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Perspective for the measurement of D + v 2 in the ALICE central barrel
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Perspective for the Perspective for the measurement of Dmeasurement of D++ v v22 in in the ALICE central barrelthe ALICE central barrel
Elena Bruna, Massimo Masera, Francesco PrinoINFN – Sezione di Torino
ECT*, Heavy Flavour workshop, Trento, September 8th 2006
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Physics motivationPhysics motivation
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Experimental observable: vExperimental observable: v22
....2cos2)cos(212 21
0 RPRP vvXddX
RPv 2cos2
Anisotropy in the observed particle azimuthal distribution due to correlations between the azimuthal angle of the outgoing particles and the direction of the impact parameter
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Sources of charmed meson vSources of charmed meson v22Elliptic flow Collective motion superimposed on top of the thermal motion
Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions
Requires strong interaction among constituents to convert the initial spatial anisotropy into an observable momentum anisotropy
Probes charm thermalization
IN PLANE
OUT OF PLANE
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Charm flow - 1st ideaCharm flow - 1st idea
Batsouli at al., Phys. Lett. B 557 (2003) 26 Both pQCD charm production without final state effects (infinite mean free
path) and hydro with complete thermal equilibrium for charm (zero mean free path) are consistent with single-electron spectra from PHENIX
Charm v2 as a “smoking gun” for hydrodynamic flow of charm
D from PYTHIAD from Hydro
B from PYTHIA
B from Hydro
e from PYTHIA
e from Hydro
130 GeV Au+Au (0-10%)
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Charm flow and coalescenceCharm flow and coalescenceHadronization via coalescence of constituent quarks successfully explains observed v2 of light mesons and baryons at intermediate pT
hint for partonic degrees of freedomApplying to D mesons: Coalescence of quarks with similar velocities
Charm quark carry most of the D momentumv2(pT ) rises slower for asymmetric hadrons ( D, Ds )
Non-zero v2 for D mesons even for zero charm v2 (no charm thermalization)
Lin, Molnar, Phys. Rev. C68 (2003) 044901
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IN PLANE
OUT OF PLANE
Sources of charmed meson vSources of charmed meson v22Elliptic flow Collective motion superimposed on top of the thermal motion
Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions
Requires strong interaction among constituents to convert the initial spatial anisotropy into an observable momentum anisotropy
Probes charm thermalization BUT contribution to D meson v2 from the light quark
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, 034909 Dainese, Loizides, Paic, EPJ C38, 461
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What to learn from vWhat to learn from v22 of D mesons? of D mesons?Low/iterm. pT (< 2-5 GeV/c)
Flow is the dominant effectTest recombination scenarioDegree of thermalization of charm
in the medium Armesto, Cacciari, Dainese, Salgado,
Wiedemann, hep-ph/0511257
Large pT (> 5-10 GeV/c): Energy loss is the dominant
effectTest path-length dependence of in-
medium energy loss in an almond-shaped partonic system Greco, Ko, Rapp PLB 595 (2004) 202
other effects dominant
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Simulation strategy for DSimulation strategy for D++ vv22 in ALICE in ALICE
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Measurement of vMeasurement of v22Calculate 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: n = Event plane (n th harmonic) =
estimator of the unknown reaction plane
Calculate particle distribution relative to the event planeCorrect for event plane resolution Resolution contains the unknown RP Can be extracted from sub-events
)](2cos[2 RPv
ii
iin nw
nwn
cossin
tan1 1
)](2cos[' 22 v
RP
vv
2
22 2cos
'
Unknown reaction plane
Event plane resolution
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Motivation and methodMotivation and methodGOAL: Evaluate the statistical error bars for measurements of v2 for D± mesons reconstructed from their K decay
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±(b, pT) events with 1 D± per event For each event
1. Generate a random reaction plane (fixed RP=0)2. Get an event plane (according to a given event plane resolution)3. Generate the D+ azimuthal angle (φD) according to the probability distribution
p(φ) 1 + 2v2 cos [2(φ-RP)]4. Smear φD with the experimental resolution on D± azimuthal angle5. Calculate v′2(D+), event plane resolution and v2(D+)
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DD±± statistics (I) statistics (I)ALICE baseline for charm cross-section and pT spectra: NLO pQCD calculations ( Mangano, Nason, Ridolfi, NPB373 (1992) 295.)
