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

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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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Project TERMALIZATION 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

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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).

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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 dont interest what is going inside QGS
• thermodynamic model (TSTM)

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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.
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PP? n ? 2 N (1) V.Babintsev
(1976) nchlt20 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)

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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.
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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 dont agree with data for nchgt10
• We must build new scheme of hadrons interactions
  for MD description. We want to get agreement for
  VHMP-region.

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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 eeannihilation,
especially parameters of hadronization. It was
one of the main causes for refusal from a scheme
with active quarks

• TSM for ee- annihilation E.Kokoulina. XI Annual
  Seminar Nonlinear Phenomena in Complex System.
  Minsk, Belarus (2002) .
• hep-ph/0209334

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Hypothesis of soft colourless for gluons on the
second stagePn(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))?z0

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)

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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-k1)/(k-1)!,
• if kgt1,
  (5) or
  1/m(1-1/m)m-1, if k1. (6)

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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.

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MD in pp scattering in Two Stage Gluon Model with
branch (TSBM)

• Pn(s) ?k0MK e-kkk/k!
• ?mkMG1/mk(m-1)(m-2)(m-k1)/(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).
• N40 and more, m2.61/-.08, ?.472/-.010,
  k2.53/-.05,
• nh2.50/-.29, ?4.89/-.10
• 
  
  

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

• If nh1.63 (fix) (below in thermodynamic model),
  than
• N40, m2.36/-.10, ?.728/-.100, k2.51/-.06,
  nh1.63,
• ?2.15/-.18, ?23.
• At this case the part of evaporated gluons is
  about 73 .

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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)

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Binomial distribution for gluons idea of
convolution of two stages? MD
-maximal possible number of evaporated
gluons from QGS
In ee- - annihilation from TSM N4-5
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From TSTM (figure)the maximal possible of
number of charged particles is 26(MEN). In TSMB
more hadrons.
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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
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Dependence of the mean multiplicities of neutral
mesons versus of charged particles.

• Bayess theorem, n1 gt nch, n2 lt 16nch - big
  distinction with experimental data at small
  multiplicity.
• The marked improvement
• Decrease top limit at low multiplicities (nchlt10)
  to n22nch.
• At bigger nch this limit n216nch.
• The low limit n1 is staying almost constant.

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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.
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Soft photons (SP)

• TSMB several of active gluons are staying inside
  of hot QGS and dont give hadron jets. New formed
  hadrons dont 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.

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The equilibrium state. We use the black body
emission spectrum

• The gluon density at the deconfinement
  temperature Tc160-200 MeV can be estimated by
  comparison with relic one
• T030K relic temperature, Ngl(160MeV)1000,
  Ngl(200MeV)2000 at L20 fm

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Table 1. The number of SP
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Conclusions

• 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.