Polarization studies with the ALICE central barrel

1
Polarization studies with the ALICE central
barrel

• Evgeny Kryshen (PNPI, Gatchina)

2
Outline

• Basic definitions
• Theoretical background
• Quarkonia polarization at fixed target and
  collider experiments
• Quarkonia polarization measurements with dimuon
  and dielectron channels in ALICE
• Methods for the reconstruction of quarkonia
  polarization
• Simulation and analysis framework for polarized
  quarkonia
• Di-electron channel
• Acceptance calculation
• Definition of a fiducial region
• Polarization vs pt, estimation of statistical
  errors
• Preliminary conclusions and future steps

3
Basic definitions

• The decay angular distribution of the vector
  particle in general case
• where ? and f the angles of the positive lepton
  in the rest frame of the decaying particle
• parameters a, ß, ?
• are related to the density matrix elements
• depend on kinematical variables
• depend on the definition of coordinate system

In most experiments flat distribution for f angle
is assumed, and integrated cross-section is
measured as a function of cos ? a 0 No
polarization a gt 0 Transverse polarization a lt
0 Longitudinal polarization
C. S. Lam and W.-K. Tung, Phys. Rev. D 18, 2447
(1978)
4
Reference systems

• Decay angular distribution depends on the choice
  of the polarization axis (z). Various
  possibilities exist
• Gottfried-Jackson reference frame
• Collins-Soper usually used in fixed target
  experiments
• Helicity frame usually used in collider
  experiments (CDF, BaBar etc)

Helicity (recoil) reference frame Z axis
coincides with the J/? direction in the
target-projectile center of mass frame

• All reference systems are equivalent for J/?
  having pt 0
• One must be careful when comparing experimental
  results with theoretical predictions

5
Theoretical overview

• Polarization in pp collisions - test of
  quarkonium production mechanisms
• CSM Color Singlet Model
• Perturbative QCD, underestimates quarkonium
  production cross-sections
• Transverse polarization
• CEM - Color Evaporation Model
• Soft gluon emission from the cc-pair during
  hadronization randomizes spin and color
• No polarization
• NrQCD Non-relativistic Quantum Chromodynamics
• Takes into account non-perturbative effects in
  quarkonium production
• Dominance of the gluon fragmentation mechanism
  for pt gtgt M, the fragmenting gluon is almost
  on-mass shell, and is therefore transversely
  polarized.
• The produced quarkonium inherits transverse
  polarization at high pt
• Khoze, Martin, Ryskin, Stirling, Eur. Phys. J.,
  C39, 163 (2005)
• Perturbative calculations only. The basic
  subprocess g(gg)8s ? J/?
• Cross sections are in agreement with CDF and RHIC
  experiments
• Transverse polarization at small pt, longitudinal
  polarization at high pt gtgt M.

• Polarization in AA collisions test for HIC
  dynamics and QGP formation
• B.L. Ioffe and D.E. Kharzeev Phys. Rev. C68
  061902 (2003)
• Quarkonium Polarization in HIC as a possible
  signature of the QGP
• Formation of quarkonia takes place in the plasma
  changes in ratio of feed-down and direct
  production non-perturbative effects are screened
  away
• Transverse polarization 0.35 - 0.4 in the case
  of QGP formation

6

• Overview of experimental results on quarkonium
  polarization
• (mostly based on R. Arnaldi talk at Physics
  Forum, March 15 2006)

7
J/? polarization in E866 experiment

• 9 million J/?s in p-Cu collisions _at_ 800 GeV
• Study vs xF, pT

• Integrating over xF and pT ? ? 0.069 ? 0.004 ?
  0.08
• NrQCD predicts 0.31 lt ? lt 0.63
• Feed-down from ?c1 (longitudinal) and ?c2
  (transverse) complicates the issue
• Nuclear effects can also play a role

Phys.Rev.Lett.,91,211801 (2003)
8
Y polarization in E866 experiment

• ? (1S) small transverse polarization at high
  pt
• Measured value ? 0.07 ? 0.04
• NRQCD predicts ? 0.28 0.31
• ? (2S) and ? (3S) strong transverse
  polarization (in agreement with CSM)

