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
Low-x 2012
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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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)