analysis of < p t > - n ch correlations in pp and pp collisions
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Analysis of <pT>-Nch Correlations in pp and pp CollisionsDenis DerkachSaint-Petersburg State University, Russia
Erice, Italy, 05.09.2006
International Subnuclear Physics School
D. Derkach, ISSP'06, Erice 205 Sep 2006
Outline
• motivation; • effective pomeron exchange model;• <pt>-Nch correlation description;
• experimental data description;• prospects for ALICE/CERN.
D. Derkach, ISSP'06, Erice 305 Sep 2006
pp Collisions
D. Derkach, ISSP'06, Erice 405 Sep 2006
Experimentally Observed pt-Nch Correlations
0 10 20 30 40 50 60 70 80 900,28
0,30
0,32
0,34
0,36
0,38
0,40
0,42
0,44
0,46
0,48
0,50
0,52
0,54
0,56
0,58
NA5 19 GeV |y|<1.5
SppS 540 GeV |y|<2.5
UA1 900 GeV |eta|<2.5
N_ch
<p_
t>N
ch
, GeV
/c
SPS 31 GeV |y|<2
UA1 200 GeV |eta|<2.5
SPS 63 GeV |y|<2
D. Derkach, ISSP'06, Erice 505 Sep 2006
Experimentally Observed pt-Nch Correlations. Features• <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.
D. Derkach, ISSP'06, Erice 605 Sep 2006
Experimentally Observed pt-Nch Correlations. Literature• 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.
D. Derkach, ISSP'06, Erice 705 Sep 2006
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
D. Derkach, ISSP'06, Erice 805 Sep 2006
String Formation
A.Capella, U.P.Sukhatme, C.-I.Tan and J.Tran Thanh Van, Phys. Rep.236(1994)225
D. Derkach, ISSP'06, Erice 905 Sep 2006
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
D. Derkach, ISSP'06, Erice 1005 Sep 2006
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
D. Derkach, ISSP'06, Erice 1105 Sep 2006
Classical Multi-Pomeron Exchange Model
n
tchnT
pgNnPwpd
dN)(),(
2
normalized cross section of simultaneous production of
n-pomeron showersnw
),( chNnPprobability for strings to give particles after
hadronization
n2 chN
)( tpgtransverse momentum distribution for particles coming from a single string
A. B. Kaidalov, K. A. Ter-Martirosyan Phys. Lett. 11B (1982) 247
D. Derkach, ISSP'06, Erice 1205 Sep 2006
Classical Multi-Pomeron Exchange Model
n
t
ch
Nynk
n
l
lzp
t t
mp
N
ynke
l
ze
nzpd
tkdN ch
))(
exp(!
)2()
!1(
),,( 222
1
02
n
tchnT
pgNnPwpd
dN)(),(
2
No correlations can be obtained from this distribution!
D. Derkach, ISSP'06, Erice 1305 Sep 2006
n
t
ch
Nynk
n
l
lzp
t tn
mp
N
ynke
l
ze
nzpd
tkdN ch
))(
exp(!
)2()
!1(
),,( 222
1
02
Modifications. Basic formula
- parameter that accounts effectively collectivity
n
t
ch
Nynk
n
l
lzp
t t
mp
N
ynke
l
ze
nzpd
tkdN ch
))(
exp(!
)2()
!1(
),,( 222
1
02
= =
D. Derkach, ISSP'06, Erice 1405 Sep 2006
Parameters
t – average string tension
k – mean number of particles produced per unit rapidity by one string
- efficient string collective coefficient
Classical model parameters:
Modificated model parameter:
D. Derkach, ISSP'06, Erice 1505 Sep 2006
Fitting
0 20 40 60 80 100
0,30
0,35
0,40
0,45
0,50
0,55
0,60
0,65
Nch
<p t>
Nch
, GeV
/c
900 GeV pp collisionsFitting was done for 11 different datasets.
Energy range covered is 17-1800 GeV.
The parameter values were extracted.
D. Derkach, ISSP'06, Erice 1605 Sep 2006
Fitting
Fitting was done for 11 different datasets.
Energy range covered is 17-1800 GeV.
The parameter values were extracted.
0 5 10 15 20 25 30
0,38
0,40
0,4263 GeV pp collisions
Nch
<p t>
Nch
, GeV
/c
D. Derkach, ISSP'06, Erice 1705 Sep 2006
Fit results
10 100 1000
-0,5
0,0
0,5
b
CM energy, GeV10 100 1000
0,00,20,40,60,81,01,21,41,61,82,0
k
CM Energy
D. Derkach, ISSP'06, Erice 1805 Sep 2006
Fit results
10 100 10000,0
0,1
0,2
0,3
0,4
0,5
0,6t,
Gev
2
CM Energy, GeV
D. Derkach, ISSP'06, Erice 1905 Sep 2006
<pt> vs. CM Energy
100 10000,000,050,100,150,200,250,300,350,400,450,50
FNAL (E735) SPS ISR FNAL(CDF) ISR(NA5)
Our Calculations for t=0.57 GeV2
Our Calculations for t=0.4 GeV2<P
T>, G
eV/c
CM Energy, GeV
D. Derkach, ISSP'06, Erice 2005 Sep 2006
Mean number of pomerons
100 1000 100000,51,01,52,02,53,03,54,04,55,05,5
Num
ber of
pom
eron
s
Energy, GeV
D. Derkach, ISSP'06, Erice 2105 Sep 2006
Dispersion in number of pomerons
100 1000 100000,0
0,5
1,0
1,5
2,0
2,5N
orm
aliz
ed d
ispe
rsio
n
Energy, GeV
D. Derkach, ISSP'06, Erice 2205 Sep 2006
LHC predictions from EPEM
0 20 40 60 80 1000,30
0,35
0,40
0,450,50
0,55
0,60
0,65
0,70
0,75
t=0.43
t=0.57
LHC predictions, | |<0.9, sqrt(s) = 14 TeV
<p t>
, GeV
/c
Nch
The predictions are made for both parameter t values. The plot should be chosen after specification of experimental data.
D. Derkach, ISSP'06, Erice 2305 Sep 2006
Conclusions
• 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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