Open%20charm%20detection%20in%20the%20ALICE%20central%20barrel

1
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
2
Physics motivation
3
Charm production pp collisions

• Hard partonic processes (q-qbar annihilation,
  gluon fusion)
• pQCD phenomenon taking place on short time-scale
  (1/mQ)
• Factorized pQCD approach

Parton Distribution Functions xa , xb momentum
fraction of partons a, b in hadrons
fragmentation z pD /pc
cross-section at hadron level
cross-section at parton level
4
Charm production AA collisions

• Hard primary production in parton processes
  (pQCD)
• Binary scaling for hard process yield
• 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

5
Binary scaling break-up

• Initial state effects
• PDFs in nucleus different from PDFs in nucleon
• Anti-shadowing and shadowing
• kT broadening (Cronin effect)
• Parton saturation (Color Glass Condensate)
• Final state effects (due to the medium)
• Energy loss
• Mainly by gluon radiation
• In medium hadronization
• Recombination vs. fragmentation

Present also in pA (dA) collisions Concentrated
at lower pT
Only in AA collisions Dominant at higher pT
6
Final state effects energy loss

• BDMPS formalism for radiative energy loss
• ? Baier et al., Nucl. Phys. B483 (1997) 291)
• 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 lt
  MQ/EQ
• Dokshitzer Karzeev, Phys. Lett. B519 (2001) 199
• Armesto et al., Phys. Rev. D69 (2004) 114003

average energy loss
distance travelled in the medium
Casimir coupling factor
transport coefficient of the medium
7
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 b0
• 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 )

8
Experimental observables
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Observables RAA

• Nuclear modification factor
• RAA?1 ?binary scaling violation
• Low pT ? main effect nuclear shadowing
• High pT ? main effect energy loss

RHIC
LHC
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Observables RDh

• Heavy-to-light ratio
• sensitive to color charge and mass dependence of
  parton energy loss
• compare gluon (? light hadrons) and charm quark
  (?D) energy loss

Charm mass effect ? only for pTlt10 GeV where also
other effects are present
Colour charge effect ? RDh gt 1 due to DEq lt DEg
? Armesto, Dainese, Salgado, Wiedemann, PRD71
(2005) 054027
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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

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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

13
Charm 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

14
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

15
What to learn from v2 of D mesons?

• Low/interediate pT (lt 2-5 GeV/c)
• recombination scenario
• estimate v2 of c quarks
• degree of thermalization of charm in the medium
• Large pT (gt 5-10 GeV/c)
• path-length dependence of in-medium energy loss
• energy loss in an almond-shaped partonic system

? Armesto, Cacciari, Dainese, Salgado, Wiedemann,
hep-ph/0511257, PLB to appear
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Parenthesis J/Y v2

• SOURCES of charmonium v2
• Charm elliptic flow
• for J/Y formed by c-cbar recombination at
  hadronization
• if charm quarks are early-thermalized
• zero J/Y v2 if charm v2 is zero
• unlike D mesons which have the contribution from
  light quark v2
• J/Y nuclear absorption
• L (length in nuclear matter) depends on f
• L larger out-of-plane than in-plane
• J/Y break-up on co-moving hadrons
• J/Y 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

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RHIC results non-photonic electrons
Nuclear modification factor
Azimuthal anisotropy
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
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Charm in ALICE central barrel
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Charm at the LHC (I)
SPS RHIC LHC
?s (GeV) 17.2 200 5500
Ncc 0.2 10 100-200
x (at y0) 10-1 10-2 10-4

• Large cross-section
• Much more abundant production with respect to SPS
  and RHIC

• Small x
• unexplored small-x region can be probed with
  charm at low pT and/or forward rapidity
• down to x10-4 at y0 and x10-6 in the muon arm

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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)
• 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
• 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

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Charmed mesons and baryons

• Weakly decaying charm states
• Mean proper length 100 mm
• Main selection tool displaced-vertex
• 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)

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ALICE at the LHC
Time Of Flight (TOF)
Transition Radiation Detector (TRD)
Muon arm
Time Projection Chamber (TPC)
Inner Tracking System (ITS)
L3 magnet
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Heavy-flavours in ALICE

• ALICE channels
• electronic (hlt0.9)
• muonic (-4lthlt-2.5)
• hadronic (hlt0.9)
• ALICE coverage
• low-pT region
• central and forward rapidity regions
• Precise vertexing in the central region to
  identify D (ct 100-300 mm) and B (ct 500 mm)
  decays

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D mesons hadronic decays

• Most promising channels for exclusive charmed
  meson reconstruction

Meson Final state charged bodies Branching Ratio Branching Ratio
D0 ?K-p 2 3.8 3.8
D0 ?K-ppp- 4 Total 7.48
D0 ?K-ppp- 4 Non resonant 1.74
D0 ?K-ppp- 4 D0 ?K-pr0 ? K-ppp- 6.2
D ?K-pp 3 Total 9.2
D ?K-pp 3 Non resonant 8.8
D ?K-pp 3 D ?Kbar0(892)p ? K-pp 1.29
D ?K-pp 3 D ?Kbar0(1430)p ? K-pp 2.33
Ds ?KK-p 3 Total 4.3
Ds ?KK-p 3 Ds ?KKbar0?KK-p 2.0
Ds ?KK-p 3 Ds ?fp?KK-p 1.8
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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
  fully-reconstructed 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

