Quarkonia polarization in ALICE Physics motivations Analysis technique for the measurement of the quarkonia (J/, ) polarization in the dimuon channel Feasibility study under different running conditions R. Arnaldi – L. Bianchi - E. Scomparin Terzo Convegno Nazionale sulla Fisica di Alice, 12-14 Novembre 2007

Basic definitions H z + y z x H + pproj ptarg J/ Quarkonia polarization is reconstructed from the angular distribution of the decay products (J/  +- ) in the quarkonia rest frame The polarization axis z can be chosen as the J/ direction in the target-projectile center of mass frame (Helicity frame) The angular distribution is parameterized as  = -1  = 0  = 1 2 > 0 Transverse polarization = 0 No polarization < 0 Longitudinal polarization

Physics motivations p-p collisions: A-A collisions: Polarization measurements are a test for different quarkonia production mechanisms, since different models predict different polarizations CSM: predicts transverse polarization CEM: predicts no polarization NRQCD: predicts transverse polarization at large pT A-A collisions: An increase of J/ polarization in heavy-ion collisions is expected in case of QGP B.L. Ioffe and D.E. Kharzeev: Phys. Rev. C68 061902 (2003): “Quarkonium Polarization in Heavy-ion collisions as a possible signature of the QGP” The physics picture emerging from several experiments (E866, CDF, HERA-B, PHENIX and NA60) is not very clear

Experimental results: J/ polarization E866 (pA@800GeV) CDF (p-p @ √s =1.8 TeV) HERA-B (p-A @ 900GeV) PRL 99, 132001 (2007) HERA-B Large transverse polarization at high pT predicted by NRQCD NOT seen NA60 (In-In @ 158GeV) Phenix (d-Au and Au-Au @ √s =200GeV) 0.1<yCM<0.8 No significant polarization effects

Experimental results:  polarization E866 experiment (pA@800GeV)  (1S): small transverse polarization at high pT  (2S) and  (3S): strong transverse polarization  (1S): NRQCD predicts  = 0.28 – 0.31 Measured value:  = 0.07  0.04 CDF (p-p @ √s =1.8 TeV) Results for (1s) show no evidence for transverse polarization (no discrepancy with NRQCD since polarization predicted for pT()>>m)

How to extract  (J/) kinematical distributions Quarkonia distribution for a certain kinematical variable obtained determining NJ/ () (y, cos, pT) correcting for acceptance effects integrating on the other kinematical variables Acceptances obtained on a 3D grid: generation and reconstruction of J/ () events (with flat y, pT and cos distributions) over the kinematical region with a fine binning 0 < pT < 20 GeV/c, -4 < y < -2.5, -1 < cos < 1 y pT Acut =0.05 Definition of a fiducial region Example: pT vs y region where A>Acut for -0.8<cos<0.8, covering the largest pT range

 acceptance matrices - Helicity -1<cos<-0.9 -0.7<cos<-0.6 -0.4<cos<-0.3 -0.1<cos<0 y pT Similar acceptances for the positive values of cosHE y, pT coverage depends on the cos range

Generated and acc. corrected distributions realistic y, pT distributions fixed degree of polarization Generation of test distributions for the  with Reconstruction Acceptance corr. and comparison to the generated spectra in the fiducial region -0.6 < cosHE <0.6 0 < pT < 20 GeV/c -3.6 < y < -3 Good agreement between the generated and acceptance corrected kinematical variables

 polarization in p-p @ 14 TeV - Helicity According to the ALICE-INT-2006-029, assuming a Luminosity = 3 1030 cm2s-1 and 107 s, we expect ~27000 ¡ Polarization can be studied in the whole pT range for -0.6 < cosHE <0.6 and -3.6 <y< -3  ~13000 ¡ reconstructed events after kinematical cuts Generated and Acc. corrected cosHE distributions are in good agreement for all the polarization values Statistical error on  ~ 0.06 – 0.11

