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Diffractive deep inelastic scattering. Cyrille Marquet RIKEN BNL Research Center. Contents. Inclusive deep inelastic scattering (DIS): e h  e X the structure functions F 2 , F T and F L Diffractive deep inelastic scattering Inclusive Diffraction: e h  e X h

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Diffractive deep inelastic scattering

Diffractive deep inelastic scattering

Cyrille MarquetRIKEN BNL Research Center


  • Inclusive deep inelastic scattering (DIS): e h  e Xthe structure functions F2, FT and FL

    Diffractive deep inelastic scattering

  • Inclusive Diffraction: e h  e X h

    the structure functions F2D, FTDand FLD

  • Exclusive vector meson production: e h  e  h, e h  e J/ hDeeply virtual Compton scattering (DVCS): e h  e  h momentum transfer and impact parameter

  • Diffactive jet production

Deep inelastic scattering dis

lh center-of-mass energyS = (l+P)2*h center-of-mass energyW2 = (l-l’+P)2photon virtualityQ2 = - (l-l’)2 > 0

transverse size

resolution 1/Q



Deep inelastic scattering (DIS)

x ~ momentum fraction of the struck parton y~ W²/S

Deep inelastic scattering dis1
Deep inelastic scattering (DIS)

FTand FL correspond to the scattering of a transversely (T) or longitudinally (L) polarized virtual photon off the hadron

experimental data are often shown in terms of

E p e x experimental data
e p  e X experimental data

measurements performed

at the HERA collider by the

H1 and ZEUS collaborations

over a broad kinematic range

at moderate x: bjorken scaling  F2(x)

scaling violations: evidence for gluons

about 15 % of the events are diffractive

Geometric scaling in dis
Geometric scaling in DIS

When plotting the same cross-section

as a function of the variable Q² x

one obtains a scaling curve:

Stasto, Golec-Biernat and Kwiecinski (2001)

x < 10-2

with Q0 1 GeV and  0.3

this scaling is called geometric scaling

it identifies an intrinsic scale of the proton

which rises as x decreases: Q0x-/2

Can we understand that scale/scaling from QCD?

It should also have consequences in diffraction

Diffractive dis

momentum transfert = (P-P’)2 < 0diffractive mass of the final stateMX2 = (P-P’+l-l’)2




Diffractive DIS

when the hadron remains intact

~ momentum fraction of the struck parton with respect to the Pomeron

xpom = x/

rapidity gap :  = ln(1/xpom)

xpom~ momentum fraction of the Pomeron with respect to the hadron

Diffractive dis1

experimental data are often shown in terms of

Diffractive DIS

in terms of photon-hadron diffractive cross-section:

Inclusive diffraction measurements

Diffractive DIS without proton tagging e p  e X Y with MY cut

H1 LRG data MY < 1.6 GeV

ZEUS FPC data MY < 2.3 GeV

Inclusive diffraction measurements

Diffractive DIS with proton tagging e p  e X p

H1 FPS data


E p e x p experimental data
e p  e X p experimental data

measurements performed

at the HERA collider by the

H1 and ZEUS collaborations

over a broad kinematic range

Collinear factorization


  • perturbative evolution of  with Q2 :


Collinear factorization

in the limit Q²   withx fixed

  • For inclusive DIS

a = quarks, gluons

not valid if x is too small

non perturbative

Factorization in ddis

for instance at the Tevatron:

predictions obtained with diffractive pdfs overestimate CDF data by a factor of about 10

a very popular approach:

use collinear factorization anyway, and apply a correction factor called the rapidity gap survival probability

Factorization in DDIS ?

