Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge",...

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Two-particle correlations on log(p t ) and the log(p t ) dependence of angular (η,Φ) correlation features in Au+Au at GeV at STAR Elizabeth Oldag for the STAR Collaboration May 7, 2012 Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge 200 = NN s

Transcript of Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge",...

Page 1: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

Two-particle correlations on log(pt) and the log(pt) dependence of angular (η,Φ) correlation features

in Au+Au at GeV at STAR

Elizabeth Oldag for the STAR Collaboration May 7, 2012

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

200=NNs

Page 2: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 2

• Correlation Measure:

• Number of correlated pairs per final state particle

• Reference Pairs

• Angular correlations use mixed pairs (tracks from two different but similar events)

• Mixed pairs in momentum space show an enhancement in the two-particle distribution due to physics

• We hypothesize our signal of interest is jets and therefore need to select a reference that is absent of jets

- Soft particle spectrum of the two-component model (ref:arXiv:0710.4504v1[hep-ph]).

• Data Set: Au+Au Collisions at 200 GeV, ~11.5 Million Minimum Bias Events, pt>0.15 GeV/c, |η| < 1, full φ

Event A

Event B

x2

x1

Sibling Pairs

x2

x1

Mixed Pairs

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Two-particle correlation measure

Efficiency corrected ref. dist.

∑∆∆

∆×

′′

′=∆

,..., zNch mixsoft

totsoft

ref ρρ

ρρρ

ρρ

ref ref

ref ref

mix sib

ρ ρ ρ

ρ ρ

ρ ρ ρ ∆

→ ∆ = − '

Page 3: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 3

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Motivation for a log(pt) measure

yt

yt

yt

yt refρρ∆

pt

pt pt

refρρ∆ pt

22 where,ln ππ

mpmm

pmy tttt

t +=

+=

Fig. pt vs. yt, the dotted line indicates a log(pt) reference

Page 4: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4

• The reference distribution was event normalized with a correction factor

– α ensures the correlation measure is zero in the absence of true correlations

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

(yt,yt) correlations – Analysis Details

( ) ( )( ) ( )1

,,

,, 2

21

2121

−=

−=

chch

ch

ttref

ttrefttsib

NNN

yyn

yynyynα

αρρ

=1 with the bias correction

mixsib NN / Centrality Bin Nch Range

0 [2,15) 1.078

1 [15,35) 1.014

2 [35,68) 1.014

3 [68,117) 1.012

[117,152) 0.998

[152,187) 0.998

… … …

4

( )2

and

1 Find

chmix

chchsib

NN

NNN

=

−=

from the real event multiplicity distribution in each multiplicity bin

For centrality info refer to arXiv:1109.4380

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E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 5

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Charge Independent (yt,yt) correlations

•All pairs •Charge Independent •pt ≥ 0.15 GeV/c

•Peak at (3,3) (1.4 GeV/c) persists through higher centralities

*STAR Preliminary

Sharp Transition (ST) in ang. corr arXiv:1109.4380 ~46-55%

Page 6: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 6

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

(yt,yt) Away-side US

•Peak ranging from 2.5 to 3.5 in yt (~1.0-2.5 GeV/C) •Amplitude grows as centrality increases but little change in peak position.

LS

•Similar behavior to US pairs

|ΦΔ| > π/2

*STAR Preliminary

Page 7: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 7

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

(yt,yt) Same-side |ΦΔ| < π/2

US •Two peaks appear from mid- to most-central collisions.

•Raises the question if this is a separation of pion and proton pairs (tbd from PID results) (ref: arXiv:0710.4504)

LS

•Signals from HBT evident along the diagonal.

*STAR Preliminary

ST

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E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 8

• Goal: To fit the correlations with a simple fit function that quantifies the main features of the correlation (the bump at (yt , yt) ~ (3,3)). – A cut window will allow us to exclude soft correlation structures and

edges. • Fit Function:

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

))/()/)*2*(((5.010

220, ∆∆ΣΣ +−−+= tyttytt yyyeAAfit σσ

21

21

ttt

ttt

yyyyyy

−=+=

Σ

yt1

yt2 ytΣ ytΔ

(yt,yt) Fitting Model

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Model Residual

Data

Peak position remains steady, similar results for LS AS

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Fitting Results (Unlike-sign away-side)

*STAR Preliminary

2/part

bin

NN

≡ν

Page 10: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 10

Model

Data

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Fitting Results (Unlike-sign same-side)

*STAR Preliminary

Residual

ST

Page 11: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 11

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Fitting Results (Unlike-sign same-side)

Cent. Bins [0-3]

One 2D Gaussian

Cent. Bins [4-10],

Two 2D Gaussians

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E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 12

• Is the peak in (yt,yt) correlations from semi-hard jet fragmentation?

• HIJING

• Interested in exploring other models: AMPT (see Lanny’s talk), SpheRio, NexSPheRio, HydJet

Plots from M. Daugherity

Jets Off

Jets On

yt

yt

yt

yt

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Model Comparisons

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E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 13

• Minimum bias angular correlations signal a change in the correlation structures as centrality increases from peripheral to central

• How are the pairs that contribution to each of these correlation features distributed in momentum space?

