UINTEGRATED GLUON DISTRIBUTION AND UINTEGRATED GLUON DISTRIBUTION AND SATURATION EFFECT IN P-P AT LHCSATURATION EFFECT IN P-P AT LHC AT AT

MPI-2012, CERN, December 3-7, 20121

Gennady Lykasov in collaboration with Vadim Bednyakov and Andrey Grinyuk

JINR, Dubna

OUTLINE OUTLINE

2. Gluon distribution in proton

3. Modified unintegrated gluon distribution

4. Saturation of gluon density at low transfer

5. Summary

2MPI-2012, CERN, December 3-7, 2012

1. Soft p-p collisions

3

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

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.

tqqtqqq

pbA=pφs

sg

exp0,;0

tggttggndg

pbAp=pφss

g

exp0,;0

12.021g mb

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

MPI-2012, CERN, December 3-7, 2012

MPI-2012, CERN, December 3-7, 2012

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

7

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 ) ,

MPI-2012, CERN, December 3-7, 2012

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) ,

2

t

Q2

0

2

t

2

0dkQ,kx,xg=Qx,xg

20

0

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.

0t

kAt our UGD goes to zero as where a

tk 1a

It has been confirmed by B.I.Ermolaev, V.Greco, S.I.Troyan, Eur.Phys.J. C 72 (2012) 1253; hep-ph/1112.1854.

2012 9

Green line is the GBW u.g.d. K. Golec-Biernat & M. Wuesthoff, Phys.Rev.D60, 114023 (1999).

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.

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)

MPI-2012, CERN, December 3-7, 2012

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.

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:

MPI-2012, CERN, December 3-7, 2012

Blue line corresponds to

fmGeVRfmGeVerR

rAMdipole 2.01;2.124.0;

1ln

4exp1 1

01

20

2

0

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

Effective dipole cross section

Red line corresponds to

20

2

04

1lnR

rdipole

SUMMARY 1. The unintegrated gluon distribution in proton at low intrinsic

transverse momenta is calculated and their parameters were found from the best fit to the LHC data.

2. At large intrinsic transverse momenta it coincides to the distributions found by GBW, H.Jung and others and at low ones it differs sizably. 3. Using the modified U.G.D. we study the saturation of the

dipole-nucleon cross section at large transverse distance between and in the dipole.4. We show that this cross section is saturated more faster if we use the modified U.G.D. In comparison to the conventional

U.G.D of type GBW.5. We found that the saturation scale Q is larger that the one obtained within the GBW model. 6.LHC data in the soft kinematical region allow us to verify this saturation scale

q qr

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

16MPI-2012, CERN, December 3-7, 2

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

HSQCD-12, Gatchina, July 2012

Longitudinal structure function within the kt-factorization

A.V. Kotikov, A.V. Lipatov, N.P. Zotov, Eur.Phys.J., C27 92003)219.H. Jung, A.V. Kotikov, A.V. Lipatov, N.P. Zotov, DIS 2007, hep-ph/07063793.

1 2

0 ,,

2222222 , ,,,,,x

Q

sduitgti

g

LitLkzkmQ

zx

Cedkz

dzQxF

,,, 22

ttgkxxgkx 2

2

20

22

0

2 ,,,tg

Q

Q

tkxdkQxxgQxxg

HSQCD-12, Gatchina, July 2012

HSQCD-12, Gatchina, July 2012

DIAGRAMS in DIAGRAMS in pppp collisions within QGSMcollisions within QGSM

p p̄

21

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

HSQCD-12, Gatchina, July 2012

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

2012 23

2012 24

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.

2012 25

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.

2012 26

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)