Transcript Document 7329544

Open charm detection in the
ALICE central barrel
Francesco Prino
INFN – Sezione di Torino
credits: Elena Bruna, Andrea Dainese, Carlos Salgado
Alessandria, Dimuon Net, March 29th 2006
Physics motivation
Charm production: pp collisions
Hard partonic processes (q-qbar annihilation, gluon fusion)
pQCD phenomenon taking place on short time-scale (≈1/mQ)
q
Q
g
q
Q
g
Q
Factorized pQCD approach
s /2
x1
s /2
x2
Q
g
Q
g
Q
g
Q
g
Q
c
D
Q2
c
D
 hhDx  PDF ( xa ) PDF ( xb )   abcc  DcD(zc )
cross-section
at hadron level
Parton Distribution Functions
xa , xb= momentum fraction of
partons a, b in hadrons
cross-section at
parton level
fragmentation
z = pD /pc
Charm production: AA collisions
Hard primary production in parton processes (pQCD)
Binary scaling for hard process yield:
dN AA / dpT  N coll  dN pp / dpT
long lifetime of charm quarks allows them to live through the
thermalization phase of the QGP and be affected by its presence
Secondary (thermal) c-cbar production in the QGP
mc (≈1.2 GeV) only 10%-50% higher than predicted temperature of
QGP at the LHC (500-800 MeV)
Thermal yield expected much smaller than hard primary production

can be observed if the pQCD production in A-A is precisely understood
Binary scaling break-up
Initial state effects
antishadowing
PDFs in nucleus different from PDFs in nucleon
shadowing
Anti-shadowing and shadowing
kT broadening (Cronin effect)

SPS
RHIC
LHC
Parton saturation (Color Glass Condensate)
Present also in pA (dA) collisions
Concentrated at lower pT
Final state effects (due to the medium)
Energy loss
A
Mainly by gluon radiation
In medium hadronization


c
u
Recombination vs. fragmentation
Only in AA collisions
Dominant at higher pT
D
c
A
D
Final state effects: energy loss
BDMPS formalism for radiative energy loss
 Baier et al., Nucl. Phys. B483 (1997) 291)
E   s CR qˆ L2
average energy loss
Casimir coupling factor
distance travelled in the medium
transport coefficient of the medium
Energy loss for heavy flavours is expected to be reduced by:
Casimir factor

light hadrons originate predominantly from gluon jets, heavy flavoured
hadrons originate from heavy quark jets

CR is 4/3 for quark-gluon coupling, 3 for gluon-gluon coupling
Dead-cone effect

gluon radiation expected to be suppressed for q < MQ/EQ
 Dokshitzer
& Karzeev, Phys. Lett. B519 (2001) 199
 Armesto et al., Phys. Rev. D69 (2004) 114003
Another medium effect: flow
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 behaviour
Isotropic expansion of the fireball:
Radial transverse flow
 Only type of flow for b=0
 Relevant observables: pT (mT) spectra
y
x
Anisotropic patterns:
Directed flow
 Generated very early when the nuclei penetrate each other x
–

Expected weaker with increasing collision energy
Elliptic flow (and hexadecupole…)
 Caused by initial geometrical anisotropy for b ≠ 0
–

z
Dominated by early non-equilibrium processes
Larger pressure gradient along X than along Y
Develops early in the collision ( first 5 fm/c )
y
x
Experimental observables
Observables: RAA
Nuclear modification factor
1 dN AA / dpT
RAA ( pT ) 
N coll dN pp / dpT
RAA≠1 binary scaling violation
 Low pT  main effect = nuclear shadowing
 High pT  main effect = energy loss
RHIC
LHC
Observables: RDh
Heavy-to-light ratio:
D
h
RD / h ( pt )  RAA
( pt ) RAA
( pt )
sensitive to color charge and mass dependence of parton energy loss
compare gluon ( light hadrons) and charm quark (D) energy loss
Colour charge effect
Charm mass effect
 RDh > 1 due to Eq < Eg
 only for pT<10 GeV where also other
effects are present
 Armesto, Dainese, Salgado, Wiedemann, PRD71 (2005) 054027
Observables: v2
Anisotropy in the observed particle azimuthal distribution due
to correlations between azimuthal angle of outgoing particles
and the direction of the impact parameter
dX X 0
1  2v1 cos(  RP )  2v2 cos2  RP   ....

