Diffractive Structure Functions
and Exclusive Production
from CDF to LHC
Konstantin Goulianos
The Rockefeller University
and the CDF Collaboration
Contents





Introduction
Elastic and total cross sections
Soft diffraction
Hard diffraction
Exclusive Production
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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p-p Interactions
Non-diffractive:
Color-exchange
Diffractive:
Colorless exchange with
vacuum quantum numbers
rapidity gap
Incident hadrons
acquire color
and break apart
CONFINEMENT
P
O
M
E
R
O
N
Incident hadrons retain
their quantum numbers
remaining colorless
pseudoDECONFINEMENT
Goal: understand the QCD nature of the diffractive exchange
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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Diffractive pp Processes
sT=Im fel (t=0)
Elastic scattering
f
h
SD
HERA&LHC, 12-16 March 2007
f
OPTICAL
THEOREM
GAP
DD
Total cross section
h
DPE
Diffraction from CDF to LHC
SDD=SD+DD
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CDF Run 1-0 (1988-89)
Elastic, diffractive, and total cross section
@ 546 and 1800 GeV
Roman Pot Spectrometers
CDF-I
Roman Pot Detectors
 Scintillation trigger counters
 Wire chamber
 Double-sided silicon strip detector
HERA&LHC, 12-16 March 2007
Roman Pots with Trackers
up to |h| = 7
Diffraction from CDF to LHC
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Run-IC
CDF-I
Run-IA,B
beam
Forward Detectors
BBC 3.2<h<5.9
FCAL 2.4<h<4.2
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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CDF-II
ROMAN POT DETECTORS
BEAM SHOWER COUNTERS:
Used to reject ND events
MINIPLUG CALORIMETER
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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The MiniPlugs @ CDF
HERA&LHC, 12-16 March 2007
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ELASTIC AND TOTAL CROSS SECTIONS
@ Tevatron: CDF and E710/811
 use luminosity independent method 
Optical
1 theorem
1 dN
s ~
2
T
el
L 1   2 dt
optical theorem

t 0
1
& s T ~ N el  N inel 
L
16 dN el
sT 
1   2 dt
t 0
1
N el  N inel
Alert:
 background Ninel yields small sT
 undetected Ninel yields large sT
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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Total Cross Sections: Regge fit
CDF
E710
CMG fit:
Covolan, Montagna, Goulianos
PLB 389 (1995) 176
Born
level
DL
Simultaneous Regge fit to
pp, p, and Kp x-sections
using the eikonal approach
to ensure unitarity
s  Se
e = 1.104 +/- 0.002

s
LHC
= 115 mb
@14 TeV
HERA&LHC, 12-16 March 2007
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sT: other approaches
eg, M. Block, arXiv:hep-ph/0601210 (2006)
 fit data using analyticity constraints
M. Block and F. Halzen, Phys. Rev. D 72, 036006
sT (LHC) =
107.3 ± 1.2 mb
HERA&LHC, 12-16 March 2007
Recall CMG Regge fit: 115 mb
Diffraction from CDF to LHC
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sT and -values from PDG
=
ratio of real/imaginary parts
of elastic scattering amplitude at t=0
CDF
E710
E811
CDF and E710/811 disagree
sT
CDF & UA4
E811
optical theorem
Im fel(t=0)
dispersion relations
Re fel(t=0)
N. Khuri and A. Martin:
measuring  at the LHC tests
discreteness of space-time
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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SOFT DIFFRACTION
Key words:
renormalization
scaling
QCD
multi-gap
HERA&LHC, 12-16 March 2007
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Renormalization
Factorization 
d 2σSD
 f IP/p (t, ξ)  σ IP p (M 2X )
dtdξ
s SD ~ s
2e
Pomeron flux
 Regge theory
sSD exceeds sT at
s  2 TeV.
 Renormalization
Pomeron flux integral
(re)normalized to unity
KG, PLB 358 (1995) 379
0.1
0
 
f IP/p (t, ξ) dξ dt  1
ξ min t  
HERA&LHC, 12-16 March 2007
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A Scaling Law in Diffraction
KG&JM, PRD 59 (1999) 114017
renormalization
2e
ds
s 1

