Diffractive deep inelastic scattering Cyrille Marquet RIKEN BNL Research Center
Jan 24, 2016
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?