1. 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, Novembre 2007

2. 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

3. 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. C (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

4. 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

5. Experimental results:  polarization
E866 experiment
 (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 √s =1.8 TeV)
Results for (1s) show no evidence for transverse polarization
(no discrepancy with NRQCD since polarization predicted for pT()>>m)

6. 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 <cos<0.8, covering the largest pT range

7.  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

8. 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

9.  polarization in p-p @ 14 TeV - Helicity
According to the ALICE-INT , assuming a Luminosity = 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

10.  polarization in p-p @ 14 TeV vs pT
Polarization is expected to depend on pT
Starting from ¡
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

11.  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

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

13. 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 14 TeV  S/B ~ 12.0
ALICE 5.5 TeV  S/B ~
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

14. 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

15. 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)
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

16. Feasibility of the J/ polarization study in running scenarios
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:
5.5 TeV
Luminosity = cm-2 s-1
time = 106 s
J/ = (central events)
J/ = (peripheral events)
Total J/=
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)

17. 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)
14 TeV
 negligible errors on J/
5.5 TeV
large background may lead to systematic error on  statistical errors expected ~±0.05
:p – 14TeV
polarization can be studied as a function of pT.
Assuming 4 pT the statistical error is ~0.02 – 0.2

18. Backup

19. 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