Hard diffraction in eA
Cyrille Marquet
RIKEN BNL Research Center
Inclusive and diffractive
structure functions
Deep inelastic scattering (DIS)
k’
k
eh center-of-mass energy
S = (k+P)2
size resolution 1/Q
*h center-of-mass energy
W2 = (k-k’+P)2
photon virtuality
Q2 = - (k-k’)2 > 0
p
Q2
Q2
x
 2
2 P.(k  k ' ) W  M h2  Q 2
x ~ momentum fraction of the struck parton
P.(k  k ' ) Q 2 / x
y

P.k
S  M h2
y ~ W²/S
Diffractive DIS
k’
when the hadron remains intact
k
momentum transfer
t = (P-P’)2 < 0
diffractive mass of the final state
MX2 = (P-P’+k-k’)2
p
p’
Q2
Q2


2( P  P' ).( k  k ' ) M X2  t  Q 2
 ~ 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
Inclusive diffraction at HERA
Diffractive DIS with proton tagging e p  e X p
H1
ZEUS
FPS data
LPS data
Diffractive DIS without proton tagging e p  e X Y with MY cut
H1
ZEUS
LRG data MY < 1.6 GeV
FPC data MY < 2.3 GeV
Collinear factorization
vs
dipole factorization
Collinear factorization
in the limit Q²   with x fixed
• for inclusive DIS
 *p X
tot
(x, Q2) 
1
 d 
(, Q2)ˆa(x/, Q2)  O(1/Q2)
a/ p
partons a x
a = quarks, gluons
• perturbative evolution
of  with Q2 :

ln (Q2)
 Κ
DGLAP

Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
not valid if x is too small
non perturbative
• for diffractive DIS
another set of pdf’s, same Q² evolution
perturbative
Factorization with diffractive jets ?
you cannot do much with the diffractive pdfs
factorization also holds for
factorization does not hold for
diffractive jet production at high Q²
diffractive jet production at low Q²
diffractive jet production in pp collisions
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
The QCD dipole picture in DIS
in the limit x  0 with Q² fixed
• deep inelastic scattering (DIS) at small xBj :
photon virtuality Q2 = - (k-k’)2 >> 2QCD
*p collision energy W2 = (k-k’+p)2
sensitive to values of x as small as xBj 
k’
k
Q
size resolution 1/Q
2
W2 Q
2
p
k’
• diffractive DIS :
k
diffractive mass MX2 = (k-k’+p-p’)2

Q2
M Q
2
X
2
xpom = x/
rapidity gap  = ln(1/xpom)
p
p’
Hard diffraction and small-x physics
the dipole scattering
amplitudfe
T=1
T << 1
dipole size r
Q 2 DIS 
Q2 DDIS
1
1

Q2
 ln(Q 2 /Q S2 ) 
1

1
1

hard diffraction is directly
sensitive to the saturation region
Forshaw and Shaw
no good fit without saturation effects
contribution of the different r regions
in the hard regime Q2  Q2S
DIS dominated by relatively hard sizes
1 Q  r  1 QS
DDIS dominated by semi-hard sizes
r ~ 1 QS
Hard diffraction off nuclei
some expectations
D,A
The ratio F2
/ F2
A
following the approach of Kugeratski, Goncalves and Navarra (2006)
ratio ~ 35 %
from Kowalski-Teaney model
at HERA saturation naturally
explains the constant ratio
plots from Tuomas Lappi
The ratio F2
•
D,A
/ F2
D,p
x dependence
following Kugeratski, Goncalves and Navarra
Au / d
full : Iancu-Itakura-Munier model
linear : linearized version of IIM
shape and normalization
influenced by saturation
•
scheme dependence for
naive :
FRWS :
Freund, Rummukainen, Weigert and Schafer
ASW :
Armesto, Salgado and Wiedemann
Pb / p