Transcript Document

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
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IV Convegno sulla fisica di ALICE, Palau, 28-30 Settembre 2008
Basic definitions
• Quarkonia polarization is reconstructed from
z
+
the angular distribution of the decay products
(  +- ) in the quarkonia rest frame
x
• The polarization axis z can be chosen as the
H
J/
pproj
y
ptarg
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quarkonium direction in the target-projectile
center of mass frame (Helicity frame)
• The angular distribution is parameterized as
dσ
 1  α cos 2θ
d cosθ
 > 0 Transverse polarization
 < 0 Longitudinal polarization
1
=0
 = -1
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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
• CSM: predicts transverse polarization
• CEM: predicts no polarization
• NRQCD: predicts transverse
NRQCD
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
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 experimental results
E866 (pA@800GeV)
CDF (p-p @ √s =1.8 TeV)
D0 (pp @ √s =1.96 TeV)
(1s)
NRQCD
(2s)
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 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
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p-p @ 14TeV: 3D acceptance technique
 distribution of a kinematic variable is obtained
• determining N (y, cos, p )
• correcting for acceptance effects
• integrating on the other kinematical variables

T
Acceptances are obtained on a 3D grid in y, pT, cos :
• generation and reconstruction of 10
 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
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-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
Generation of  events with realistic y and pT distributions
Reconstruction of  and acceptance correction
(neglecting background contribution)
pT bin (GeV/c)
0 < pT < 20
αgen
αrec (HE)
1
1.09  0.11
0
0.02  0.09
-1
-1.04  0.05
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)
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p-p @ 14TeV: results vs. pT
According to NRQCD, polarization should increase with pT
pT bin
(GeV/c)
0 < pT < 3
3 < pT < 5
5 < pT < 8
8 < pT < 20
αgen

Υrec after
kin.cuts
(#Υgen = 27100)
HE
HE
1
-0.21  0.25
0
-0.11  0.18
-1
-0.02  0.13
1
-0.05  0.16
0
0.14  0.12
-1
0.10  0.07
1
0.10  0.18
0
-0.04  0.12
-1
-0.14  0.08
1
0.02  0.14
0
-0.02  0.09
-1
0.01  0.04
important to study the pT dependence
=1
 = -1
5100
5600
=0
5100
4000
• reasonable agreement between gen and rec
• statistical error on rec between 0.03 and 0.19
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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
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MC templates technique
MC templates:
Data:
• obtained generating and • obtained generating and reconstructing  with realistic y
reconstructing two large
samples of  with = ± 1
and realistic y and pT
distributions
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
  1   

 2 1    

 TL  cos    3    TT  cos    Bkg  cos   FS B  cos 
1



 



The coefficients of the linear superposition give the  degree of polarization
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Inv. mass spectrum for Pb-Pb @ 5.5 TeV
Generation of the invariant mass spectrum:
5 years data taking
• 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
bb  B 0B   X  D                  X
cc  D   D 0  X       X
dimuons obtained from muons originated
from uncorrelated bb – cc pairs
• Uncorrelated background:
generated through a parametrization and
reconstructed with fast simulation
•  and K contribution:
negligible in the  region
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
ALICE PPR – Volume 11
II
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
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Mass spectrum fit
-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.
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Mass spectrum fits
-0.9<cosθ<-0.8
-0.5<cosθ<-0.4
-0.4<cosθ<-0.3
-0.8<cosθ<-0.7
-0.7<cosθ<-0.6
-0.6<cosθ<-0.5
-0.3<cosθ<-0.2
-0.2<cosθ<-0.1
-0.1<cosθ<0
0.4<cosθ<0.5
0<cosθ<0.1
0.1<cosθ<0.2
0.2<cosθ<0.3
0.3<cosθ<0.4
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

 Ei   i
 Di
 2  2  Ei  i  Di   Di ln 
i


 i
   i  Si   Si ln 

 Si
 

 
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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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
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Other degrees of polarizations
1 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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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:
the bck shape is exponential
 the bck is well estimated
This bias increases with , since for large
 the shape of the cos distribution is
dominated by the most peripheral bins
Edges of the cos distributions:
the bck is not an exponential
 its contribution is underestimated
the signal shape is wider
 is bigger
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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
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The (2s) and (3s) polarization can be done only after several years of data taking
Backup
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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
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MC templates technique
MC templates:
 = -1
=1
• obtained generating and reconstructing
two large samples of  with = ± 1 and
realistic y and pT distributions
Data:
-0.4<cosθ<-0.3
• obtained generating and reconstructing  with realistic y
(5 yr of data taking,
=-1)
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
• 3 gaussian with asymmetric tails (for the 3 )
• exponential for the background
• in the  region (9.2-9.7 GeV) the S+B and B are evaluated:
• S+B  with a counting technique
• B  integrating the exponential fz.
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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
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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
when injecting =0 we get:
• pT>7 GeV/c:  = -0.03 ± 0.05
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)
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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
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Comparison J/ Gen and Calc
S/B= 3.13
peripheral Pb-Pb
(J/ bck subtr)
(J/ + bck)
-
Pb-Pb @ 5.5 TeV
S/B= 0.2
central Pb-Pb
(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
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