Gluons in the proton and exclusive hard diffraction

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Gluons in the proton and exclusive hard
diffraction

• Aharon Levy
• Tel Aviv University and MPI

• 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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HERA Kinematics
Ee27.5 GeV EP920 GeV s(kP)2 (320 GeV)2
Transverse distance scale
McAllister, Hofstadter Ee188 MeV rmin0.4
fm Bloom et al. 10 GeV 0.05 fm CERN,
FNAL fixed target 500 GeV 0.007
fm HERA 50 TeV 0.0007 fm
where t is the square of the 4-momentum transferre
d to the proton
Impact parameter
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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
soft and hard studied by W (or x1/W2)
dependence of the cross section.
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soft
Donnachie and Lanshoff universal behavior of
total hadron-hadron cross section
high energy behavior ?tot ? s0.08
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Regge trajectories
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hard
DIS
The rise of F2 with decreasing x is strongly
dependent on Q2.
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soft ? hard
Below Q2 ?0.5 GeV2, see same energy dependence as
observed in hadron-hadron interactions. Start to
resolve the partons.
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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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Exclusive VM electroproduction

• (V0 ? ? DVCS)

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soft to hard transition

• 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
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Photoproduction
process becomes hard as scale (mass) becomes
larger.
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?(W) ?0
Fix mass change Q2
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?(W) - ?, J/?, ?
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? (Q2M2) - VM
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?(Q2)
Fit to whole Q2 range gives bad ?2/df (70)
VM n comments
? 2.440.09 Q2gt10 GeV2
? 2.750.13 0.07 Q2gt10 GeV2
J/? 2.4860.0800.068 All Q2
? 1.540.09 0.04 Q2gt3 GeV2
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b(Q2) ?0, ?
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b(Q2M2) - VM
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Frankfurt - Strikman
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Information on ?L and ?T
Use ?0 decay angular distribution to get r0400
density matrix element
using SCHC
? - ratio of longitudinal- to transverse-photon
fluxes ( lt?gt 0.996)
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R?L/?T (Q2)
When r0004 close to 1, error on R large and
asymmetric ? advantageous to use
r0004 rather than R.
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Photon configuration - sizes
?T large size small size
strong color forces color screening
large cross section small cross
section
? ?T, ?L ?T both sizes, ?L small
size
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?L/?tot(W)
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?L/?tot(t)
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?(W) - DVCS
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
?0 photoproduction
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Effective Pomeron trajectory
?0 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 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
  (2-dim 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 softhard
  Pomeron for an effective evolution.
  Eur. Phys. J. C 51, 83
  (2007).

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Q2
KMW good for Q2gt2GeV2 miss Q20 DF miss most
Q2 FSS Gauss better than DGKP

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Q2
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.