 polarization in p-p @ 14 TeV vs pT Polarization is expected to depend on pT Starting from 27000 ¡ Define 4 pT bins, as done in CDF: pT y cosHE Rec. ¡ after kin cuts 0-3 -3.6, -3 -0.6, +0.6 ~5000 3-5 -3.9, -2.9 -0.7, +0.7 ~5600 5-8 -4, -2.7 ~5100 8-20 -4, -2.85 -0.9, +0.9 ~4000 0<pT<3 GeV/c 3<pT<5 GeV/c 5<pT<8 GeV/c 8<pT<20 GeV/c For each pT range a fiducial range is defined -0.9<cosHE <0.9 -0.6<cosHE <0.6 -0.7<cosHE <0.7

 polarization in p-p @ 14 TeV vs pT Comparison generated and acc. corr distributions (Helicity) 0<pT<3 GeV/c 3<pT<5 GeV/c 5<pT<8 GeV/c 8<pT<20 GeV/c

 polarization in p-p @ 14 TeV vs pT in each pT bin Statistical errors on the  ~0.03 -0.20

J/ polarization The same approach can be used to study J/ polarization However, to better take into account the background under the J/, another approach was used, similar to the technique used by CDF ALICE p-p @ 14 TeV  S/B ~ 12.0 ALICE Pb-Pb @ 5.5 TeV  S/B ~ 0.2 - 3 The amount of background is negligible The amount of background is important the subtraction of the bkg is less crucial, since the bkg should not bias the J/ polarization measurement the bkg contribution has to be subtracted, since it may bias the J/ polarization measurement

Comparison J/ Gen and Calc – p-p @ 14 TeV (J/ bck subtr) (J/ + bck) The bias on the evaluation of the J/ polarization due to the background is not very large (as expected) Even in this case, the subtraction of the background improves the measurement, compensating for the small discrepancy between Gen and Calc With this statistics (200K) the error on J/ is < 0.02 0.02 is the statistical error

Comparison J/ Gen and Calc - Pb-Pb @ 5.5 TeV S/B= 3.13 peripheral Pb-Pb S/B= 0.2 central Pb-Pb (J/ bck subtr) (J/ + bck) (J/ bck subtr) (J/ + bck) The background clearly washes out the original J/ polarization In both cases, the subtraction of the background allows to correct for the bias on the J/ polarization measurement Small systematic effect still visible small system after bck subtraction

Feasibility of the J/ polarization study in running scenarios p-p @ 14 TeV Luminosity = 3 1030 cm-2 s-1 time = 107 s J/ = 2.8 106 The number of J/ is enough to perform a detailed study as a function of pT. Assuming 200000 reconstructed J/ in p-p @ 14 TeV (all the statistics we have) 1<pT<4 GeV/c:  = -0.02 ± 0.02 4<pT<7 GeV/c:  = -0.03 ± 0.04 pT>7 GeV/c:  = -0.03 ± 0.05 when injecting =0 we get: Pb-Pb @ 5.5 TeV Luminosity = 5 1026 cm-2 s-1 time = 106 s J/ = 133000 (central events) J/ = 21700 (peripheral events) Total J/= 6.8 105 supposed 20 shifts of 10 hours+campo magnetico The number of J/ is enough to perform a study as a function of centrality. Absolute statistical error ~±0.05 for all centralities (for peripheral, smaller statistics compensated by the smaller background)

Conclusions Polarization study is clearly feasible in ALICE for the J/ and ¡ Various algorithms to extract ¡ and J/ polarization have been implemented and applied to the foreseen data taking conditions J/ : Polarization can be determined both as a function of pT (p-p collisions) and centrality (Pb-Pb) p-p @ 14 TeV  negligible errors on J/ Pb-Pb @ 5.5 TeV large background may lead to systematic error on  statistical errors expected ~±0.05 ¡ :p – p @ 14TeV polarization can be studied as a function of pT. Assuming 4 pT the statistical error is ~0.02 – 0.2

Backup

Error on the polarization degree The error on the  parameter (for a fixed number of events) depends on the degree of polarization: it is smaller for LONGITUDINAL polarization, larger for TRANSVERSE polarization same number of events It depends on the lever arm of the fit