1. Small-x Physics and Diffraction: HERA Results
Allen Caldwell, Max Planck Institute for Physics
Munich, Germany
Topics:
Inclusive measurements (structure functions, photon-proton cross sections)
Fits to inclusive cross sections
Diffraction (‘inclusive’, VM production, DVCS)
Factorization in diffraction
Forward jets
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

2. Structure of hadrons and nuclei at an electron-ion collider
Structure Functions k k’
New Results/fits
New results
Not relevant at small x
Transverse resolution
Momentum fraction
Inelasticity
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

3. Structure of hadrons and nuclei at an electron-ion collider
Small-x
F2 x-
HERA Discovery!
The rise of the parton densities (and of F2) with decreasing x is strongly dependent on Q2. Implies very large density of partons in the proton when probe at high energies !
Small fraction of HERA data
Typically define small x as x<0.01
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

4. A classic HERA plot: the dependence of the rise of F2 on Q2
Parametrize:
Below Q2 0.5 GeV2, see same x (energy) dependence as observed in hadronic interactions. Start to resolve the (constituent) quarks and see the partons at larger Q2.
I will show an update of this plot later
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

5. Recent development: combined ZEUS and H1 Data sets/fits
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

6. Range of validity of DGLAP not clear
all is not well …
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.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

7. Structure of hadrons and nuclei at an electron-ion collider
Brand New : FL from HERA
Need to measure differential cross section at two beam energies (at least).
small Q2
LO pQCD
Expected to dominate
at small-x F2
Available luminosity (pb-1)
HER Ep=920 GeV e+p >300
e-p >200
MER Ep=575 GeV e+p 8
LER Ep=460 GeV e+p 14 r
F2-FL 1
y2/Y+
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

8. Reduced Cross Sections
FL expected to produce turnover at small-x (assuming F2 continues as x-λ)
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

9. Structure of hadrons and nuclei at an electron-ion collider
Preliminary results just out …
H1 results consistent with NLO pQCD expectations from H1 fits, ZEUS data somewhat lower. H1 results now published, ZEUS still preliminary.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

10. Hadron-Hadron Cross Section
HERA: total photoproduction cross section
ZEUS prel.
  (W2) e
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

11. Structure of hadrons and nuclei at an electron-ion collider
The rise at small x revisited
Look in proton rest frame
Parameterize: D 2P BH
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

12. Structure of hadrons and nuclei at an electron-ion collider
Data Sets for Fitting
Bayesian analysis based on Markov Chain Monte Carlo
Hep-ph
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

13. Structure of hadrons and nuclei at an electron-ion collider
Fixed Target
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

14. Structure of hadrons and nuclei at an electron-ion collider
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

15. Structure of hadrons and nuclei at an electron-ion collider
ZEUS
Summary:
2P gives best fits
D also OK
BH does not fit
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

16. Structure of hadrons and nuclei at an electron-ion collider
Slope of the cross section with l increases with Q
Extrapolation of the cross section with the D parameterization:
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

17. Structure of hadrons and nuclei at an electron-ion collider
Data extrapolated with this form indicates a merging of cross sections.
Crossing is unphysical, eventually expect all cross sections to behave similarly at large l, independent of the starting scale.
Is the distance scale meaningful ?
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

18. Structure of hadrons and nuclei at an electron-ion collider
Look at the effective slope with all available data. See indications of a turnover at the highest Q.
The data prefers the 2P parameterization. In this case, there is a saturation of the growth of the cross section with Q (so there would not be a unique l for crossing as could happen in the D parameterization).
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

19. The second HERA surprise
rapidity
Color-neutral object
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

20. Structure of hadrons and nuclei at an electron-ion collider
Evidence of Hard Diffraction at HERA
10% of events have large rapidity gap !
Implies scattering on color neutral cluster: at least two gluons.
Nearly constant ratio of diffraction to total as a function of W for fixed MX,Q2
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

21. Structure of hadrons and nuclei at an electron-ion collider
Diffractive PDF’s
where
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

