UNINTEGRATED GLUON DISTRIBUTION UNINTEGRATED GLUON DISTRIBUTION AND GLUON SATURATION IN P-P AT LHC AND GLUON SATURATION IN P-P AT LHC

Gennady Lykasov* in collaboration withH.Jung**,V.Bednyakov* A. Lipatov***, A.Pikelner*, N. Zotov*** *JINR, Dubna

** DESY, Hamburg ***MSU, Moscow

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OUTLINEOUTLINE

1. Quark –Gluon-String Model (QGSM) and gluons in proton.

2. Gluon distribution in proton 3. Inclusive spectra of charge hadrons in p-p within QGSM including gluons

4. Modified un-integrated gluon distribution Low-x 2012

5. Structure functions and H1 data

6. Summary

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DIAGRAMS in DIAGRAMS in pppp collisions within QGSMcollisions within QGSM

p p̄

4

Fig. 1. The one-cylinder graph (at the left) and the multi-cylinder graph (at the right) for the inclusive pp hX process.

A.Capella, J.Tran Thanh Van, Phys.Lett., B114, 450 (1982)

A.B.Kaidalov, Phys.Lett., B116, 459 (1982)A.B.Kaidalov, K.A.Ter-Martirosyan, Phys.Lett., B117, 247 (1982)

QGSM

DPM

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5

So, the inclusive spectrum is presented in the following form:

Aq = 11.91 ± 0.39, bq = 7.29 ± 0.11Ag = 3.76 ± 0.13 bg = 3.51 ± 0.02

ρ (x= 0, p t )=ρq ( x=0, pt )+ρg (x= 0, p t )

Here

tggttggndg

pbAp=pφs

s

exp0,;0

tqqtqqq

pbA=pφs

s

exp0,;0

V.A. Bednyakov, A.V. Grinyuk, G.L., M. Poghosyan, Int. J.Mod.Phys. A 27 (2012) 1250012. hep-ph/11040532 (2011); hep-ph/1109.1469 (2011); Nucl.Phys. B 219 (2011) 225.

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In the light cone dynamics the proton has a general decomposition:

One-Pomeron exchange (left) and the cut one-Pomeron exchange (right); P-proton, g-gluon, h-hadron produced in PP

,...,, quudquudguud S.J.Brodsky, C.Peterson, N.Sakai, Phys.Rev. D 23 (1981) 2745.

The cut one-pomeron exchange

ρ (x,pht )=F ( x+ ,pht ) F ( x− ,pht )

1t

11t11t

2 kp,x

xG,kxfkddx=p,xF ht

+hqq1ht+

Gqh ( z,k t )=zD q

h ( z,k t )

qqgP

Here

where

,,

where is the splitting function of a gluon to the quark-antiquark pair

PP

qqgq Pg=f

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UN-INTEGRATED GLUON UN-INTEGRATED GLUON DISTRIBUTION IN PROTON DISTRIBUTION IN PROTON

9

where R0=C1(x/x0)λ/2 , C1=1/GeV K.Golec-Biernat & M.Wuesthoff, Phys.Rev. D60, 114023 (1999); Phys.Rev. D59, 014017 (1998)H.Jung, hep-ph/0411287, Proc. DIS'2004 Strbske Pleco, Slovakia

xA ( x,k t2 ,Q 0

2 )=3σ 0

4π2 α s

R 02 ( x ) k t

2 exp (−R 02 ( x ) k t

2 ) ,

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xg ( x,k t ,Q0 )=C 0 C 3 (1−x )bg (R 02 (x ) k t

2 +C 2 (R0 ( x ) k t )a )

exp (−R0 ( x ) k t−d (R0 ( x ) k t )3) ,

xg ( x,Q02)=

0

Q 02

xg ( x,k t2 ,Q0

2 )dk t2

C 3

C 0=3σ0 / (4π 2 α s (Q02 ))

A.Grinyuk, H.Jung, G.L., A.Lipatov, N.Zotov, hep-ph/1203.0939; Proc.MPI-11, DESY, Hamburg, 2012.

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Green line is the GBW u.g.d. K.Golec-Biernat & M.Wuesthoff,

Red line is the modified u.g.d. A.Grinyuk, H.Jung, G.L., A.Lipatov, N.Zotov, hep-ph/1203.0939; Proc.MPI-11, DESY, Hamburg, (2012.)

Phys.Rev. D60, 114023 (1999).

