pt-inclusive 2-particle correlations; p-p, Cu-Cu, Au-Au BES

Transcription

1 pt-inclusive 2-particle correlations; p-p, Cu-Cu, Au-Au BES Duncan May 7,

2 Agenda Review of Methods Minimum-bias Jets in pp - the reference system Review 200, 62 GeV Au-Au Compare Cu-Cu to Au-Au Beam Energy Scan 200, 62, 39, 27, 19, 11 and 7 GeV Au-Au 2

3 Correlation Measures We can construct a correlation measure from the standard definition: Cov( x, y ) Corr ( x, y ) = σ xσ y Pearson's correlation coefficient: [ 1,1] the gold-standard correlation measure for the last 100 years. ρ(p1,p2) = 2 particle density in momentum space sibling p 1, p 2 Event 1 Event 2 reference p 1, p 2 Covariance Δρ = object - reference p 1, p 2 = sib p 1, p 2 ref p 1, p 2 = 2 p 1, p 2 1 p 1 1 p 2 In this talk I use a pt integral measure. ( 1, 2) independent of project onto ( 1, 2) nearly independent of project onto 1 na nb = ρ ref Normalize σ aσ b ε aε b Δρ(n) ρref 2D autocorrelation on (, ) from 6D space is a per-particle measure This measure comes from a direct application of the standard 3 pairs correlation function, and all we have to do is count

4 p-p collisions at 200 GeV are well described by Hijing with jets minbias hard AS jet minbias hard SS jet Data Hijing, with jets soft projectile fragments HBT soft minbias hard Data has HBT, e+e-, possible pileup Well described by Hijing with jets Hijing without jets does not look like pp at 200 GeV Hijing, no jets soft 4

5 Fit Function (5 easy pieces) STAR Preliminary Proton-Proton fit function Δρ ρref soft Δρ ρref = φδ + φδ ηδ φδ ηδ hard Δρ ρref ηδ For 200, 62 GeV Au-Au 1D Gaussian is important only in peripheral collisions longitudinal fragmentation 1D gaussian HBT, e+e2d exponential Au-Au fit function Use proton-proton fit function plus cos(2φδ) quadrupole term (~ elliptic flow). Include cos(2 ) in proton-proton fit? What about cos(3 )? dipole Away-side -cos(φ) Same-side Minijet Peak, 2D gaussian cos(2φδ) φδ 5 quadrupole ηδ

6 Multiplicity dependence of 200 GeV proton-proton collision 2 N tracks 4 5 N tracks 7 8 N tracks N tracks N tracks 18 STAR PRELIMINARY With cos(2 ) Without cos(2 ) Minbias A2D SS AD/2 SS STAR PRELIMINARY 2AQ Evolution with multiplicity/centrality Including cos(2 ) improves 2, minimal changes of other parameters 2/DOF 12 M collisions 6

7 200 GeV p-p Centrality nch b/b0 S from data H from rescale minimum-bias distribution with soft S and hard H components assumption (DIS): hard (QCD) processes occur at smaller radii, larger nch curves: Au-Au Glauber model adapted to p-p b/b0 ν jets b/b0 AQ ν Au-Au systematics b/b0 b/b0 AQ jet structure nonjet quadrupole 7

8 Review of 200, 62 GeV AuAu data and fits. AuAu200 Data 84-93% 55-65% 38-46% 9-18% 1-5% residuals 200 GeV AuAu (2001) 62 GeV AuAu (2004) 200 GeV pp minbias Fit captures large scale structure SS amplitude increase with centrality, beam energy SS width increases with centrality, not beam energy AS dipole follows SS amplitude Quadrupole shape is same, amp depends on beam energy 8

9 Au-Au cos(3 ) is redundant If we include cos(3 ) in Estruct fit model the 2D exponential and 1D Gaussian on do not change. Changes in Fourier components are st st st A S cos 3 AQ A Q cos 2 A D A D cos A 0 A 0 where st refers to standard fit without cos(3 ) % 55-65% ST 38-46% 9-18% 200 GeV 62 GeV Maximum set to A2D value for each centrality cos(3 ) describes part of the same-side peak. SS 1D peak not systematically significant. 200 GeV 9 62 GeV 1-5%

