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The description of pp-interactions with very high multiplicity at 70 GeV/c by Two Stage Gluon Model. E.S.Kokoulina, Gomel STU, Belarus V.A.Nikitin, JINR, Russia.

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E s kokoulina gomel stu belarus v a nikitin jinr russia

The description of pp-interactions with very high multiplicity at 70 GeV/c by Two Stage Gluon Model

E.S.Kokoulina, Gomel STU, Belarus

V.A.Nikitin, JINR, Russia


Project “ with very high multiplicity at 70 GeV/c by Two Stage Gluon ModelTERMALIZATION” Collective behaviors of secondary particles in proton-proton interactions at 70 GeV/cJ.Manjavidze and A.Sissakian (Phys.Rep., 2001)A.Sissakian (Usp.Phys.Nauk, 2003)

QCD: proton consists from quarks and gluons.

Two stage gluon model for the description of high energy multiparticle production (MP) is supposed.

I stage (quark-gluon division): QCD and thermodynamical aproaches;

II stage (hadronization): the phenomenological description


Our model investigations had shown that with very high multiplicity at 70 GeV/c by Two Stage Gluon Modelquark division of initial protons at 70 GeV/c is absent.MP is realized by active gluons.

The idea P.Carruthers about a passive role quarks: “labels and sources of colour perturbation in the vacuum: meanwhile the gluons dominates in collisions and MP.” (1984)

The domination of gluons was first proposed by S.Pokorski and L.Van Hove (1975).


One of the most generally accepted methods for study of multiparticle dynamics is the Multiplicity Distributions (MD)analysis. Using this methods it is possible to known about the development of study processes.

Two schemes are supposed. They are distinguished only by quark-gluon (QG) stage:

(I) we want to study gluon division inside QG system (QGS) – branch model (TSMB)

we don’t interest what is going inside QGS –

thermodynamic model (TSTM)


In both schemes some of gluons (not of all) leave QGS and convert to real hadrons. We named such gluons active ones. In the thermodynamic idea we can say that active gluons are evaporated from hot QGS. After evaporation they pass stage of hadronization.


P p n 2 n 1 v babintsev 1976 n ch 20 in present experiment it is planned to get events with n 40 60
P+P leave QGS and convert to real hadrons. We named such gluons  n  +2 N (1) V.Babintsev (1976) nch<20 in present experiment it is planned to get events with n=40-60

At very high multiplicity (VHMP) and near the threshold of reaction (1) all particles have small relative momentum and than the large density of hadron system will be reached. According to generally accepted conception at these conditions that system should be in QGP state. (V.Boiko, L.Enkowsky (1991) E.Shuryak (1984)


The possible signal for QGP – direct photon production. Direct means that photons should not be decay products of hadrons. The explanation of the experimental increase of the rate of direct soft ’s as the results of Compton QG scattering in comparison with calculations based on the bremsstrahlung and radiative decays of hadrons is proposed. These photons give the information about early stage of QG interactions.


Basing for choice of scheme
Basing for choice of scheme Direct means that photons should not be decay products of hadrons. The explanation of the experimental increase of the rate of direct soft

  • The choice of MP scheme is based on comparison with experimental data.

  • Quark model O.Chikilev, P.Chliapnikov (1992)

  • Generator PYTHIA don’t agree with data for nch>10

  • We must build new scheme of hadrons interactions for MD description. We want to get agreement for VHMP-region.


At the beginning researches we took model where some of quarks and gluons from proton take part in the formation of hadron jets. Parameters of that model had values which were differed a lot from parameters obtained in Two Stage Model(TSM) for the description of MD in e+e—annihilation, especially parameters of hadronization. It was one of the main causes for refusal from a scheme with active quarks

TSM for e+e- annihilation: E.Kokoulina. XI Annual Seminar Nonlinear Phenomena in Complex System. Minsk, Belarus (2002) .

[hep-ph/0209334]


Hypothesis of soft colourless for gluons on the second stage:Pn(s) = m PmP(s) PnH(m,s) (2)Generation function (GF) for MD are determined by convolution of two stages Q(s,z) = m PmP(s) (QH(z))m = QP(s, QH(z)) (3) Pn(s) = 1/n! n/zn Q (s, QH(z))z=0 QH, QP – GF for MD at hadronization and in QGS

How much active gluons are into QGS at the first time after the impact of protons? We assume that their number may grow from 0 (analogue of impact parameter for nucleus). Only in the case of elastic scattering active gluons are absent. The simplest MD is Poisson (k– mean multiplicity)

Pk = e-kkk/k! (4)


Tsm with branch

TSM with branch stage:

On the first stage in the moment of impact some active gluons may appear. The energy of colliding protons is transformed into internal energy of QGS. The temperature of this system is raised. QCD: gluons may become nearly free particles. We use (4) for them. These active gluons in QGS have some energy. If their energy is large they may give branch process (A.Giovannini, 1979). MD for k active gluons (m –mean multiplicity) from Farry MD:

PmB(s) = 1/mk(1-1/m)m-k(m-1)(m-2)…(m-k+1)/(k-1)!,

if k>1, (5) or 1/m(1-1/m)m-1, if k=1. (6)


On the second stage some of active gluons may leave QGS and transform to real hadrons. We named that gluons evaporated. We introduce the parameter  - the ratio of evaporated gluons, leaving QGS, to all active gluons, which may transform to hadrons.

