Diffraction for all:from Tevatron to LHC and Beyond
HEP 2006, December 11-15, Valparaiso, Chile
Konstantin Goulianos
The Rockefeller University
Recent referencesDiffraction at the Tevatron: CDF resultshttp://pos.sissa.it//archive/conferences/035/016/DIFF2006_016.pdf
Renormalized diffractive parton densitieshttp://pos.sissa.it//archive/conferences/035/044/DIFF2006_044.pdf
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ContentsIntroductionElastic and Total Cross SectionsDiffractionExclusive Production
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p-p InteractionsDiffractive:Colorless exchange with vacuum quantum numbers
Non-diffractive:Color-exchange
Incident hadrons retain their quantum numbersremaining colorless
pseudo-DECONFINEMENT
Incident hadrons acquire colorand break apart
CONFINEMENT
POMERON
Goal: understand the QCD nature of the diffractive exchange
rapidity gap
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Elastic Scattering
DIFFRACTION PATTERN
PROTON BEAM
TARGETPROTON
PROTON-PROTON ELASTIC SCATTERING
p p' dtdσ
2
π
)(p4
R
cGeV13b
m1R
e~bte~dtdσ 2
2
−
−
⎟⎠⎞
⎜⎝⎛≈⇒=
θ
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Diffraction DissociationRT
RL
M
P0
P0
Δ PT Δ PL,
m p
sM
PΔPξ
2
L
L ==
025.02
2
−=tdMdt
d σ
Momentum loss fraction
COHERENCE CONDITION 1.0
mm
p
≈< πξξ< 0.1
d
?M1~
dMdσwhyBut 22
Tevatron M 0.6 TeVLHC 4.4 TeV
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Rapidity Gaps
ξ1~
dξdσ
M
1~dM
dσconstantΔηddσ
220t
⇒⇒≈⎟⎟⎠
⎞⎜⎜⎝
⎛
=
p pX p
ξp
Particle production Rapidity gap
η
φ
-ln ξln MX2
ln s
X
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Diffractive pp Processes
η
φ
Elastic scattering Total cross section
SD DD DPE SDD=SD+DD
σT=Im fel (t=0)
OPTICALTHEOREM
η
φGAP
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Rapidity Gaps in Fireworks
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The PhysicsElastic and Total Cross Sections:……….pp pp and pp X
Fundamental Quantum MechanicsFroissart Unitarity Bound……….σT < C ln2s Optical theorem………………………..σT ~Im f(t=0)Dispersion relations………………....Re f(t=0)~Im f(t=0)Is space-time discrete? Measure σT and ρ-value at LHC!
Diffraction Dissociation:………………pp pX, XgX, pXp, pXgX, …Non-perturbative QCD
Soft & hard diffractionFactorizationMulti-gap diffractionDiffraction in QCD:…….……what is the Pomeron?Dark energy?
Exclusive Production:………………….…..pp pp+H (jet+jet, γ+γ, …, H0)Discovery channel
Diffractive Higgs production at the LHC (?)
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Tevatron Experiments
InfoExp
RomanPots El σT
Soft diffraction Hard diffraction
p, pbar
CDF-0 p, pbar x x sd
pbar
pbar
p, pbar
D0-I JJ,W,Z,JGJ, …
E710/811Scint. Counters
x x sd
CDF-I sd,dd,dpe,sdd JJ,b,J/ψ,W,JGJ
CDF-II sd JJ,W,Z,JGJExclusive JJ,γγ,...
D0-II x x sd,dpe,… JJ,W,Z,JGJ,…Exclusive ???
