GLUON DOMINANCE MODEL

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GLUON DOMINANCE MODELGLUON DOMINANCE MODEL

Kokoulina E.

GSTU, Belarus & JINR,Dubna

The unified approach to multiplicity distribution (MD) description in high energy interactions:

- annihilation,

ee

Proton (nucleus) collisionsProton-antiproton- annihilation

JINR, LPPJINR, LPP GSTU, GSTU, LPRLPR

ISMD35, ISMD35, KROMĚŘÍŽKROMĚŘÍŽ, ,

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The region of high multiplicity (HMHM): n >> n(s) – mean muliplicity. Pn - multiplicity distribution (MDMD), Q(s,z) - generating function (GFGF) Q(s,z)= Σ Pn (s) z n .

• -annihilation - MD, moments… (the QCD Markov branching process + hadronization);

• pp- interactions from 69 to 800 GeV/c by two schemes with and without gluon branch on 1st stage, modification of 2nd scheme by clan mechanism at higher energies;

• -annihilation (~10-100 GeV/c).

ee

pp

V. Kuvshinov and E.K. Acta Phys.Polon.B13(1982) 533.

-



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First stage (cascade):

a) gluon fission; b) quark bremsstrahlung; c) quark pair creation.

hadronsgqqqZee ?),()( 0

Second stage:

Hadronization. BD

).()(

),1(~

)(2)()(2)()(

)()()(

gqggg

gqq

QQBQQAdY

dQ

QQAdY

dQ

.)1(1PN

p

hpH

p zN

nQ

Convolution: of two stages

.!

)1)...(1(pk

p

p

m

p

pppm km

k

km

m

m

mkkkP

quark fission -> NBD

K.Konishi et.al.NPB157(1979)45 A.Giovannini.NPB161(1979)429.

ee++ee- - - annihilation- annihilation

JINR, LPPJINR, LPP

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Mg

m

nNmhnhn

Nm

k

p

p

m

p

pppn N

n

N

nC

km

k

km

m

m

mkkkP

p

0

)2(

)2( 1!

)1)...(1(

,/1~ 01 cETk

p

,),(!

1

0

z

n

n

n zsQzn

P

Parameters: mean multiplicity of gluons on 1st stage, kp, [V.Kuvshinov, E.K. Vesti AN BSSR (1978)];

mean (max possible) number of hadrons, formed from one quark on the 2nd-stage,

m

)(Nn h

./ qg NN

Results: .62~;2.~);172(20)14(1.~;10~ 2 GeVGeVmk p



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N

mm

k

mf

p

222

22

22 )1( nnnf

________

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Pn in -annihilation at 14, 50, 91.4, 172 and 189 GeV; H(q) at 91.4 GeV.

14GeV50GeV 91.4GeV

172GeV 189GeV

91.4GeV

Pn Pn Pn

Pn PnH(q)

ee

E. K. Minsk, NPCS (2002)[hep-ph/0209334]; ISMD32,2002.



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Hadronization gluon parameters ( ), 14 -189 GeV.

s s

gNhgn

hgg nN ,

)( hgg nN maximal (mean) multiplicity of hadrons from

one gluon while its passing through of hadronization. 2.~/ qg NN hadronization of gluon are softer than

quark.



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Project ““THERMALIZATITHERMALIZATIOONN” ” (JINR , IHEP, SINP MSU,

GSTU)

1. Experimental data pp (70 GeV).

2. Quark model. Yad.Fiz. 55 (1992) 820. Collisions of quark pairs.

3. MC PHYTHIA code underestimates the σ(nch) by two orders of

magnitude at nch=20.

mbnch )(

chn

nch=20

The study of MP at pp (pA) interactions in HM region: nch>20-30.

The goal:

)(/ snnz chch V.V.Avdeichikov et al. JINR-P1-2004-190, Feb 2005. Proposal ”THERMALIZATION”.