• p-Cu collisions _at_ 800 GeV (2 mln events 8.1 lt
  Mµµ lt 15 GeV)
• Studied vs xF and pt

Phys.Rev.Lett.,86,2529 (2001)
9
J/? polarization in CDF
Run 1

• p p _at_ vs 1.8 TeV
• 180000 J/?, 1800 ? (Run 1)

J/? prompt

• Disagreement at high pt with NrQCD predictions.
  But in agreement with approach of Khoze et al.
• Zero polarization for J/? from B decays
• Inconsistency between Run1 and Run2

?
Run 2
J/? from B decay
Phys.Rev.Lett.85,2886 (2000)
10
J/? polarization in NA60

• In-In _at_ 158 AGeV
• Statistics 30K J/?
• Negligible background at J/? mass (2-3)
• ? vs Npart, pt, xF measured
• Result ? close to 0

In the case of QGP formation ? 0.3-0.4 is
predicted by Ioffe and Kharzeev

• R. Arnaldi et al. (NA60 Coll.), Eur. Phys. J.
  C43, 167 (2005 )

11
J/? polarization in PHENIX

• AuAu _at_ 200 AGeV, dAu _at_200 AGeV
• J/? ?e e-
• Central arm ?lt0.35, p gt 0.2 GeV
• Low statistics
• Consistent with zero polarization
• J/? ?µ µ- is under studies
• Larger statistics is expected

d-Au
? 0.15 0.26(stat) 0.04(syst)
dAu _at_200 GeV
Au-Au
d-Au ? vs pt
? 0.06 0.28(stat) 0.05(syst)
12
Other experiments

• Fixed target experiments E537, E672, E771, CIP
  showed unpolarized results.
• BaBar (ee- annihilation) J/? are produced
  mostly longitudinally polarized
• plt3.5 GeV/c a -0.46 - 0.21
• pgt3.5 GeV/c a -0.80 - 0.09

Most experimental results are in contradiction
with theoretical predictions polarization
measurements in the Alice experiment should help
to clarify this puzzle
13
Dimuon vs dielectron channel in ALICE
J/? ? µ µ-
J/? ? e e-

• Extension of polarization measurements to the
  mid-rapidity region which is expected to be
  baryon free different physics
• ITS allows to measure and separate secondary J/?
  from B decays (17) and study polarization of
  prompt J/? only

Run 1 - TRD will be only partially installed
reduced acceptance
ALICE PPR, Volume II
14
Methods for polarization measurements

• 3D-acceptance correction method (used in E866,
  NA60)
• Invariant mass distributions are plotted in bins
  of pt, xF and cos ? and fitted to a Gaussian peak
  background.
• The number of events under the peak give the
  triple-differential yield
• Uncorrected cos ? distributions are plotted in
  each (pt, xF) bin
• 3D acceptance plot is calculated with predicted
  distribution in pt, xF and cos ?.
• Acceptance-corrected cos ? distributions are
  obtained for each (pt, xF) bin
• cos ? distributions are fitted with the function
  f(cos ?) N(1 a cos2 ?)
• Advantage exact knowledge of the differential
  cross-section is not crucial
• Requirement significant statistics in each (pt,
  xF and cos ?) bin or negligible background

• Inclusive acceptance correction (used in Phenix)
• In the case of low statistics polarization is
  measured inclusively in a wide kinematical range,
  where quarkonium cross-section changes
  significantly.
• Inclusive acceptance is calculated in this
  kinematical range with realistic kinematical
  distributions as an input.
• Acceptance-corrected cos ? distributions are
  fitted with the function f(cos ?) N(1 a cos2
  ?)
• Disadvantage is sensitive to J/? kinematics.
  Non-negligible systematic error