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CDF Run 1-0 (1988-89)Elastic, diffractive, and total cross section
@ 546 and 1800 GeV
Roman Pot Spectrometers
Roman Pot DetectorsScintillation trigger countersWire chamber Double-sided silicon strip detector
Roman Pots with Trackersup to |η| = 7
CDF-I
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CDF-I
DIPOLE MAGNETS
ROMAN POTS at 57 m
p- CDF
Scintillator fiber xy-tracker 270 pitch, 2 m lever armx<0.97
x=1
μ
Acceptance: 0 < |t| < 1, 0.03< < 0.1ξ
Run-IC Run-IA,B
HADRON
END PLUG EM
CENTRAL EMCES
EM
Forward(Not-To-Scale)
CPR
CENTRAL MUON
CENTRAL MUON UPGRADE
STEEL ABSORBER
η = 0
Silicon Vertex Detector
Central Muon Extension
Z
Vertex Tracking Chamber
CHAMBERTRAKCING
INTERACTION POINT
DetectorCDF
η = 4.2
η = 2.4
η = 0.9
PLUG
ENDHADRONCENTRAL
BBC
WALL
CENTRAL
SOLENOID
HADRON
END
HADRON
Forward DetectorsBBC 3.2<η<5.9FCAL 2.4<η<4.2
beam
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CDF-IIROMAN POT DETECTORS
BEAM SHOWER COUNTERS:Used to reject ND events
MINIPLUG CALORIMETER
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The MiniPlugs @ CDF
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CDF & D0 - Run II
Z(m)
D SQ2Q3Q4S A1A2
P1U
P2I
P2O
P1DD2 D1
233359 3323057
Q4Q3Q2
D0
From Barreto’s talk in small-x
LM 2.5<η<4.4VC 5.2<η<5.9
Z(m)
p
D Q2Q3Q4
p
RP3 RP1
2332 3223057
Q4Q3Q2
MP 3.5<η<5.5BSC1 5.5<η<7.5
RP2
S S
BSC4 BSC2BSC3 BSC2 BSC3CDF
CDF & D0:COMPLIMENTARY
COVERAGE
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ELASTIC AND TOTAL CROSS SECTIONS
@ Tevatron: CDF and E710/811use luminosity independent method
Optical theorem
Alert:background Ninel yields small σTundetected Ninel yields large σT
( )
inelelt
elT
inelelTt
elT
NNdtdN
NNLdt
dNL
++=⇒
++
=
=
1116
1~&1
11~
02
02
2
ρπσ
σρ
σ
optical theorem
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σT and ρ-values from PDG
E710
ρ = ratio of real/imaginary partsof elastic scattering amplitude at t=0
E811
CDF
CDF & UA4
CDF and E710/811 disagree
σT
optical theoremIm fel(t=0)
dispersion relationsRe fel(t=0)E811
N. Khuri and A. Martin:measuring ρ at the LHC tests discreteness of space-time
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Total Cross Sections: Regge fitCMG: Covolan, Montagna, and G
PLB 389 (1995) 176
Simultaneous Regge fit to pp, πp, and Kp x-sections using the eikonal approachto ensure unitarity
σ Sε
ε = 1.104 +/- 0.002
σLHC = 115 mb@14 TeV
Bornlevel
DL
E710CDF
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Other Approaches
σT (LHC) = 107.3 ± 1.2 mb
eg, M. Block, arXiv:hep-ph/0601210 (2006)
fit data using analyticity constraintsM. Block and F. Halzen, Phys. Rev. D 72, 036006
Recall CMG Regge fit: 115 mb
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TOTEM experiment @ LHCTotal Cross Section, Elastic Scattering, and Diffraction Dissociation
Aim at 1% accuracy on σT
RP stations
RP stations
CMS
CMS/TOTEM LOI: Prospects for Diffractive and Forward Physics at the LHC
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SOFT DIFFRACTIONKey words:
renormalization
scaling
QCD
multi-gap
Dark energy ???
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Regge theoryσSD exceeds σT at
RenormalizationPomeron flux integral(re)normalized to unity
Renormalization)(Mσξ)(t,f
dtdξσd 2
XpIPIP/pSD
2
−•=
KG, PLB 358 (1995) 379
TeV.2s ≈
1dtdξξ)(t,f0.1
ξIP/p
0
tmin
=∫ ∫−∞=
εσ 2~ sSD
Pomeron fluxFactorization
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A Scaling Law in Diffraction
14 GeV (0.01 < ξ < 0.03)
20 GeV (0.01 < ξ < 0.03)
546 GeV (0.005 < ξ < 0.03)
1800 GeV (0.003 < ξ < 0.03)
1____
(M2)1+Δ.....
←_____ 546 GeV std.flux prediction
← 1800 GeV std.flux prediction
Δ = 0.05 ________→
Δ = 0.15 _________→
renorm. fluxprediction
_________→
std. and renorm.flux fits
|↑
KG&JM, PRD 59 (1999) 114017
ε≡Δ
Factorization breaks down so as to ensure M2-scaling!
