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Study of the  polarization in the muon channel

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. 2. z.  = 1.  +.  = 0. x.

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Study of the  polarization in the muon channel

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  1. 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

  2. 2 z  = 1 +  = 0 x J/ H pproj ptarg  = -1 y 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 • > 0 Transverse polarization • < 0 Longitudinal polarization

  3. NRQCD Physics motivations p-p 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 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

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

  5.  expected statistics in ALICE Pb-Pb @ s= 5.5A TeV L= 51026 cm-2 s-1 t= 106 s p-p @ s= 14 TeV L=31030 cm-2 s-1 t= 107 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

  6. -0.9 < cos θ < 0.9 -0.6 < cos θ < 0.6 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 Results are extracted in a fiducial region, to reduce too large variations in the acceptance values

  7. 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) 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)

  8.  = 1  = 0 p-p @ 14TeV: results vs. pT According to NRQCD, polarization should increase with pT • important to study the pT dependence  = -1 • reasonable agreement between gen and rec • statistical error on recbetween 0.03 and 0.19

  9. 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

  10. MC templates technique • 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 • MC templates: • obtained generating and reconstructing two large samples of with= ± 1 and realistic y and pT distributions 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

  11. ALICE PPR – Volume II 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 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

  12. Central collisions Semi-central collisions Peripheral collisions 1 year of data taking 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

  13. -0.4<cosθ<-0.3 (5 yr of data taking, =-1) Mass spectrum fit 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.

  14. Mass spectrum fits -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

  15. 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)

  16. 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

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

  18. 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

  19. 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

  20. 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

  21. Backup

  22. 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

  23. -0.4<cosθ<-0.3 (5 yr of data taking, =-1) MC templates technique • MC templates: • 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: • 3 gaussian with asymmetric tails (for the 3 ) • exponential for the background • S+B  with a counting technique • B  integrating the exponential fz.

  24. CDF (p-p @ √s =1.8 TeV) 0.1<yCM<0.8 Experimental results: J/ polarization E866 (pA@800GeV) 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) No significant polarization effects

  25. 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: 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)

  26. (J/ bck subtr) (J/ + bck) Comparison J/ Gen and Calc – p-p @ 14 TeV • 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

  27. (J/ bck subtr) (J/ bck subtr) (J/ + bck) (J/ + bck) Comparison J/ Gen and Calc - Pb-Pb @ 5.5 TeV S/B= 3.13peripheral Pb-Pb S/B= 0.2central Pb-Pb • 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

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