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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 1
Preliminary Examination
Tom DanielsonUniversity of Wisconsin
13 December 2004
Investigation of QCD Evolution through Jets with the ZEUS Detector at HERA
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 2
OutlineOutlineOutlineOutline
• Framework for QCD• Deep Inelastic Scattering and proton structure• Quark-parton model• Color charge and QCD• QCD Evolutions (DGLAP and BFKL)
• Methods for investigation• HERA accelerator• ZEUS detector• Jets and jet finding• Multiple jets
• Present Status• H1 and ZEUS Multijet results• Comparison between data and leading order Monte Carlo
• Conclusions and future plans
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 3
Classification of ParticlesClassification of ParticlesClassification of ParticlesClassification of Particles
• Hadrons: particles that interact strongly
• Bound states of structure-less particles (quarks)
• Quark-parton model• Quark properties:
mass, electric charge, spin
• Quarks treated as point-like, non-interacting
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 4
Parton StudiesParton StudiesParton StudiesParton Studies
Main objective: Study structure of particles• Scattering via probe exchange
• Photon → Electric charge
• W, Z Bosons → Weak charge
• Wavelength
• Special case: Deep Inelastic Scattering (DIS)
• High energy lepton transfers momentum to nucleon via probeprobe
lepton
Q
Q: related to momentum of probe
Size of proton ~ 1 fm HERA can probe to ~ 0.001 fm
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 5
DIS KinematicsDIS KinematicsDIS KinematicsDIS Kinematics
quantitiest independen 2Only
tyInelastici
partonstruck by carried momentumproton ofFraction 2
tualityPhoton vir )(
Energy CM Squared )(
2
2
2'22
2
sxyQ
kp
qpy
qp
Qx
kkqQ
epkps
Bj
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 6
DIS Cross SectionDIS Cross SectionDIS Cross SectionDIS Cross Section
Express cross section in terms of DIS kinematics and proton structure
• F2, FL, F3 → proton structure functions • F2 → interaction between transversely polarized
photon and partons• FL → interaction between longitudinally polarized
photon and partons• xBjF3 → parity violating term from weak interaction
),(),(),(2
),()( 2
3222
24
22
2
2
QxFxQxFyQxFQx
QxdQdx
pedBjBjBjLBj
Bj
EBj
Bj
2)1(1 y
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 7
Quark-Parton ModelQuark-Parton ModelQuark-Parton ModelQuark-Parton Model
• Proton contains only valence quarks• Partons considered point-like particles
• Structure functions describing individual particles’ momenta distribution depend only on xBj
• No Q2 dependence (Bjorken scaling):
• fi(x) → Parton density functions (PDF’s)• Must be experimentally determined
i
BjiBji xfxeF )(22)(),( 2
BjiBji xFQxF
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 8
QCD and Colored GluonsQCD and Colored GluonsQCD and Colored GluonsQCD and Colored Gluons
Problems with Quark-Parton Model• Statistics for Fermion ++
• ++ comprised of 3 u quarks• Violation of Exclusion principle under QPM
• Sum rule for F2
• If QPM correct:
• Value of integral shown to be ~0.5 by experiment• Quarks carry roughly half proton momentum
• Single quarks never observed• Quantum Chromodynamics: gluons with color quantum
number• ++ quark composition: uRuBuG
• Mediator of strong force → gluon• Gluons carry roughly half proton momentum
• Observed particles “colorless” → color conservation• Isolated quarks not observed → Confinement
1)(1
0
2 BjBj dxxF
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 9
QCD and Scaling ViolationQCD and Scaling ViolationQCD and Scaling ViolationQCD and Scaling Violation
Quark-parton model: F2 independent of Q2
QCD: F2 depends on Q2
• Slope of F2 vs. Q2 depends on xBj
• x > ~.25: F2 decreases as Q2 increases
• x < ~.25: F2 increases with Q2
• Prediction of QCD validated
scaling violation
