Transcript Document

Model of pp and AA collisions for the description
of long-range correlations
V. Kovalenko, V. Vechernin
Saint Petersburg State University
The XXI International Baldin Seminar on High Energy Physics Problems
"Relativistic Nuclear Physics and Quantum Chromodynamics"
Joint Institute for Nuclear Research, Dubna, 10-15 September
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p-p interaction:
parton distributions
Inclusive momentum distributions are taken from [1,2]:
At n>1 the sea quarks and antiquarks have the same
distribution as the valence quarks.
Poisson distribution for the number of quark-antiquark
(diquark) pairs (n) is assumed with some parameter λ
[1] A.B. Kaidalov, O.I.Piskunova. Zeitschrift fur Physik C 30(1):145-150, 1986
[2] G.H. Arakelyan, A.Capella, A.B.Kaidalov, and Yu.M.Shabelski. Eur.Phys.J (C), 26(1):81-90, 2002
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p-p interaction:
parton distributions
Corresponding exlusive distribution of the momentum
fractions:
Valence quark is labelled by N-1, the diquark by N, and the
other refers to sea quarks and antiquarks.
N=2*n
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p-p interaction:
parton distributions
Corresponding exlusive distribution of the momentum
frations:
Valene quark is labelled by N-1, the diquark by N, and the
other refers to sea quarks and antiquarks.
N=2*n
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p-p interaction:
color dipoles
The probability amplitude for the сollision of two dipoles with сoordinates
(r1,r2), (r3,r4) [3,4]:
Confienment is taken into account by introduction of some cut off at
rmax ≃ 0.2 − 0.3fm. It leads:
The total probability of the inelastic interaction of two protons
in the eikonal approximation:
[3] G. Gustafson, Acta Phys. Polon. B40, 1981 (2009)
[4] C. Flensburg, G. Gustafson, and L. Lonnblad, Eur. Phys. J. (C) 60, 233 (2009)
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p-p interaction:
string fusion
The interaction of colour strings in transverse plane is carried out in the
framework of local string fusion model [5]
with the introduction of the lattice in the impact parameter plane.
The finite rapidity length of strings is taken into account [6-8].
Sk – area, where k strings are overlapping, σ0 single string transverse
area, μ0 and p0 – mean multiplicity and transverse momentum from one
string
[5] Braun, M.A. and Pajares, C. Eur. Phys. J. (C),16,349,2000
[6] V. Vechernin and R. Kolevatov, Physics of Atomic Nuclei 70, 1797 (2007)
[7] V. Vechernin and R. Kolevatov, Physics of Atomic Nuclei 70, 1809 (2007)
[8] Vechernin, V. V. and Kolevatov, R. S., Simple cellular model of long-range multiplicity and
pt correlations in high-energy nuclear collisions 2003 http://arxiv.org/abs/hep-ph/0304295v1
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string fusion
mechanism versions
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p-p interaction:
parameter fixing
tot
σinel
, mb
rstr=0.2, αs= 0.7, μ0=0.92 ✔, p0=0.36
Сечение . Pt в backup
rstr=0.3, αs= 0.5, μ0=1.02, p0=0.35
rstr=0.4, αs= 0.5, μ0=1.12, p0=0.346
Connection of λ with collision energy ->
Long-range correlations
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Scaled variables:
B → B / <B> , F → F / <F>
Correlation function
f (F) = <B>F
approximation:
а+b x
Correlation
coefficients:
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n-n correlation function
effects of string fusion
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n-n, pt-n, pt-pt
correlation functions
pp, 7 TeV
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Dependence of correlation coefficients
on the width of backward rapidity window
Rapidity windows used:
y
0.6 0.8
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Dependence of correlation coefficients
on the width of forward rapidity window
Rapidity windows used:
Fit:[6,7,9]
y
-0.8 -0.6
[9] V. Vechernin. Long-Range Rapidity Correlations in the Model with Independent Emitters,
XX Baldin ISHEPP, 2010, arXiv:1012.0214v1 [hep-ph]
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Dependense of n-n, pt-n, pt-pt
correlations on the rapidity gap
pp, 7 TeV
Δy=0.8
AA interactions
Compare with Glauber's model
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Number of participant, number of binary collisions, their variations and scaled
variatons and correlator for σinelNN =34mb, calculated in the model of this work:
250
1000
900
800
700
600
500
400
300
200
100
0
NpartA
NpartAB
N_C
200
150
100
50
0
0
2
4
6
8
1000
900
DnpartAB 800
700
DN_C*
600
500
400
300
200
100
0
10 12 14 16 18
DNPartA
10 12 14 16 18
0
2
4
6
8
3,5
70
correlator*
60
D/N
50
D_C/N_C
3
2,5
2
40
1,5
30
1
20
0,5
10
0
0
2
4
6
8
10
12
14
16
0
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The same for the Glauber's model (σNN =34mb) :
1000
900
800
700
600
500
400
300
200
100
0
250
200
NpartAB
N_C
70
correlator*
60
D/N
5
D_C/N_C
50
4
40
2000
3
30
1500
2
20
1
10
DNPartA
4500
DnpartAB
4000
DN_C*
150
7
6
5000
NpartA
3500
3000
2500
100
50
1000
500
0
2
4
6
8
10
12
14
16
18
0
0
0
2
4
6
8
10 12 14 16 18
0
0
2
4
6
8
10
12
14
16
0
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AA interaction:
charged multiplicity
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PbPb, 2.76TeV
[10]
[10] K. Aamodt et al (ALICE Collaboration).Phys. Rev. Lett.,106, 032301, 2011.
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AA interaction:
correlation coefficients
PbPb, 2.76TeV
Fixed impact parameter
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Conclusions
Long-range correlations are calculated in the framework of the
string fusion model, taking into account finite rapidity length of
the strings.
n-n, pt-n and pt-pt correlation functions demonstrating nonlinear behaviour are found.
Dependence of the correlation coefficients on the width of
rapidity windows and the gap between them is calculated.
The model enables to describe the AA interactions without
referring to the Glauber picture of nucleon-nucleon collisions.
The number of soft binary collisions is proved to be less than in
the Glauber approach.
Correlation coeficients for Pb-Pb collisions are estimated in
case of fixed impact parameter.
In Pb-Pb collisions at LHC energy the strength of pt-pt
correlation is larger compared to pt-n correlation.

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Backup
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Backup
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Backup
Mean pt
rstr=0.2, αs= 0.7, μ0=0.92, p0=0.36 ✔
Сечение . Pt в backup
rstr=0.3, αs= 0.5, μ0=1.02, p0=0.35
rstr=0.4, αs= 0.5, μ0=1.12, p0=0.346
Connection of λ with collision energy ->
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Backup
Pt-pt correlation