Gluons in the proton and
exclusive hard diffraction
Aharon Levy
Tel Aviv University and DESY
• Introduction
• soft, hard interactions
• gluons
• data on exclusive vector meson electroproduction
• sizes of gluon cloud
• sizes of photon configurations
• effective Pomeron trajectory
• comparison to theory
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LHeC
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Deep Inelastic kinematics
Spin
[20 fb-1 /point]
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e
HERA
Kinematics

Ee=27.5 GeV
EP=920 GeV
s=(k+P)2 = (320 GeV)2
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c
b
t
p
r

Transverse distance scale:
McAllister, Hofstadter Ee=188 MeV
Bloom et al.
10 GeV
CERN, FNAL fixed target
500 GeV
HERA
50 TeV
Impact parameter:
*
b
c
0.2 fm
r

Q Q(GeV )
rmin=0.4 fm
0.05 fm
0.007 fm
0.0007 fm
where t is the square of the 4-momentum
transferred to the proton
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Proton  momentum frame
Partons frozen during time of
interaction. Virtual photon
samples the quark distribution.
Assume that partons form incoherent
beam. The parton density distributions
are meant to be universal quantities.
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Proton rest-frame
e

*
r
q
p
b
q

qq , qqg , …..
Photon fluctuates into
states, which interact with the proton.
r large  interaction soft,
r small  interaction hard.
soft and hard – studied by W (or x~1/W2)
dependence of the cross section.
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soft
  p,   p
pp, pp
Donnachie and Lanshoff – universal behavior of total
hadron-hadron cross section :
 tot (h  h)  As
IP
(0) 1
high energy behavior
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 Bs IR (0)1
tot  s0.08
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Regge trajectories
 (t )   (0)   ' t
 IP (t )  1.08  0.25t
 IR (t )  0.45  t
 tot (h  h)  As
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IP
(0) 1
 Bs IR (0)1
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hard
2
d

*
DIS:

F


(

p)
2
tot
2
dxdQ
The rise of F2 with decreasing x
is strongly dependent on Q2.
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at small x
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F2
x
  (Q2 )
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soft  hard
  s0.08
Below Q2 0.5 GeV2, see same energy
dependence as observed in hadronhadron interactions. Start to resolve
the partons.
F2
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x
  (Q2 )
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F2  parton densities. * ‘sees’ partons. parton
density increases with decreasing x.
QCD based fits can
follow the data
accurately, yield parton
densities. BUT:
• many free parameters
(18-30) (only know how
parton densities evolve)
• form of
parameterisation fixed
by hand (not given by
theory)
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all is not well …
From Pumplin, DIS05
There are signs that DGLAP (Q2
evolution) may be in trouble at
small x (negative gluons, high 2
for fits).
Need better data to test whether
our parton densities are
reasonable. The structure
function FL will provide an
important test.
Can also get information on gluon
density from exclusive hard processes.
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arXiv:0711.1721
Date: Mon, 12 Nov 2007 07:49:56 GMT (288kb)
Title: Status of Deeply Inelastic Parton Distributions
Authors: Johannes Bl\"umlein
From EDS07
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Exclusive VM electroproduction
 p V p
*
0
V   ,  , , J / , 
0
(V0 =   DVCS)
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soft to hard transition
 (W )  W
IP

d
 b|t |
e
dt
‘soft’
g
g
‘hard’
• Expect
 to increase from soft (~0.2, from ‘soft
Pomeron’ value) to hard (~0.8, from xg(x,Q2)2)
• Expect b to decrease from soft (~10 GeV-2) to
hard (~4-5 GeV-2)
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ingredients
Use QED for photon wave function.
Study properties of V-meson wf and the gluon density in the proton.
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Mass distributions
  K K 
J /     
  
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Photoproduction
 W

process becomes hard as
scale (mass) becomes
larger.
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(W) –
0
ρ
Fix mass – change Q2
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(W) - , J/, 
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 (Q2+M2) - VM
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  Q  M
2

2 n
(Q2)
Fit to whole Q2 range
gives bad 2/df (~70)
 p p
*
1
0
VM
Q2(GeV2)
n
comments
ρ
2.44±0.09
Q2>10 GeV2

2.75±0.13
±0.07
Q2>10 GeV2
2.486±0.080
±0.068
All Q2
1.54±0.09
±0.04
Q2>3 GeV2
J/

