Diffractive deep inelastic scattering

Cyrille Marquet

RIKEN BNL Research Center

Contents• Inclusive deep inelastic scattering (DIS): e h e X

the structure functions F2, FT and FL

Diffractive deep inelastic scattering

• Inclusive Diffraction: e h e X hthe structure functions F2

D, FTD and FL

D

• 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)2

photon virtualityQ2 = - (l-l’)2 > 0

222

22

Q

Q)'.(2

Q

hMWllPx

transverse sizeresolution 1/Q

hadron

P

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

2

2 /Q.

)'.(

hMS

xlPllPy

Deep inelastic scattering (DIS)

FT and 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

with Q0 1 GeV and 0.3

Stasto, Golec-Biernat and Kwiecinski (2001)When plotting the same cross-section

as a function of the variable Q² x

one obtains a scaling curve:

this scaling is called geometric scaling

it identifies an intrinsic scale of the proton

which rises as x decreases: Q0 x-/2

Can we understand that scale/scaling from QCD?

It should also have consequences in diffraction

x < 10-2

Inclusive diffraction

Diffractive DIS

momentum transfert = (P-P’)2 < 0

diffractive mass of the final stateMX

2 = (P-P’+l-l’)2

when the hadron remains intact

22

22

Q

Q)').('(2

Q

tMllPPX

xpom = x/ rapidity gap : = ln(1/xpom)

hadron

P

P

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

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

Diffractive DIS

in terms of photon-hadron diffractive cross-section:

experimental data are often shown in terms of

Inclusive diffraction measurements

Diffractive DIS with proton tagging e p e X p

H1 FPS data ZEUS LPS data

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

H1 LRG data MY < 1.6 GeVZEUS FPC data MY < 2.3 GeV

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

)Q/1()Q,/(ˆ)Q,()Q,( 222/

12* Oxdx apa

apartons x

Xptot

in the limit Q² with x fixed

perturbative

non perturbative

• For inclusive DIS

a = quarks, gluons

DGLAPΚ

)(Qln 2Dokshitzer-Gribov-Lipatov-Altarelli-Parisi

• perturbative evolution of with Q2 :

not valid if x is too small

Factorization in DDIS ?

factorization does not hold for

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

but: you cannot do much with the diffractive pdfs

collinear factorization for F2D similar with diffractive parton densities

factorization also holds for

diffractive jet production at high Q²

for instance at the Tevatron:

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

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

a very popular approach:

The dipole picture of DISvalid in the small-x limit

k

k’

p

r : dipole size

in diffraction:

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

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

)Q,( 2r )Q,( 2r

pp’

Elastic/inelastic components

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

dissocelasdiff

can also be expressed in the dipole picture

same object for inclusiveand diffractive cross-section

Measuring FLD

FLD is higher twist:

it cannot be predicted from pdfs

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

What about geometric scalinggeometric 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 lineare lines of constant densities

along which scattering is constant

0.3

x < 10-2

C.M. and L. Schoeffel (2006)

Geometric scaling in diffractionAt fixed , the scaling variable should be

diffractive cross-section in bins of

xpom < 10-2

consistent with the HERA data

0.3

Success of the dipole model

MX=1.2 GeV

MX=3 GeV

MX=6 GeV

MX=11 GeV

MX=20 GeV

MX=30 GeV

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

Iancu, Itakura and Munier (2003)

CGC = saturation model

Ratio diffractive/inclusivesaturation naturally explains the constant ratio

Exclusive vector meson productionand

Deeply virtual Compton scattering

Exclusive vector-meson production

)Q,,( 2zr

- collinear factorization with generalized parton densities

)M,,( 2VzrV

)M,,()Q,,()M,Q,( 2V

22V

2 zrzrdzr V

22V

2.22*

)M,Q,();,(16

1 rexbrTbdrddt

d biqqq

VppVM

in the dipole picture:

with the overlap function:

sensitive to instead of

access to impact parameter

- determination of the t slope: tMxBVppVM Vedt

d )²,Q,(*

lots of data from HERA (especially J/Psi)

)²,Q,(*

txdt

d VppVM

²)Q,(* xVppVM

measurements:

rho productionS. Munier, A. Stasto and A. Mueller (2001)

S(1/r 1Gev, b 0, x 5.10-4) 0.6

HERA is entering the saturation regime

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

yellow band: cannot be trusted, too sensitiveto large t region where there is no data

J-Psi productionH. 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

),(Q/Q)()²,Q,( 2s

2 txgtftxdtd

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

Btetf )(form factor with B = const

saturation scale

need data at fixed t for

different values of x and Q²

Diffractive tri-jet production

Diffractive tri-jet production

k : gluon transverse momentum

final state configuration: tri-jet + gap + proton

k

the gluon jet is the most forward in the proton directionother configurations are suppressed by ln(1/ )

idea: measure the transverse momentumspectrum of the gluon jet

kddk 2

2

0 k

k²1/k²

k0

modeldependent

modelindependent

modelindependent

k0: typical unitarization scale

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

observable strongly

sensitive to unitarity effects

Study of with a saturation modelkddk 2

2

marked bump for k = kmax kmax/QS = independent of Q², QS 1.5Can 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

Predictions of the GBW model with

and the parameters and x0

taken from the F2 fits:

In the HERA energy range

2/0Gev.1)(Q

pompomS xxx

= 0.288 and x0 = 3.10-4

for full lines (no charm)

= 0.277 and x0 = 4.10-5

for dashed lines (charm included)

need points in different bins

ZEUS did measure 4 points forkd

dk 22

Conclusions

• Inclusive diffraction

measure FLD

• Exclusive vector meson production/DVCS

measurements in different t bins with large Q² and x ranges

• Diffractive tri-jet production

potential to bring evidence for saturation?