d 2
v2  cos2  RP 
Sources of charmed meson v2
Elliptic flow
Requires strong interaction among constituents to convert the initial
spatial anisotropy into an observable momentum anisotropy
Probes charm thermalization
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
Scattering on pions
Due to elliptic flow, azimuthal distribution of
pions is anisotropic
Charm flow - 1st idea
130 GeV Au+Au (0-10%)
D from PYTHIA
D from Hydro
B from PYTHIA
B from Hydro
e from PYTHIA
e from Hydro
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
Charm flow and coalescence
Hadronization via coalescence of constituent quarks successfully
explains observed v2 of light mesons and baryons at intermediate pT
hint for partonic degrees of freedom
Lin Molnar, Phys. Rev. C68 (2003) 044901
Coalescence of quarks with similar velocities
Charm quark carry most of the D momentum
 v2(pT)
rises slower for asymmetric hadrons (D, Ds)
non-zero v2 for D mesons even for zero charm v2
(no charm thermalization)
Greco Ko Rapp, Phys. Lett. B595 (2004) 202
Prediction for v2 of electrons from D decay
What to learn from v2 of D mesons?
Low/interediate pT (< 2-5 GeV/c)
recombination scenario
 estimate v2
of c quarks
 degree of thermalization of charm in
the medium
Large pT (> 5-10 GeV/c):
path-length dependence of inmedium energy loss
 energy
loss in an almond-shaped
partonic system
 Armesto, Cacciari, Dainese, Salgado, Wiedemann, hep-ph/0511257, PLB to appear
Parenthesis: J/ v2
SOURCES of charmonium v2:
Charm elliptic flow
for J/ formed by c-cbar recombination at hadronization
if charm quarks are early-thermalized
zero J/ v2 if charm v2 is zero

unlike D mesons which have the contribution from light quark v2
J/ nuclear absorption
L (length in nuclear matter) depends on f

