Diffractive deep inelastic scattering
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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

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Diffractive deep inelastic scattering

Cyrille MarquetRIKEN BNL Research Center


  • Inclusive deep inelastic scattering (DIS): e h  e Xthe structure functionsF2, FT and FL

    Diffractive deep inelastic scattering

  • Inclusive Diffraction: e h  e X h

    the structure functionsF2D, 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

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 partony~ W²/S

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

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

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

Inclusive diffraction

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

experimental data are often shown in terms of

Diffractive DIS

in terms of photon-hadron diffractive cross-section:

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

H1LRG data MY < 1.6 GeV

ZEUSFPC data MY < 2.3 GeV

Inclusive diffraction measurements

Diffractive DIS with proton tagging e p  e X p

H1FPS 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


  • 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

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



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

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 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

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

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

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

saturation naturally explains the constant ratio

Exclusive vector meson productionandDeeply virtual Compton scattering

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

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

H. Kowalski and D. Teaney (2003)

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

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 production











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

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

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?

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