4-7 June 2003 K. Goulianos, Low-x Workshop, Nafplion 1
Konstantin GoulianosThe Rockefeller University & The CDF Collaboration
Low-x Workshop, Nafplion, Greece, 4-7 June 2003 • Introduction• Run I review• Run II results• Conclusion
Aspects of Diffraction at CDFAspects of Diffraction at CDF
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Introduction
What is hadronic diffraction?
X
p
X
L
L
m
m
S
M
P
P
2
ξ
Diffractiondissociation
2
2
dMdtd
1
~dt
d
KG, Phys. Rep. 101 (1983) 171
cohe
rence
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Non-diffractive interactions: Diffractive interactions:
rapidity gaps are regions of rapidity devoid of particles
Gaps are exponentially suppressed
From Poisson statistics:
dy
dneP y )(
(r=particle density in rapidity space)
2lnlnln Msy
constant~1
~22 yd
d
MdM
d
large rapidity gaps are signatures for diffraction
rapidity gaps are formed bymultiplicity fluctuations
rapidity gaps, like diamonds,‘live for ever’
Diffraction and Rapidity GapsDiffraction and Rapidity Gaps
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Quark/gluon exchange across a rapidity gap:
POMERON
No particles radiated in the gap:
the exchange is COLOR-SINGLET with quantum numbers of vacuum
Rapidity gap formation: NON-PERTURBATIVE
Diffraction probes the large distance aspects of QCD:
POMERON CONFINEMENT
PARTONIC STRUCTURE FACTORIZATION
?
The PomeronThe Pomeron
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Elastic scattering Total cross section Diffraction
PRD PRL PRL PRL50 (1994) 5535 87 (2001)141802 to be sub’d submitted
SOFT diffraction
HARD diffraction
Control sample
W 78 (1997) 2698 JJ 74 (1995) 855 JJ 85 (2000) 4217
JJ 79 (1997) 2636 JJ 80 (1998) 1156
b-quark 84 (2000) 232 JJ 81 (1998) 5278
J/ 87 (2001) 241802
JJ 84 (2000) 5043
JJ 88 (2002) 151802
with roman pots
PRL reference
PRD 50 (1994) 5518
PRD 50 (1994) 5550
Diffraction at CDF in Run IDiffraction at CDF in Run I
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Factorization & Renormalization
Soft diffraction
)'(),(/
2
ytyfdtyd
dpIPpIP
Renormalize to unityKG, PLB 358(1995)379
Gap probability )0(
)(
pIP
IPIPIP tg
y
y
'y
sln2ln XM
ysy ln
XM
yo e
2)(tFeC pyt
COLORFACTOR
tt '1)( PI
Pomerontrajectory
1)0(ln IPses os
ooT
parton model
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ReggeonsReggeons
sMs
sIPRR
sMs
sIP
s
M
ssRIPIP
s
M
ssIPIPIP
~21~~
~12
21~1~
2~5.0212
2~
5.021/1~
2~12
2~
1~
Key players:
• Both rise at small but integral does not fit data;• M2-dependence of IP-IP-R does not fit low-s data;=> KG: Renormalize IP-IP-IP
• Reggeon contribution: important at large
KG & JM: use renormalized IP-IP-IP plus -IP with only g IP-IP-IP as free parameter
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X)pp(p)pp( Total cross section
KG, PLB 358 (1995) 379Differential cross section
KG&JM, PRD 59 (114017) 1999
2~ s
12
2
2 )(M
s
dM
dREGGE
122 )(
1
MdM
dRENORM
s-independent Differential shape agrees with Regge Normalization is suppressed by factor ~ Renormalize Pomeron flux factor to unity
2sM2 SCALING
Soft Single Diffraction DataSoft Single Diffraction Data
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CDF Single Diffraction Data and FitsCDF Single Diffraction Data and Fits
Data versus MC based on triple-Pomeron plus Reggeon
CDF PRD 50 (1994) 5535
Data at |t|=0.05 GeV2 corrected for acceptance
KG&JM, PRD 59 (114017) 1999
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Double diffraction
Plot #Events versus
Double Pomeron Exchange
Measure
Plot #Events versus log()
ieEs
iTp
particlesall
1
SDD: single+double diffraction Central gaps in SD events
Central and Double GapsCentral and Double Gaps
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Differential shapes agree with Regge predictions
One-gap cross sections require renormalization
DD SDD DPE
Two-gap/one-gap ratios are 17.0
Central and Double-Gap ResultsCentral and Double-Gap Results
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Soft Double Pomeron ExchangeSoft Double Pomeron Exchange
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colorfactor
1y 2y1y 2y
1y1y 2y2y
2t1t 21 yyy 7 independent variables
2122
gaps21
71
7
)( yyop
yt
ii
etFeCdV
dii
Gap probability Sub-energy cross section(for regions with particles)ye 2~Integral 2~ s
Renormalization removes the s-dependence SCALING
Two-Gap Diffraction (hep-ph/0205141)Two-Gap Diffraction (hep-ph/0205141)
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5 region-centers1 sum of all gaps4 t-values
Vi
10 variables
ytetyf )'(),(
Renormalize gap probability to calculate multigap cross sections
Use amplitude at t=0 for x-section
Use amplitude squared for gaps
Pgap depends on sum of gaps
form factors
17.0)(
)(
t
tg
Renormalize: set integral of Pgap to unity
Amplitude
one factorfor each gap
Multigap Diffraction (hep-ph/0205141)Multigap Diffraction (hep-ph/0205141)
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Hard diffraction in Run I
BBC 3.2<<5.9FCAL 2.4<<4.2
BBCFCAL
Diffractive dijets
CDF Forward Detectors
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SINGLE DIFFRACTION DOUBLE DIFFRACTIONJetJetpp gapgap Xpp
1.45 (0.25)J/
0.62 (0.25)b
0.65 (0.04)0.75 (0.10)JJ
1.15 (0.55)W
D0CDFX
SD/ND gap fraction (%) at 1800 GeV DD/ND gap fraction at 1800 GeV
• All SD/ND fractions ~1%
• Gluon fraction
• Suppression by ~5 relative to HERA
15.054.0 gf
Just like in ND except for the suppression due to gap formation
Hard Diffraction Using Rapidity GapsHard Diffraction Using Rapidity Gaps
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),,,( 2QxtF SD
ISSUES: 1) QCD factorization > is FSD universal?
