analysis of - n ch correlations in pp and pp collisions

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.


pp Collisions

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

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.


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.


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


String Formation

A.Capella, U.P.Sukhatme, C.-I.Tan and J.Tran Thanh Van, Phys. Rep.236(1994)225


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


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



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



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!


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

= =


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:

Fitting

0 20 40 60 80 100

0,30

0,35

0,40

0,45

0,50

0,55

0,60

0,65

Nch



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.

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



Nch

, GeV

/c


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


Fit results

10 100 10000,0

0,1

0,2

0,3

0,4

0,5

0,6t,

Gev

2

CM Energy, GeV

<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, G

eV/c

CM Energy, GeV


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


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

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



, GeV

/c

Nch

The predictions are made for both parameter t values. The plot should be chosen after specification of experimental data.


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 “ ”.

analysis of < p t > - n ch correlations in pp and pp collisions

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