Saturation dynamics

2

0

2

0 4exp1,

Rr

rxGBW

dipole

2/0

10 / xxGeVR at 0xx 0 dipolewe have

Saturation becomes when 02~ Rr I leads to . It leads to 0~ T

when 10 QR or 0/1 RQ

K. Golec-Biernat, M Wuesthoff , Phys.Rev. D60, 114023 (1999); D59, 014017 (1998)

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Effective dipole cross section and unintegrated gluon distribution

tst

t

t

dipolekxxgrkJ

kdk

rx ,,13

4,

02

2

0J

sHere is the QCD running constant, is the Bessel

function of the zero order.

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Effective dipole cross section

xRr

rxGBW

dipole 2

0

2

0 4exp1, Green line:-

xRra

xRra

rxGBW

dipole 2

0

2

2

0

1

0exp1, Red line:

fmGeVR 2.01 1

0

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Blue line corresponds to

fmGeVRfmGeVerR

rAMdipole 32.06.1;2.124.0;

1ln

4exp1 1

01

20

2

0

Javier L. Albacete,Cyrille Marquet,arXiv:1001.137 [hep-ph]

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Kt-factorization

σ= dzz

d2 k t σ part ( xz

,k t2)F ( z,k t

2 )

Photo-production cross section

Here is the un-integrated parton density function,F ( z,k t2 )

Classification scheme:

xG (x,k t2 ) describes the DGLAP type UGD

xF ( x,k t2 ) is used by BFKL

describes the CCFM type UGD with an xA ( x,k t2 , Q̄ 2 )

Q̄

σ part ( x / z,k t2 ) is the partonic cross section.

additional factorization scale (such as ) α s (Q̄2 )≤1

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Longitudinal structure function within the kt-factorization

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1 2

0 ,,

2222222 , ,,,,,x

Q

sduitgti

g

LitLkzkmQ

zx

Cedkz

dzQxF

,,, 22

ttgkxxgkx 2

2

20

22

0

2 ,,,tg

Q

Q

tkxdkQxxgQxxg

F L as a function of at W=276 GeV and Q2 μR2 =127 Q 2

-The-The-The-The-

SUMMARY

1. The inclusion of the gluon distributions in proton allows us to apply the QGSM to analyze the hadron production in p-p at transverse momenta less than 2 – 3 GeV/c.

2. The unintegrated gluon distributions in proton at low intrinsic transverse momenta were calculated and their parameters were found fitting the LHC data.

3. At large intrinsic transverse momenta they coincide to the distributions found by GBW, J.Hannes and others. 5. The modified UGDF allows us to describe the H1 data on at low x and rather satisfactorily. 6. The H1 data on the longitudinal structure function in dependence on at are described also satisfactorily using the modified UGDF.

F L ( x,Q 2 ) Q2

Q2 W= 276 G eV

F L

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THANK YOU VERY MUCH FOR THANK YOU VERY MUCH FOR YOUR ATTENTION !YOUR ATTENTION !

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Effective dipole cross section

Red line corresponds to

20

2

04

1lnR

rdipole

The x-dependence of at assuming and , where

F L

μR2 =KQ2 K= 127μR

2 =Q 2

Q 2= 2 . 2 (G eV / c )2

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Inclusive hadron production in central region and the AGK cancellation

According to the AGK, the n-Pomeron contributions to the inclusive hadron spectrum at y=0 are cancelled and only the one-Pomeron contributes. This was proved asymptotically, i.e., at very high energies.

Using this AGK we estimate the inclusive spectrum of the charged hadrons produced in p-p at y=0 as a function of the transverse momentum including the quark and gluon components in the proton.

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ρg (x= 0, pt )=φg (0, pt )∑n=2

(n−1 ) σ n (s )=

φg (0, p t ) (gsΔ−σ nd )

Inclusive hadron production in central region and the AGK cancellation

According to the AGK, the n-Pomeron contributions to the inclusive hadron spectrum at y=0 are cancelled and only the one-Pomeron contributes. This was proved asymptotically, i.e., at very high energies.

Using this AGK we estimate the inclusive spectrum of the charged hadrons produced in p-p at y=0 as a function of the transverse momentum including the quark and gluon components in the proton.

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ρg (x= 0, pt )=φg (0, pt )∑n=2

(n−1 ) σ n (s )=

φg (0, p t ) (gsΔ−σ nd )

Effective dipole cross section

Blue line corresponds to

2

20

20

2

04

1ln4 r

R

R

rdipole

N.Nikolaev,B.Zakharov,Z.Phys.C49, 607 (1990)