L larger out-of-plane than in-plane
J/ break-up on co-moving hadrons
J/ break-up by QGP hard gluons
parton density is azimuthally anisotropic
 Heiselberg Mattiello, Phys. Rev. C60 (1999) 44902
 Wang Yuan, Phys. Lett. B540 (2002) 62
RHIC results: non-photonic electrons
Nuclear modification factor
(1) q_hat = 0 GeV2/fm
Azimuthal anisotropy
Greco,Ko,Rapp: PLB595(2004)202
(4) dNg / dy =
1000
(2) q_hat = 4 GeV2/fm
(3) q_hat = 14
GeV2/fm
The medium is so dense that c quarks
lose energy (by gluon radiation)
The medium is so strongly
interacting that c quarks suffer
significant rescattering and
develop azimuthal anisotropy
Charm in ALICE central barrel
Charm at the LHC (I)
s (GeV)
Ncc
x (at y=0)
SPS
17.2
≈ 0.2
≈ 10-1
RHIC
200
≈10
≈ 10-2
LHC
5500
≈100-200
≈ 10-4
Large cross-section
Much more abundant production with respect to SPS and RHIC
cc
cc
 LHC
 10  20   RHIC
Small x
x1 
A1 M cc ycc
e
Z1 s pp
x2 
A2 M cc  ycc
e
Z 2 s pp
unexplored small-x region can be
probed with charm at low pT and/or
forward rapidity
to x~10-4 at y=0 and x~10-6 in
the muon arm
 down
muon
arm
central
barrel
Charm at the LHC (II)
p-p collisions
Test of pQCD in a new energy and x regime
Test for saturation models
 Enhancement of charm production at low pT
due to non-linear gluon evolution ?
Reference for Pb-Pb (necessary for RAA)
c(DGLAP+non-linear)
c(DGLAP)
p-Pb collisions
Probe nuclear PDFs at LHC energy
Disentangle initial and final state effects
Pb-Pb collisions
Probe the medium formed in the collision
charm
WARNING: pp, pPb and PbPb will have
different s values
Need to extrapolate from 14 TeV to 5.5 TeV
to compute RAA
 Small
(≈ 10%) theoretical uncertainty on the
ratio of results at 14 and 5.5 TeV
12%
Charmed mesons and baryons
Weakly decaying charm states
Mean proper length ≈ 100 mm
Main selection tool: displacedvertex
Tracks from open charm decays are
typically displaced from primary
vertex by ≈100 mm
Need for high precision vertex
detector (resolution on track
impact parameter ≈ tens of
microns)
primary vertex
q
track impact parameter
decay vertex
Meson
D  (cd )
Mass (MeV)
1869
c (µm)
312
D 0 (cu )
Ds (cs )
1865
1968
123
147
c (udc)
 c (usc )
2285
2466
60
132
 0c (dsc )
 0c ( ssc )
2472
2698
34
21
ALICE at the LHC
Time Of Flight (TOF)
Transition Radiation Detector (TRD)
Time Projection
Chamber (TPC)
Inner Tracking
System (ITS)
L3 magnet
Muon arm
Heavy-flavours in ALICE
ALICE channels:
muonic (-4<h<-2.5)
hadronic (|h|<0.9)
ALICE coverage:
low-pT region
central and forward
rapidity regions
Precise vertexing in the
central region to
identify D (c ~ 100-300
mm) and B (c ~ 500 mm)
decays
pT of Q-hadron [GeV]
electronic (|h|<0.9)
1 year pp 14 TeV @ nominal lumin.
100
ATLAS/CMS
(b)
LHCb
(b)
10
ALICE
(b)
(c)
1
-2
0
ALICE
(c/b)
2
4
h of Q-hadron
6
D mesons: hadronic decays
Most promising channels for exclusive charmed meson reconstruction
Meson
Final state
# charged
bodies
Branching Ratio
K-
2
3.8%
D0
K-
D+
K-
4
3
Total
7.48%
Non resonant
1.74%
D0 K-r0  K-
6.2%
Total
9.2%
Non resonant
8.8%
D+ Kbar0*(892)  K-
1.29%
D+ Kbar0*(1430)  K- 2.33%
Ds+
K+K-
3
Total
4.3%
Ds+ K+Kbar0*K+K-
2.0%
Ds+ fK+K-
1.8%
D mesons in central barrel
No dedicated trigger in the central barrel  extract the signal from
Minimum Bias events
Large combinatorial background (benchmark study with dNch/dy = 6000 in
central Pb-Pb!)
SELECTION STRATEGY: invariant-mass analysis of fullyreconstructed topologies originating from displaced vertices
build pairs/triplets/quadruplets of tracks with correct combination of
charge signs and large impact parameters
particle identification to tag the decay products
calculate the vertex (DCA point) of the tracks
good pointing of reconstructed D momentum to the primary vertex
Inner Tracking System
6 cylindical layers of silicon detectors:
Layer Technology Radius
(cm)
1
2
3
4
5
6
Pixel
Pixel
Drift
Drift
Strip
Strip
±z
(cm)
4.0
7.2
15.0
23.9
38.5
43.6
14.1
14.1
22.2
29.7
43.2
48.9
Spatial resolution (mm)
rf
z
12
100
12
100
38
28
38
28
20
830
20
830
provide also
dE/dx for
particle
idetification
Silicon Pixel Detectors (2D)
Silicon Drift Detectors (2D)
Silicon Strip Detectors (1D)
L= 97.6 cm
R= 43.6 cm
Time Projection Chamber
Main tracking detector
Characteristics:
Rin
90 cm
Rext
250 cm
Length (active volume)
500 cm
Pseudorapidity coverage:
-0.9 < h < 0.9
Azimuthal coverage:
2
# readout channels
≈560k
Maximum drift time:
88 ms
Gas mixture:
90% Ne 10% CO2
Provides:
Many 3D points per track
Tracking efficiency > 90%
Particle identification by dE/dx