2) Regge factorization >
(not detected)
pBjx
i
eEs
xjets
iT
pBj
#
1
Bjorken-x of antiproton
),( 2QxF ND Nucleon structure function
Diffractive structure function
),,,( 2QxtF SD
),(),(),,,( 2flux
2 QftfQtF IPIPSD
/x?
momentum fraction of parton in IP
METHOD of measuring FSD : measure ratio R(,t) of SD/ND rates for given ,t set R(,t)=FSD/FND
evaluate FSD = R * FND
Diffractive Dijets with Leading AntiprotonDiffractive Dijets with Leading Antiproton
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)(DJJF
mnDJJ CF ),(
Test Regge factorizationTest QCD factorization
Regge factorization holdsSuppressed at the Tevatronrelative to predictions basedon HERA parton densities exchangePomeron1m !!!
Dijets in Single DiffractionDijets in Single Diffraction
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(not detected)
R(SD/ND)
R(DPE/SD)
Test of factorization
equal?
SDND
DPESD RR 5
Factorization breaks down
The second gap is un-suppressed!!!
Dijets in Double Pomeron ExchangeDijets in Double Pomeron Exchange
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Run II Diffraction at the Tevatron
CDF Forward Detectors
MiniPlug calorimeters (3.5<<5.5) Beam Shower Counters (5.5<<7.5) Antiproton Roman Pot Spectrometer
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Run II Forward Detector LayoutRun II Forward Detector Layout
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MiniPlug Run II DataMiniPlug Run II Data
ADC counts in MiniPlug towersin a pbar-p event at 1960 GeV.• “jet” indicates an energy cluster and may be just a hadron.• Approximately 1000 counts = 1 GeVMultiplicity distribution in SD and ND events
MiniPlug tower structure
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J5 At least one cal tower with ET > 5 GeV
RP inclusive Three-fold coincidence in RP trigger counters
RP+J5 Single Diffractive dijet candidates
RP+J5+BSC-GAP_p Double Pomeron Exchange dijet candidates
Triggers
Results presented are from ~26 pb-1 of data The Roman Pot tracking system was not operational for these data samples The of the (anti)proton was determined from calorimeter information:
iiT
X eEs
)(
towerscal
1
(-)+ is for (anti)proton
Run II Data SamplesRun II Data Samples
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Diffractive Dijet SampleDiffractive Dijet Sample
ND+SD & SD+MBoverlap events
~ 1SD
events
0.03<<0.1
ondistributiXp
constantlog
1
d
d
d
dFlat region
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Diffractive Dijet Structure FunctionDiffractive Dijet Structure Function
Ratio of SD to ND dijet eventratesas a function of xBj
for different values of Q2=ET2
Ratio of SD to ND dijet event ratesas a function of xBj
compared with Run I data
No dependence observed within 0.03 < <0.1(confirms Run I result)
No appreciable Q2 dependence observed within 100 < Q2 < 1600 GeV
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Dijets in DPEDijets in DPE
In SD data with RP+J5 triggerselect events with rapidity gapin both the BSC_p and MP_p
(3.5 < <7.5)
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Data SelectionData SelectionDPE dijet candidatesDPE: RP+J5+BSC_GAP_p
Single Diffractive dijet candidatesSD: RP+J5
Tower with ET > 5 GeVND: J5
Prescale=5
Prescale=280
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DPE Dijet KinematicsDPE Dijet Kinematics
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Inclusive/Exclusive DPE Dijet Predictions Inclusive/Exclusive DPE Dijet Predictions
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Limit on Exclusive DPE Dijets (Run I)Limit on Exclusive DPE Dijets (Run I)
σ
CL)(95%nb3.7e)σ(exclusiv
nb21.6(syst)stat)(4.444.6e)σ(inclusiv
Observed ~100 DPE dijet events
0.035 < < 0.095 Jet ET > 7 GeV Rapidity gap in 2.4 < < 5.9
Dijet mass fraction X
jjjj M
MR
MJJ based on energy within cone of 0.7=> look for exclusive dijets in window 0.7 < RJJ < 0.9
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Run II: Exclusive DPE Dijets ?Run II: Exclusive DPE Dijets ?
No exclusive dijetbump observed
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Double Pomeron Exchange Dijet EventsDouble Pomeron Exchange Dijet Events
Rjj=0.81, Jet1(2)=33.4(31.5) GeV Rjj=0.36, Jet1(2)=36.2(33.3) GeV
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SUMMARY
Soft and hard conclusions
Soft Diffraction
Hard Diffraction Pay a color factor for each gap
Use the reduced energy cross section
Get gap size from renormalized Pgap
Diffraction is an interaction between low-x partons subject to color constraints