15
Simulation framework

• Generator of polarized quarkonia
• Standalone class AliQuarkoniumDecayer public
  AliDecayer is used instead of AliDecayerPythia,
  supports dilepton decays for J/?, Y etc.
• AliQuarkoniumDecayerSetForceDecay (Int_t
  decay)decay kDiElectron, kDiMuon both
  dilepton channels can be forced
• AliQuarkoniumDecayerSetLambda (Double_t
  lambda)sets polarization parameter
• AliQuarkoniumDecayerSetPolarizPtHistogram
  (TH1D histo)allows to set a sample histogram
  for the pt-dependant polarization parameter
• AliQuarkoniumDecayerSetRefSystem (Int_t
  refSystemID)only helicity reference frame is
  implemented at the moment

• Simulation environment
• Aliroot HEAD 9 March 2006
• Generator AliGenParam, CDF scaled
  parametrization
• Fast simulation for electrons response LUT (J.F.
  Grosse-Oetringhaus), reduced efficiencies for
  expected background dNch/d? 4000 are taken into
  account
• Fast simulation for muons response LUT (FASTSIM
  package)
• Full simulation and reconstruction with ESD
  tracks tested

16
Simulation of J/? in the central barrel

• Fast simulation was used
• Acceptance is calculated with statistics 108 J/?
  in the rapidity range accessible for the central
  barrel y lt 1 -gt negligible errors
• PbPb run is considered (L 5 x 1026 cm-2 s-1,
  running time 106 s)
• dNch/d? 4000
• For 10 most central events expected signal J/?
  S 110 700
• pt range 1 GeV/c lt pt lt 10 GeV/c (where
  significant signal is expected)
• signal error is set with (SB)1/2 for
  corresponding pt bin

S, B, S/B ratio and SGN vs pt
Satisfactory acceptance coverage in cos ?
reconstruction of J/? polarization seems feasible
Signal is significant enough even if calculated
in bins of cos ? for each pt range lowest SGN
8
obtained from PPR by appropriate scaling
17
3D acceptance analysis

• Triple-differential acceptance is calculated with
  the flat distribution in bins of pt, y and cos ?.
  Considered y-pt range
• -1 lt y lt 1 20 bins
• 0 GeV/c lt pt lt 10 GeV/c 10 bins
• -1 lt cos ? lt 1 20 bins

• Acceptance strongly depends on the considered bin
  in cos ?.
• Acceptance reduces at the edges of cos ? range.
  The most significant effect for low pt.
• Acceptance vanishes at some pt-y bins these
  bins must be excluded from the analysis

18
Definition of fiducial region - I

• In order to perform acceptance correction, bins
  with zero acceptance must be excluded from the
  analysis necessary to define fiducial region in
  pt-y space where acceptance is higher than a
  certain cut value for each ? range
• Cut bins with acceptance lt 0.025

• Accessible pt-y space strongly narrows with the
  growing cos ? value
• cut value to be optimized

19
Definition of fiducial region And matrices

• the accessible kinematical region, common for all
  bins in a given cos ? range, should be
  deteremined the and matrices were created

cos ? lt 0.7
cos ? lt 0.8
cos ? lt 0.9
The accessible kinematical region strongly
narrows if wider range in cos ? is considered
Accessible y-pt kinematical region is divided
into 5 pt ranges and corresponding range in cos ?
is selected
20
Optimization of cos ? ranges
Reconstructed a values vs considered cos ? range
Reconstructed a uncertainty vs considered cos ?
range
Optimized cos ? range

• In order to optimize cos ? range, longitudinally
  polarized J/? were generated and polarization
  parameter was extracted from the fit
• The range, which gives the lowest uncertainty, is
  selected

21
Integrated acceptance in pt bins

• Integrated acceptance distributions in 5 pt
  ranges were obtained by simulations with
  realistic CDF-scaled parameterization
• Total statistics 108 events in the acceptance
  region

1 GeV/c lt pt lt 2 GeV/c
4 GeV/c lt pt lt 6 GeV/c
8 GeV/c lt pt lt 10 GeV/c

• Larger acceptance at high pt compensates low
  statistics
• Acceptance values depend on the J/? kinematical
  distributions - systematic uncertainties should
  be checked