in the low-momentum region

in the relativistic rise
Time Of Flight
Multigap Resistive Plate Chambers
for pion, kaon and proton PID
Characteristics:
Rin
370 cm
Rext
399 cm
Length (active volume)
745 cm
# readout channels
≈160k
Pseudorapidity coverage:
-0.9 < h < 0.9
Azimuthal coverage:
2
TOF
Provides:
pion, Kaon identification (with contamination
<10%) in the momentum range 0.2-2.5 GeV/c
proton identification (with contamination <10%)
in the momentum range 0.4-4.5 GeV/c
Pb-Pb, dNch/dy=6000
Tracking: momentum resolution
without vertex constrain
with vertex constrain
(=50 mm)
Track impact parameter in Pb-Pb
Resolution on track impact parameter mainly provided by the 2 layers
of Silicon Pixel Detectors
Interaction point (primary vertex)
x and y coordinates known with high precision from beam position given by LHC
(beam=15 mm)
z coordinate measured from cluster correlation on the two layers of SPD
central Pb–Pb
< 60 mm (rf)
for pt > 1 GeV/c
Two layers:
r = 4 cm
r = 7 cm
Track impact parameter in p-p
Interaction point (x and y) known from LHC with less precision
Due to the need of reduce the luminosity by beam defocusing (beam=150 mm
instead of 15 mm)
3D reconstruction of primary vertex with (primary) tracks
Contribution to track impact parameter resolution from primary vertex
uncertainty not negligible (especially for low multiplicity events)
pp low multiplicity
pp high multiplicity
Particle Identification
Hadron identification in ALICE barrel based on:
Momentum from track parameters
Velocity related information (dE/dx, time of flight, Čerenkov light...)
specific for each detector
Different systems are efficient in different momentum ranges
and for different particles
D meson simulation and
reconstruction
Charm production at the LHC
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-Pb

System
Pb-Pb
(0-5% centr.)
p-Pb
(min. bias)
pp
sNN
5.5 TeV
8.8 TeV
14 TeV
ccNN w/o shadowing
6.64 mb
8.80 mb
11.2 mb
Cshadowing (EKS98)
0.65
0.80
1.
ccNN with shadowing
4.32 mb
7.16 mb
11.2 mb
Ncctot
115
0.78
0.16
D0+D0bar
141
0.93
0.19
D++D-
45
0.29
0.06
Ds++Ds-
27
0.18
0.04
c++c-
18
0.12
0.02
D0 K-+ : selection of candidates
0
D
central Pb-Pb
+
K :
Results (I)
S/B
S/B
Significance
initial
final
S/S+B
(M3)
(M1)
(M1)
Pb-Pb
Central
~35
5  10-6
10%
(for 107 evts,
~1 month)
(dNch/dy = 6000)
pPb
min. bias
pp
~30
2  10-3
5%
(for 108 evts,
~1 month)
~40
2  10-3
10%
(for 109 evts,
~7 months)
With dNch/dy = 3000 in Pb-Pb, S/B larger by  4
and significance larger by  2
D0 K-+: Results (II)
inner bars: stat. errors
outer bars: stat.  pt-dep. syst.
not shown: 9% (Pb-Pb), 5% (pp, p-Pb)
normalization errors
1 year at nominal luminosity
(107 central Pb-Pb events,
109 pp events)
+ 1 year with 1month of p-Pb running
(108 p-Pb events)
Down to pt ~ 0 in pp and p-Pb (1 GeV/c in Pb-Pb)
important to go to low pT for charm cross-section measurement
D+ K-++ : motivation
Determination of charm cross section
D0/D+ ratio puzzle

Expected value = 3.08 (from spin degeneracy of D and D* and decay B.R.)
0
*
*
0
*0
*0
0
D 0 D prompt  D  BR ( D  D )  D  BR ( D  D ) 1  3  0.68  3 1
 

 3.08

*
*

*0
*0

D
D prompt  D  BR ( D  D )  D  BR ( D  D ) 1  3  0.32  3  0

Measured value = 2.32 (ALEPH at LEP)
Different systematics
Different selection strategies due to:


D+ has a “longer” mean proper length (c ~312mm compared to ~123 mm of
the D0)
D+ fully reconstructable from a 3-charged body decay instead of the 2 (or 4)
body decay of D0
+
D
→
+
+
K   vs.
0
D
→
+
K
Advantages
1. D+ has a longer mean proper length (c ~312 mm compared to ~123
mm of the D0)
2. D+ → K-++ has a larger branching ratio (9.2% compared to 3.8%
for D0 → K-+)
3. Possibility to exploit the resonant decay through Kbar0* to enhance
S/B
Drawbacks
1. Larger combinatorial background (3 decay products instead of
the 2 of the D0 → K-+)
2. Smaller <pT> of the decay products (~ 0.7 GeV/c compared to ~ 1
GeV/c of the D0 decay products)
3. D+ less abundant than D0 (factor 2-3)
D+ → K-++: selection of candidates
Single track cuts (pT and d0)
Build K pairs
cut on the distance between the
DCA point of the 2 tracks and the
primary vertex
Build K triplets from accepted K
pairs
Signal
d0K x d02
d0K x d02
Background
d0K x d01
Cut on d0…
d0K x d01
D+→K-++: decay vertex reconstruction
Calculate the point of minimum distance from the 3 tracks
Tracks approximated as straight lines (analytical method)
Minimize the quantity D2=d12+d22+d32 with:
2
 xk  x0   yk  y0   z k  z0 
 