10 Comparison of CuCu and AuAu, 200 and 62 GeV A2D SS AD/2 2AQ SS 200 GeV AuAu 62 GeV AuAu 200 GeV CuCu 62 GeV CuCu 2/DOF 200 GeV CuCu: same-side amplitude and width increase is at slightly higher than AuAu. Amplitude does not turn over, turn over in AuAu is probably not geometric 62 GeV CuCu: hard to see increase above LGS in same-side amplitude but width increase at same place as 200 GeV CuCu cos(2 ) seems to be pushed up in b. We are investigating possibility of centrality fluctuation causing these differences. 10

11 Lévy Gaussian Width Fluctuations fluctuation tails Gaussian relative η width variance: A 2D { 1 1 2n 1/ n 0 2 n } 1/4n =σ σ2 η/σ 2 η { } 1 A2D exp 2 2 PRC 81, (2010) Sec. IV-C 11 width fluctuations produce non-gaussian tails

12 fluctuation tails 10-20% fit ν 3.6 n= GeV Cu-Cu data STAR PRELIMINARY data-quad-offset residuals ν 4 n= % STAR PRELIMINARY jets jet width fluctuations just above sharp transition no ridge, no v3 12

13 Beam Energy Scan STAR has data at beam energies of 200, 62, 39, 27, 19, 11 and 7 GeV 84-93% 55-65% 38-46% 9-18% STAR PRELIMINARY %

14 Beam Energy Scan, kinematic differences with energy Beam rapidity changes at 200 GeV ybeam = 6.06 STAR TPC acceptance ~ 1/6 at 11 GeV ybeam = 3.15 STAR TPC acceptance ~ 1/3 Away-side may show more curvature because of larger relative acceptance 40-50% 30-40% Ebeam ymax % 19 GeV AuAu, 2D exponential subtracted At 200 and 62 GeV the away-side was flat for these centralities Standard fit sometimes has trouble converging, offset plus 1D Gaussian have three DOF but only need two { } 1 A0 A G exp 2 2 A'0 A p 2 (npos/nneg increases with lower beam energy, particle production channels change) 14

15 11 GeV need same-side peak, 7 GeV does not 11 GeV AuAu 30-40% 20-30% 7 GeV AuAu 30-40% 10-20% 20-30% 10-20% Data Residuals, no SS peak Residual with SS peak Significant difference when SS peak included Note that 2D exponential tries to fit sharp peak and broad SS peak. SS peak makes no difference 15

16 Au-Au Beam Energy Scan fit parameters A2D SS SS 200 GeV 62 GeV 39 GeV 27 GeV 19 GeV 11 GeV 7 GeV STAR PRELIMINARY AD/2 2/DOF 2AQ 7 GeV fit without same-side 2D Gaussian Don't have track efficiencies for 39 GeV and lower, amplitudes will change cos(2 ) shape is independent of beam energy. Same-side width is independent of beam energy. 16

17 Conclusions Proton-proton collisions; SS peak is due to hard scattering Charge multiplicity is a proxy for centrality SS peak amplitude, AS cos( ) increase with centrality cos(2 ) looks like it exists and centrality trend makes sense Cu-Cu collisions; SS peak amplitude does not turn over for most central collisions SS peak amplitude, width has sharp transition at slightly higher than Au-Au Peak of cos(2 ) shape pushed to slightly higher than for Au-Au dependence may be affected by centrality fluctuations, currently under study Au-Au collisions; For peripheral collisions SS peak is just like proton-proton peak. Adding cos(3 ) re-arranges terms, is a description of SS peak, not a new phenomenon. Need to understand tracking efficiencies, changes due to kinematic limits, but: Centrality dependence of cos(2 ) amplitude independent of beam energy SS peak required down to beam energy of 11 GeV broadening of SS peak independent of beam energy 17

18 Interplay between same-side width and 1D Gaussian width? SS 1D Gauss Peripheral 19 GeV AuAu. 2D exponential, cos( ), cos(2 ) subtracted. (This is not pileup.) 80-90% 70-80% 60-70% Fit with Ap instead of 1D Gaussian (Ap, fit parameters) A2D SS AD/2 2AQ SS SS width changes for peripheral bins SS amplitude and width may follow trends better BUT... not a good reason to favor this parameterization. cos(2 ) amplitude does not change. 2/DOF 18