Diffrazione ad HERA
Marcella Capua – INFN e Universita’ della Calabria
• Diffrazione inclusiva ad HERA → DiffPDF
• Produzione di mesoni vettori
• DVCS
IFAE 2004
Torino 13–15 aprile 2004
Diffractive γ*p interactions at HERA
Q2
Standard Deep Inelastic Scattering in a frame in
which the proton is very fast (Breit frame):
x = fraction of proton’s momentum carried by
struck quark  Q2/W2
W
W = photon-proton centre of mass energy
Diffraction: exchange of color singlet producing
a rapidity GAP in the particle flow
Q2
*(q)
W

fraction of the p momentum carried by the IP:
X
xIP
IP
x IP
q  ( p  p' ) Q 2  M X2

 2
q p
Q W 2
fraction of the IP momentum carried by the struck quark:
t
IFAE04 Torino
aprile 2004
Q2
Q2
x

 2

2q  ( p  p' ) Q  M X2
x IP
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INFN e Universita' della Calabria
2
Inclusive diffraction γ*p  Xp
DIS probes the partonic structure of the proton
Q2
Structure function:

d 2
4 2 
y2
2

1

y


 F2 ( x , Q )
2
4
2
dxdQ
xQ 
2[1  R( x , Q )] 
W
diffractive structure function (assumes FLD  0 ):
Q2
D( 4)
2
F
*(q)
W

Q 4
d 4 D epe ' Xp '
(  , Q , x IP , t ) 

4 2 (1  y  y 2 / 2) d dQ 2dx IP dt
2
diffractive γ*p cross section:
X
xIP
d D* p
IP
dM X
t

d 4 epD e ' Xp '
 (1  (1  y ) ) dQ 2dM X dWdt
2
F2D(4)  fIP (xIP,t) F2IP(,Q2)
Naively, if IP were particle:
Flux of Pomerons
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aprile 2004

Q 2W
“Pomeron structure function”
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INFN e Universita' della Calabria
3
Large Rapidiy Gap method
X system and e’ measured
System Y not measured, some theoretical
and experimental uncertanties
Integrate over t<1GeV2 and MY<1.6 GeV
High acceptance
Diffractive peak
xL 
p'z
 1  x IP
pz
p tag method
Measurement of t
Free of p-diss background
Higher MX range
Lower acceptance
MX method
High acceptance
t measurement not possible
systematics from p-diss
NB: if scattered proton not detected, background from proton dissociative events
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aprile 2004
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INFN e Universita' della Calabria
4
H1 Diffractive Structure Function vs 
Diffraction
x
x
Proton

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aprile 2004
Weak  dependence – not a “normal” hadron !
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INFN e Universita' della Calabria
x
5
Diffractive Structure Function vs Q2
Proton
Diffraction
Q2
Positive scaling violations
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
Q2
6
(Diffractive) hard scattering factorisation
Diffractive DIS, like inclusive DIS, is factorisable into a hard part and a soft part
[QCD Hard Scattering factorization:Trentadue, Veneziano; Berera, Soper; Collins…]:
 ( * p  Xp)  f q p ( x IP , t , x , Q 2 )  ˆ  q ( x , Q 2 )
*
At fixed xIP and t diffractive parton distribution
functions evolve according to DGLAP

