1. Perspective for the measurement of D+ elliptic flow
F. Prino1, E. Bruna2, M. Masera2
1 INFN – Sezione di Torino
2 Dip. Fisica Sperimentale, Università di Torino
Alice Physics Week, December

2. Alice Physics Week, December 5-9 2005
Elliptic flow
Anisotropy in particle azimuthal distribution due to collective motion (flow) of particles
Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions
Fourier expansion of particle azimuthal distribution relative to the reaction plane
Reaction plane (YRP) defined by beam direction and impact parameter
Elliptic flow x y
YRP
Alice Physics Week, December

3. Alice Physics Week, December 5-9 2005
Flow and anisotopy
Elliptic Flow not the only source of correlations between D± azimuthal angles and the reaction plane
D± azimuthal anisotropy may also originate from:
Parton energy loss
Smaller in-medium length L in-plane
(parallel to reaction plane) than out-of-plane
(perpendicular to the reaction plane)
Drees, Feng, Jia, Phys. Rev. C71,
Dainese, Loizides, Paic, EPJ C38, 461
Scattering on pions
Due to elliptic flow, azimuthal distribution
of pions is anisotropic
more pions in-plane than out-of-plane
What is measured is v2 (which is not only due to flow)
Alice Physics Week, December

4. Alice Physics Week, December 5-9 2005
Measurement of v2
Calculate the 2nd order coefficient of Fourier expansion of particle azimuthal distribution relative to the reaction plane
The reaction plane is unknown.
Estimate the reaction plane from particle azimuthal anisotropy:
Yn = Event plane (n th harmonic) = estimator of the unknown reaction plane
Calculate particle distribution relative to the event plane
Correct for event plane resolution
Resolution contains the unknown YRP
Can be extracted from sub-events
Unknown reaction plane
Event plane resolution
Alice Physics Week, December

5. Alice Physics Week, December 5-9 2005
Motivation and method
GOAL: Evaluate the statistical error bars for measurements of v2 for D± mesons decaying in Kpp
v2 vs. centrality (pT integrated)
v2 vs. pT in different centrality bins
TOOL: fast simulation (ROOT + 3 classes + 1 macro)
Assume to have only signal
Generate ND±(Db, DpT) events with 1 D± per event
For each event
Generate a random reaction plane (fixed YRP=0)
Get an event plane (with correct event plane resolution)
Generate the D+ azimuthal angle (φD) according to the probability distribution p(φ)  1 + 2v2 cos [2(φ-YRP)]
Smear φD with the experimental resolution on D± azimuthal angle
Calculate v′2(D+), event plane resolution and v2(D+)
Alice Physics Week, December

6. Event plane simulation
Simple generation of particle azimuthal angles () according to a probability distribution
Faster than complete AliRoot generation and reconstruction
Results compatible with the ones in PPR chapter 6.4
Our simulation
PPR chap 6.4
Alice Physics Week, December

7. Event plane resolution scenario
Event plane resolution depends on v2 and multiplicity
Ntrack = number of p, K and p in AliESDs of Hijing events with b = <b>
bmin-bmax
<b>
Ntrack v2
0-3
1.9
7000
0.02
3-6
4.7
5400
0.04
6-9
7.6
3200
0.06
9-12
10.6
1300
0.08
12-18
14.1
100
0.10
Hadron integrated v2 input values (chosen ≈ 2  RHIC v2)
Alice Physics Week, December

8. D± azimuthal angle resolution
From recontructed D+
200 events made of 9100 D+ generated with PYTHIA in -2<y<2
Average  resolution = 8 mrad = 0.47 degrees
Alice Physics Week, December

9. Alice Physics Week, December 5-9 2005
D± statistics
Nevents for 2·107 MB triggers
Ncc = number of c-cbar pairs
Includes shadowing
Shadowing centrality dependence from Emelyakov et al., PRC 61,
D± yield calculated from Ncc
Fraction ND±/Ncc (≈0.38) from tab. 6.7 in chapt. 6.5 of PPR
Geometrical acceptance and reconstruction efficiency
Extracted from 1 event with D± in full phase space
B. R. D± Kpp = 9.2 %
Selection efficiency
No final analysis yet
Assume e=1.5% (same as D0)
bmin-bmax (fm)
s (%)
Nevents
(106)
Ncc / ev.
D± yield/ev.
0-3
3.6
0.72
118
45.8
3-6 11
2.2 82
31.8
6-9 18 42
16.3
9-12
25.4
5.1
12.5
4.85
12-18
8.4
1.2
0.47
Alice Physics Week, December

10. Results: v2 vs. centrality
2·107 MB events
bmin-bmax
N(D±)selected
s(v2)
0-3
1070
0.024
3-6
2270
0.015
6-9
1900
0.016
9-12
800
0.026
12-18
125
0.09
Error bars quite large
Would be larger in a scenario with worse event plane resolution
May prevent to draw conclusions in case of small anisotropy of D mesons
Alice Physics Week, December

