Study of the  polarization in the muon channel Roberta Arnaldi Livio Bianchi Enrico Scomparin INFN e Universita’ di Torino Physics motivations Analysis techniques Feasibility study IV Convegno sulla fisica di ALICE, Palau, 28-30 Settembre 2008

Basic definitions Quarkonia polarization is reconstructed from the angular distribution of the decay products (  +- ) in the quarkonia rest frame The polarization axis z can be chosen as the quarkonium direction in the target-projectile center of mass frame (Helicity frame) The angular distribution is parameterized as y z x H + pproj ptarg J/  = -1  = 0  = 1 2 > 0 Transverse polarization < 0 Longitudinal polarization

Physics motivations p-p collisions: A-A collisions: NRQCD 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 quarkonium 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, D0, HERA-B, PHENIX and NA60) is not very clear

 experimental results E866 (pA@800GeV) CDF (p-p @ √s =1.8 TeV) D0 (pp @ √s =1.96 TeV) (1s) NRQCD D0-Note 5089-conf (2s) NRQCD discrepancies between results from different experiments disagreement between (1s) polarization and NRQCD no contradiction between (2s) polarization and NRQCD at high pT

 expected statistics in ALICE p-p @ s= 14 TeV L= 31030 cm-2 s-1 t= 107 s Pb-Pb @ s= 5.5A TeV L= 51026 cm-2 s-1 t= 106 s ALICE-INT-2006-029 Different amount of background in p-p and Pb-Pb different techniques to extract  polarization p-p: background negligible  3D acceptance correction matrices Pb-Pb: background not negligible  MC templates techniques ALICE PPR – Volume II

p-p @ 14TeV: 3D acceptance technique  distribution of a kinematic variable is obtained determining N (y, cos, pT) correcting for acceptance effects integrating on the other kinematical variables Acceptances are obtained on a 3D grid in y, pT, cos : generation and reconstruction of 106  with flat input distributions in y, pT and cos over the kinematical region with a fine binning 0 < pT < 20 GeV/c, -4 < y < -2.5, -1 < cos < 1 -0.9 < cos θ < 0.9 -0.6 < cos θ < 0.6 Results are extracted in a fiducial region, to reduce too large variations in the acceptance values

p-p @ 14TeV: results Generation of  events with realistic y and pT distributions Reconstruction of  and acceptance correction (neglecting background contribution) Results from ~27000 (1s) (expected for L=31030cm-2s-1 in 107 s) pT bin (GeV/c) αgen αrec (HE) 0 < pT < 20 1 1.09  0.11 0.02  0.09 -1 -1.04  0.05 after kinematic cuts (0<pT<20 GeV/c, -3.6<y<-3, -0.6<cos<0.6) only ~13000  are left good agreement between gen and rec statistical error varies between 0.05 and 0.11 ALICE expected statistics in 1 year ~ 3 times  CDF statistics (Run I, 3 yr)

p-p @ 14TeV: results vs. pT According to NRQCD, polarization should increase with pT important to study the pT dependence pT bin (GeV/c) αgen  Υrec after kin.cuts (#Υgen = 27100) HE 0 < pT < 3 1 -0.21  0.25 5100 -0.11  0.18 -1 -0.02  0.13 3 < pT < 5 -0.05  0.16 5600 0.14  0.12 0.10  0.07 5 < pT < 8 0.10  0.18 -0.04  0.12 -0.14  0.08 8 < pT < 20 0.02  0.14 4000 -0.02  0.09 0.01  0.04  = 1  = -1  = 0 reasonable agreement between gen and rec statistical error on rec between 0.03 and 0.19

pros and cons of the 3D acceptance technique Advantages: if a fine binning is used in the acceptance grid evaluation independence from the input distributions of the kinematic variables with the same approach it is possible to study also the other kinematical variables Drawbacks: approach is robust only if background is negligible  the required fine binning and the limited  statistics do not allow the background subtraction in each y, pT, cos cell Alternative approach based on Monte Carlo templates (already used by CDF) This approach is tested in Pb-Pb @ 5.5 TeV, i.e. in the worst conditions for what concerns the amount of background

MC templates technique obtained generating and reconstructing two large samples of  with = ± 1 and realistic y and pT distributions Data: obtained generating and reconstructing  with realistic y and pT distributions and a certain degree of polarization. signal (S) and backgrounds (B) are summed. data are divided in 20 cos bins and from each inv. mass spectrum the S+B and the B contributions are evaluated The S+B cos distribution is fitted to a superposition of the templates plus the background contribution previously evaluated The coefficients of the linear superposition give the  degree of polarization

