SC(m,n) / <v ><v m > n..8 ALICE Pb Pb s NN =.76 ev SC(,)/<v ><v > : SP method ( η>.8) SC(,)/<v ><v > : Cumulant method SC(,)/<v ><v > : SP method ( η>.8) SC(,)/<v ><v > : Cumulant method HIJING SC(,) SP / Cumulant method ratio.5 SP / Cumulant method ratio Ratio.5 Ratio SC(m,n) with HIJING are compatible with zero for both methods here are some systematic differences (especially for SC(,)) between two methods 9. We are not sure whether different methods respond differently to flow fluctuations or if we can rule out non-flow effects in the end 9 different sensitivities to flow fluctuations and non-flow effects Flow harmonic correlations November, 6 9 /

30 Results ransvers momentum dependence of SC(m,n) with SP method Extend to hihger p bins up to minimum cut =.5GeV/c SC(m,n) ALICE Pb Pb s NN =.76 ev SC(,) (SP, η >.8) SC(,) (SP, η >.8) < p < 5. GeV/c.8 < p < 5. GeV/c.9 < p < 5. GeV/c. < p < 5. GeV/c. < p < 5. GeV/c.5 < p < 5. GeV/c As same as QC results, clear p dependence for SC(m,n) Also p dependence of normalized SC(m,n) is shown SC(m, n)/<v ><v n > m.5 5 < 5. GeV/c ) Ratio to ( < p SC(,) SC(,).8 < p < 5. GeV/c.9 < p < 5. GeV/c. < p < 5. GeV/c. < p < 5. GeV/c.5 < p < 5. GeV/c ALICE Pb Pb s.5 NN =.76 ev SC(,)/<v ><v > (SP, η >.8) SC(,)/<v ><v > (SP, η >.8) 5 < p < 5. GeV/c.8 < p < 5. GeV/c.9 < p < 5. GeV/c. < p < 5. GeV/c. < p < 5. GeV/c.5 < p < 5. GeV/c.5 5 Flow harmonic correlations November, 6 /

31 Summary Summary We have measured SC(m,n) which quantify the relationship between event-by-event fluctuations of two different flow harmonics. cos(mϕ +nϕ mϕ nϕ ) c = vm v n v m v n Symmetric cumulants (SC) and normalized SC (NSC), which quantify the relationship between flow harmonics are measured and we found SC(,) and SC(,) are negative(anti-correlated) and SC(,), SC(5,) and SC(5,) are positive(correlated) for all centralities. Higher order SC (SC(5,), SC(5,), SC(,)) are smaller than lower order SC(SC(,), SC(,)), while NSC are comparable Also from model comparison differenent order harmonic correltions have different sensitivities to the initial conditions and the system properties. In most central collision region (%-%, where the fluctuation dominant), the sign of correlation is different between data and hydrodynamic model calculation VISH+ with large η/s failed to cpature the centrality dependence of SC(m,n), espeically for higher orders From p dependence study SC results with various min p cuts shows clear p dependence of SC. No significant difference in Normalized SC up to p =.7 GeV/c might indicate that p dependence of SC(m,n) mainly comes from p dependence of v n rather than p dependent correlation between flow harmonics within the errors. Flow harmonic correlations November, 6 /

32 backup Backup Slides Backup pages Flow harmonic correlations November, 6 /

33 ε ε ε ε backup Results from short SC paper (arxiv:6.766) SC(m,n) v SC(m,n)/ v m n SC(m,n) / ε ε ε m n ALICE Pb-Pb SC(,) SC(,) Hydrodynamics s =.76 ev NN SC(,), η/s= SC(,), η/s() param SC(,), η/s() param SC(,), η/s= SC(,), η/s() param SC(,), η/s() param SC(,)/ v v SC(,)/ v Hydrodynamics MC-Glauber v SC(,)/ v SC(,)/ v SC(,)/ v SC(,)/ v SC(,) SC(,) SC(,) SC(,) / ε / ε / ε / ε v v v v ε ε ε ε, η/s=, η/s() param,,,, η/s=, η/s() param,,,, WN, BC, WN, BC AMP: String Melting SC(,) SC(,) AMP: String Melting SC(,)/ v SC(,)/ v SC(,)/ v v v v SC(,)/ v v v and v are correlated, v and v are anti-correlated in all centralities, the centrality dependence can not be described quantitively by any existing calculations. Normalized SC(,) is sensitive to initial conditions and insensitive to η/s, normalized SC(,) is sensitive to both SC(m,n) measurements provide strong constrains on the η/s in hydro in combination with the individual flow harmonics, discriminating the inputs to hydro model with different parameterizations of η/s. SC(m, n) provides strong constrains to initial conditions and η/s. Flow harmonic correlations November, 6 /

