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Saturation Model for exclusive processes at HERA, DVCS, F2, including evolution and impact parameter dependence Henri Kowalski DESY DIS 2007 Munich, 17 th of April 2007. NNPZ, GLM, FKS, GBW, MMS DGKP, BGBK, IIM, FSS…… KT - Kowalski, Teaney KMW - Kowalski, Motyka, Watt. Dipole Models - PowerPoint PPT Presentation
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Saturation Model for exclusive processesat HERA, DVCS, F2,
including evolution and impact parameter dependence
Henri KowalskiDESY
DIS 2007
Munich, 17th of April 2007
)2
exp(12*21
0
2*
bddzrdptot
2*1
0
22 |)2
exp(12|16
1*
VM
bip
VM dzebdrddt
d
)2/exp(~)(
)exp(~
2 BbbT
tBdt
d diff
NNPZ, GLM, FKS, GBW, MMS DGKP, BGBK, IIM, FSS……KT - Kowalski, TeaneyKMW - Kowalski, Motyka, Watt
proton shape
)(),()( 2222
bTxxgrN s
C
Glauber Mueller
0)t,(WImAW
1σ 2
el2γptot
Dipole Models equivalent to LO perturbative QCD for small dipoles
),( zr
OpticalTheorem
KT
x < 10-2
universal rate of rise of all hadronic cross-sections
tottot xWp )/1(~)(~ 2*
Total *p cross-section
6.520
202
2 )1(1
),( xx
Axxgr
C g
g
KT
KMW
tot
b-CGC
b-Sat
Inclusive Diffraction
-LPS
F2 C
KT
Dipole Model - gluon density convoluted with dipole wave functions simultaneous prediction/description of many reactions
Inclusive Diffraction
BGBK
Diffractive Di-jets Q2 > 5 GeV2
-RapGap
Satrap
H. Kowalski, L. Motyka, G. Watt
Exclusive Vector Meson Production
Effective modification of Fourier Trans by Bartels, Golec-Biernat, Peters
)1( 2
Real part correction
Skewedness correction Martin, Ryskin Teubner
))2/exp(1(2 2
bd
d)(),()( 222
2
bTRxxgrN gs
C
Wave Functions
Boosted Gaussian – NNPZ, FKS, FS Gaussian distribution of quark 3-momentum in the meson rest frame
then boosted to LC
Gauss LC - KTGaussian distribution of quark 2-momentum in LC, factorization of r, z components- strong endpoint suppression in T
)2
exp()1(2
),(2
2
2LL
L R
rzz
R
Nzr
)
2exp()1(
2),(
2
222
2TT
T R
rzz
R
Nzr
Parameters of WF fixed by normalization conditions and the values of mesons decay constant, fV
WF Overlaps
from gluon density convoluted with dipole wave functions we obtain simultaneous prediction/description of many reactions
KMW
Vector Mesons
DVCS
Note: educated guesses for VM wf work surprisingly well
KMW
WVpp ~*
evolution of a saturated gluon density Rates of rise of the VM cross-sections
At EIC it should be possible to reduce the errors by a large factor, O(100), study of t-dependent rate of rise study of b-dependent Pomeron evolution – direct insight into saturation inside the proton or nuclei
KMW properties of wave functions Ration of longitudinal/transverse x-sections
)2/exp(~)( )exp(~ 2GD
diff
BbbTtBdt
d
Exponential fall of t-distributions
gaussian shape of the proton in the impact parameter b
)2/exp(~)( )exp(~ 2GD
diff
BbbTtBdt
d
KMW
BG BG
))1(( rzbibi ee
Description of the size of interaction region BD
Modification by Bartels, Golec-Biernat, Peters
fm 68.03 2 Gp BR
2G
p
GeV 48.6B
fm 008.0870.0R
the gluonic proton radius smaller than the quark radius
t-distributions of DVCS
universal rate of rise of all hadronic cross-sections
tottot xWp )/1(~)(~ 2*
Rate of rise of the *p cross-section In the impact parameter dipole models of DIS with the gaussian proton shape the fit of the rate of rise of *p requires QCD evolution which is DGLAP-like DGLAP-like strong interdependence between and Q2
What have we learnt from HERA about small-x
Large fraction of *p comes from the region of large b where matter density is low
median
40% )2/exp(~)( 2 GMEDIAN BbbT
Saturation scale (a measure of gluon density at which gluon re-scattering starts to be substantial)
HERA RHIC
22
22
22
GeV 3.1
fm 7 1000
1
1
4
S
C
CsS
Q
Rdy
dN
dy
dN
RN
NQ
qSqSF
CgS QQ
C
NQ )(
4
9)()( 222
QSRHIC (x=10-2)
~ QSHERA(x=10-4)
22 2
SS r
Q
))()/,(32
exp(12 ),( 2
022
2
2bTQrCxxgr
bd
rxds
universal rate of rise of all hadronic cross-sections
Is saturated state observed at HERA perturbative?
properties gluon densityRandom walk in the impact parameter
Study of the Glue
t-distributions for exclusive diffractive meson production on proton and nuclei at EIC
first estimate of the expected measurement precision:
pT < 30 MeV, t ~ pT2
t < 0.01 GeV2
for proton and light nuclei
What are the lessons/open questions for EIC from exclusive diffraction at HERA
Precise study of gluon density, tested with dipoles of various sizes,measure gluon diffusion evolution effects
Diffractive vector mesons scattering - an excellent probe of nuclear matter, why is the gluonic radius smaller than the quark radius?? >>>>> Measure t distribution on (polarized) nuclei <<<<<<>>>>> Obtain holographic picture of nuclei !!!! <<<<<<
BGBK – DGLAP evolution & saturation
GBW - saturation only
More about saturation
with impact parameter without impact parameter
properties of the gluon density Rise of the DVCS cross-sections
))(),(
32exp(1
2
),( 222
2bATxxgr
Abd
rxdWSs
Aqq
Smooth Gluon Cloud
Q2 (GeV2) C 0.74 1.20 1.70 Ca 0.60 0.94 1.40
Hard Diffraction – the HERA surprise
Non-Diffractive Event
Diffractive Event expected before HERA <0.01%, seen over 10% at Q2=10 GeV2
Diffraction at HERA is so large because it is a shadow of DIS (i.e. inelastic processes) dipole picture
fm 10001011
xmE p
0)t,(WImAW
1σ 2
el2pγ
tot
*
A glimpse into nuclei
Naïve assumption for T(b): Wood-Saxon like, homogeneous, distribution of nuclear matter
)2/exp(~)(
)exp(~
2 BbbT
tBdt
d diff
DIS on Nuclei
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