Inv. mass spectrum for Pb-Pb @ 5.5 TeV Generation of the invariant mass spectrum: Signal: (1S), (2S) and (3S) generated with AliGenParam and reconstructed with full simulation. Generation done with several degrees of polarization Correlated background: generated with Pythia by Rachid* and reconstructed with fast simulation Uncorrelated background: generated through a parametrization and reconstructed with fast simulation  and K contribution: negligible in the  region 5 years data taking dimuons obtained from muons originated from uncorrelated bb – cc pairs ALICE PPR – Volume II Results are given for 1,3 and 5 years of data taking (L= 51026 cm-2 s-1) *ALICE-INT-2005-018 version 1.0

Inv. mass spectrum for Pb-Pb @ 5.5 TeV (2) The relative weight of correlated and uncorrelated backgrounds is taken from PPR Vol II The contribution of each type of background is different in the 5 centrality classes  5 different data samples have been prepared for each degree of polarization Central collisions Semi-central collisions Peripheral collisions 1 year of data taking

Mass spectrum fit S+B Bck Fit to the inv. mass spectrum with: -0.4<cosθ<-0.3 (5 yr of data taking, =-1) S+B Bck Fit to the inv. mass spectrum with: 3 gaussian with asymmetric tails (for the 3 ) exponential for the background In the  region (9.2-9.7 GeV): S+B  obtained with a counting technique B  obtained integrating the exponential fz.

Mass spectrum fits 1 year of data taking, longitudinal polarization -0.9<cosθ<-0.8 -0.8<cosθ<-0.7 -0.7<cosθ<-0.6 -0.6<cosθ<-0.5 -0.5<cosθ<-0.4 -0.4<cosθ<-0.3 -0.3<cosθ<-0.2 -0.2<cosθ<-0.1 -0.1<cosθ<0 0<cosθ<0.1 0.1<cosθ<0.2 0.2<cosθ<0.3 0.3<cosθ<0.4 0.4<cosθ<0.5 0.5<cosθ<0.6 0.6<cosθ<0.7 0.7<cosθ<0.8 0.8<cosθ<0.9 1 year of data taking, longitudinal polarization

Fit to the cos spectrum The template fit to the cos spectrum is done minimizing the quantity where: Di = signal+background ev. Si = background ev. Ei = expected number of signal ev. i = expected number of bck. ev. Data (S+B) Fit MC temp.+Bck Warning: the formula is correct if S+B and B errors are poissonian. In our case this assumption is not completely correct, because bck. errors are not obtained from an ev. counting technique Bck CDF note: CDF/DOC/JET/PUBLIC/3126 (1995)

Fit to the cos spectrum (2) Input degree of polarization  = -1 1 year of data taking 5 year of data taking Similar plots have been obtained for other degrees of polarizations

Other degrees of polarizations 1 year of data taking 5 years of data taking =0 =1

Final results for Pb-Pb @ 5.5 TeV The adopted technique allows to extract a degree of polarization in reasonable agreement with the one used as input. The statistical error (after 1 year) is between 0.06 and 0.15

the signal shape is wider Bias on high values of  Small bias (mainly) for transverse degree of polarization and low statistics  related to the background shape in the peripheral cos regions. Central cos bins: Edges of the cos distributions: the bck shape is exponential  the bck is well estimated the bck is not an exponential its contribution is underestimated the signal shape is wider  is bigger This bias increases with , since for large  the shape of the cos distribution is dominated by the most peripheral bins

Conclusions We have carried out the analysis of the  polarization in the muon channel, similarly to what we did for the J/ Two different techniques based on: 3D acceptance correction MC templates have been investigated according to the amount of background in the  region Results: The (1s) polarization study is feasible in p-p and Pb-Pb collisions p-p @ 14TeV we expect high  statistics, so that, in 1 year of data taking at nominal luminosity, it will be possible to study the (1s) polarization also as a function of pT Pb-Pb @ 5.5 TeV in 1 year of data taking we can extract the (1s) polarization integrated over centrality with an error of ~0.1. Integrating over some years of data taking, the pT or centrality dependence of the polarization can be investigated The (2s) and (3s) polarization can be done only after several years of data taking

Backup

Errore su  same number of events The error on  increases with  (if samples of reconstructed events with the same statistics are compared) This is related to the error calculation within the least square method: if f(x) = p0(1+αx2) σα ∝ 1/p0

MC templates technique obtained generating and reconstructing two large samples of  with = ± 1 and realistic y and pT distributions  = -1  = 1 Data: obtained generating and reconstructing  with realistic y and pT distributions and a certain degree of polarization. signal (S) and backgrounds (B) are summed. data are divided in 20 cos bins and from each of them the inv. mass is fitted with in the  region (9.2-9.7 GeV) the S+B and B are evaluated: -0.4<cosθ<-0.3 (5 yr of data taking, =-1) 3 gaussian with asymmetric tails (for the 3 ) exponential for the background S+B  with a counting technique B  integrating the exponential fz.

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

J/ polarization studies 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: supposed 20 shifts of 10 hours+campo magnetico 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 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)

Comparison J/ Gen and Calc – p-p @ 14 TeV (J/ bck subtr) (J/ + bck) 0.02 is the statistical error 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

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) small system after bck subtraction 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