22
Reconstructed cos ? distributions vs pt

• Invariant mass distributions were reconstructed
  in bins of pt and cos ?
• ? distributions in pt bins were corrected for the
  acceptance and compared to the simulated spectrum

1 GeV/c lt pt lt 2 GeV/c
4 GeV/c lt pt lt 6 GeV/c
8 GeV/c lt pt lt 10 GeV/c

• Uncertainty on reconstructed a 0.02 0.05
• a uncertainty is not very sensitive to the number
  of reconstructed J/? (if this number is
  significant enough)

23
Tests on different polarization values
Similar studies made for several simulated
polarization patterns
Longitudinal polarization
No polarization
Transverse polarization
polarization, dependent on pt

• Performance of reconstruction algorithm - wholly
  satisfactory results for different patterns
• Uncertainties up to 0.13 in the case of
  transverse polarization
• underestimation of polarization parameter in the
  case of pt-dependent polarization - additional
  investigation is required

24
Conclusions and future steps

• Conclusions
• Quarkonium polarization measurement is an
  important test for our understanding of
  quarkonium production mechanisms and HIC dynamics
• J/? polarization measurement with the central
  barrel is feasible for PbPb collisions
• The technique for polarization measurement is
  well established, acceptance properties
  understood.
• Polarization parameter can be extracted in 5 pt
  ranges. Statistical uncertainties on
  reconstructed a 0.02 - 0.13.
• To do
• Analysis of acceptance for the reduced number of
  installed TRD modules
• Feasibility of polarization measurements in Run 1
  (pp, 200 hours)
• Realistic background simulation
• Optimization of fiducial regions and acceptance
  cut
• Optimization of pt and cos ? binning
• Estimation of systematic errors, check the
  consequences of unknown kinematical
  distributions, check the convergence of the
  method
• Bottomium polarization measurements
• Polarization of J/? from B meson decays

25
Backup slides

• J/? polarization measurements with the muon
  spectrometer

26
General information

• Fast simulation (FASTSIM package) was used
• Acceptance is calculated with statistics 108 J/?
  in the ? range of the muon spectrometer 1710 lt
  ? lt1780 -gt negligible errors
• pp Run 1 is considered (L 1030 cm-2 s-1, run
  time 7.2 x 105 s) - estimated statistics of
  collected J/? 67 000

27
pt-y acceptance plots in cos ? bins

• 0.9 lt cos ? lt 1.0

0.8 lt cos ? lt 0.9
0.7 lt cos ? lt 0.8
0.6 lt cos ? lt 0.7
0.3 lt cos ? lt 0.4
0.0 lt cos ? lt 0.1
28
Fiducial regions (cut 0.05)
0.9 lt cos ? lt 1.0
0.8 lt cos ? lt 0.9
0.7 lt cos ? lt 0.8
0.6 lt cos ? lt 0.7
0.3 lt cos ? lt 0.4
0.0 lt cos ? lt 0.1
29
And matrices (cut 0.05)
Cos ? lt 0.5
Cos ? lt 0.6
Cos ? lt 0.7
Cos ? lt 0.8
Cos ? lt 0.9
Cos ? lt 1.0
30
Optimization of ? range
Optimized cos ? ranges
31
Acceptance in pt-bins and reconstruction
1 lt pt lt 4
4 lt pt lt 7
7 lt pt lt 20
32
a vs pt
33

• Some Backup slides

34
Gottfried-Jackson and Collins-Soper reference
systems
Decay angular distribution depends on the choice
of the polarization axis (z). Various
possibilities exist
Collins-Soper Z axis is parallel to the
bisector of the angle between beam and target
directions in the quarkonium rest frame
Gottfried-Jackson Z axis is parallel to the
incoming beam axis in the quarkonium rest frame
Viewed from J/? rest frame

• These reference systems are mainly used at fixed
  target experiments

35
Dielectron channel - Polarization dependent on pt

• Reconstruction is performed correctly
• Fit procedure needs careful treatment

• Possible solutions
• use wider bins in order to improve significance
  of reconstructed distribution
• remove out-of-order points from the fit