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 “TERMALIZATION” Collective behaviors of secondary particles

in proton-proton interactions at 70 GeV/c

J.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 quark 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)

(II) 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) 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• 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 Pm

P(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

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):

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-2

mN (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), thanN=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)

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):

!mmeP

mm

m

Binomial distribution for gluons + idea of convolution of two stages MD

ME

m

nmNhnhn

mN

mm

n Nn

Nn

mmesP C

0

)2(22 ,1

!)(

,20.48.2,12.63.1,13.24.4,2~2 mnN h

6.2~

ME -maximal possible number of evaporated gluons

from QGS

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

From TSTM (figure):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.

.036.1, 000

hh nmnn

The simplification on the second stage as TSM:tot

htot

h

ch

hch

Nn

Nn

Nn

0

0

.ochtot nnn where

13.57.20 n

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.

2

1

2

1

)(

))((),(0 n

nnn

n

nnchn

ch

sP

nnsPsnn

Centauro events with large charged particles and practically no accompanying neutrals may be realized in the region

VHMP. AntiCentauro events with a large number of neutrals and very

small charged must be absent.

Soft photons (SP)

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 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

1

8 3

3

Th

ecd

d

337

0

)(10479.5)(

fm

TTTgl

Table 1. The number of SP

 p, MeV/c

 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

 

Conclusions1. The two stage gluon model for the description of MD in

pp-interactions with VHMP at 70 GeV/c was proposed.

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

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

4. The number of soft photons is calculated.5. It is ascertained that Centauro events may be discovered

in the VHMP charged region. The existence of AntiCentauro events is rejected.