UINTEGRATED GLUON DISTRIBUTION AND SATURATION EFFECT IN P-P AT LHC AT
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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.
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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
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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.
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)