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pp - interactions pp - interactions

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Gluon Dominance modelGluon Dominance model (GDM)(GDM)

• After an inelastic collision of two protons the part of energy are converted into the thermal and one or few gluons become free,

• Gluons may give cascade;

• Some of gluons (not of all) leave Quark-Gluon System (QGS) – are evaporated and are converted to hadrons.

1st stage

2nd stage



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Our model investigations had shown : quarks of initial protons are staying in leading particles (from 70 to 800

GeV/c).Multiparticle production (MP) is realized

by gluons. We name them active.

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

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



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The Multiplicity Distributions (MD) analysis are used to study MP-

processes.

Scheme with the gluon branch in QGS – branch model (TSMB)

orScheme without the gluon branch –Thermodynamical model (TSTM)

E.K. and V.Nikitin. 7th Int. school-seminar The actual problems of Microworld Physics, Gomel, Belarus. 1 (2004) [hep-ph/0308139]



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TSMB –convolution gluon and hadron MD

• MD for active gluons at the moment of impact – Poisson

• MD for branch of gluons – Furry

• MD for hadronization stage – Binomial (BD)

!/ kke kk

)!1(

)1)...(2)(1(11

1

k

kmmm

mm

km

k

)2(2

2 1

nmN

h

n

hnmN N

n

N

nC

““THERMALIZATION”THERMALIZATION” GSTU, LFIGSTU, LFIISMD35, ISMD35, KROMĚŘÍŽKROMĚŘÍŽ

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.11

1)!1(

)1)...(2)(1(1

!

)2(

0

2

2

nmNMk

k

Mg

km

hnhnmN

km

k

kk

n N

n

N

nC

mk

kmmm

mk

keP

Scheme with branch (TSMB):Scheme with branch (TSMB):

- ratio of evaporated gluons to all active ones

, N – parameters of hadronization for gluon

hn

N ~40. This value is taking into account not only second hadrons but also it is very likely (soft) photons. P.Lichard & L.Van Hove. Phys.Let. B245 (1990) 605.


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)1( Some of active gluons (<50%) are staying inside QGS and don’t give hadron jets. New formed hadrons catching up them, are excited and throw down excess of energy by soft photons (SP).

We found very weak branching of active gluons at 69 GeV/c.

“…the fraction of gluons freed in the collision obeys c ≈ ½. ” A.H. Mueller. Nucl.Phys. A715 (2003) 20.


“To reconcile RHIC data with the theory one has assume that …such effects could be due to non-perturbative thermalization leading to formation of QGP in which partons would loss energy.” Yu.V. Kovchegov [hep-ph/0507134].

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Gluons leave QGS and fragment to hadrons (without branch):

MD = Poisson & Binomial D.

M - max number of evaporated gluons is rising (from 6 to 10)max number of hadrons is limited by M*N(~ 24-26 for charged particles at 69 GeV/c)

E.K. Acta Phys.Polon. B35(2004)295

Me

m

nmNhnhnmN

mm

n nN

n

N

nC

m

meP

0

)2(2

2 ).2(,1!

TSTMTSTM



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p, GeV/c

Mg

N

69 2.48 +/-.20 6 4.24 +/-.13

1.63 +/-0.12

~2 ~2

102 2.75 +/.08 8 3.13 +/-.56

1.64 +/-0.04

~2 2.2

205 2.82 +/-.20 8 4.50 +/-.10

2.02 +/-0.12

~2 2.0

300 2.94 +/-.34 10 4.07 +/-.86

2.22 +/-0.23

~2 9.8

405 2.70 +/-.30

9 4.60 +/-.24

2.66 +/-0.22

~2 16.4

800 3.41 +/-2.55

10 20.3 +/-10.4

2.41 +/-1.69

~2 10.8

m hn 2

Table 1. TSTM parameters



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69 GeV/c 102 GeV/c 205 GeV/c

405 GeV/c 800 GeV/c

63.1hn 64.1hn 02.2hn

66.2hn 41.2hn

300 GeV/c

26.2hn



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Semenov S. et al. Sov.J. Nucl. Phys.22(1975) 792

TSMT -

KNO - - - - -

),628.6/35.125.8exp(

)39.985.18/1.0()( 1042

vPn n nk

nk

n nk

nk

n

nkkkP

)(!