22. Structure of hadrons and nuclei at an electron-ion collider
The ‘inclusive’ diffractive cross section has the same x dependence as the total cross section. There is an indication of universal behavior:
Similar at small x
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

23. Forward neutron production - electron - pion scattering
Same x dependence as inclusive
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

24. Structure of hadrons and nuclei at an electron-ion collider
Small x partons
Message: at small-x, data suggests that source of partons (photon, pion, proton, pomeron) is not critical – the gluon density is a universal quantity. Fundamental aspect of matter at small distances.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

25. Ratio of diffractive to total cross section versus scale
Logarithmic decrease of diffractive cross section at fixed W, MX
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

26. Factorization in Diffractive Scattering
Factorization has been proven for Diffractive DIS and exclusive hard diffraction (Collins, Berera&Soper, Trentadue&Veneziano).
However, factorization is not expected to hold for diffractive hadron-hadron scattering. The cross sections for large rapidity gap events at the Tevatron are well below expectations based on HERA diffractive pdfs.
What about diffractive photoproduction ? The photon can behave both as a point particle and as a composite (hadronic) particle.
The ratio of dijet measurement to NLO prediction is photoproduction is a factor smaller than the same ratio in DIS. However, no dependence on xgamma found.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

27. Factorization in Diffractive Scattering
ZEUS also sees some evidence of suppression of dijets in diffractive photoproduction, but less than H1. Could be related to higher ET.
Summary:
Diffractive charm – no hint of factorization breaking observed
Diffractive dijets – in photoproduction, data favor a global suppression relative to NLO QCD diff pdfs. Factorization breaking observed at low ET but no xgamma dependence.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

28. Structure of hadrons and nuclei at an electron-ion collider
Exclusive Processes e p
,VM
A long list of processes have been measured:
N is low mass system
and
QCD
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

29. Structure of hadrons and nuclei at an electron-ion collider
Data can be parameterized as smooth function of
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

30. Structure of hadrons and nuclei at an electron-ion collider
The dependence of R on W is not the expected one (much less W dependence than initially expected). Maybe due to wavefunction effects.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

31. Structure of hadrons and nuclei at an electron-ion collider
The Upsilon is now seen with 5 sigma with the full HERA data.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

32. Structure of hadrons and nuclei at an electron-ion collider
DVCS has also been measured – consistent interpretation withing the CDM (see talk by H. Kowalski)
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

33. Forward Jet Production in DIS
High x
Small x
Idea (A. Mueller): selection of events with large rapidity interval visible in the detector – laboratory for studying QCD radiation.
NLOJET++: Fixed order QCD partonic cross section, on mass shell ME + DGLAP , (collinear factorisation)
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

34. Structure of hadrons and nuclei at an electron-ion collider
MC Models
LEPTO: LO ME on mass shell + PS in DGLAP
Strong ordering in kT
CASCADE: LO off mass shell ME + PS based on kT factorized CCFM evolution
At small xBj no ordering in kT
ARIADNE: implementation of Color Dipole Model (CDM)
Random walk in kT like in BFKL
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

35. Structure of hadrons and nuclei at an electron-ion collider
Inclusive Forward Jet
• Lepto too low
• Ariadne “default “ too high
• Ariadne “tuned”(by H1) is fine
CASCADE has problem with shape of distributions
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

36. Trijet with Forward Jet
NLOJET++ is below the data – more partons needed. LEPTO also too low, default ARIADNE too high, tuned ARIADNE OK.
Summary: Only CDM (ARIADNE MC), with BFKL-like kT parton cascade, can describe all data on forward jets. However, parameter tuning was necessary.
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider

37. Structure of hadrons and nuclei at an electron-ion collider
Summary
Understanding the small-x physics is still a work in progress, but:
new data from HERA still coming in (FL, VM updates, total photoproduction cross section)
The data has simple features
indications of universality in small-x behavior
at small enough x, forget the source – gluons are fundamental aspect of nature
Phenomenological studies can give insight
need for new round of experiments, e.g., EIC. What will it bring for the small-x aspects of QCD ?
July 15, 2008
Structure of hadrons and nuclei at an electron-ion collider