34 backup Hydro results from RHIC to LHC, v n vs η/s( ) v n { } v { },v { } / (a) η/s = η/s =param η/s =param η/s =param η/s =param LHC.76 ev Pb +Pb p =[ ALICE v n { } 5.] GeV centrality [%] (b) η/s = RHIC GeV Au +Au η/s =param p =[.5.] GeV η/s =param η/s =param η/s =param SAR v { } SAR v { } / centrality [%] v { } v { } (a) η/s =. η/s = η/s =. η/s =param LHC.76 ev Pb +Pb p =[ 5.] GeV { } ALICE v centrality [%] (b) η/s =. LHC.76 ev Pb +Pb η/s = p =[ 5.] GeV η/s =. η/s =param ALICE v { } centrality [%] H. Niemi, K.J. Eskola, R.Paatelainen (arxiv:55.677) Flow harmonic correlations November, 6 /

35 backup Hydro results from RHIC to LHC, SC(m,n) vs η/s( ) hv v i hv ihv i hv v i hv ihv i.8 6 /s =.6 /s = param. /s = param /s = param. /s = param centrality [%] LHC.76eVPb + Pb p =...5. GeV centrality [%] / v v v v / v v v v η/s = η/s =param η/s =param η/s =param η/s =param centrality [%] LHC.76 ev Pb +Pb p = 5. GeV centrality [%] H. Niemi, K.J. Eskola, R.Paatelainen (arxiv:55.677) Flow harmonic correlations November, 6 /

36 backup AMP results from RHIC to LHC SC m,n,-m,-n -6 AMP.76 ev.5 SC = v,,-,- SC = v.5,,-, v - v v v - v v centrality percentile SC m,n,-m,-n -6 AMP GeV 8 v v - v v v - v 6 v v - v v v - v v v - v v v - v Ante Bilandzic et al., Phys. Rev. C 89, 69 () v v v v v v (mb) (mb) (mb, no rescattering) (mb) (mb) (mb, no rescattering) 5 6 centrality percentile Flow harmonic correlations November, 6 5 /

37 backup initial energy density profile from RHIC to LHC e [GeV/fm ] e [GeV/fm ] 5 pqcd ebc 5 ewn 5 % 5 (a) y [fm] 5 % (c) pqcd ebc ewn y [fm] LHC Pb +Pb.76 ev x [fm] RHIC Au +Au GeV x [fm] e [GeV/fm ] e [GeV/fm ] % (b) pqcd ebc ewn y [fm] 8 6 % (d) pqcd ebc ewn y [fm] LHC Pb +Pb.76 ev x [fm] RHIC Au +Au GeV x [fm] Figure: Energy density profiles, H. Niemi, K.J. Eskola, R.Paatelainen (arxiv:55.677) Flow harmonic correlations November, 6 6 /

38 backup Can we rule out non-flow effects? SC(m,n) results with HIJING are zeros for all centralities for both method, even with the high p bins ( see B?? ). hose suggested that SC(m,n) is insensitive to non-flow effect. In additional to HIJING results, we now have studied it explicitly with PYHIA jet particles on SC(m,n), this implies the largest effect from the particles which stem from jets in PYHIA in mid central collisions. dn/dp /N evt Centrality 5 Centrality 5 Centrality Centrality Centrality Centrality 5 Centrality 5 6 PYHIA phard > 5 [GeV/c] Setup same oymc as previous slides. Use PYHIA8 to impose jets into oymc. implement PYHIA jet particles for every events. s =.76eV PhaseSpace : phatmin> 5 GeV /c Ratio Pythia/Data p [GeV/c] Flow harmonic correlations November, 6 7 /

39 backup Comparison two method : SC(m,n) results with oymc From low to high multiplicity Calculate SC analytically based on MC study. SC(m,n) SC(,) with oymc Input SC value SC(,) : SP SC(,) : QC SC(m,n) SC(,) with oymc Input SC value SC(,) : SP SC(,) : QC Ratio..5. SP / QC ratio Multiplicity Ratio.5. SP / QC ratio Multiplicity we observe discrepancy between two methods. his effect is most pronounced in lowest multiplicity % QC method recover better the input value than SP method SP method results are always smaller than QC for all multiplicity bins. p8 Flow harmonic correlations November, 6 8 /

40 backup oymc + Jet results SC(m,n). SC(m,n) SC(,) with oymc Input SC value SC(,) : SP SC(,) : QC SC(,) : SP + Jet SC(,) : QC + Jet.5.5 SC(,) with oymc Input SC value SC(,) : SP SC(,) : QC SC(,) : SP + Jet SC(,) : QC + Jet Ratio Multiplicity Ratio Multiplicity When we implement particles from jets in PYHIA (Open markers), strengths of correlation from both SP and QC methods are getting smaller. he response to particles from jet are similar for both QC and SP methods. few % difference in central collisions and % effect in 5-6% centrality bin. hese observations hold both for SC(,) and SC(,). Flow harmonic correlations November, 6 9 /