2
2 1e
dM
(M )
 e
 Independent of S over 6
orders of magnitude in M2 !
Factorization breaks down so as to ensure M2-scaling!
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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The QCD Connection
f
y  ln s
y
Total cross section:
power law increase versus
~1/s
s
s T ( s)  s o ee y  s o s e
The exponential rise of sT(y’) is due
to the increase of wee partons with y’
(E. Levin, An Introduction to Pomerons,Preprint DESY 98-120)
f
y  ln s
Im f el ( s, t )  e e   t y
HERA&LHC, 12-16 March 2007
y
Elastic cross section:
forward scattering amplitude
Diffraction from CDF to LHC
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Single Diffraction in QCD
(KG, hep-ph/0205141)
t
2 independent variables:
dσ
dM 2
y 
y
t , y
s 2ε

2 1 ε
(M
)
REGGE
color
factor
d 2s
2
e   t y 2
e y
 C  Fp (t )  e
  s o e
dt dy




Gap probability
~e
2e y

y ln s
ymin
Renormalization removes the s-dependence
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
s
2e y
 s 2e
SCALING
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Multi-gap Renormalization
(KG, hep-ph/0205141)
y1
5 independent variables
t1
y1
y2
y1
y2
y  y1  y2
d 5s
e   ti yi
2
 C  Fp (t1 ) e
i 1- 2
 dVi

i 15
Gap probability
~e

HERA&LHC, 12-16 March 2007
y ln s
ymin
s
t2
color
factors

 s o e
2
e  y1  y 2 

Sub-energy cross section
(for regions with particles)
2e y
2e y

2
y2
 s 2e
Same suppression
as for single gap!
Diffraction from CDF to LHC
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Central and Double Gaps @ CDF
 Double Diffraction Dissociation
 One central gap
 Double Pomeron Exchange
 Two forward gaps
 SDD: Single+Double Diffraction
 One forward + one central gap
HERA&LHC, 12-16 March 2007
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Central & Double-Gap CDF Results
Differential shapes agree with Regge predictions
DD
SDD
DPE
 One-gap cross sections are suppressed
 Two-gap/one-gap ratios are    0.17
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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Gap Survival Probability
S=
gap
S12gap/0
gap/1gap (1800 GeV)  0.23
gap
S12gap/0
gap/1gap (630 GeV)  0.29
Results similar to predictions by:
Gotsman-Levin-Maor
Kaidalov-Khoze-Martin-Ryskin
Soft color interactions
HERA&LHC, 12-16 March 2007
Diffraction from CDF to LHC
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HARD DIFFRACTION
 Diffractive fractions
 Diffractive structure function
 factorization breakdown
 Restoring factorization
 Q2 dependence
 t dependence
 Hard diffraction in QCD
dN/dh
h
HERA&LHC, 12-16 March 2007
JJ, W, b, J/y
Diffraction from CDF to LHC
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Diffractive Fractions @ CDF
pp  (
 X )  gap
Fraction(%)
Fraction:
SD/ND ratio
at 1800 GeV
HERA&LHC, 12-16 March 2007
W
1.15 (0.55)
JJ
0.75 (0.10)
b
0.62 (0.25)
J/y
1.45 (0.25)
All ratios ~ 1%
~ uniform suppression
~ FACTORIZATION !
Diffraction from CDF to LHC
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Diffractive Structure Function:
Breakdown of QCD Factorization
b = momentum fraction
of parton in Pomeron
H1
Using preliminary pdf’s from
HERA&LHC, 12-16 March 2007
The diffractive structure function at
the Tevatron is suppressed by a
factor of ~10 relative to expectation
from pdf’s measured by H1 at HERA
Similar suppression factor
as in soft diffraction
relative to Regge expectations!
Diffraction from CDF to LHC
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Restoring QCD Factorization
R(SD/ND)
R(DPE/SD)
DSF from two/one gap:
factorization restored!
The diffractive structure function measured on the proton side in events with
a leading antiproton is NOT suppressed relative to predictions based on DDIS
HERA&LHC, 12-16 March 2007
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Diffractive Structure Function:
Q2 dependence
ETjet ~ 100 GeV !
Small Q2 dependence in region 100 < Q2 < 10,000 GeV2
 Pomeron evolves as the proton!
HERA&LHC, 12-16 March 2007
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Diffractive Structure Function:
t- dependence
Fit ds/dt to a double exponential:
 No diffraction dips
 No Q2 dependence in slope
from inclusive to Q2~104 GeV2
HERA&LHC, 12-16 March 2007
 Same slope over entire region of
0 < Q2 < 4,500 GeV2
across soft and hard diffraction!
Diffraction from CDF to LHC
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Hard Diffraction in QCD
p
p
deep sea
Derive diffractive
from inclusive PDFs
and color factors
valence quarks
valence quarks
antiproton
x=x
proton
HERA&LHC, 12-16 March 2007
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EXCLUSIVE PRODUCTION
Measure exclusive jj & gg