ε
εσ+∝ 12
2
2 )(Ms
dMd
renormalization
1
Independent of S over 6 orders of magnitude in M2 !
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The QCD Connection
( ) ytel etsf Δ′+∝ αε),(Im
yφ sy ln=Δ
The exponential rise of σT(Δy’) is dueto the increase of wee partons with Δy’
(E. Levin, An Introduction to Pomerons,Preprint DESY 98-120)
εε σσσ ses oy
oT == ′Δ)(y
φ sy ln=′ΔTotal cross section:power law increase versus s
Elastic cross section:forward scattering amplitude
∼1/αs
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y′ΔyΔ
yt Δ,2 independent variables:
( ){ } { }yo
ytp eetFC
yddtd ′ΔΔ′+ ••••=
Δεαε σκσ 22
2
)(
Gap probability
Renormalization removes the s-dependence SCALING
Single Diffraction in QCD
ye Δε2~εε 22ln
minsyssy
y ≈Δ∫ =ΔΔ
t
colorfactor
(KG, hep-ph/0205141)
ε12
2ε
REGGE2 )(M
sdMdσ
+∝
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Multi-gap Renormalization
ye Δε2~εε 22ln
minsyssy
y ≈Δ∫ =ΔΔ
Same suppressionas for single gap!
1y′Δ 2y′Δ1yΔ 2yΔ
1y′ 2y
1t 21 yyy Δ+Δ=Δ5 independent variables
2t
( ){ } ( ){ }2122
2-1i1
2
51
5
)( yyo
ytp
ii
eetFCdV
dii ′Δ+′Δ
=
Δ′+
−=
××= ∏∏εαε σκσ
Gap probability Sub-energy cross section(for regions with particles)
colorfactors
(KG, hep-ph/0205141)
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p
p
IP
IPp p
η0ηp_ ηp
p
pIP
M1
M2
η
dNdη
ηη maxmin
ln M1 ln M22 2
ln s
ηη maxminp
0η
ln M1 ln M22 2
ln1/ξp ln s’ln s
p p
IP tpM1
IP tp
M2
Double Diffraction Dissociation
One central gap
Double Pomeron Exchange
Two forward gaps
SDD: Single+Double Diffraction
One forward + one central gap
Central and Double Gaps @ CDF
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1
10
10 2
10 102
103
√s (GeV)
σ DD (
mb)
for
Δη >
3.0
ReggeRenormalized gap
CDFUA5 (adjusted)
10-1
1
103
sub-energy √s--, (GeV)
gap
frac
tion
Δη >
3.0 CDF: one-gap/no-gap
CDF: two-gap/one-gapRegge predictionRenorm-gap prediction
2-gap
1-gap
210
0
0.1
0.2
0.3
0.4
0.5
103
√s⎯
(GeV)F
ract
ion
of E
vent
s w
ith ξ
p <
0.02
CDF Data: DPE/SD ratio (Preliminary)
Regge + Factorization
Gap Probability Renorm.
Pomeron Flux Renom.
One-gap cross sections are suppressedTwo-gap/one-gap ratios are 17.0=≈ κ
Central & Double-Gap CDF ResultsDifferential shapes agree with Regge predictions
10
10 2
10 3
10 4
10 5
10-6
10-5
10-4
10-3
10-2
10-1
1ξp
X
MX2
Num
ber
of E
vent
s pe
r Δl
ogξ
= 0
.1
Data
DPE MC
SD MC
DPE+SD MC
√s⎯
= 1800 GeV
0.035 ≤ ξ- p ≤ 0.095
| t- p | ≤ 1.0 GeV2
( GeV 2 )1 10 10
210
310
410
510
6CDF Preliminary
10
10 2
10 3
10 4
10 5
0 1 2 3 4 5 6 7
√s=1800 GeV
DATADD + non-DD MCnon-DD MC
Δη0=ηmax-ηmin
even
ts
10 2
10 3
10 4
10 5
0 1 2 3 4 5 6 7Δη0
exp=ηmax-ηmin
even
ts
√s=1800 GeVDATASDD + SD MCSD MC
DD SDD DPE
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Dark Energy
P(Δy) is exponentially suppressed
dydN
ρ,ey)P( particlesΔyρ ==Δ −
Rapidity gaps are formed bymultiplicity fluctuations:
Non-diffractive interactions
Δy2εe~0ty)P( =Δ
2lnlnln Msy −=−≈Δ ξ
Rapidity gaps at t=0 grow with Δy:
Diffractive interactions
2ε: negative particle density!