• Further evidence gathered by selecting pairs from distinct momentum regions and fitting with a well studied 11 parameter fit function

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Angular Correlations

arXiv:1109.4380

84-93% 18-28 % 55-64% 0-5% ST

Page 14: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 14

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Momentum dependence of angular correlation structures

5

η Δ Φ Δ

ref ρ ρ ∆

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0 1 2 3 4 5 6

8 7 9 10 11 12

13 14 15 16 17

18 19 20 21

22 23 24

25 26

27

y t,1

y t,2

∑ ∆ ≈ ∆

i ref ref,tot

i ref

yt all ref N N

ρ ρ

ρ ρ ,

,

2D Fit

Weighting factors are applied to each cut bin to accurately compare fit values

1D Gaussian

2D Gaussian

Page 15: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 15

Fitting ambiguities with higher order harmonics • p+p and peripheral Au+Au data clearly show 4 corr structures which can be described with a choice of 4 fit

model components. Each are required (otherwise the omitted structure appears in the residuals).

• With increasing centrality the fit model fails due to the development of an additional structure. Another model

component is required that can describe it (we chose a quadrupole)

• The data can be fit with higher-order harmonics but in the absence of a clear signal in the residuals such

terms are not required. Including them introduces fitting ambiguities.

– v3 conspires with v1 and v2 to fit the away-side structure which is fit equally well with just a v1 and v2 term.

– v3 on the same side is representing the η elongation of the same-side peak

– The v3 amplitude is not representing a required cos(3ΦΔ) term and instead obscuring the interpretation of the other fit

components.

dipole quadrupole sextupole D’+Q’+S

Difference:

Net effect of v3 is a SS 1DG

D+Q

+

+ +

=

=

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E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 16

• Map back onto (yt,yt) space the features of interest, for example: – Volume of the 2D Gaussian – The integral of the 2D Gaussian over a range of ηΔ – Amplitude of the dipole, quadrupole

• Prefactor applied in order to get the number of correlated pairs in an

angular correlation feature, for pairs in a (yt,yt) bin, per final state particle on yt

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Displaying Fit Results

softtsoftt dydN

dydN

,2,,1,

1

yt

Volume

= yt

×

Page 17: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 17

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Momentum dependence of same-side peak

*STAR Preliminary

Page 18: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 18

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Momentum dependence of same-side peak as a function of ηΔ

*STAR Preliminary

Peak position does not soften in yt as the cut region moves towards the edge of the 2D Gaussian

ηΔ ΦΔ

ηΔ ΦΔ

ηΔ ΦΔ

Page 19: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 19

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Momentum dependence of dipole

*STAR Preliminary

Page 20: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 20

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Momentum dependence of quadrupole

*STAR Preliminary

Page 21: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 21

• The extended correlation on ηΔ, commonly referred to as the

“ridge”, is not comprised of softer pairs relative to the center of

the 2D Gaussian peak.

• We are unable to determine if correlated pairs in the same-

side structure originate from one or more physical processes.

– Until then we should not assume that pairs beyond a

certain ηΔ value are not correlated from jets

Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Ridge discussion

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E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 22

• Momentum correlations complete the six dimensional correlation space (pt1,Φ1,η1,pt2,Φ2,η2).

– A broad peak is observed extending from yt of 2-4 (0.5-4.0 GeV/c) – The peak position remains constant as centrality increases. – HIJING, which models peripheral Au+Au collisions, suggests this broad peak in

(yt,,yt) is due to jet fragmentation.

• The correlated pairs that contribute to the 2D Gaussian structure, hypothesized to be from minijets, have a momentum distribution peaked around (yt,1,yt,2)=(3,3) (1.4 GeV/c).

• The dipole (hypothesized to be the dijet away-side) does not soften with an increase in centrality.

• In Progress: Repeat same cut scheme but with identified particles. Study correlations of baryons vs. mesons and strange vs. non-strange particles.

Conclusion Outline: •Momentum Correlations •Relationship to Angular Corr. •Implications for ridge

Page 23: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

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Back-Up Slides

Page 24: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 24

pt integrated 2D Gaussian amplitude versus centrality

arXiv:1109.4380

Page 25: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 25

arXiv:0710.4504

Page 26: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 26

Comparing Χ2 of fit model with and without sextupole

• Corresponding to slide 15 – 9-18% Au-Au 200 GeV

• No sextupole (standard model) Χ2/dof = 3.91 • With sextupole Χ2/dof = 3.67

Page 27: Two-particle correlations on log(pt) and the log(pE. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 4 • The reference distribution was event normalized with a correction

E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 27

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Construct ratio of 2D histograms:

Ratios of 2D histograms are computed bin-by-bin

Exact decomposition

Details to weighted sum of (yt,yt) dependent axial correlations (slide 14)