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Inner Tracking System

• 6 cylindical layers of silicon detectors

Layer Technology Radius (cm) z (cm) Spatial resolution (mm) Spatial resolution (mm)
Layer Technology Radius (cm) z (cm) rf z
1 Pixel 4.0 14.1 12 100
2 Pixel 7.2 14.1 12 100
3 Drift 15.0 22.2 38 28
4 Drift 23.9 29.7 38 28
5 Strip 38.5 43.2 20 830
6 Strip 43.6 48.9 20 830
provide also dE/dx for particle idetification
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Time Projection Chamber

• Main tracking detector
• Characteristics
• Rin 90 cm
• Rext 250 cm
• Length (active volume) 500 cm
• Pseudorapidity coverage -0.9 lt h lt 0.9
• Azimuthal coverage 2p
• readout channels 560k
• Maximum drift time 88 ms
• Gas mixture 90 Ne 10 CO2
• Provides
• Many 3D points per track
• Tracking efficiency gt 90
• Particle identification by dE/dx
• in the low-momentum region
• in the relativistic rise

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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 lt h lt 0.9
• Azimuthal coverage 2p
• Provides
• pion, Kaon identification (with contamination
  lt10) in the momentum range 0.2-2.5 GeV/c
• proton identification (with contamination lt10)
  in the momentum range 0.4-4.5 GeV/c

TOF
Pb-Pb, dNch/dy6000
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Tracking momentum resolution
without vertex constrain
with vertex constrain (s50 mm)
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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 (sbeam15 mm)
• z coordinate measured from cluster correlation on
  the two layers of SPD

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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 (sbeam150 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)

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Particle Identification

• Hadron identification in ALICE barrel based on
• Momentum from track parameters
• Velocity related information (dE/dx, time of
  flight, Cerenkov light...) specific for each
  detector
• Different systems are efficient in different
  momentum ranges and for different particles

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D meson simulation and reconstruction
34
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 scc 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
sccNN w/o shadowing 6.64 mb 8.80 mb 11.2 mb
Cshadowing (EKS98) 0.65 0.80 1.
sccNN with shadowing 4.32 mb 7.16 mb 11.2 mb
Ncctot 115 0.78 0.16
D0D0bar 141 0.93 0.19
DD- 45 0.29 0.06
DsDs- 27 0.18 0.04
LcLc- 18 0.12 0.02
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D0? K-p selection of candidates
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D0? K-p Results (I)
S/B initial (M?3s) S/B final (M?1s) Significance S/?SB (M?1s)
Pb-Pb Central (dNch/dy 6000) 5 ? 10-6 10 35 (for 107 evts, 1 month)
pPb min. bias 2 ? 10-3 5 30 (for 108 evts, 1 month)
pp 2 ? 10-3 10 40 (for 109 evts, 7 months)
central Pb-Pb
With dNch/dy 3000 in Pb-Pb, S/B larger by ? 4
and significance larger by ? 2
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D0? K-p 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

38
D? K-pp 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.)
• Measured value 2.32 (ALEPH at LEP)
• Different systematics
• Different selection strategies due to
• D has a longer mean proper length (ct 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

39
D ? K-pp vs. D0 ? K-p
Advantages

1. D has a longer mean proper length (ct 312 mm
   compared to 123 mm of the D0)
2. D ? K-pp has a larger branching ratio (9.2
   compared to 3.8 for D0 ? K-p)
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-p)
2. Smaller ltpTgt 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)

40
D ? K-pp selection of candidates

• Single track cuts (pT and d0)
• Build Kp pairs
• cut on the distance between the DCA point of the
  2 tracks and the primary vertex
• Build Kpp triplets from accepted Kp pairs

Signal
Background
d0K x d0p2
d0K x d0p2
Cut on d0
d0K x d0p1
d0K x d0p1
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D?K-pp decay vertex reconstruction

• Calculate the point of minimum distance from the
  3 tracks
• Tracks approximated as straight lines (analytical
  method)
• Minimize the quantity D2d12d22d32 with

42
D ? K-pp decay vertex resolution
p
p
K-
bending plane
D
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D ? K-pp selection of vertices
BLACK signal vertices RED BKG Kpp vertices
BLACK signal vertices RED BKG Kpp vertices
Track dispersion around decay vertex Distance
primary - secondary vertex Cosine of pointing
angle
BLACK signal vertices RED BKG Kpp vertices
The histograms are normalized to the same area
44
D ? K-pp 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) s
  from D mass

Selection Kept signal S/event Kept BKG triplets B/event (MD1s) S/B
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
Kp 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 primary-secondary vertex 60 1 10-3 2.5 0.08 10-2
Pointing angle 100 1 10-3 12 0.01 0.1
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Ds? KK-p motivation
I. Kuznetsova and J. Rafelski

• 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 (gsgt1) is a signature
  of deconfinement
• Ds v2 important test for coalescence models
• Molnar, J. Phys. G31 (2005) S421.

