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Multi-pomeron exchange model for pp and pp collisions at ultra-high energy
E. O. Bodnyaa;b, D. A. Derkachc, V. N. Kovalenkoa, A. M. Puchkova and G. A. Feofilova
a b c

Saint Petersburg State University, Russia University of California, Berkeley, USA Oxford University, UK

QFTHEP'2013, Repino Saint Petersburg, Russia


Experimentally Observed pt-Nc Correlations
0,58 0,56 0,54 0,52

h

UA1 900 GeV |eta|<2.5 ISR 540 GeV |y|<2.5

N , GeV/c

0,50 0,48 0,46 0,44 0,42 0,40 0,38 0,36 0,34 0,32 0,30 0,28 0 10 20 30 40 50 60 70 80 90

ch

UA1 200 GeV |eta|<2.5 ISR 63 GeV |y|<2

NA5 19 GeV |y|<1.5 ISR 31 GeV |y|<2

N_ch

2


Regge-Gribov multipomeron approach
Probability of production of n pomerons
' '

where n ­ cross section of n cut-pomeron ex c hange :

Each cut-pomeron corresponds to pair of strings

3


Regge-Gribov multipomeron approach

Numerical values of parameters used [1]:

[1] Lakomov I. A., Vechernin V. V. , PoS (Baldin ISHEPP XXI) 072 (2012)
4


Regge-Gribov multipomeron approach
Mean and variance of the number of pomerons:

Variance

Mean

5


Description of multiplicity
Probability for n strings to give N
ch

particles: ,

where k ­ is mean multiplicity per rapidity unit from one pomeron; ­ acceptance i.e. width of (pseudo-)rapidity interval Probability to have N
ch

particles in a given event:

Mean charged multiplicity:
6


Description of transverse momentum
Schwinger mechanism of particles production from one string [2]:
~

pt-Nch correlation function in the model is calculated as:

[2] Schwinger J. Phys. Rev. 1951. Vol. 82, P. 664 ­ 679

7


Description of transverse momentum
Schwinger mechanism of particles production from one string [2]:
~

pt-Nch correlation function in the model is calculated as:

[2] Schwinger J. Phys. Rev. 1951. Vol. 82, P. 664 ­ 679

8


Distribution of N

ch

and particles over pt
Probability distribution Probability of production of n pomerons Poisson distribution of the charged particles from 2n string Modified Schwinger mechanism
9


Determination of the parameter k
from experimental data on charged multiplicity:

Fitted by


pt-Nch correlations
The data on pt-Nch correlations are analyzed in wide energy region: from 17 GeV to 7 TeV Values of the parameters and t are obtained. Examples of fitting:
pp, 17 GeV pp, 19 GeV pp, 22 GeV pp, 31 GeV pp, 63 GeV
Data (points): NA49 Collaboration Data (points): UA1 Collaboration

pp, 200 GeV pp, 540 GeV pp, 900 GeV pp, 1800 GeV pp, 1800 GeV pp, 2360 GeV
Data (points): CMS Collaboration Data (points): CMS Collaboration

pp, 7000 GeV

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Dependence of the parameters and t on collision energy

t = 0.566 GeV

2

t = 0.428 GeV

2

Fitted by 12


LHC predictions at 14 TeV
The predictions are made for several parameter t values. The plot should be chosen after specification of experimental data.

t = 0.731 GeV t = 0.676 GeV t = 0.566 GeV
t = 0.731 GeV2 ­ parabola fit applied t = 0.676 GeV2 ­ as at 7 TeV t = 0.566 GeV2 ­ averaged over all experimental data

2 2 2

13


relation to String Fusion

=>

independently on energy

­ mean multiplicity from one source ­ characteristic transverse momentum from one source 14


relation to String Fusion
Ratio of mean multiplicity from one source over characteristic pt from one source


Conclusions
·

Experirmental results on pt-Nch correlation are studied in a wide energy range and model parameters are obtained: ­ Logarithmic growth of mean multiplicity from one pomeron (k) with energy is obtained ­ Smooth growth of parameter , accounting string collectivity ­ The parameter t is found to be constant. ­ Numerical agreement with string fusion model

·

predictions for pt-Nch correlation behavior at the collision energy of 14 TeV have been made
16


Backup slides

17




20


Distribution of N
200 GeV

ch
900 GeV

2360 GeV

7000 GeV

21


Mean transverse momentum


String Formation

[2] A. B. Kaidalov and K. A. Ter-Martirosyan, Phys. Lett. B 117 (1982) 247

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String Formation


Collective effects are observed. Possible solution ­ string interactions. [3]

[3] M. A. Braun and C. Pajares, Phys. Lett. B 287 (1992) 154; Nucl. Phys. B 390 ( 1993) 542, 549

24


Experimentally Observed pt-Nc Correlations. Features

h

Experimentally Observed pt-Nch Correlations. Features

25

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

26


Classical Multi-Pomeron Exchange Model
dN = 2 d pT


n

w n P ( n,N ch ) g ( p t )

w

normalized cross section of simultaneous production of

n

n-pomeron showers probability for hadronization transverse momentum distribution for particles coming from a single string

P ( n,N ch )

2n strings to give

N

ch

particles after

g ( pt )

A. B. Kaidalov, K. A. Ter-Martirosyan Phys. Lett. 11B (1982) 247

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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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