11. Alice Physics Week, December 5-9 2005
Results: v2 vs. pT
2·107 MB events
pT limits
N(D±)sel
s(v2)
0-0.5
140
0.06
0.5-1
280
0.04
1-1.5
390
1.5-2
360
2-3
535
0.03
3-4
250
0.05
4-8
265
8-15 50
0.11
pT limits
N(D±)sel
s(v2)
0-0.5
120
0.06
0.5-1
230
0.05
1-1.5
330
0.04
1.5-2
300
2-3
450
0.03
3-4
210
4-8
220
8-15 40
0.11
pT limits
N(D±)sel
s(v2)
0-0.5 50
0.10
0.5-1
100
0.07
1-1.5
140
0.06
1.5-2
125
2-3
190
0.05
3-4 90
4-8 95
8-15 20
0.15
Alice Physics Week, December

12. Combinatorial background
Huge number (≈1010) of combinatorial Kpp triplets in a central event
≈108 triplets in invariant mass range 1.84<M<1.90 GeV/c2 (D± peak ± 3s )
Final selection cuts not yet ready
Signal almost free from background only for pT>5-6 GeV/c
Need to separate signal from background in v2 calculation
FIRST IDEA: sample candidate Kpp triplets in bins of azimuthal angle relative to the event plane (Dφ= φ-Y2)
Build invariant mass spectra in bins of Dφ and centrality / pT
Alice Physics Week, December

13. Analysis in bins of Dφ (I)
Extract number of D± in 90º “cones”:
in-plane (-45<Dφ<45 U 135<Dφ<225)
out-of-plane (45<Dφ<135 U 225<Dφ<315)
Alice Physics Week, December

14. Analysis in bins of Dφ (II)
Fit number of D± vs. Dφ with A[1 + 2v2cos(2Dφ) ]
0<b<3
3<b<6
6<b<9
v2 values and error bars compatible with the ones obtained from <cos(2Dφ)>
Alice Physics Week, December

15. Other ideas for background
Different analysis methods to provide:
Cross checks
Evaluation of systematics
Apply the analysis method devised for Ls by Borghini and Ollitrault [ PRC 70 (2004) ]
To be extended from pairs (2 decay products) to triplets (3 decay products)
Extract the cos[2(φ-YRP)] distribution of combinatorial Kpp triplets from:
Invariant mass side-bands
Different sign combinations (e.g. K+p+p+ and K-p-p-)
Alice Physics Week, December

16. Alice Physics Week, December 5-9 2005
Conclusions
Large stat. errors on v2 of D± → Kpp in 2·107 MB events
How to increase the statistics?
Sum D0→Kp and D±→Kpp
Number of events roughly 2 → error bars on v2 roughly /√2
Sufficient for v2 vs. centrality (pT integrated)
Semi-peripheral trigger
v2 vs. pT that would be obtained from 2·107 semi-peripheral events ( 6<b<9 )
pT limits
N(D±)sel
s(v2)
0-0.5
645
0.03
0.5-1
1290
0.02
1-1.5
1800
0.017
1.5-2
1650
0.018
2-3
2470
0.015
3-4
1160
4-8
1225
8-15
220
0.05
Alice Physics Week, December

17. Alice Physics Week, December 5-9 2005
BACKUP SLIDES
Alice Physics Week, December

18. Worse resolution scenario
Low multiplicity and low v2
Large contribution to error bar on v2 from event plane resolution
Alice Physics Week, December

19. Glauber calculations (I)
N-N c.s.:
scc from HVQMNR
+ shadowing
Pb Woods-Saxon
Alice Physics Week, December

20. Glauber calculations (II)
N-N c.s.:
scc from HVQMNR
+ shadowing
Pb Woods-Saxon
Alice Physics Week, December

21. Shadowing parametrization
Rg(x~10-4,Q2=5 GeV2) = 65%
from EKS98
Eskola et al., Eur. Phys. J C 9 (1999) 61.
Emel’yanov et al., Phys. Rev. C 61 (2000)
Alice Physics Week, December

22. More details on v2 error bars
High resolution scenario
bmin-bmax
N(D±)selected
s(v2’)
RCF
s(RCF)
s(v2) (from v2’ + from RCF)
0-3
1070
0.0213
0.896
0.006
0.024 (= √ ( )
3-6
2270
0.0148
0.9708
0.0009
0.015 (= √ ( )
6-9
1900
0.0159
0.9771
0.0007
0.016 (= √ ( )
9-12
800
0.025
0.971
0.001
0.026 (= √ ( )
12-18
125
0.061
0.65
0.06
0.09 (= √ ( )
Low resolution scenario
bmin-bmax
N(D±)selected
s(v2’)
RCF
s(RCF)
s(v2) (from v2’ + from RCF)
0-3
1070
0.022
0.76
0.014
0.029 (= √ ( )
3-6
2270
0.015
0.934
0.002
0.016 (= √ ( )
6-9
1900
0.016
0.953
0.017 (= √ ( )
9-12
800
0.025
0.004
0.027 (= √ ( )
12-18
125
0.061
0.57
0.08
0.11 (= √ ( )
Alice Physics Week, December