  

 



 x   y   z 
dk
2
Straight Line
Approximation
d (μm)
2
2
PT = 0.5 GeV/c
Secondary vertex
Primary
vertex
d (μm) = distance between the
secondary vertex and the tangent
line
Decay dist (μm)
D+ → K-++: decay vertex resolution
y
y’
π+
x’
π+
K-
rotated
bending plane
D+
x
D+ → K-++: selection of vertices
BLACK: signal vertices
RED: BKG K vertices
BLACK: signal vertices
RED: BKG K vertices
Track dispersion around decay vertex
Distance primary - secondary vertex
Cosine of pointing angle
BLACK: signal vertices
RED: BKG K vertices
The histograms are normalized to the same area
D+ → K-++: preliminary results
Preliminary because:
Limited statistics of simulated events
Perfect PID assumed
Cuts tuned using all BKG triplets and not only the ones with invariant mass
within 1 (or 3)  from D+ mass
Kept S/event Kept BKG B/event S/B
Selection
signal
triplets (M ±1)
D
No cut
100%
0.1
100%
3 106
3 10-8
Single track cuts
9.2%
9.2 10-3
0.2%
6 103
10-6
K pairs vertex
63%
6 10-3
5%
3 102
2 10-5
Products of impact
parameters
100%
6 10-3
75%
2 102
3 10-5
3-track vertex
dispersion
50%
2 10-3
1.5%
3
7 10-4
Distance primarysecondary vertex
60%
1 10-3
2.5%
0.08
10-2
Pointing angle
100%
1 10-3
12%
0.01
0.1
Ds+ K+K-+ : motivation
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 (gs>1) is a
signature of deconfinement
Ds v2 important test for coalescence
models

Molnar, J. Phys. G31 (2005) S421.
I. Kuznetsova and J. Rafelski
Ds
+
+
+
K K
vs.
+
D
→
+
+
K 
Advantages
1.
Smaller combinatorial background if particle identification is
efficient (kaons are less abundant than pions)
2. Larger fraction of Ds+ → K+K-+ from resonant decays (through
Kbar0* or f) with respect to D+
Drawbacks
1.
Ds+ has a smaller mean proper length (c =147 mm compared to
312 mm of the D+)
2. Ds+ → K+K-+ has a smaller Branching Ratio (4.3%) with respect
to D+ → K-++ (BR=9.2%)
Analysis in progress by Rosetta Silvestri
Perspective for D0 energy loss
D0 K-+ : RAA
1 year at nominal luminosity
1 month
 107 central Pb-Pb events
10 months
 109 pp events
Low pT (< 6–7 GeV/c)
Also nuclear shadowing
D
/ dpt
1 dN AA
R ( pt ) 
D
N coll dN pp
/ dpt
D
AA
‘High’ pT (6–15 GeV/c)
Only parton energy loss
D0 K-+ : heavy-to-light ratios
1 year at nominal luminosity
1 month
 107 central Pb-Pb events
10 months
 109 pp events
D
h
RD / h ( pt )  RAA
( pt ) RAA
( pt )
Perspective for D+ v2
Motivation and method
GOAL: Evaluate the statistical error bars for measurements of
v2 for D± mesons decaying in K
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
2.
Get an event plane (with correct 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 angle
5.
Calculate v′2(D+), event plane resolution and v2(D+)
±
D
statistics
Nevents for 2·107 MB triggers
bmin-bmax
(fm)
 (%)
0-3
3.6
0.72
118
45.8
MNR + EKS98 shadowing
3-6
11
2.2
82
31.8
Shadowing centrality dependence
from Emelyakov et al., PRC 61, 044904
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
Nevents
Ncc / ev.
D± yield/ev.
Ncc = number of c-cbar pairs
(106)
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 20000
D± in full phase space
B. R. D± K = 9.2 %
Selection efficiency
No final analysis yet
Assume e=1.5% (same as D0)
Event plane resolution scenario
Event 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
Ntrack = number
of , K and p in
AliESDs of
Hijing events
with b = <b>
Hadron
integrated v2
input values
(chosen ≈ 2
 RHIC v2)
Results: v2 vs. centrality
2·107 MB events
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
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
Results: v2 vs. pT
2·107 MB events
pT limits
N(D±)sel
v2)
pT limits
N(D±)sel
v2)
pT limits
N(D±)sel
v2)
0-0.5
140
0.06
0-0.5
120
0.06
0-0.5
50
0.10
0.5-1
280
0.04
0.5-1
230
0.05
0.5-1
100
0.07
1-1.5
390
0.04
1-1.5
330
0.04
1-1.5
140
0.06
1.5-2
360
0.04
2-3
535
0.03
1.5-2
300
0.04
1.5-2
125
0.06
3-4
250
0.05
2-3
450
0.03
2-3
190
0.05
4-8
265
0.05
3-4
210
0.05
3-4
90
0.07
8-15
50
0.11
4-8
220
0.05
4-8
95
0.07
8-15
40
0.11
8-15
20
0.15
Worse resolution scenario
Low multiplicity and low v2
Large contribution to error bar on v2
from event plane resolution
Combinatorial background
Huge number (≈1010) of combinatorial K triplets in a central event
≈108 triplets in invariant mass range 1.84<M<1.90 GeV/c2 (D± peak ± 3 )
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 K triplets in bins of azimuthal
angle relative to the event plane (φ= φ-2)
Build invariant mass spectra in bins of φ and centrality / pT
Analysis in bins of φ (I)
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)
Analysis in bins of φ (II)
Fit number of D± vs. φ with A[1 + 2v2cos(2φ) ]
0<b<3
3<b<6
6<b<9
v2 values and error
bars compatible with
the ones obtained
from <cos(2φ)>
Other ideas for background
Different analysis methods to provide:
1.
Cross checks
2.
Evaluation of systematics
Apply the analysis method devised for s by Borghini and
Ollitrault [ PRC 70 (2004) 064905 ]
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---)
Conclusions on v2
Large stat. errors on v2 of D± → K in 2·107 MB events
How 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
Backup
Glauber calculations (I)