Theoretical uncertainty = factor 2-3 Average between cross-sections obtained with MRSTHO and CTEQ5M
sets of PDF ≈ 20% difference in cc between MRST HO and CTEQ5M
Binary scaling + shadowing (EKS98) to extrapolate to p-Pb and Pb-PbSystem
Pb-Pb(0-5% centr.)
p-Pb (min. bias) pp
sNN 5.5 TeV 8.8 TeV 14 TeVcc
NN w/o shadowing 6.64 mb 8.80 mb 11.2 mb
Cshadowing (EKS98) 0.65 0.80 1.cc
NN with shadowing 4.32 mb 7.16 mb 11.2 mb
Ncctot 115 0.78 0.16
D0+D0bar 141 0.93 0.19D++D- 45 0.29 0.06Ds
++Ds- 27 0.18 0.04
c++c
- 18 0.12 0.02
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DD±± statistics (II) statistics (II)Nevents for 2·107 MB triggersNcc = number of c-cbar pairs MNR + EKS98 shadowing Shadowing centrality
dependence from Emelyakov et al., PRC 61, 044904
D± yield calculated from Ncc Fraction ND±/Ncc ≈0.38
Geometrical acceptance and reconstruction efficiency Extracted from 1 event with
20000 D± in full phase space
B. R. D± K = 9.2 %Selection efficiency No final analysis yet Assume =1.5% (same as D0)
bmin-bmax
(fm) (%) 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 3.6 42 16.3
9-12 25.4 5.1 12.5 4.85
12-18 42 8.4 1.2 0.47
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Event plane simulationEvent plane simulationSimple 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
RPvddN
cos21 2
PPR chap 6.4 Our simulation
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Hadron integrated v2 input values (chosen ≈ 2 RHIC v2)
Ntrack = number of , K and p in AliESDs of Hijing events with b = <b>
Event plane resolution scenarioEvent plane resolution scenarioEvent plane resolution depends on v2 and multiplicity
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
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DD±± azimuthal angle resolution azimuthal angle resolution
From 63364 recontructed D+ 200 events made of
9100 D+ generated with PYTHIA in -2<y<2
Average resolution = 8 mrad = 0.47 degrees
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Simulated results for DSimulated results for D++ v v22
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vv22 vs. centrality vs. centrality
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
bmin-bmax N(D±)selected 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
2·107 MB events
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vv22 vs. p vs. pTT
pT limits N(D±)sel v2)
0-0.5 120 0.06
0.5-1 230 0.05
1-1.5 330 0.04
1.5-2 300 0.04
2-3 450 0.03
3-4 210 0.05
4-8 220 0.05
8-15 40 0.11
pT limits N(D±)sel v2)
0-0.5 140 0.06
0.5-1 280 0.04
1-1.5 390 0.04
1.5-2 360 0.04
2-3 535 0.03
3-4 250 0.05
4-8 265 0.05
8-15 50 0.11
pT limits N(D±)sel v2)
0-0.5 50 0.10
0.5-1 100 0.07
1-1.5 140 0.06
1.5-2 125 0.06
2-3 190 0.05
3-4 90 0.07
4-8 95 0.07
8-15 20 0.15
2·107 MB events
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Worse resolution scenarioWorse resolution scenarioLow multiplicity and low v2
Large contribution to error bar on v2 from event plane resolution
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First conclusions about DFirst conclusions about D++ v v22
Large stat. errors on v2 of D± → K in 2·107 MB eventsHow to increase the statistics? Sum D0→K and D±→K
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 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 0.02
4-8 1225 0.02
8-15 220 0.05
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How to deal with the backgroundHow to deal with the background
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Combinatorial backgroundCombinatorial background
Huge number (≈1010 without PID) of combinatorial Ktriplets in a HIJING central event ≈108 triplets in mass range 1.84<M<1.90 GeV/c2 (D± peak ± 3 )
Final selection cuts not yet defined Signal almost free from background only for pT > 6 GeV/c At lower pT need to separate signal from background in v2
calculation
1 HIJING central event 1 HIJING central event
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First ideas for backgroundFirst ideas for backgroundSample candidate K triplets in bins of azimuthal angle relative to the event plane (φ= φ-2) Build invariant mass spectra of K triplets in φ bins Extract number of D± in φ bins from an invariant mass analysis
Quantify the anisotropy from numbers of D± in the φ bins
x
y
2
D+
φ
φ
Event plane (estimator of the unknown reaction plane)
D meson momentum as reconstructed from the K triplet
produced particles (mostly pions)
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Analysis in 2 bins of Analysis in 2 bins of φφNon-zero v2 difference between numbers of D ± in-plane and out-of-planeExtract number of D± in 90º “cones”: in-plane (-45<φ<45 U 135<φ<225) out-of-plane (45<φ<135 U 225<φ<315)
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Analysis in more bins of Analysis in more bins of φφ16 Δφ binsFit number of D± vs. φ with K[1 + 2v2cos(2φ) ]
0<b<3 3<b<6 6<b<9
v2 values and error bars compatible with the ones obtained from <cos(2φ)>
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Other ideas for backgroundOther ideas for backgroundDifferent analysis methods to provide:
1. Cross checks2. Evaluation of systematics
Apply the analysis method devised for s by Borghini and Ollitrault [ PRC 70 (2004) 064905 ]
Used by STAR for s To be extended from pairs (2 decay products) to triplets (3 decay
products)Extract the cos[2(φ-RP)] distribution of combinatorial K triplets from:
Invariant mass side-bands Different sign combinations (e.g. K+++ and K---)
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BackupBackup
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Flow = collective motion of particles (due to high pressure arising from compression and heating of nuclear matter) superimposed on top of the thermal motion Flow is natural in hydrodynamic language, but flow as intended in heavy
ion collisions does not necessarily imply (ideal) hydrodynamic behaviourIsotropic expansion of the fireball: Radial transverse flow
Only type of flow for b=0 Relevant observables: pT (mT) spectra
Anisotropic patterns: Directed flow
Generated very early when the nuclei penetrate each other– Expected weaker with increasing collision energy
Dominated by early non-equilibrium processes Elliptic flow (and hexadecupole…)
Caused by initial geometrical anisotropy for b ≠ 0– Larger pressure gradient along X than along Y
Develops early in the collision ( first 5 fm/c )
Flow in the transverse planeFlow in the transverse plane
x
y
x
y
z
x
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Ds probe of hadronization: String fragmentation:
Ds+ (cs) / D+ (cd) ~ 1/3
Recombination:Ds
+ (cs) / D+ (cd) ~ N(s)/N(d) (~ 1 at LHC?)Chemical non-equilibrium may cause a shift in relative yields of charmed hadrons:
Strangeness oversaturation (s>1) is a signature of deconfinement
Ds v2 important test for coalescence models Molnar, J. Phys. G31 (2005) S421.