hard partonic cross section
fi/pD(x,Q2,xIP,t): probability to find, with probe of resolution Q2, in a proton,
parton i with momentum fraction x, under the condition that proton remains
intact, emerging with small energy loss and momentum transfer given by xIP, t
A new type of PDFs, with same dignity as standard PDFs. Applies when
vacuum quantum numbers are exchanged.
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
7
Regge phenomenology - “resolved IP model”
 ( * p  Xp)  f IP p ( x IP , t )  pq p (  , Q 2 )  ˆ  p (  , Q 2 )
*
Regge motivated pomeron flux
f IP / p ( x IP , t ) 
e
Bt
2 ( t ) 1
x IP
Shape of diffractive pdfs
independent of xIP and t
There is no evidence of the  or Q2 dependence when xIP changes → Regge factorization
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
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NLO DGLAP QCD fits to the H1 data
-Regge factorization
-Singlet Σ and gluon g with Q20=3GeV2
-NLO DGLAP evolution
-Fit medium Q2 (6 < Q2 < 120 GeV2)
-Experimental and theor incertainties
Diff PDF’s:
Extended to large z
Gluon dominate
Σ well constrained
Gluon momentum fraction
75 ±15 % at Q2 = 10 GeV2
and remains large up to high
Q2
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
9
Test of QCD factorization NLO Comparisons with Diff DIS Jets
Use diff PDFs to predict the rate of
diffractive dijet production:
jet
jet
Good agreement with prediction
with NLO fit at medium Q2
• Normalisation and shape of data described ok
• Same conclusion for charm production
Hard scattering factorisation works in diffractive DIS at HERA
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
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?
(= F2D)
Test factorisation in pp events
FDJJ
Diff PDFs crucial e.g. to estimate
rates of diffractive processes at
LHC/Fermilab (eg diffractive Higgs)
Violation of factorisation understood in terms of
(soft) rescattering corrections of the spectator
partons (Kaidalov, Khoze, Martin, Ryskin):
(x =xIP)
NB several other important approaches:
F2D
Predictions based
on rescattering
assuming HERA
diffractive PDFs
CDF data

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aprile 2004
o) Bjorken (1993)
o) Gotsman, Levin, Maor (1993)
o) Goulianos (1995)
o) Buchmueller, Gehrmann, Hebecker (1997)
o) Cox, Forshaw, Loennblad (1999)
o) Enberg, Ingelman, Timneanu (2000)
o) Erhan, Schlein (2000)
o) Bialas, Peschanski (2002)
o) ...
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NLO DGLAP QCD fits to the ZEUS data
•MX>2 GeV, xIP<0.01, Q2>2 GeV2
•NLO DGLAP fit
•Regge factorisation assumption
possible for this small data set
•initial scale Qo2=2 GeV2
QCD fit describes data
(  2 / ndf  37.9 / 36)
fractional gluon momentum is
(82  8( stat )  9( sys ))%
Similar to H1!
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INFN e Universita' della Calabria
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The colour dipole picture
Virtual photon fluctuates to qq, qqg states (colour dipoles)
q

q
*
1
Q 2  M q2q
*
q
q
g
 E ~ W 2 ~ 1 x
•Lifetime of dipoles very long  it is the dipole that interacts with the proton
•Transverse size
 1/  (Q2+ Mqq2)
•This is why can do diffraction in ep collisions !
Transverse size of incoming hadron beam can be reduced
at will. Can be so small that strong interaction with proton
becomes perturbative (colour transparency) !
Two models:
IFAE04 Torino
aprile 2004
Saturation Model (Golec-Biernat and M. Wusthoff)
BEKW model (Bartels, Ellis, Kowalski and Wüsthoff)
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INFN e Universita' della Calabria
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Saturation vs data (LPS) (Bartels, Golec-Biernat, Kowalski)
Inclusive diffraction:
Inclusive DIS:
Data well described by BGK saturation model
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
Q2
14
BEKW vs data (LPS) (Bartels, Ellis, Kowalski and Wüsthoff)
Transition to a constant cross
section as Q2 0
(similar to total cross section)
Main features of the data
described by BEKW
parametrization (xIP<0.01)
FqTq ~  (1   )
medium β
FqTqg ~ (1   )
small β
qqg fluctuations dominant at low Q2
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
15
Vector Meson production
Large variety of processes to study dynamics versus scales: MV2, Q2, t
V
V
(JPC=1--): r, f, J/y,U,...
W
IP
p
p
p
p
2-gluon exchange:
LO realisation of vacuum
quantum numbers in QCD
Gluon density in the proton
Cross section proportional to probability
of finding 2 gluons in the proton:
growth with decreasing x (increasing W)
at large Q2+ MV2 reflecting large gluon
density at low x
  [ x g(x,  2 )]2
!
x   2 W2
 2  (Q 2  M 2V )
[Ryskin (1993), Nikolaev et al (1994), Brodsky et al (1994),...]
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aprile 2004
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INFN e Universita' della Calabria
16
VM: sensitivity to gluons in proton
with d  4(P(0) -1)
 (p
Vp), Q2=0
 W0.2
MV
 W0.8
•At small MV (MV2  1 GeV2): Incoming
dipole behaves like a normal-size
hadron. Flat  vs W reflects flat
gluon distribution for Q2  0
•At large MV :Fast growth of  with W
reflects growth of gluon distribution
with decreasing x
xg(x)
Fit:  ~
Wd
 W1.7
(not the most recent)
W  1/  x
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Marcella Capua
INFN e Universita' della Calabria
x
17
VM: sensitivity to models
 (p
Vp), Q2=0
High precision data
Large MV supplies a scale for
hard processes  apply QCD
models
Now able to dicriminates
theory models
MV
LLA
W  1/  x
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Marcella Capua
INFN e Universita' della Calabria
18
Deeply Virtual Compton Scattering
*