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Fit
b(Q2) – ρ0, 
d
 e b|t |
dt
:
 p p
*
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0
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b(Q2+M2) - VM
g
g
‘hard’
 r 2  b  ( c)2
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DVCS
Frankfurt - Strikman
Kornelija Passek-Kumaricki - EDS07
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Information on L and T
Use 0 decay angular distribution to get r0400 density matrix element
f (cos  h )  (1  r0004 )  (3r0004  1) cos 2  h
 L 1 r0004
R

 T  1  r0004
using SCHC
 - ratio of longitudinal- to transversephoton fluxes ( <> = 0.996)
L
L
r 

 L   T  tot
04
00
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R=L/T
2
(Q )
When r0004 close to 1, error on R large and asymmetric
 advantageous to use r0004 rather than R.
 *p  0 p
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Photon configuration - sizes
small kT
large
config.
large
kT
small
config.
T: large size
small size
strong color forces
color screening
large cross section
small cross section
*:
*T, *L
*T – both sizes,
*L – small size
Light VM: transverse size of qq ~ size of proton
Heavy VM: qq size small  cross section much smaller
(color transparency) but due to small size (scale given
by mass of VM) ‘see’ gluons in the proton   ~ (xg)2
 large 
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L/tot(W)
 L and T same W dependence
L  qq
in small configuration
T  qq in small and large
configurations
small configuration  steep W dep
large configuration  slow W dep
 large qq configuration is
suppressed
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L/tot(t)
bL  bT
 size of *L  *T
 large qq configuration
suppressed
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(W) - DVCS
 p  p
*
Final state  is real  T
using SCHC  initial * is *T
but W dep of  steep
 large *T configurations
suppressed
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Effective Pomeron trajectory
Get effective Pomeron trajectory from d/dt(W) at fixed t
Regge:
d
(W )  F (t )W 2[2 IP ( t ) 2]
dt
ρ0 photoproduction
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Effective Pomeron trajectory
ρ0 electroproduction
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Comparison to theory
• All theories use dipole picture
• Use QED for photon wave function
• Use models for VM wave function – usually
take a Gaussian shape
• Use gluon density in the proton
• Some use saturation model, others take
sum of nonperturbative + pQCD calculation,
and some just start at higher Q2
• Most work in configuration space, MRT
works in momentum space. Configuration
space – puts emphasis on VM wave function.
Momentum space – on the gluon distribution.
• W dependence – information on the gluon
• Q2 and R – properties of the wave
function
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0
ρ
data - Comparison to theory
• Martin-Ryskin-Teubner (MRT) – work in momentum
space, use parton-hadron duality, put emphasis on
gluon density determination.
Phys. Rev. D 62, 014022 (2000).
• Forshaw-Sandapen-Shaw (FSS) – improved
understanding of VM wf. Try Gaussian and DGKP (2dim Gaussian with light-cone variables).
Phys. Rev. D 69, 094013 (2004).
• Kowalski-Motyka-Watt (KMW) – add impact
parameter dependence, Q2 evolution – DGLAP.
Phys. Rev. D 74, 074016 (2006).
• Dosch-Ferreira (DF) – focusing on the dipole cross
section using Wilson loops. Use soft+hard Pomeron
for an effective evolution.
Eur. Phys. J. C 51, 83 (2007).
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2
Q
KMW – good for
Q2>2GeV2 miss Q2=0
DF – miss most Q2
FSS – Gauss better
than DGKP
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2
Q
Data seem to prefer
MRST99 and CTEQ6.5M
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W dependence
KMW - close
FSS:
Sat-Gauss – right W-dep.
wrong norm.
MRT:
CTEQ6.5M – slightly
better in W-dep.
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L/tot(Q2)
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L/tot(W)
All models have mild W dependence.
None describes all kinematic regions.
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Summary and conclusions
• HERA data shows transition from soft to hard interactions.
• The cross section is rising with W and its logarithmic derivative in
W, , increases with Q2.
• The exponential slope of the t distribution decreases with Q2 and
levels off at about b = 5 GeV-2. Transverse size of gluon density
(0.6 fm) inside the charge radius of the proton (0.8 fm).
• The ratio of cross sections induced by longitudinally and
transversely polarised virtual photons increases with Q2, but is
independent of W and t. The large configurations of the
transversely polarised photon are suppressed.
• The effective Pomeron trajectory has a larger intercept and
smaller slope than those extracted from soft interactions.
• All these features are compatible with expectations
of perturbative QCD.
• None of the models which have been compared to the
measurements are able to reproduce all the features of the data.
• Precision measurements of exclusive vector meson
electroproduction can help determine the gluon density in the
proton.
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