Transcript Study of Bose-Einstein Correlations at 0.9 and 7 TeV with

Study of Bose-Einstein Correlations
at 0.9 and 7 TeV with ATLAS
Y.Kulchitsky¹⁾²⁾, E.Plotnikova¹⁾, N.Rusakovich¹⁾, P.Tsiareshka¹⁾²⁾
¹⁾ JINR Dubna
²⁾ Institute of Physics, National Academy of Sciences of Belarus, Minsk
ATLAS/JINR meeting at 20.12.2011
Abstract: We present the results of a study of pp collisions at √s = 0.9 TeV and 7 TeV collected by the
ATLAS experiment at the LHC collider. The Bose-Einstein correlations of the π±π± two boson system have
been studied in the minimum-bias and high-multiplicity events. The research was carried out on a sample of
≈350 000 events at 0.9 TeV; ≈20000000 events at 7 TeV (minimum-bias trigger) and ≈14000 at 7 TeV (high
multiplicity trigger). The two pion correlations have been retrieved. The final results were corrected on the
coulomb interactions. Five different reference samples were compared and discussed. A significant two-pion
correlation enhancement near origin is observed. This enhancement effect has been used to evaluate the
radius of the two-pion emitter source. A comparison between 4 different parameterizations of C2(Q) function
is given. We studied BEC in dependent of charged hadron multiplicity, transverse momentum of π±π± two
boson system and transverse momentum of each hadrons from two boson system . For the first time we
studies BEC at very high multiplicity region. We found that BEC radius become saturated at high
multiplicity of charged hadrons.
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Gaussian Approximation
• If the source is approximated with Gaussian:
source
S(x,k)
x2
x1
• Then the correlation function is also Gaussian:
Y1,2
k1 k2
detector
• These radii are the so-called HBT radii
• If transformed to the out-side-long system (not invariant)
• Out: direction of the mean transverse momentum of the pair
• Side: orthogonal to out
• Long: beam direction
• Not necessarily reflecting the geometrical size
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Two-particle Correlations
“Away-side” (∆φ~ π) jet correlations:
correlation of particles between back-to-back jets
Bose-Einstein correlations for identical
particles with (∆φ,∆η) ~ (0,0)
Momentum conservation:
~ -cos(∆φ)
“Near-side” (∆φ~ 0) jet peak: correlation
of particles with a single jet
Short-range correlations (|∆η|<2):
resonances, string fragmentation, “clusters”
Corrected 2-particle correlation distribution functions in ∆η and ∆φ for 7 TeV. By construction, these plots
are symmetric around ∆η = 0 and ∆φ is plotted from −π/2 to 3π/2 to avoid splitting the away-side region.
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JINR Contribution
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0.9 TeV data samples
Official MinBias D3PD samples for Experimental data and MC are used
Experimental data samples:
data09_900GeV.00142383.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120524_00_r15.6.7.8Newtrk
data09_900GeV.00142195.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120485_00_r15.6.7.8Newtrk
data09_900GeV.00142193.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120419_00_r15.6.7.8Newtrk
data09_900GeV.00142191.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120365_00_r15.6.7.8Newtrk
data09_900GeV.00142189.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120305_00_r15.6.7.8Newtrk
data09_900GeV.00142174.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120272_00_r15.6.7.8Newtrk
data09_900GeV.00142171.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120239_00_r15.6.7.8Newtrk
data09_900GeV.00142166.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120206_00_r15.6.7.8Newtrk
data09_900GeV.00142165.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120173_00_r15.6.7.8Newtrk
data09_900GeV.00142154.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid120032_00_r15.6.7.8NewtrkGLS
data09_900GeV.00142149.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid119999_00_r15.6.7.8Newtrk
data09_900GeV.00141811.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid119768_00_r15.6.7.8Newtrk
data09_900GeV.00141749.physics_MinBias.merge.ESDtoD3PD.r1093_p101_tid119702_00_r15.6.7.8Newtrk
Number of selected events = 357,523
Number of selected tracks = 4,532,663
MC data sample: (non-diffractive)
mc09_900GeV.105001.pythia_minbias.merge.NTUP_MINBIAS.e500_s771_s767_r1234_p137_tid130221_00
Number of selected events = 975,742
Number of selected tracks = 12,363,168
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7 TeV data samples
Experimental data samples:
data10_7TeV.00152221.physics_MinBias.merge.NTUP_MINBIAS.f239_p127_tid125125_00
data10_7TeV.00152166.physics_MinBias.merge.NTUP_MINBIAS.f239...
data10_7TeV.00152214.physics_MinBias.merge.NTUP_MINBIAS.f239...
data10_7TeV.00152345.physics_MinBias.merge.NTUP_MINBIAS.f239...
data10_7TeV.00152409.physics_MinBias.merge.NTUP_MINBIAS.f239...
data10_7TeV.00152441.physics_MinBias.merge.NTUP_MINBIAS.f239...
data10_7TeV.00152508.physics_MinBias.merge.NTUP_MINBIAS.f241...
Number of selected events: ~20 M events
MC sample: ( non-diffractive samples)
mc09_7TeV.105001.pythia_minbias.merge.NTUP_MINBIAS.e517_s764_s767_r1229_p137
Number of selected events: ~14 M events
7 TeV Data with the high multiplicity trigger
Experimental data sample:
user.jmonk.00166850.physics.MinBias.NTUP_HIGHMULT.f296.v2/
Number of selected events = 13,985
Number of selected tracks = 2,070,633
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Event/Tracks characteristics of 0.9 TeV and 7 TeV
Trigger:
 L1_MBTS_1 | L1_MBTS_2 | L1_MBTS_1_1 trigger
 good run/lumiblocks
Vertex Selection:
 Pile-up Removal cut
 ≥ 1 vertex
 ≥ 2 "selected" track (as vertex requires 2 tracks)
Track Selection:








pT ≥ 100. MeV
|ƞ| < 2.5
|d0| < 1.5 mm
|z0 sinθ| < 1.5 mm
b-layer hit if one expected
≥ 1 pixel hit
≥ 2,4,6 SCT hits for pT > 100,200,300 MeV
χ2 prob > 0.01 for pT > 10 GeV (to remove the mis-measured tracks).
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Event/Tracks characteristics of
7 TeV with the high multiplicity trigger**
Trigger:
 mbSpTrkVtxMh
 Another Luminosity blocks
Vertex:
 at least one good primary vertex (type 1). Removed pile-up cut as defined
by the MB 2.0 analysis. Instead if second vertex has higher multiplicity than the
primary, skip event.
At least 108 tracks with:
 |η| < 2.5
 pT ≥ 100. MeV
 Reconstructed by the inside-out or low- pT tracking algorithms.
 ≥ 1 pixel hit*
 ≥ 6 SCT hits
 |d0| < 1.5 mm
 |z0sinθ| < 1.5 mm
 fit probability ≥ 0.01 for pT > 10 GeV
*No b-layer requirement. After MB 2.0 definition of expectHitInBLayer changed.
**http://indico.cern.ch/getFile.py/access?contribId=6&resId=0&materialId=slides&confId=106091
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0.9 TeV dataset properties
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7 TeV HMT dataset properties
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C2 functions: experimental approach
For each track pair we reconstruct the quantity Q.

 2
2
Q = E1  E2    p1  p2 
The Q++, Q- - , Q+-,Q-+ are the quantities for pairs of the like/unlike sign
(“ls”/”us”) particles.
The C2(Q) correlation function is a ratio of the like sign particle (track)
pairs Q distributions' sum (signal distributions N(Q)(with BEC)) and the
unlike sign particle (track) pairs Q distribution (reference distribution
Nref(Q)(without BEC,but contain all other correlations.))
We construct the C2(Q) correlation function
It is a problem!!!
++ and -- track pair combinations
N
(
Q
)
C
(
Q
) ref
2
N(
Q
)
N(Q)
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+- track pair combinations
two particles Q distribution
- identical
particles used
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Reference functions
All of the reference samples that we have used are obtained from data.
These are:
 Unlike-charge pairs (“UCP”) – us
non-identical track pairs taken from the same event.
 Opposite-hemisphere pairs (“OHP”) – us/ls
inversion in space the three-momentum of one of the two particles:


E, p  E, p
 Rotated particles (“RP”) – us/ls
inversion the x and y components of the three-momentum of one of the two
particles:
p , p , p    p , p , p 
x
y
z
x
y
z
 Event mixing reference function (“MixE”) – us/ls
the same particle type track pairs created from different events.
 Double ratio (“DR”) – us/ls
Data
C
C2(Q) correlation function MC corrected.
С2DR Q  2MC
 
