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Study of the polarization in the

muon channel

IV Convegno sulla fisica di ALICE, Palau, 28-30 Settembre 2008

Roberta ArnaldiLivio Bianchi

Enrico ScomparinINFN e Universita’ di Torino

• Physics motivations• Analysis techniques• Feasibility study

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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

θcos α1cosθ d

dσ 2

> 0 Transverse polarization < 0 Longitudinal polarization

= -1

= 0

2

y

z

x H

+

pproj ptarg

J/

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Physics motivations

p-p collisions:

Polarization measurements are a test for different quarkonia production mechanisms, since different models predict different polarizations

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

NRQCD• CSM: predicts transverse polarization• CEM: predicts no polarization• NRQCD: predicts transverse polarization at large pT

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experimental resultsE866 (pA@800GeV) CDF (p-p @ √s =1.8 TeV)

D0 (pp @ √s =1.96 TeV)

(2s)

NRQCD

(1s) NRQCD

D0-Note 5089-conf

• discrepancies between results from different experiments• disagreement between (1s) polarization and NRQCD • no contradiction between (2s) polarization and NRQCD at high pT

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expected statistics in ALICE

p-p @ s= 14 TeVL= 31030 cm-2 s-1 t= 107 s

ALICE-INT-2006-029

Pb-Pb @ s= 5.5A TeV

L= 5 51026 cm-2 s-1 t= 106 s

ALICE PPR – Volume II

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

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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

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p-p @ 14TeV: results

pT bin (GeV/c) αgen αrec (HE)

0 < pT < 20

1 1.09 0.11

0 0.02 0.09

-1 -1.04 0.05

Generation of events with realistic y and pT distributions

Reconstruction of and acceptance correction (neglecting background contribution)

Results from ~27000 (1s) (expected for L=31030cm-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)

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p-p @ 14TeV: results vs. pT

According to NRQCD, polarization should increase with pT

pT bin (GeV/c)

αgen

Υrec after kin.cuts

(#Υgen = 27100)

HE HE

0 < pT < 3

1 -0.21 0.25

51000 -0.11 0.18

-1 -0.02 0.13

3 < pT < 5

1 -0.05 0.16

56000 0.14 0.12

-1 0.10 0.07

5 < pT < 8

1 0.10 0.18

51000 -0.04 0.12

-1 -0.14 0.08

8 < pT < 20

1 0.02 0.14

40000 -0.02 0.09

-1 0.01 0.04

• reasonable agreement between gen and rec

• statistical error on rec between 0.03 and 0.19

= 1 = -1

= 0

important to study the pT dependence

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Advantages:if a fine binning is used in the acceptance grid evaluation independence from the input distributions of the kinematic variableswith 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

pros and cons of the 3D acceptance technique

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

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MC templates technique

The S+B cos distribution is fitted to a superposition of the templates plus the background contribution previously evaluated

MC templates:

• 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

2 11cos cos cos cos

1 3L T S BT T Bkg F

The coefficients of the linear superposition give the degree of polarization

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Inv. mass spectrum for Pb-Pb @ 5.5 TeV

Results are given for 1,3 and 5 years of data taking (L= 51026 cm-2 s-1)

5 years data taking

Generation of the invariant mass spectrum:

*ALICE-INT-2005-018 version 1.0

0

0

bb B B X D X

cc D D X X

dimuons obtained from muons originated from uncorrelated bb – cc pairs

• 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

ALICE PPR – Volume II

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Inv. mass spectrum for Pb-Pb @ 5.5 TeV (2)

Central collisions

Semi-central collisions

Peripheral collisions

1 year of data taking

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

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Mass spectrum fit

-0.4<cosθ<-0.3(5 yr of data taking, =-1)

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 techniqueB obtained integrating the exponential fz.

S+B

Bck

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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

0.4<cosθ<0.50.3<cosθ<0.40.2<cosθ<0.30.1<cosθ<0.20<cosθ<0.1

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

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Fit to the cos spectrum

The template fit to the cos spectrum is done minimizing the quantity

2 2 ln lni i ii i i i i i i

i i i

EE D D S S

D S

where:

Di = signal+background ev.Si = background ev.Ei = expected number of signal ev.i = expected number of bck. ev.

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

CDF note: CDF/DOC/JET/PUBLIC/3126 (1995)

Data (S+B)

Fit MC temp.+Bck

Bck

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1 year of data taking 5 year of data taking

Fit to the cos spectrum (2)

Input degree of polarization = -1

Similar plots have been obtained for other degrees of polarizations

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Other degrees of polarizations1 year of data taking 5 years of data taking

=0

=1

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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

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Small bias (mainly) for transverse degree of polarization and low statistics

related to the background shape in the peripheral cos regions.

Bias on high values of

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

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Conclusions

The (1s) polarization study is feasible in p-p and Pb-Pb collisions

p-p @ 14TeVwe 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 TeVin 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

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:

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Backup

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The error on The error on increases increases with with (if samples of (if samples of reconstructed events reconstructed events

with the same statistics with the same statistics are compared)are compared)

This is related to the This is related to the error calculation within error calculation within

the least square method: the least square method: if f(x) = pif f(x) = p00(1+(1+ααxx22))

σσα α 1/p∝ 1/p∝ 00

same number of events

Errore su

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MC templates technique

MC templates:

• 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 of them the inv. mass is fitted with

• in the region (9.2-9.7 GeV) the S+B and B are evaluated:

= -1 = 1

-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.

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Experimental results: J/ polarization

E866 (pA@800GeV)

PRL 99, 132001 (2007)

NA60 (In-In @ 158GeV)

0.1<yCM<0.8

CDF (p-p @ √s =1.8 TeV)

Large transverse polarization at high pT predicted by NRQCD NOT seen

Phenix (d-Au and Au-Au @ √s =200GeV)

HERA-B (p-A @ 900GeV)

HERA-B

No significant polarization effects

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p-p @ 14 TeV

Luminosity = 3 1030 cm-2 s-1

time = 107 sJ/ = 2.8 106

Pb-Pb @ 5.5 TeV

Luminosity = 5 1026 cm-2 s-1

time = 106 sJ/ = 133000 (central events)J/ = 21700 (peripheral events)Total J/= 6.8 105

The number of J/ is enough to perform a detailed study as a function of pT.

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)

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 ± 0.05when injecting =0 we get:

J/ polarization studies

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(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

Comparison J/ Gen and Calc – p-p @ 14 TeV

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Comparison J/ Gen and Calc - Pb-Pb @ 5.5 TeV

S/B= 0.2 central Pb-PbS/B= 3.13 peripheral 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