)1)...(1(

A.Giovannini, R.Ugocioni[hep-ph/0405251]

nn /

NBD - - - - -

TSMT

Clan as independent intermediate gluon source.

Ln (NBD) ~ Farry (TSMB)

Ln (NBD) ~ Binom. (TSMT)

Our results: clans consist from gluons! Change of fragmentation ( ) to

recombination mechanism (hh, AA) .

Comparisons:

ee



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tot

htoth

ch

hch

N

n

N

n

N

n

0

0

MD of neutral mesons at 69 GeV/cThe simplification on the second stage of TSM:

Our results: max of neutral mesons = 16

max of total multiplicity =42

Mean multiplicity of π0 versus the number of nch

2

1

2

1

/)()(0

n

nn

n

nnnchtotnch

tot tot

tottotPnnPnn

a) top and bottom limits is determined by condition:420 nnch

b) The noticeable improvement is reached if we decrease top limit at charged multiplicities <10 to )(22 choch nnnn Our result: Centaur events may be realized in the region of HM. AntiCentaur events must be absent.

a)

b)

JINR, LPPJINR, LPP

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pp -> npp -> nchch . ISR (30-60 GeV) . ISR (30-60 GeV)

Modification. Superposition of clans:clans consist from one, two (or more) gluons of fission:

62 GeV

E.K., Nikitin V. et al. ISHEPP2004.hep-ph/0503254.

.1!

1!

)(

)2(22

22

2

22

)2(2

2

1

11

2

2

2

2

22

1

1

1

1

11

nNmhnh

nNm

M

m

mm

nNmhnhn

Nm

M

m

mm

n

N

n

N

nC

m

me

N

n

N

nC

m

mesP

14.23.3 hn

)1( 21

.13/9/,8.1~/

,25.015.1,03.059.32

21

21

ndf

mm

Soft ( ) & semi-hard ( ) components, and so on.

1 2



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PHENIX [nucl-exp/0410003]; X.Zhang, G.Fai.[hep-ph/0306227]

pp

GeVs 200

PHENIX

From GDM the ratio of charged hadrons to neutral mesons in p+p is:

70 GeV/c: 1.19+/-0.25;

800 GeV/c: 1.49+/-0.33;

(cms) 62 GeV : ~ 1.6 ( )

h

hch

h

ch

n

n

nsmh

n

sn

000 2

1

)(

1)/(

2/)(

076.10 hn

The ratio of h/π=1.6 is the value measured in experiment : p+p reactions (53 GeV) and

Au-Au (200 GeV/N) peripheral interactions (60-92%) RHIC. The assumption: The specific feature of our GDM approach is the dominance of a lot of active gluons at MP. We expect the emergence of them in nucleus collisions (RHIC) and the formation of new kind of matter QGP.

JINR, LPPJINR, LPP

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Soft Photons – the signature of Soft Photons – the signature of hadronizationhadronization 1.0)(,40,4 nTnmbmb inin

The black body emission spectrum:1

8 3

3

T

h

ecd

dn

383

10112.4/)()(725.2,2

244.0)(

mVTnMVBKT

hc

kTVTn rr

3

3

3968

3

101010112.4/)()(,)()(

fm

T

TVTnT

T

TTnTn

rrr

Excess of soft photons:

)1016.11()(5010~ 10 KMeVMeVpt

(the density)

)()(3 TLnTL L(fm) L(fm)

10 11. 30 3.5

15 6.9 40 2.6

25 4.1 50 2.0

tp tp2 tppT

Our result: L - the size of hadronization region

M.Volkov,E.K., E.Kuraev. Part. and Nucl., Let., №5 (2004)122. [hep-ph/0402163]

JINR, LPPJINR, LPP

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-annihilation -annihilation (exper.data):(exper.data):

pp1) The second correlation moment of negative

hadrons ( ) in pp-interactions and -annihilation.