DDss++ K K++KK--++ : motivation : motivation
I. Kuznetsova and J. Rafelski
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Glauber calculations (I)Glauber calculations (I)
mb
mbccNN
inelNN
64.6
60
ABABinelNN
inelAB bTbP )(11)(
)()( bTABbN ABinelNNcoll
)()( bTABbN ABccNNcc
N-N c.s.:
cc from HVQMNR + shadowing
Pb Woods-Saxon
fmdfmrfme
rdrr
549.0624.616.01
)(
0
30
00
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Glauber calculations (II)Glauber calculations (II) AB
ABinelNN
inelAB bTbb )(112)(
)(2)( bTABbb ABccNN
ccAB
InelPbPb
bc
ccPbPb
bc
bcccPbPb
db
dbN
0
00
mb
mbccNN
inelNN
64.6
60
N-N c.s.:
cc from HVQMNR + shadowing
Pb Woods-Saxon
fmdfmrfme
rdrr
549.0624.616.01
)(
0
30
00
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Shadowing parametrizationShadowing parametrization
Eskola et al., Eur. Phys. J C 9 (1999) 61. Emel’yanov et al., Phys. Rev. C 61 (2000) 044904.
Rg(x~10-4,Q2=5 GeV2) = 65%from EKS98
),(),(
2
2
QxfQxf
C pg
Pbg
shad
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Why elliptic flow ?Why elliptic flow ?
At t=0: geometrical anisotropy (almond shape), momentum distribution isotropicInteraction among consituents generate a pressure gradient which transform the initial spatial anisotropy into a momentum anisotropy Multiple interactions lead to thermalization
limiting behaviour = ideal hydrodynamic flow
The mechanism is self quenching The driving force dominate at early times Probe Equation Of State at early times
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In-plane vs. out-of-planeIn-plane vs. out-of-plane ....2cos2)cos(21
2 210 RPRP vvX
ddX
Elliptic flow coefficient:v2>0 In plane elliptic flowv2<0 Out of plane elliptic flow
Isotropic
V2=10%V2= - 10%
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More details on vMore details on v22 error bars error bars
bmin-bmax N(D±)selected v2’) RCF RCF) v2) (from v2’ + from RCF)
0-3 1070 0.0213 0.896 0.006 0.024 (= √ (0.0242+ 0.00022)
3-6 2270 0.0148 0.9708 0.0009 0.015 (= √ (0.0152+ 0.000012)
6-9 1900 0.0159 0.9771 0.0007 0.016 (= √ (0.0162+ 0.000032)
9-12 800 0.025 0.971 0.001 0.026 (= √ (0.0262+ 0.000062)
12-18 125 0.061 0.65 0.06 0.09 (= √ (0.092+ 0.0022)
bmin-bmax N(D±)selected v2’) RCF RCF) v2) (from v2’ + from RCF)
0-3 1070 0.022 0.76 0.014 0.029 (= √ (0.0292+ 0.00022)
3-6 2270 0.015 0.934 0.002 0.016 (= √ (0.0162+ 0.000072)
6-9 1900 0.016 0.953 0.002 0.017 (= √ (0.0172+ 0.000062)
9-12 800 0.025 0.934 0.004 0.027 (= √ (0.0272+ 0.00022)
12-18 125 0.061 0.57 0.08 0.11 (= √ (0.1072+ 0.022)
High resolution scenario
Low resolution scenario
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Analysis in 2 bins of Analysis in 2 bins of φφ
Extract number of D± in 90º “cones”: in-plane (-45<φ<45 U 135<φ<225) out-of-plane (45<φ<135 U 225<φ<315)