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C2
Q 
Q 
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Reference samples of 0.9 TeV
C2(Q) with UCP us ref.
C2(Q) with OHP ls ref.
DR C2(Q) with UCP us ref.
Problem Region
Problem Region
C2(Q) with RP ls ref.
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C2(Q) with MixE us ref.
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Reference samples of 7 TeV HMT
C2(Q) with UCP us ref.
C2(Q) with OHP ls ref.
Problem Region
C2(Q) with RP ls ref.
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C2(Q) with MixE us ref.
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Coulomb correction
The measured N(Q) distribution for the like or unlike signed particle (track) pairs
in presence of the Coulomb interaction is given by:
Nmeas Q = GQN Q
where Nmeas(Q) is the measured distribution, N(Q) is the distribution free
of Coulomb correlations.
Gamow penetration G(Q) factor
G(Q)=
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2 πη
e2 πη − 1
Sommerfeld parameter η
± αm
η=
Q
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Coulomb correction of 0.9 TeV C2(Q)
We have to correct any reference sample to this Coulomb interaction to make our
final C2(Q) function free of the coulomb correlations.
Comparison of the same C2(Q) function:
blue – primary data C2(Q),
red – C2(Q) corrected to Coulomb
correction.
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Ratio of the same C2(Q) function –
with and without correction on
Coulomb correction.
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Coulomb correction of 7 TeV HMT C2(Q)
Comparison of the same C2(Q) function:
blue – primary data C2(Q),
red – C2(Q) corrected to Coulomb
correction.
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Ratio of the same C2(Q) function –
with and without correction on
Coulomb correction.
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Efficiency correction
Corrections on some efficiencies (functions of η and pt):

“reconstruction track efficiency”

“trigger efficiency”

“vertex reconstruction efficiency”
ε(pt, η)
ε(pt)
η
Pt, GeV/c
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Pt (GeV/c)
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Efficiency correction of 0.9 TeV C2(Q)
To exclude the region of possible two track fake reconstruction a small Q
threshold was introduced, Q > 20 MeV, as a minimal Q between two tracks.
Comparison of the same C2(Q) function:
blue – primary data C2(Q),
red – C2(Q) corrected to different
Efficiency correction.
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Ratio of the same C2(Q) function –
with and without correction on
Efficiency correction.
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Parametrization Models
Several models have been constructed to describe the shape of the Bose-Einstein
enhancement at Q = 0, based on different assumptions.


GSSg model. The Goldhaber spherical source model.
 R 2Q 2 

C2 1 = C0 1+ λe
1+ Qε 


GSSe model. Empirical model. Used since it represents well the shape of
the correlation.




C22 = C0 1+ λe RQ 1+Qε 
R is the source radius
λ is the incoherence factor (0,1) introduced empirically.
QOg model. Quantum Optics model.
2 2
 R 2Q 2
2  2R Q 

C23 = C0 1+ 2p 1  p e
+p e
1+ Qε 
QOe model. Empirical but inspired to the Quantum Opticsmodel.


C24 = C0 1+ 2p1  pe RQ + p 2e2RQ 1+ Qε 
p is the chaoticity: =0 ( =1) for purely coherent (chaotic) sources.
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Different models’ fit of 0.9 TeV C2(Q)
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Excluded region
400-800 MeV
Excluded region
400-800 MeV
Excluded region
400-800 MeV
Excluded region
400-800 MeV
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Different models’ fit of 7 TeV HMT C2(Q)
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Comparison of the C2(Q) correlation functions of
two different energy data samples: 0.9 TeV and 7 TeV HMT
Blue line – Data 0.9 TeV C2(Q)
Red line – Data 7 TeV HMT C2(Q)
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Ntracks , pT & kT slices' statistics of 0.9 TeV
The BEC are studied on:
 Regions of track multiplicity Ntracks
 Regions of track transverse momentum pT
 Regions of transverse momentum of the tracks’ pair kT