2) The differences at 14.75, 22, 32 and 100 GeV/c remain significant for all multiplicities and have local max and min.

2f

J.Rushbrooke and B.Webber. Phys.Rep. C44(1978)1.

pp)()( pppp nn

mNhm zNnzQzmQ )1(/1),1(),(

m m

mNhG

m

mNhG

m zN

nPzcz

N

nPczQ )1(1)1(1)( 2

20

.)1(144

mN

m

hG

m zN

nPzc

1)

2)

GDM:

““THERMALIZATION”THERMALIZATION” GSTU, LFIGSTU, LFI

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GDM - annihilation (10 – 100 GeV/c)pp

GDM – 14.75 GeV/c)()()( pppppppp nnn

nn /Pn =

a) second Correlative moments of negative charged particles:

b) differences between pp and pp inelastic topological cross sections:

22 )1( nnnf

__________

Nnm hG /)(~ 2

Superposition of intermediate topologies (“0”, “2” –valent q’s, “4”- valent +

vacuum q’s+ GDM Pn-description.

_

,05.0:40:15:: 420 ccc

.5.1~/.61.074.1,18.036.3 2 ndfnm h


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Conclusions (I):Conclusions (I):• GDMGDM describes MD, moments, correlations in MP -

e+e--, pp-, pp-interactions in wide energy region;• GDMGDM confirms the realization of the

fragmentation mechanism of hadronization in e+e-

- annihilation and the transition to the recombination one in hadron interactions;

• GDMGDM shows that gluons play an active role at MP, the part of them (almost one half ) produce new hadrons;

• GDMGDM explains the shoulder structure in MD at higher energies by means of the independent evaporation of gluon sources of hadrons which may be realized by single gluons and also groups from two or more fission gluons.

_



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Conclusions (II):Conclusions (II):• GDM GDM agrees with the experimental ratio of the

charged hadrons to π0 for pp- and peripheral nuclear interactions;

• GDMGDM describes MD and explains the negative and positive values of f2 in pp – annihilation by the inclusion of intermediate quark topology at few tens GeV/c;

• GDMGDM proposes a mechanism of the soft photons production as a sign of hadronization and estimates the emission region size of them;

• GDM GDM drows a conclusion about possible existing of Centauro at the region of HM and absenting of Anti Centauro.

_



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DĕkujuDĕkuju



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Second correlative moments for charged hadrons ( ) in e+e- annihilation:2

2 )1( nnnf _________

N

mm

k

mf

p

222

22

a) at

b) at

);2.,1,1(0,9 2 mkfGeVs p

).2.,1,1~(0,9 2 mkfGeVs p



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“THERMALIZATION”Search for pentaquark Search for pentaquark + +

[hep-ex/0401024][hep-ex/0401024]

Drift tubes

Drift tubes tracker

tracker

PREL

IMIN

ARY

PREL

IMIN

ARY



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SVD-2 setup

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Second correlative moments (Second correlative moments (ff22))

Mg

m

mNhmm

zN

n

m

emzzsQ

0

2 ,)1(1!

),(GF -

Nnmf h 1

122

a)

b)

c)

);4~,1~,1(0, 20 Nnmfss h;0, 20 fss

).1,1(0, 20 hnmfss



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• the inclusion energy and momentum distribution in GDM;

• application of GDM to π+/- p, K+/- p and p+/-

p interactions at various energy region;• study of hadronization stage for different

kinds of hadrons by GDM;• Search of collective phenomena in pp-

interactions at HM events...

Outlook:Outlook:



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GLUON DOMINANCE MODEL

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