inel
inel
PAB
(b) 1  1   NN
TAB (b)
N-N c.s.:

AB
inel
 NN
 60 mb
cc
 NN
 6.64 mb
cc from HVQMNR
+ shadowing
inel
N coll (b)  AB NN
TAB (b)
Pb Woods-Saxon
r (r ) 
r0
r  r0
d
1 e
r 0  0.16 fm3
r0  6.624 fm
d  0.549 fm
cc
N cc (b)  AB NN
TAB (b)
Glauber calculations (II)
 (b)  2b1  1   T (b)  
N-N c.s.:
inel
AB
inel
NN AB
AB
inel
 NN
 60 mb
cc
 NN
 6.64 mb
cc from HVQMNR
cc
cc
 AB
(b)  2b  AB NN
TAB (b)
+ shadowing
Pb Woods-Saxon
r (r ) 
r0
r  r0
d
1 e
r 0  0.16 fm3
r0  6.624 fm
d  0.549 fm
cc
 N PbPb

bc
0



bc
0
bc
0
cc
db PbPb
Inel
db PbPb
Shadowing parametrization
Cshad 


f gPb ( x, Q 2 )
p
g
2
f ( x, Q )
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) 044904.
Effect of charm mass at the LHC
mass effect visible only for pT<10 GeV
where other competing processes are in
Directed flow
dX X 0
1  2v1 cos(  RP )  2v2 cos2  RP   ....

d 2
Directed flow coefficient
v1  cos  RP 
Why elliptic flow ?
At t=0: geometrical anisotropy (almond
shape), momentum distribution isotropic
Interaction 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
In-plane vs. out-of-plane
dX X 0
1  2v1 cos(  RP )  2v2 cos2  RP   ....

d 2
Isotropic
V2=10%
Elliptic flow coefficient:
v2>0 In plane elliptic flow
v2<0 Out of plane elliptic flow
V2= - 10%
“Glauber” calculations
Optical approximation
 Czyz and Maximon, Annals Phys. 52 (1969) 59.
Nucleus thickness
functions
Nucleus-nucleus
thickness function
Nucleon-nucleon
collision probability
Event plane simulation
Simple generation of particle azimuthal angles () according to a
probability distribution
dN
 1  2v2 cos  RP 
d
Faster than complete AliRoot generation and reconstruction
Results compatible with the ones in PPR chapter 6.4
PPR chap 6.4
Our simulation
D± 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