p
p
• Similar to elastic VM production,
but  instead of VM in final state
• No VM wavefunction involved
• Again rapid increase of cross section
with W – a reflection of the large gluon
density at low x
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
19
DVCS vs GPDs
GPD-based calculations, NLO QCD(!) - Freund & with 2 sets of GPDFs
Colour dipole models Donnachie &, Favart &
Both theoretical approaches consistent with measurements
• Sensitivity to GPDs (so far) in DVCS (large Q2) and U production
• A field in its infancy. Holds the promise of mapping parton-parton
correlations and transverse distribution of partons in the proton
• Important to find how to extract GPDs from data
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aprile 2004
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INFN e Universita' della Calabria
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Conclusioni
• E’ possibile discutere la diffrazione in termini di pQCD
• Sappiamo determinare le PDF diffrattive confermando la fattorizzazione in
diffrazione ad HERA.
• L’oggetto scambiato e’ essenzialmente gluonico (alta’ densita’ gluonica nel
protone 75 ±15 % )
• L’ipotesi del rescattering offre la possibilita’ di interpretare anche i dati del
Tevatron e quindi di parlare di universalita’ delle PDF.
• Il color dipole model e’ una finestra nella regione di transizione dal perturbativo
al non perturbativo.
• Processi di VM offrono la possibilita’ di misurare le densita’ gluoniche e la
precisione dei nostri dati e’ in grado di discriminare tra modelli teorici di pQCD.
• Sensibilita’ alle GPDs e quindi alle correlazioni tra partoni.
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INFN e Universita' della Calabria
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Hard diffraction sensitive to parton-parton correlations
in the proton
In general, x1  x2:
*
x1
p
  [x g(x)] 2
x2
p
  [H(x 1, x 2 )]2
Generalised PDFs: sensitive to parton-parton correlations in the proton
Hard diffraction sensitive to proton structure and
calculable in QCD
GPD
Hard diffraction sensitive to parton correlations and
transverse distribution of partons in proton via GPDs
Ingredient for estimating diffractive cross sections at LHC
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
GPD
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Diffractive γ*p interactions at HERA
 No activity in the forward direction
 Proton almost intact after the collision
- large kinematic range and cross section:
~ 10 % of DIS is diffractive
- 4 acceptance: important for * diss system
- point-like probe
- wide Q2 range: to access the transition region
from soft to hard processes
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
Three different
selections method
23
Color dipole models
qq
(Golec-Biernat and M. Wusthoff)
• pQCD: sqq  r2  1/Q2 (colour transparency)
Saturation
pQCD
e.g. Saturation Model
npQCD
• As Q2  0, sqq   violation of unitarity
• Growth by sqq saturating at sqq  s(rp)
r
e.g. BEKW model
(Bartels, Ellis, Kowalski and Wüsthoff)
FTqq ~β(1- β), weak Q2 dep.
FTqqg ~(1- β)γ , ln (1+Q2/Q20), Q20=1GeV2
energy dep. for both :
FLqq only at high β
from fits to the data
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aprile 2004
Marcella Capua
INFN e Universita' della Calabria
x IP
 ndiff ( Q 2 )
24