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, Settembre 2008

2. 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

3. 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. C (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.  experimental results
E866
CDF √s =1.8 TeV)
D0 √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

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

7. 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)

8. 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

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 5.5 TeV, i.e. in the worst conditions for what concerns the amount of background

10. 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

11. 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 version 1.0

12. 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

13. 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 ( GeV):
S+B  obtained with a counting technique
B  obtained integrating the exponential fz.

14. 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

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. 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

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
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
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. 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 ( 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.

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

25. J/ polarization studies
14 TeV
Luminosity = cm-2 s-1
time = 107 s
J/ =
The number of J/ is enough to perform a detailed study as a function of pT.
Assuming reconstructed J/ in 14 TeV
(all the statistics we have)
1<pT<4 GeV/c:  = ± 0.02
4<pT<7 GeV/c:  = ± 0.04
pT>7 GeV/c:  = ± 0.05
when injecting =0 we get:
supposed 20 shifts of 10 hours+campo magnetico
5.5 TeV
Luminosity = cm-2 s-1
time = 106 s
J/ = (central events)
J/ = (peripheral events)
Total J/=
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. 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

27. Comparison J/ Gen and Calc - Pb-Pb @ 5.5 TeV
S/B= peripheral Pb-Pb
S/B= 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