pT 1  pT 2
kT 
2
900 GeV
900 GeV
900 GeV
pT slice
Tracks' pairs
(%)
N slice
Tracks' pairs
(%)
kT slice
Tracks' pairs
(%)
100 - 300
30.9%
2-9
6.4%
100 - 200
2.4%
300 - 500
32.7%
10 - 15
14.1%
200 - 300
13.6%
500 - 1000
36.4%
16 - 22
21.2%
300 - 400
19.4%
23 - 29
20.7%
400 - 500
18.2%
30 - 38
19.9%
500 - 600
14.4%
39 - 70
17.4%
600 - 700
10.7%
700 - 1200
21.4%
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Ntracks , pT & kT slices' statistics of 7 TeV HMT
7 TeV HMT
7 TeV HMT
7 TeV HMT
kT slice
Tracks' pairs
(%)
N slice
Tracks' pairs
(%)
pT slice
Tracks' pairs
(%)
100 - 200
9.2%
108 - 129
2.8%
100 - 300
12.2%
200 - 300
13.0%
130 - 145
26.4%
300 - 500
20.5%
300 - 400
13.9%
146 - 157
28.7%
500 - 1000
47.7%
400 - 500
12.9%
158 - 190
37.6%
1000 - 2000
19.6%
500 - 600
11.1%
> 190
4.5%
600 - 700
9.2%
700 - 1000
18.2%
1000 - 1500
12.5%
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R&λ
distributions
of 0.9 TeV
C2(Q)
Dependence of R and λ:
 On track multiplicity
Ntracks
 On track pT threshold
 On pair’s pT threshold
“kT”
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R&λ
distributions
of 7 TeV HMT
C2(Q)
Dependence of R and λ:
 On track multiplicity
Ntracks
 On track pT threshold
 On pair’s pT threshold
“kT”
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R and λ distributions vs N
of different energy data C2(Q):
0.9 TeV, 7 TeV and 7TeV HMT
Dependence of λ parameter
on track multiplicity N
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Dependence of R parameter
on track multiplicity N
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CMS Results
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R and λ distributions vs pT
of different energy data C2(Q):
0.9 TeV, 7 TeV and 7TeV HMT
Dependence of λ parameter
on track pT
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Dependence of R parameter
on track pT
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R and λ distributions vs kT
of different energy data C2(Q):
0.9 TeV, 7 TeV and 7TeV HMT
Dependence of λ parameter
on track pair’s kT
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Dependence of R parameter
on track track pair’s kT
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World results
Comparison with previous
measurements
Preliminary
ATLAS √s = 7 TeV HMT
ATLAS √s = 900 GeV
Most of the previous experiments
provided r measurement with a “traditional”
Gaussian fit. The comparison can be done
between first momentum
with a scale factor √ :
r  rgauss / 
0.9 TeV
r = 0.73
7 TeV HMT r = 0.91
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Systematic Effects
The systematic uncertainties were estimated by comparing the C2(Q) function
parameters estimated from different analysis approaches and different fitting
and selection conditions.
The study for 0.9 TeV and 7 TeV HMT is done for the case of using “UCP us” as
the reference distribution.
Sources of systematics for BEC studies:
 Bin sizes
 Fit intervals
 Qmin thresholds
 Reference distributions
 Monte Carlo types (for DR C2(Q) 0.9 TeV case)
 Track Reconstruction Efficiency (only for 0.9 TeV data sample)
 Splitting and merging of the tracks
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Systematic Effects – more details (1)
Systematics due to binning
• We fit the C2(Q) functions on interval (20-2000) MeV
• The interval is divided to 20 MeV bins
• We compared the results for bin size 10, 20 and 30 MeV
• The impact to the fit parameters is at level :
I.
0.9 TeV :
σλ - 5 ÷ 9%, σR - 3 ÷ 5% for different fit models.
II. 7 TeV HMT : σλ - 7 ÷ 12%, σR - 3 ÷ 8% for different fit models.
Systematic uncertainty due to fit
• The region of resonances should be removed from fit
• BEC groups (Dubna, Pisa, Bratislava) choose to exclude the interval (400-800)
MeV
• The systematics was assumed as a standard deviation for various boundaries:
• The result for fit parameters is:
I.
0.9 TeV :
σλ - 2 ÷ 3%, σR - 3 ÷ 5% for different fit models.
II. 7 TeV HMT : σλ - 2 ÷ 3%, σR - 3 ÷ 8% for different fit models.
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Systematic Effects – more details (2)
Systematics for Qmin threshold
• The ATLAS detector has a finite resolution on Q, 5 MeV at low Q, 20 MeV at 1
GeV
• The default minimum of Q is set to 20 MeV
• We compared the results with Qmin = 10, 20 and 30 MeV
• The impact to fit parameters is:
I.
0.9 TeV :
σλ - 12 ÷ 36%, σR - 10 ÷ 26% for different fit models.
II. 7 TeV HMT : σλ - 8 ÷ 17%, σR - 5 ÷ 13% for different fit models.
Systematics due to the reference distribution
• We reconstructed the C2(Q) functions using a few reference distributions (as
mentioned before) but for the detail study we used only 3 most interesting for
us reference types:
UCP us, OHP ls and DR UCP us (only for 0.9 TeV data sample)
• The default reference distribution was choose the UCP us function.
• The impact to the fit parameters is at level:
I.
0.9 TeV :
σλ - 22 ÷ 55%, σR - 18 ÷ 22% for different fit models.
