Transcript Analysis of pT-Nch Correlations in pp and pp Collisions

Analysis of <pT>-Nch
Correlations in pp
and pp Collisions
Denis Derkach
Saint-Petersburg State University,
Russia
Erice, Italy, 05.09.2006
International Subnuclear Physics School
Outline
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motivation;
effective pomeron exchange model;
<pt>-Nch correlation description;
experimental data description;
prospects for ALICE/CERN.
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pp Collisions
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Experimentally Observed pt-Nch
Correlations
UA1 900 GeV |eta|<2.5
0,58
0,56
SppS 540 GeV |y|<2.5
0,54
0,52
<p_t>
N ch
, GeV/c
0,50
0,48
0,46
0,44
UA1 200 GeV |eta|<2.5
0,42
0,40
SPS 63 GeV |y|<2
0,38
0,36
0,34
NA5 19 GeV |y|<1.5
0,32
SPS 31 GeV |y|<2
0,30
0,28
0
10
20
30
40
50
60
70
80
90
N_ch
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Experimentally Observed pt-Nch
Correlations. Features
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<pt>Nch does not grow with energy at low
Nch.
<pt>Nch flattens at high Nch.
Experiments can be divided into two
groups depending on the value of <pt> at
Nch close to 0.
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Experimentally Observed pt-Nch
Correlations. Literature
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NA49 collab. arXiv:hep-ex/0311009.
A. Breakstone et al. (ABCDHW Collaboration),
Phys. Lett. 132B (1983) 463.
UA1 collab., Nucl Phys 335B (1990) 261.
F.Abe et.al, Phys.Rev.Lett. 61 (1988) 1819.
C.De Marzo et al. Phys. Rev. 29D (1984) 363.
V.V. Aivazyan et al., Phys.Lett. 209B (1988) 103.
T. Alexopoulos et al., Phys. Lett. 336B (1994) 599.
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Classical Multi-Pomeron Exchange
Model
Pomeron is a virtual particle that is
exchanged during the inelastic scatering
process with vacuum quantum numbers
flow.
It can be considered as a pair of strings.
The number of pomerons exchanged rises with energy.
Collective effects are not included in the model.
A. B. Kaidalov and K. A. Ter-Martirosyan, Phys. Lett. B 117 (1982) 247
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String Formation
A.Capella, U.P.Sukhatme, C.-I.Tan and J.Tran Thanh Van, Phys. Rep.236(1994)225
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Dual Parton Model calculations
In this model an additional
assumption was made: a
transverse momentum of
sea quarks was introduced
as a parameter.
This parameter was fitted
to be 1.1 GeV.
P. Aurenche, F. W. Bopp and J. Ranft,
Phys. Lett. 147B, (1984) 212
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String Formation


Collective effects are
observed.
Possible solution –
string interactions.
M. A. Braun and C. Pajares, Phys. Lett.
B 287 (1992) 154; Nucl. Phys. B 390
(1993) 542, 549
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Classical Multi-Pomeron Exchange
Model
dN
  wn P(n, N ch ) g ( pt )
2
d pT
n
normalized cross section of simultaneous production of
wn
n-pomeron showers
probability for 2 n strings to give
P(n, Nch )
N ch
particles after
hadronization
g ( pt )
transverse momentum distribution for particles coming from a
single string
A. B. Kaidalov, K. A. Ter-Martirosyan Phys. Lett. 11B (1982) 247
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Classical Multi-Pomeron Exchange
Model
dN
  wn P(n, N ch ) g ( pt )
2
d pT
n
N ch
2
2
n 1 l
p


(
p

m
)
dN( , k , t )
z
(
2
nk

y
)
z
 2 nky
t
  (1  e  )e
exp(
)
2
d pt
Nch!
t
n nz
l 0 l!
No correlations can be obtained from this distribution!
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Modifications. Basic formula
=
=
N ch
2
2
n 1 l
p


(
p

m
)
dN( , k , t )
z
(
2
nk

y
)
z
 2 nky
t
  (1  e  )e
exp(
)
2

d pt
Nch!
nt t
n nz
l 0 l!

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- parameter that accounts effectively collectivity
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Parameters
Classical model parameters:
t – average string tension
k – mean number of particles produced per unit rapidity
by one string
Modificated model parameter:

- efficient string collective coefficient
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Fitting
900 GeV pp collisions
0,65
Fitting was done for
11 different datasets.
0,55
0,50
Energy range covered is
17-1800 GeV.
0,45
ch
<p t> N , GeV/c
0,60
The parameter values
were extracted.
0,40
0,35
0,30
0
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20
40
Nch
60
80
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100
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Fitting
63 GeV pp collisions
0,42
<p t> N , GeV/c
Fitting was done for
11 different datasets.
0,40
ch
Energy range covered is
17-1800 GeV.
The parameter values
were extracted.
0,38
0
5
10
15
20
25
30
Nch
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Fit results
0,5
k
b
0,0
-0,5
10
100
1000
2,0
1,8
1,6
1,4
1,2
1,0
0,8
0,6
0,4
0,2
0,0
10
CM energy, GeV
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100
1000
CM Energy
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Fit results
0,6
0,5
t, Gev
2
0,4
0,3
0,2
0,1
0,0
10
100
1000
CM Energy, GeV
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<P T >, GeV/c
<pt> vs. CM Energy
0,50
0,45
0,40
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
FNAL (E735)
SPS
ISR
FNAL(CDF)
ISR(NA5)
Our Calculations for t=0.57 GeV
Our Calculations for t=0.4 GeV
100
2
2
1000
CM Energy, GeV
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Mean number of pomerons
5,5
Number of pomerons
5,0
4,5
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
100
1000
10000
Energy, GeV
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Dispersion in number of pomerons
Normalized dispersion
2,5
2,0
1,5
1,0
0,5
0,0
100
1000
10000
Energy, GeV
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LHC predictions from EPEM
0,75
0,70
t=0.57
0,65
<p t>, GeV/c
The predictions are
made for both
parameter t values.
The plot should be
chosen after
specification of
experimental data.
LHC predictions, |
|<0.9, sqrt(s) = 14 TeV
0,60
0,55
t=0.43
0,50
0,45
0,40
0,35
0,30
0
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40
60
Nch
80
100
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Conclusions
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Experirmental results on mean pt and on pt-n correlation are
summarized in a wide energy range.
Negative and positive correlations are reproduced in one approach
of modified multi-Pomeron exchange model.
Smooth behavior of parameter “  ” with energy is observed.
Logarithmic growth of number of Pomerons and their dispersions
with energy in the region 17 GeV – 1.8 TeV are related to observed
experimental correlations.
First results on pp collisions in ALICE at the LHC at 5.5 TeV on the
pt-Nch corelation at midrapidity should clarify the functional
dependence of “  ”.
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