Gravitational repulsion?
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HARD DIFFRACTIONDiffractive fractionsDiffractive structure function
factorization breakdownRestoring factorizationQ2 dependencet dependenceHard diffraction in QCD
η
dN/dη
JJ, W, b, J/ψ
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All ratios ~ 1% ~ uniform suppression~ FACTORIZATION !
Diffractive Fractions @ CDF
gap)( ++→ Xpp
1.45 (0.25)J/ψ
0.62 (0.25)b
0.75 (0.10)JJ
1.15 (0.55)W
Fraction(%)Fraction:SD/ND ratioat 1800 GeV
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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!
Diffractive Structure Function:Breakdown of QCD Factorization
CDF
H1
β = momentum fractionof parton in Pomeron
Using preliminary pdf’s from
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Restoring QCD Factorization
0.1 1
0.1
1
10
100
β
FD jj(β
)
from DPE/SD , 0.01 ≤ ξ ≤ 0.03
from SD/ND , 0.035 ≤ ξ ≤ 0.095
p
p
ND jetjet
0p
p
p
IP
SD jetjet
p
0
p
p
IP
IP
DPE jetjet
p p
η0ηp_ ηp
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
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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!
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Diffractive Structure Function:t- dependence
No diffraction dipsNo Q2 dependence in slopefrom inclusive to Q2~104 GeV2
Fit dσ/dt to a double exponential:
Same slope over entire region of0 < Q2 < 4,500 GeV2
across soft and hard diffraction!
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valence quarks
antiproton
x=ξ
Hard Diffraction in QCD
proton
deep sea
Derive diffractivefrom inclusive PDFsand color factors
antiproton
valence quarks
p
p
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EXCLUSIVE PRODUCTION
H
Measure exclusive jj & γγ Calibrate predictions for H production rates @ LHC
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/0308283B. Cox, A. Pilkington,PRD 72, 094024 (2005)OTHER…………………………
Search for exclusive dijets:Measure dijet mass fraction
Look for signal as Mjj 1
( )rscalorimeteallMM
RX
jjjj =
Search for exclusive γγ
3 candidate events found1 (+2/-1) predictedfrom ExHuME MC* background under study
* See talk by V. Khoze
KMR: σH(LHC) ~ 3 fbS/B ~ 1 if ΔM ~ 1 GeVClean discovery channel
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Exclusive Dijet Signal
b-tagged dijet fractionDijet fraction – all jets
Exclusive b-jets are suppressedby JZ= 0 selection rule
Excess over MC predictions at large dijet mass fraction
DIJETS
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RJJ(excl): Data vs MC
Shape of excess of events at high Rjjis well described by both models
ExHuME (KMR): gg gg processuses LO pQCD
Exclusive DPE (DPEMC)non-pQCD based on Regge theory
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jjexcl: Exclusive Dijet Signal
COMPARISONInclusive data vs MC @ b/c-jet data vs inclusive
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JJexcl : x-section vs ET(min)Comparison with hadron level predictions
ExHuME (red)Exclusive DPE in DPEMC (blue)
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JJexcl : cross section predictionsExHuME 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.
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Looking forward @ LHC
TOTEM/CMS ATLAS
FP420 project: http://www.fp420.com/Measure protons at 420 m from the IP during normal high luminosity running to be used in conjunction with CMS and ATLASFeasibility study and R&D for Roman Pot detector development
Physics aim :pp → p+ X + p (Higgs, New physics, QCD studies)Status: Project funded by the UK
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SummaryTEVATRON – what we have learntM2 – scalingNon-suppressed double-gap to single-gap ratiosPomeron: composite object made up from underlying pdf’s subject to color constraints
LHC - what to doElastic and total cross sections & ρ-valueHigh mass ( 4 TeV) and multi-gap diffraction Exclusive production (FP420 project)
Reduced bgnd for std Higgs to study propertiesDiscovery channel for certain Higgs scenarios