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
2
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= 31030 cm-2 s-1 t= 107 s
Pb-Pb @ s= 5.5A TeV
L= 51026 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=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)
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
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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= 51026 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+αx2)
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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