1. Polarization studies with the ALICE central barrel Evgeny Kryshen (PNPI, Gatchina)

2. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 2Outline 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 p t, estimation of statistical errors Preliminary conclusions and future steps

3. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 3 In most experiments flat distribution for φ angle is assumed, and integrated cross- section is measured as a function of cos θ: α = 0 – No polarization α > 0 – Transverse polarization α < 0 – Longitudinal polarization Basic definitions The decay angular distribution of the vector particle in general case: where θ and φ – the angles of the positive lepton in the rest frame of the decaying particle parameters α, β, γ are related to the density matrix elements depend on kinematical variables depend on the definition of coordinate system  = -1  = 0  2 C. S. Lam and W.-K. Tung, Phys. Rev. D 18, 2447 (1978)

4. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 4 Reference systems All reference systems are equivalent for J/  having p t = 0 One must be careful when comparing experimental results with theoretical predictions All reference systems are equivalent for J/  having p t = 0 One must be careful when comparing experimental results with theoretical predictions y z x HH ++ projectiletarget J/  Helicity (recoil) reference frame: Z axis coincides with the J/  direction in the target-projectile center of mass frame 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) 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)

5. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 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 p t >> M, the fragmenting gluon is almost on-mass shell, and is therefore transversely polarized. The produced quarkonium inherits transverse polarization at high p t Khoze, Martin, Ryskin, Stirling, Eur. Phys. J., C39, 163 (2005): Perturbative calculations only. The basic subprocess: g(gg) 8s  J/ψ Cross sections are in agreement with CDF and RHIC experiments Transverse polarization at small p t, longitudinal polarization at high p t >> M. 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 p t >> M, the fragmenting gluon is almost on-mass shell, and is therefore transversely polarized. The produced quarkonium inherits transverse polarization at high p t Khoze, Martin, Ryskin, Stirling, Eur. Phys. J., C39, 163 (2005): Perturbative calculations only. The basic subprocess: g(gg) 8s  J/ψ Cross sections are in agreement with CDF and RHIC experiments Transverse polarization at small p t, longitudinal polarization at high p t >> 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 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. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 6 Overview of experimental results on quarkonium polarization (mostly based on R. Arnaldi talk at Physics Forum, March 15 2006)

7. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 7 J/ ψ polarization in E866 experiment 9 million J/  s in p-Cu collisions @ 800 GeV Study vs x F, p T 9 million J/  s in p-Cu collisions @ 800 GeV Study vs x F, p T Integrating over x F and p T  = 0.069  0.004  0.08 NrQCD predicts 0.31 < < 0.63 Feed-down from  c1 (longitudinal) and  c2 (transverse) complicates the issue Nuclear effects can also play a role Integrating over x F and p T  = 0.069  0.004  0.08 NrQCD predicts 0.31 < < 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. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 8 Y polarization in E866 experiment p-Cu collisions @ 800 GeV (2 mln events 8.1 < M μμ < 15 GeV) Studied vs x F and p t p-Cu collisions @ 800 GeV (2 mln events 8.1 < M μμ < 15 GeV) Studied vs x F and p t Phys.Rev.Lett.,86,2529 (2001)  (1S): small transverse polarization at high p t : Measured value:  = 0.07  0.04 NRQCD predicts  = 0.28 – 0.31  (2S) and  (3S): strong transverse polarization (in agreement with CSM)  (1S): small transverse polarization at high p t : Measured value:  = 0.07  0.04 NRQCD predicts  = 0.28 – 0.31  (2S) and  (3S): strong transverse polarization (in agreement with CSM)

9. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 9 J/ ψ polarization in CDF Disagreement at high pt with NrQCD predictions. But in agreement with approach of Khoze et al. Zero polarization for J/ψ from B decays Inconsistency between Run1 and Run2 Disagreement at high pt with NrQCD predictions. But in agreement with approach of Khoze et al. Zero polarization for J/ψ from B decays Inconsistency between Run1 and Run2 Phys.Rev.Lett.85,2886 (2000) Run 2 Run 1 J/ψ prompt Ψ’Ψ’ J/ψ from B decay p – p @ √s = 1.8 TeV 180000 J/ ψ, 1800 ψ ’ (Run 1) p – p @ √s = 1.8 TeV 180000 J/ ψ, 1800 ψ ’ (Run 1)

10. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 10 R. Arnaldi et al. (NA60 Coll.), Eur. Phys. J. C43, 167 (2005 ) J/ ψ polarization in NA60 In-In @ 158 AGeV Statistics: 30K J/ψ Negligible background at J/ψ mass (~2-3%) λ vs N part, p t, x F measured Result: λ close to 0 In-In @ 158 AGeV Statistics: 30K J/ψ Negligible background at J/ψ mass (~2-3%) λ vs N part, p t, x F measured Result: λ close to 0 In the case of QGP formation λ ~ 0.3-0.4 is predicted by Ioffe and Kharzeev

11. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 11 J/ ψ polarization in PHENIX AuAu @ 200 AGeV, dAu @200 AGeV J/ψ  e + e - Central arm: |η| 0.2 GeV Low statistics Consistent with zero polarization J/ψ  μ + μ - is under studies Larger statistics is expected AuAu @ 200 AGeV, dAu @200 AGeV J/ψ  e + e - Central arm: |η| 0.2 GeV Low statistics Consistent with zero polarization J/ψ  μ + μ - is under studies Larger statistics is expected dAu @200 GeV λ = 0.15 ± 0.26(stat) ± 0.04(syst) λ = 0.06 ± 0.28(stat) ± 0.05(syst) Au-Au d-Au d-Au: λ vs p t

12. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 12 Other experiments Fixed target experiments E537, E672, E771, CIP showed unpolarized results. BaBar (e + e - annihilation) –J/ψ are produced mostly longitudinally polarized: p*<3.5 GeV/c: α = -0.46 +- 0.21 p*>3.5 GeV/c: α = -0.80 +- 0.09 Fixed target experiments E537, E672, E771, CIP showed unpolarized results. BaBar (e + e - annihilation) –J/ψ are produced mostly longitudinally polarized: p*<3.5 GeV/c: α = -0.46 +- 0.21 p*>3.5 GeV/c: α = -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. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 13 Dimuon vs dielectron channel in ALICE 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/ψ from B decays (~17%) and study polarization of prompt J/ψ only 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/ψ from B decays (~17%) and study polarization of prompt J/ψ only ALICE PPR, Volume II J/ψ  μ + μ - SystemRunning time, sLuminosity, cm -2 s -1 S (x 10 3 )S/BSignificance Pb-Pb, c1 class10 6 5 x 10 26 1300.20150 Pb-Pb, c2 class10 6 5 x 10 26 2300.27220 p-p10 7 5 x 10 30 4 67012.62081 p-p, run 17.2 x 10 5 1 x 10 30 6712.6250 SystemRunning time, sLuminosity, cm -2 s -1 S (x 10 3 )S/BSignificance Pb-Pb, 10% cent.10 6 5 x 10 26 1101.2 245 p-p10 7 5 x 10 30 700 p-p, run 17.2 x 10 5 1 x 10 30 ? J/ψ  e + e - Run 1 - TRD will be only partially installed – reduced acceptance

14. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 14 Methods for polarization measurements 3D-acceptance correction method (used in E866, NA60) Invariant mass distributions are plotted in bins of p t, x F and cos θ and fitted to a Gaussian peak + background. The number of events under the peak give the triple-differential yield Uncorrected cos θ distributions are plotted in each (p t, x F ) bin 3D acceptance plot is calculated with predicted distribution in p t, x F and cos θ. Acceptance-corrected cos θ distributions are obtained for each (p t, x F ) bin cos θ distributions are fitted with the function: f(cos θ) = N(1 +α cos 2 θ) Advantage: exact knowledge of the differential cross-section is not crucial Requirement: significant statistics in each (p t, x F and cos θ) 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 θ distributions are fitted with the function: f(cos θ) = N(1 +α cos 2 θ) Disadvantage: is sensitive to J/ψ kinematics. Non-negligible systematic error

15. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 15 Simulation framework Generator of polarized quarkonia: Standalone class AliQuarkoniumDecayer: public AliDecayer is used instead of AliDecayerPythia, supports dilepton decays for J/ψ, Y etc. AliQuarkoniumDecayer::SetForceDecay (Int_t decay): decay = {kDiElectron, kDiMuon} – both dilepton channels can be forced AliQuarkoniumDecayer::SetLambda (Double_t lambda): sets polarization parameter AliQuarkoniumDecayer::SetPolarizPtHistogram (TH1D* histo): allows to set a sample histogram for the p t -dependant polarization parameter AliQuarkoniumDecayer::SetRefSystem (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 dN ch /dη = 4000 are taken into account Fast simulation for muons: response LUT (FASTSIM package) Full simulation and reconstruction with ESD tracks tested

16. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 16 Simulation of J/ψ in the central barrel Fast simulation was used Acceptance is calculated with statistics 10 8 J/ψ in the rapidity range accessible for the central barrel : |y| negligible errors PbPb run is considered (L = 5 x 10 26 cm -2 s -1, running time = 10 6 s) dN ch /dη = 4000 For 10% most central events expected signal J/ψ: S = 110 700 p t range: 1 GeV/c < p t < 10 GeV/c (where significant signal is expected) signal error is set with (S+B) 1/2 for corresponding p t bin Fast simulation was used Acceptance is calculated with statistics 10 8 J/ψ in the rapidity range accessible for the central barrel : |y| negligible errors PbPb run is considered (L = 5 x 10 26 cm -2 s -1, running time = 10 6 s) dN ch /dη = 4000 For 10% most central events expected signal J/ψ: S = 110 700 p t range: 1 GeV/c < p t < 10 GeV/c (where significant signal is expected) signal error is set with (S+B) 1/2 for corresponding p t bin Satisfactory acceptance coverage in cos θ – reconstruction of J/ψ polarization seems feasible S, B, S/B ratio and SGN vs p t :* *obtained from PPR by appropriate scaling Signal is significant enough even if calculated in bins of cos θ for each p t range: lowest SGN ~ 8

17. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 17 3D acceptance analysis Triple-differential acceptance is calculated with the flat distribution in bins of p t, y and cos θ. Considered y-p t range: –-1 < y < 120 bins –0 GeV/c < p t < 10 GeV/c10 bins –-1 < cos θ < 120 bins Triple-differential acceptance is calculated with the flat distribution in bins of p t, y and cos θ. Considered y-p t range: –-1 < y < 120 bins –0 GeV/c < p t < 10 GeV/c10 bins –-1 < cos θ < 120 bins Acceptance strongly depends on the considered bin in cos θ. Acceptance reduces at the edges of cos θ range. The most significant effect – for low p t. Acceptance vanishes at some pt-y bins – these bins must be excluded from the analysis Acceptance strongly depends on the considered bin in cos θ. Acceptance reduces at the edges of cos θ range. The most significant effect – for low p t. Acceptance vanishes at some pt-y bins – these bins must be excluded from the analysis 0.0 < cos θ < 0.1 0.6 < cos θ < 0.7 0.8 < cos θ < 0.9

18. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 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 p t -y space where acceptance is higher than a certain cut value for each θ range Cut bins with acceptance < 0.025 In order to perform acceptance correction, bins with zero acceptance must be excluded from the analysis – necessary to define fiducial region in p t -y space where acceptance is higher than a certain cut value for each θ range Cut bins with acceptance < 0.025 0.0 < cos θ < 0.1 0.6 < cos θ < 0.7 0.8 < cos θ < 0.9 Accessible pt-y space strongly narrows with the growing |cos θ| value cut value to be optimized Accessible pt-y space strongly narrows with the growing |cos θ| value cut value to be optimized

19. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 19 Definition of fiducial region – And matrices the accessible kinematical region, common for all bins in a given cos θ range, should be deteremined – the “and” matrices were created | cos θ | < 0.7 | cos θ | < 0.8 | cos θ | < 0.9 The accessible kinematical region strongly narrows if wider range in cos θ is considered Accessible y-p t kinematical region is divided into 5 p t ranges and corresponding range in cos θ is selected

20. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 20 Optimization of cos θ ranges In order to optimize cos θ range, longitudinally polarized J/ψ were generated and polarization parameter was extracted from the fit The range, which gives the lowest uncertainty, is selected In order to optimize cos θ range, longitudinally polarized J/ψ were generated and polarization parameter was extracted from the fit The range, which gives the lowest uncertainty, is selected Reconstructed α values vs considered cos θ range Reconstructed α uncertainty vs considered cos θ range Optimized cos θ range

21. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 21 1 GeV/c < p t < 2 GeV/c 4 GeV/c < p t < 6 GeV/c 8 GeV/c < p t < 10 GeV/c Integrated acceptance in p t bins Larger acceptance at high pt compensates low statistics Acceptance values depend on the J/ψ kinematical distributions - systematic uncertainties should be checked Larger acceptance at high pt compensates low statistics Acceptance values depend on the J/ψ kinematical distributions - systematic uncertainties should be checked Integrated acceptance distributions in 5 p t ranges were obtained by simulations with “realistic” CDF-scaled parameterization Total statistics: 10 8 events in the acceptance region Integrated acceptance distributions in 5 p t ranges were obtained by simulations with “realistic” CDF-scaled parameterization Total statistics: 10 8 events in the acceptance region

22. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 22 Reconstructed cos θ distributions vs p t p t range, GeV/c Reconstructed α 1 ÷ 2-1.016 ± 0.035 2 ÷ 4-0.967 ± 0.025 4 ÷ 6-1.002 ± 0.021 6 ÷ 8-0.999 ± 0.030 8 ÷ 10-0.978 ± 0.047 Uncertainty on reconstructed α ~ 0.02 ÷ 0.05 α uncertainty is not very sensitive to the number of reconstructed J/ψ (if this number is significant enough) Uncertainty on reconstructed α ~ 0.02 ÷ 0.05 α uncertainty is not very sensitive to the number of reconstructed J/ψ (if this number is significant enough) Invariant mass distributions were reconstructed in bins of p t and cos θ θ distributions in p t bins were corrected for the acceptance and compared to the simulated spectrum 1 GeV/c < p t < 2 GeV/c 4 GeV/c < p t < 6 GeV/c 8 GeV/c < p t < 10 GeV/c

23. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 23 Tests on different polarization values 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 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 Longitudinal polarizationNo polarizationTransverse polarization Similar studies made for several simulated polarization patterns polarization, dependent on p t

24. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 24 Conclusions and future steps Conclusions: Quarkonium polarization measurement is an important test for our understanding of quarkonium production mechanisms and HIC dynamics J/ψ 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 p t ranges. Statistical uncertainties on reconstructed α ~ 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 p t and cos θ binning Estimation of systematic errors, check the consequences of unknown kinematical distributions, check the convergence of the method Bottomium polarization measurements Polarization of J/ψ from B meson decays

25. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 25 Backup slides J/ψ polarization measurements with the muon spectrometer

26. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 26 General information Fast simulation (FASTSIM package) was used Acceptance is calculated with statistics 10 8 J/ψ in the θ range of the muon spectrometer : 171 0 negligible errors pp Run 1 is considered (L = 10 30 cm -2 s -1, run time = 7.2 x 10 5 s) - estimated statistics of collected J/ψ: 67 000 Fast simulation (FASTSIM package) was used Acceptance is calculated with statistics 10 8 J/ψ in the θ range of the muon spectrometer : 171 0 negligible errors pp Run 1 is considered (L = 10 30 cm -2 s -1, run time = 7.2 x 10 5 s) - estimated statistics of collected J/ψ: 67 000

27. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 27 pt-y acceptance plots in cos θ bins 0.9 < cos θ < 1.0 0.8 < cos θ < 0.9 0.7 < cos θ < 0.8 0.6 < cos θ < 0.7 0.3 < cos θ < 0.4 0.0 < cos θ < 0.1

28. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 28 Fiducial regions (cut =0.05) 0.9 < cos θ < 1.0 0.8 < cos θ < 0.9 0.7 < cos θ < 0.8 0.6 < cos θ < 0.7 0.3 < cos θ < 0.4 0.0 < cos θ < 0.1

29. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 29 And matrices (cut =0.05) | Cos θ | < 0.5 | Cos θ | < 0.6 | Cos θ | < 0.7 | Cos θ | < 0.8 | Cos θ | < 0.9 | Cos θ | < 1.0

30. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 30 Optimization of θ range Optimized cos θ ranges:

31. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 31 Acceptance in pt-bins and reconstruction 1 < p t < 4 4 < p t < 7 7 < p t < 20

32. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 32 α vs p t

33. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 33 Some Backup slides

34. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 34 Gottfried-Jackson and Collins-Soper reference systems p projectile p target z axis GJ p µ+ y x Viewed from J/  rest frame p projectile p target z axis CS p µ+ y x Viewed from J/  rest frame 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 These reference systems are mainly used at fixed target experiments

35. Evgeny Kryshen 3rd DIMUONnet Workshop, 29 March 2006 35 Dielectron channel - Polarization dependent on p t Reconstruction is performed correctly Fit procedure needs careful treatment 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 Possible solutions: use wider bins in order to improve significance of reconstructed distribution remove out-of-order points from the fit