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