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A prediction of unintegrated parton

distributionRuan Jianhong Zhu Wei

East China Normal University

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outline

Introduction

The models

Our scheme

Conclusion

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1 Introduction

① The integrated parton distributuion ),( 2xxa

evolution according to DGLAP equation, input parton distribution such as

GRV,MRST,CTEQ… can be used to describe inclusive processes

well decided by the global fit of structure function F2

:),( 2xxa ),( 2xxv),( 2xxs),( 2xxg

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② the unintegrated parton distribution ),,( 22 tkxf

For less inclusive processes, the distributions unintegrated over the tranverse momentum have to be considerd.

),(),,( 2

0

222

22

xxakxfk

dkta

t

t

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2 The models① CCFM evolution equation:

The unintegrated gluon distribution satisfies the CCFM evolution equation based on angular ordering.

The solution of the CCFM equation has only proved practically with Monte Carlo generators.

The interactions among initial partons are neglected in the CCFM equation.

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② Golec-Biernat-Wusthoff gluon distribution

Based on the parametrization of the dipole-nucleon cross section with parameters fitted to the HERA data

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③ Kharzeev-Levin gluon distribution

based on the idea of gluon saturation, the gluon distribution is parametrized.

It was claimed that the gluon distribution leads to a good description of the recent RHIC rapidity distributions.

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Kimber, Martin and Ryskin proposed that the two scale UPDFs can be derived from the single-scale unintegrated distribution, and its dependence on the second scale μ is introduced by using the Sudakov factor.

④ KMR scheme

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3 Our method: KMR scheme

MD_DGLAP

equation

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the initial quark and gluon densities (GRV-like)

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our result

The unintegrated gluondensity in proton at μ=10 GeV

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The unintegrated gluondistributions in Pb(A=208)

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Comparison of our predicted (RZ)-gluon(solid curves) with other models

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Published in physics review c 80,045209(2009)

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① Two component model

Ⅰcentral region

Ⅱ fragmentation region

gg →g mechanism

quark recombination model

Particle multiplicities and limiting fragmentation

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),)2

(,(),)2

(,()(1

1

4 2,

2,,2

2,

2,,1,

22,

2

,2

gtgtgtp

ggtgtgtp

gsgtgtc

c

gt

Ipp

pqp

xFpqp

xFqdpN

N

pdyd

d

Ⅰcentral region

Ⅱ fragmentation region

x

tptpt

IIpp

in

pxxsxxpxvxdxx

x

dxdp

d0

211

21112

),())(1(2

1),(

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1

d

dN

d

dN

d

dN IIpp

Ipppp

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Proton-proton collisions

ssd

dN pp 20 ln023.0ln25.05.2

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② Fragmentation limiting

beamy '

)/ln( Nbeam msy

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5 Conclusion:

① we predict the unintegrated parton distributions in proton and nucleus by using the KMR scheme incorporating the shadowing and antishadowing corrections②We find that the suppression of the unintegrated gluon distribution when kt→ 0 arises from the valence-like input rather than the nonlinear saturation effect, although the nonlinear shadowing effect is obvious.③We use two complementary production mechanisms: hard gluon-gluon fusion in the central rapidity region and soft quark recombination in the fragmentation region to study the particle multiplicity distributions in hadron-hadron collisions at high energies.

④We find that the limiting fragmentation hypothesis, which generally appear in present data of hadron collisions is partly violated if the observations are across over a wide range between the RHIC-LHC energies.

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Thank You!