Our binomial distribution for MD of hadrons from evaporated gluons are

PnH = Cn-2mN (nh/N)n-2(1-nh/N)mN-(n-2) , (9)

N and nh – maximal possible and average multiplicities of hadrons from one active gluon on the second stage. Effect of two leading protons is taking into account.


Md in pp scattering in two stage gluon model with branch tsbm
MD in pp scattering in Two Stage Gluon Model with branch (TSBM):

Pn(s) =k=0MK e-kkk/k!

m=kMG1/mk(m-1)(m-2)…(m-k+1)/(k-1)! (1-1/m)m-k

C n-2mN (nh/N)n-2 (1-nh/N)mN-(n-2) , (10)

2 ~1 (70 GeV/c), ~10 (69 GeV/c).

N=40 and more, m=2.61+/-.08, =.472+/-.010, k=2.53+/-.05,

nh=2.50+/-.29, =4.89+/-.10


The maximal possible number of hadrons from gluon N> or ~ 40 –very much like the number of partons in the glob of cold QGP L.Van Hove.

If nh=1.63 (fix) (below in thermodynamic model), than

N=40, m=2.36+/-.10, =.728+/-.100, k=2.51+/-.06, nh=1.63,

=2.15+/-.18, 2~3.

At this case the part of evaporated gluons is about 73 %.


Thermodynamical model tstm

Thermodynamical model (TSTM) or ~ 40 –very much like the number of partons in the glob of cold QGP L.Van Hove.

After the impact some of active gluons may

leave QGS (evaporate) and fragment

to hadron jets. We describe evaporated

gluons by Poisson MD as (4):


Binomial distribution for gluons idea of convolution of two stages md

Binomial distribution for gluons + or ~ 40 –very much like the number of partons in the glob of cold QGP L.Van Hove.idea of convolution of two stages MD

-maximal possible number of evaporated gluons

from QGS

In e+e- - annihilation from TSM N~4-5


From TSTM (figure): or ~ 40 –very much like the number of partons in the glob of cold QGP L.Van Hove.the maximal possible of number of charged particles is 26(ME*N). In TSMB more hadrons.


From figure we see the maximal possible number of neutrals from tstm is 16 so for total 42
From figure we see the maximal possible number of neutrals from TSTM is 16, so for total – 42.

The simplification on the second stage as TSM:

where


Dependence of the mean multiplicities of neutral mesons versus of charged particles
Dependence of the mean multiplicities of neutral mesons versus of charged particles.

Bayess theorem, n1 > nch, n2 < 16+nch - big distinction with experimental data at small multiplicity.

The marked improvement:

Decrease top limit at low multiplicities (nch<10) to n2=2nch.

At bigger nch this limit n2=16+nch.

The low limit n1 is staying almost constant.


Centauro versus of charged particles.events with large charged particles and practically no accompanying neutrals may be realized in the region VHMP. AntiCentauroevents with a large number of neutrals and very small charged must be absent.


Soft photons sp

Soft photons (SP) versus of charged particles.

TSMB: several of active gluons are staying inside of hot QGS and don’t give hadron jets. New formed hadrons don’t contain inside themselves. They are catching up small energetic gluons which were free. Gluons have possibility to stick to them (confinement). Hot hadrons are exited. This energy may be thrown down by means of photon radiation. We want to estimate the number of them.


The equilibrium state we use the black body emission spectrum

The equilibrium state. We use the black body emission spectrum

The gluon density at the deconfinement temperature Tc=160-200 MeV can be estimated by comparison with relic one

T0=30K – relic temperature, Ngl(160MeV)~1000, Ngl(200MeV)~2000 at L=20 fm


Table 1 the number of sp

p, MeV/c spectrum

10

15

20

30

L, fm

N

N

N

N

50

75

100

120

3.96

13.36

31.61

64.87

13

45

107

209

32

107

253

495

107

361

855

1670

Table 1. The number of SP


Conclusions
Conclusions spectrum

1. The two stage gluon model for the description of MD in pp-interactions with VHMP at 70 GeV/c was proposed.

  • The important role of active gluons in the formation of new hadrons is shown.

  • The maximal possible number of charged and neutral mesons are obtained.

  • The number of soft photons is calculated.

  • It is ascertained that Centauro events may be discovered in the VHMP charged region. The existence of AntiCentauro events is rejected.


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