46
Ds? KK-p vs. D ? K-pp
Advantages

1. Smaller combinatorial background if particle
   identification is efficient (kaons are less
   abundant than pions)
2. Larger fraction of Ds ? KK-p from resonant
   decays (through Kbar0 or f) with respect to D

Drawbacks

1. Ds has a smaller mean proper length (ct 147 mm
   compared to 312 mm of the D)
2. Ds ? KK-p has a smaller Branching Ratio (4.3)
   with respect to D ? K-pp (BR9.2)

Analysis in progress by Rosetta Silvestri
47
Perspective for D0 energy loss
48
D0? K-p RAA

• 1 year at nominal luminosity
• 1 month ? 107 central Pb-Pb events
• 10 months ? 109 pp events

49
D0? K-p heavy-to-light ratios

• 1 year at nominal luminosity
• 1 month ? 107 central Pb-Pb events
• 10 months ? 109 pp events

50
Perspective for D v2
51
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
• Get an event plane (with correct event plane
  resolution)
• Generate the D azimuthal angle (fD) according to
  the probability distribution p(f) ? 1 2v2 cos
  2(f-YRP)
• Smear fD with the experimental resolution on D
  azimuthal angle
• Calculate v'2(D), event plane resolution and
  v2(D)

52
D statistics

• Nevents for 2107 MB triggers
• Ncc 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) 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? Kpp 9.2
• Selection efficiency
• No final analysis yet
• Assume e1.5 (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 3.6 42 16.3
9-12 25.4 5.1 12.5 4.85
12-18 42 8.4 1.2 0.47
53
Event plane resolution scenario

• Event plane resolution depends on v2 and
  multiplicity

bmin-bmax ltbgt 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
54
Results v2 vs. centrality
2107 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

55
Results v2 vs. pT
2107 MB events
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 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 s(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 s(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
56
Worse resolution scenario

• Low multiplicity and low v2

Large contribution to error bar on v2 from event
plane resolution
57
Combinatorial background

• Huge number (1010) of combinatorial Kpp triplets
  in a central event
• 108 triplets in invariant mass range 1.84ltMlt1.90
  GeV/c2 (D peak 3s )
• Final selection cuts not yet ready
• Signal almost free from background only for
  pTgt5-6 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
  (Df f-Y2)
• Build invariant mass spectra in bins of Df and
  centrality / pT

58
Analysis in bins of Df (I)

• Extract number of D in 90º cones
• in-plane (-45ltDflt45 U 135ltDflt225)
• out-of-plane (45ltDflt135 U 225ltDflt315)

59
Analysis in bins of Df (II)

• Fit number of D vs. Df with A1 2v2cos(2Df)

60
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) 064905
• To be extended from pairs (2 decay products) to
  triplets (3 decay products)
• Extract the cos2(f-YRP) distribution of
  combinatorial Kpp triplets from
• Invariant mass side-bands
• Different sign combinations (e.g. Kpp and
  K-p-p-)

61
Conclusions on v2

• Large stat. errors on v2 of D ? Kpp in 2107 MB
  events
• How to increase the statistics?
• Sum D0?Kp and D?Kpp
• Number of events roughly ?2 ? error bars on v2
  roughly /v2
• Sufficient for v2 vs. centrality (pT integrated)
• Semi-peripheral trigger
• v2 vs. pT that would be obtained from 2107
  semi-peripheral events ( 6ltblt9 )

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 0.02
4-8 1225 0.02
8-15 220 0.05
62
Backup
63
Glauber calculations (I)

• N-N c.s.
• scc from HVQMNR
• shadowing
• Pb Woods-Saxon

64
Glauber calculations (II)

• N-N c.s.
• scc from HVQMNR
• shadowing
• Pb Woods-Saxon

65
Shadowing parametrization
Rg(x10-4,Q25 GeV2) 65 from EKS98

• Eskola et al., Eur. Phys. J C 9 (1999) 61.
• Emelyanov et al., Phys. Rev. C 61 (2000) 044904.

66
Effect of charm mass at the LHC
mass effect visible only for pTlt10 GeV where
other competing processes are in
67
Directed flow
68
Why elliptic flow ?

• At t0 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

69
In-plane vs. out-of-plane
Isotropic
V210
V2 - 10
70
Glauber calculations

• Optical approximation
• ? Czyz and Maximon, Annals Phys. 52 (1969) 59.

Nucleus thickness functions
Nucleus-nucleus thickness function
Nucleon-nucleon collision probability
71
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

72
D azimuthal angle resolution

• From 63364 recontructed D
• 200 events made of 9100 D generated with PYTHIA
  in -2ltylt2
• Average ? resolution 8 mrad 0.47 degrees