two-particle correlations on log(pt) and the log(pe. oldag, u.t. austin, int workshop - the...
TRANSCRIPT
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
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 ∆
→ ∆ = − '
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
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
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%
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
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
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
E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 9
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
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
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
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
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
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
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
+
+ +
=
=
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
×
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
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
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
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
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
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
E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 23
Back-Up Slides
E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 24
pt integrated 2D Gaussian amplitude versus centrality
arXiv:1109.4380
E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 25
arXiv:0710.4504
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
E. Oldag, U.T. Austin, INT Workshop - The "Ridge", May 2012 27
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Ratios of 2D histograms are computed bin-by-bin
Exact decomposition
Details to weighted sum of (yt,yt) dependent axial correlations (slide 14)