II. 7 TeV HMT : σλ - 32 ÷ 54%, σR - 30 ÷ 41% for different fit models.
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Systematic Effects – more details (3)
Systematic uncertainty for the Double ratio of the C2(Q) functions of 0.9 TeV data
sample due to MC production
• Pythia, PhoJet and Perugia0 MC productions were compared.
• The fit parameters change at level:
I.
0.9 TeV :
σλ - 14 ÷ 22%, σR - 10 ÷ 14% for different fit models.
II. 7 TeV HMT : NO MC for this data
Systematics due to Track Reconstruction Efficiency for 0.9 TeV data sample
• The efficiency of track reconstruction at ATLAS is only 10% for 100 MeV
• We expect a low affect to C2(Q) function (we use a ratio of two distributions).
• For restoring this systematics we used several C2(Q) functions – one with the
usual efficiency and two another with adding and subtraction of a weight equal
to the inverse efficiency.
I.
0.9 TeV :
σλ - 0 ÷ 4%, σR - 2÷ 2.2% for different fit models.
II. 7 TeV HMT : NO INFO
Splitting/ merging of tracks
• Assumed to be negligible
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R & λ tables of the total systematics:
0.9 TeV and 7 TeV HTM
0.9 TeV
7 TeV HTM
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Conclusions
1. We present the results of a study of pp collisions at √s = 0.9 TeV and 7 TeV
collected by the ATLAS experiment at the LHC collider.
2. The Bose-Einstein correlations of the π±π± two boson system have been studied in
the minimum-bias and high-multiplicity events. The research was carried out on a
sample of ≈350 000 events at 0.9 TeV; ≈20000000 events at 7 TeV (minimum-bias
trigger) and ≈14000 at 7 TeV (high multiplicity trigger).
3. The two pion correlations have been retrieved. The multiplicity distribution was
corrected on track reconstruction efficiency. The final results were corrected on the
coulomb interactions.
4. Five different reference samples were compared and discussed.
5. A significant two-pion correlation enhancement near origin is observed. This
enhancement effect has been used to evaluate the radius and haoticity of the twopion emitter source.
6. A comparison between 4 different parameterizations of C2(Q) function is given.
7. We studied BEC in dependent of charged hadron multiplicity, transverse momentum
of π±π± two boson system and transverse momentum of each hadrons from two
boson system . The radius of the emission source measured from the fit is
Rg=1.30±0.03 (0.9 TeV); Rg=1.61±0.02 (7 TeV HMT). It is in agreement with
world results.
8. For the first time we studies BEC at very high multiplicity region. We found that
BEC radius become saturated at high multiplicity of charged hadrons.
BACKUP SLIDES
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The HBT effect
• History
 „Interference between two different photons can
never occur.” P. A. M. Dirac, The Principles of Quantum
Mechanics, Oxford, 1930
 Robert Hanbury Brown and Richard Q. Twiss,
(engineers, worked in radio astronomy) found
correlation between photons from different sources.
 „In fact to a surprising number of people the idea that
the arrival of photons at two separated detectors can
ever be correlated was not only heretical but patently
absurd, and they told us so in no uncertain terms, in
person, by letter, in print, and by publishing the
results of laboratory experiments, which claimed to
show that we were wrong …”
Click to edit Master text styles
• Astronomical usage
 Intensity interferometry in radio astronomy
 Angular diameter of a main sequence star measured.
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Bose-Einstein Correlations
source
• Two plane-waves:
• Bosons: need for symmetrization
S(x,k)
x2
x1
Y1,2
• Spectrum:
S(x,k) is the source distribution
• Two-particle spectrum (momentum-distribution):
k k2
1
detector
• Approximations: Plane-wave, no multiparticle symmetrization, thermalization …
• The invariant correlation function depends on relative and average moments
• Uses Fourier-transformed form of the source
• We can get the source from correlation
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ATLAS Detector
A Toroidal LHC ApparatuS
Minimum Bias Trigger Scintillator (MBTS)
Inner Detector (ID)
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ATLAS Inner Detector
Includes different tracking subdetectors such as Pixel detectors,
silicon SemiConducter Tracker (SCT) and Transition Radiation
Tracker (TRT), pseudorapidity coverage |η|<2.5
 Main detector to measure charged tracks
 Well modeled by Monte Carlo
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Minimum Bias Trigger Scintillator
 32 independent wedge-shaped plastic scintillators
(16 per side) read out by PMTs, 2.09<|η|<3.84
 Designed to for triggering on min bias events, >99% efficiency
 MBTS timing used to veto halo and beam gas events
 Also being used as gap trigger for various diffractive subjects
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