collinear factorization for F2Dsimilar with diffractive parton densities

but: you cannot do much with the diffractive pdfs

factorization does not hold for

diffractive jet production at low Q² diffractive jet production in pp collisions

factorization also holds for

diffractive jet production at high Q²

The dipole picture of dis



r : dipole size


in diffraction:

at large Nc, 1 dipole emitting N-1 gluons = N dipoles

The dipole picture of DIS

valid in the small-x limit

Elastic inelastic components



Elastic/inelastic components

elas: involves the quark-antiquark final state, dominant for small diffractive mass (large  )

same object for inclusiveand diffractive cross-section

dissoc: involves higher order final states: qqg, …dominant for large diffractive mass (small  )

can also be expressed in the dipole picture

Measuring f l d
Measuring FLD

Contributions of the different final states to the diffractive cross-section:

at small  : quark-antiquark-gluon

at intermediate  : quark-antiquark (T)

at large  : quark-antiquark (L)

large  measurements FLD

FLD is higher twist:

it cannot be predicted from pdfs

What about geometric scaling

x < 10-2

 0.3

What about geometric scaling

geometric scaling can be easily understood as a consequence of large parton densities

what does the proton look like in (Q², x) plane:

lines parallel to the saturation line

are lines of constant densities

along which scattering is constant

Geometric scaling in diffraction
Geometric scaling in diffraction

At fixed  , the scaling variable should be

C.M. and L. Schoeffel (2006)

 0.3

consistent with the HERA data

diffractive cross-section in bins of 

xpom < 10-2

Success of the dipole model

MX=30 GeV

MX=20 GeV

MX=11 GeV

MX=6 GeV

MX=3 GeV

MX=1.2 GeV

Success of the dipole model

CGC = saturation model

Iancu, Itakura and Munier (2003)

Forshaw and Shaw have not been able to find a good fit without saturation effects

Ratio diffractive inclusive
Ratio diffractive/inclusive

saturation naturally explains the constant ratio

Exclusive vector meson production and deeply virtual compton scattering

Exclusive vector meson productionandDeeply virtual Compton scattering

Exclusive vector meson production

in the dipole picture:

with the overlap function:

sensitive to instead of

 access to impact parameter

Exclusive vector-meson production


lots of data from HERA (especially J/Psi)

- collinear factorization with generalized parton densities

- determination of the t slope:

Rho production
rho production

S. Munier, A. Stasto and A. Mueller (2001)

the S-matrix (S=1-T ) is extracted from the  data

yellow band: cannot be trusted, too sensitive

to large t region where there is no data

S(1/r 1Gev, b  0, x  5.10-4)  0.6 HERA is entering the saturation regime

J psi production
J-Psi production

H. Kowalski and D. Teaney (2003)

E. Gotsman, E. Levin, M. Lublinsky,U. Maor and E. Naftali (2003)

What about geometric scaling1
What about geometric scaling

t integrated cross-sections

d/dt cross-sections

C.M., R. Peschanski and G. Soyez (2005)

saturation scale

form factor

with B = const

need data at fixed t for

different values of x and Q²

Diffractive tri jet production1











Diffractive tri-jet production

C.M. and K. Golec-Biernat (2005)

final state configuration: tri-jet + gap + proton

k0: typical unitarization scale

idea: measure the transverse momentum

spectrum of the gluon jet


the gluon jet is the most forward in the proton direction

other configurations are suppressed by ln(1/ )

k : gluon transverse momentum

  • observable strongly

    sensitive to unitarity effects

Study of with a saturation model

kmax/QS = independent of Q², QS

 1.5

Can we experimentally test this? extract QS?

important limitation: at HERA QS< 1 Gev and k > 3 Gev one does not have access to the whole bump

Study of with a saturation model

marked bump for k = kmax

In the hera energy range
In the HERA energy range

Predictions of the GBW model with

and the parameters  andx0

taken from the F2 fits:

  • = 0.288 andx0 = 3.10-4

    for full lines (no charm)

 = 0.277 andx0 = 4.10-5

for dashed lines (charm included)

need points in different bins

ZEUS did measure 4 points for


  • Inclusive diffractionmeasure FLD

  • Exclusive vector meson production/DVCSmeasurements in different t bins with large Q² and x ranges

  • Diffractive tri-jet productionpotential to bring evidence for saturation?