1. Small-x and Diffraction in DIS at HERA I Henri Kowalski DESY 12th CTEQ Summer School Madison - Wisconsin June 2004

2. H1 detector ZEUS detector Ep = 920 GeV, Ee = 27.5 GeV, # bunches = 189
Ip = 110 mA, Ie = 40 mA
Linst= 2 x 1031 cm-2 s-1

3. ZEUS detector Q2 ~ 2 –100 GeV2 Q2 ~ 0.05-0.6 GeV2
Q virtuality of the incoming photon
W CMS energy of the incoming
photon-proton system
x Fraction of the proton momentum
carried by struck quark x ~ Q2/W2

4. Infinite momentum frame Proton looks like a cloud of
y – inelasticity
Q2 = sxy
Infinite momentum frame
Proton looks like a cloud of
noninteracting quarks and gluons
F2 measures parton density
in proton at scale Q2
F2 = f e2f x q(x,Q2)

5. there is a change of slope at small-x, near Q2 = 1 GeV2

6. Gluon density
Gluon density dominates F2 for x < 0.01

7. Gluon density known with good precision at larger Q2.
For Q2 ~1 GeV2 gluons tends to go negative.
NLO, so not impossible
BUT – cross sections such as L also negative !

8. MX - invariant mass of all particles seen in the central detector
t momentum transfer to the diffractively scattered proton

9. Diffractive Signature
DY ~ log(W2 / M 2X)
diff
Non-
diff
Non-Diffraction Diffraction
- Rapidity
uniform, uncorrelated particle emission along the
rapidity axis =>
probability to see a gap DY is ~ exp(-<n>DY)
<n> - average multiplicity per unit of rapidity
dN/ dM 2X ~ 1/ M 2X =>
dN/dlog M 2X ~ const

10. Slow Proton Frame
incoming virtual photon fluctuates into a quark-antiquark
pair which in turn emits a cascade-like cloud of gluons
Transverse size of the quark-antiquark cloud
is determined by r ~ 1/Q ~ cm/ Q (GeV)
Diffraction is similar to the elastic scattering:
replace the outgoing photon by the diffractive final state
r , J/Y or X = two quarks
Rise of sgptot with W is a measure of radiation intensity

11. Radiation process
emission of gluons is ordered in rapidities
QCD Toy Model:
integrals over transverse momenta are independent
of each other
Rise of sgptot with W is a measure of radiation intensity

12. Dipole description of DIS

13. Q2~1/r2
exp(-mq r)

14. GBW Model K. Golec-Biernat, M. Wuesthoff Scaling in
Geometrical Scaling
A. Stasto & Golec-Biernat
J. Kwiecinski
Parameters fitted to DIS F2 data:
s0 = 23 mb l = x0 =

15. Parameters fitted to HERA DIS data: c2 /N ~ 1
s0 = 23 mb l = x0 =

16. Saturation Model
Predictions for Diffraction

17. Geometrical Scaling
A. Stasto & Golec-Biernat
J. Kwiecinski

18. GBW model, in spite of its compelling success has some obvious
shortcomings:
The treatment of QCD evolution is only rudimentary
remedy => incorporate DGLAP into dipole cross-section
J. Bartels, K. Golec-Biernat, H. Kowalski
The dipole cross section is integrated over the transverse coordinate
although the gluon density is expected to be a strongly varying function
of the impact parameter.
Recently: BFKL motivated Ansatz proposed by
Iancu, Itakura, Munier

19. Impact Parameter Dipole Saturation Model
H. Kowalski
D. Teaney
hep-ph/
Proton
b – impact parameter
well motivated:
Glauber
Mueller
Levin
Capella
Kaidalov
T(b) proton shape

20. Derivation of the GM dipole cross section
probability that a dipole at b
does not suffer an inelastic
interaction passing through
one slice of a proton
S2 -probability that a dipole
does not suffer an inelastic
interaction passing through
the entire proton
<= Landau-Lifschitz

21. t-dependence of the diffractive cross sections determines the b distribution

22. mu = 0.05 GeV Q02 = 0.8 GeV2 c2/N = 0.8 x < 10-2 Q2 > 0.25 GeV2
mc = 1.30 GeV
Fit parameters
lg = C= 4.0
Q02 = 0.8 GeV2
c2/N = 0.8
x < 10-2

23. GBW Model
IP Saturation Model

24. Smaller dipoles  steeper rise Large spread of leff characteristic for
universal rate of rise of all
hadronic cross-sections
Smaller dipoles  steeper rise
Large spread of leff characteristic for
Impact Parameter Dipole Models

25. Saturation region

26. All quarks
Charmed quark

27. Gluon density Charm structure function

28. Photo-production of Vector Mesons

29. Absolute values of cross sections are strongly dependent on mc

33. Absorptive correction to F2 from AGK rules
Martin
M. Ryskin
G. Watt
Example in Dipole Model
F ~ -
Single inclusive
pure DGLAP
Diffraction

34. Fit to diffractive data using MRST Structure Functions
A. Martin M. Ryskin G. Watt

35. A. Martin M. Ryskin
G. Watt

36. rS - dipole size for which proton consists of one int. length
Density profile
grows with diminishing x and r
approaches a constant value
Saturated State Color Glass Condensate
S2 -probability that a dipole
does not suffer an inelastic
interaction passing through
the entire proton
Saturated state =
= high interaction
probability
S2 => 0
multiple scattering
rS - dipole size for
which proton consists
of one int. length

37. Saturation scale = Density profile at the saturation radius rS
lS = 0.25
lS = 0.15

38. Saturation in the un-integrated gluon distribution
kT factorisation formula
dipole formula

39. GBW - - - - - - - - - - - - - - - - - - - - -
x = 10-6
BGBK ___________________________________
x = 10-2
GBW
x = 10-4
BGBK ___________________________________
x = 10-2
- numerical evaluation

40. Diffractive production of a qq pair_
Diffractive production of a qq pair

42. Inclusive Diffraction
LPS - Method

43. END of Part I