Bialas, Landshoff,
Phys.Lett. B 256,540 (1991)
Khoze, Martin, Ryskin,
Eur. Phys. J. C23, 311 (2002);
C25,391 (2002);C26,229 (2002)
C. Royon, hep-ph/0308283
B. Cox, A. Pilkington,
PRD 72, 094024 (2005)
OTHER…………………………
Clean discovery channel
KMR: sH(LHC) ~ 3 fb
S/B ~ 1 if M ~ 1 GeV
 3 candidate events found
 1 (+2/-1) predicted
from ExHuME MC*
 background under study
M jj
M X all calorimete rs 
Look for signal as Mjj 1
HERA&LHC, 12-16 March 2007
H
Search for exclusive gg
Search for exclusive dijets:
Measure dijet mass fraction
R jj 
Calibrate predictions for
H production rates @ LHC
* See talk by V. Khoze
Diffraction from CDF to LHC
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Exclusive Dijet Signal
D
I
J
E
T
S
Dijet fraction – all jets
Excess over MC predictions
at large dijet mass fraction
HERA&LHC, 12-16 March 2007
b-tagged dijet fraction
Exclusive b-jets are suppressed
by JZ= 0 selection rule
Diffraction from CDF to LHC
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RJJ(excl): Data vs MC
ExHuME (KMR): gggg process
 uses LO pQCD
Exclusive DPE (DPEMC)
 non-pQCD based on Regge theory
Shape of excess of events at high Rjj
is well described by both models
HERA&LHC, 12-16 March 2007
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jjexcl: Exclusive Dijet Signal
COMPARISON
Inclusive data vs MC @ b/c-jet data vs inclusive
HERA&LHC, 12-16 March 2007
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JJexcl : x-section vs ET(min)
Comparison with hadron level predictions
HERA&LHC, 12-16 March 2007
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JJexcl : cross section predictions
ExHuME Hadron-Level Differential Exclusive Dijet Cross Section vs Dijet Mass
(dotted/red): Default ExHuME prediction
(points): Derived from CDF Run II Preliminary excl. dijet cross sections
Statistical and systematic errors are propagated from measured cross section
uncertainties using ExHuME Mjj distribution shapes.
HERA&LHC, 12-16 March 2007
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Summary
TEVATRON – what we have learnt
 M2 – scaling
 Non-suppressed double-gap to single-gap ratios
 Pomeron: composite object made up from underlying
pdf’s subject to color constraints
LHC - what to do
 Elastic and total cross sections & -value
 High mass (4 TeV) and multi-gap diffraction
 Exclusive production (FP420 project)
 Reduced bgnd for std Higgs to study properties
 Discovery channel for certain Higgs scenarios
HERA&LHC, 12-16 March 2007
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