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 10
Perturbative QCD (pQCD)Perturbative QCD (pQCD)Perturbative QCD (pQCD)Perturbative QCD (pQCD)
Splitting functions give probability quark or gluon to split into parton pair
• Leading Order quark and gluon splitting diagrams shown
pQCD–perturbative series summed over terms in expansion of s
• Methods of summation: next slide
S SS
photon
quark
lepton
gluon
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 11
BFKL and DGLAP EvolutionsBFKL and DGLAP EvolutionsBFKL and DGLAP EvolutionsBFKL and DGLAP Evolutions
QCD evolution:
Done by summing over diagrams
DGLAP: Sum over diagrams contributing ln(Q2) terms
• Widely used
BFKL: Sum over diagrams contributing ln(1/xBj) terms
),(),( 2200 QxfQxf
1
222
2
2
)],()(),()([2
)(
)ln(
),(
x
gqggS Qzq
z
xPQzg
z
xP
z
dzQ
Q
Qxg
Splitting Functions
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 12
BFKL-DGLAP ApplicabilityBFKL-DGLAP ApplicabilityBFKL-DGLAP ApplicabilityBFKL-DGLAP Applicability
BFKL and DGLAP apply in different kinematic regions
• DGLAP: high Q2, xBj
• Approximations do not include ln(1/xBj)
• BFKL: low Q2, xBj
Aim to study the ranges of validity
Limiting case of large gluon density
Non-perturbative region
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 13
Parton Energy and Parton Energy and kkTT Ordering OrderingParton Energy and Parton Energy and kkTT Ordering Ordering
•DGLAP: ordering in both kT and x
•BFKL: Strong ordering in x, but not ordered in kT
•Differences• Expect more partons with higher kt in
forward region with BFKL than with DGLAP
• DGLAP: Scattered partons correlated in Energy, azimuthal and polar angles
• BFKL: Scattered partons not necessarily strongly correlated
1,2,2,1,, ... ttntntnt kkkkk
121 ... xxxx nn
121 ... xxxx nn
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 14
JetsJetsJetsJets
• Colored partons produced in hard scatter → “Parton level”
• Colorless hadrons form through hadronization → “Hadron level”
• Collimated “spray” of particles → Jets
• Particle showers observed as energy deposits in detectors → “Detector level”
Produced Observed
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 15
HERA Collider at DESYHERA Collider at DESYHERA Collider at DESYHERA Collider at DESY
920 GeV protons27.5 GeV e- or e+
318 GeV CMS Energy• Equivalent to ~50 TeV
fixed target
220 Bunches• Not all filled
Beam Currents• Proton: 140 mA• Electron: 58 mA
Instantaneous Luminosity
• 1.8 x 1031cm-2s-1
BH
unpunptottot RIIRL
)(
DESY
Hamburg, Germany
ZEUS
H1
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 16
HERA LuminosityHERA LuminosityHERA LuminosityHERA Luminosity
1992 – 2000 total integrated luminosity: 193 pb-1
2002 – 2004 total integrated luminosity: 84 pb-1
ZEUS Luminosities (pb-1) # events (106)
Year HERA ZEUS on-tape Physics
e-: 93-94, 98-99 27.37 18.77 32.01
e+: 94-97, 99-00 165.87 124.54 147.55
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 17
ZEUS DetectorZEUS DetectorZEUS DetectorZEUS Detector
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 18
ZEUS CalorimeterZEUS CalorimeterZEUS CalorimeterZEUS Calorimeter
• Alternating layers of depleted uranium and scintillator• Energy resolutions in test beam
• Electromagnetic: 18% / √E• Hadronic: 35% / √E
• 99.7% solid angle coverage (-3.5 < < 4.0)
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 19
Central Tracking Detector (CTD)Central Tracking Detector (CTD)Central Tracking Detector (CTD)Central Tracking Detector (CTD)
Drift chamber inside 1.43 T solenoid
Measures event vertex
Vertex resolution• longitudinal (z): 4mm
• transverse (x-y): 1mm
e p
Side ViewView Along Beam Pipe
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 20
ZEUS TriggerZEUS TriggerZEUS TriggerZEUS Trigger10 MHz crossing rate, 100 kHz Background rate, 10Hz
physics rateFirst level: Use data subset: 10 MHz → 500 Hz
• Dedicated custom hardware• Pipelined without deadtime• Global and regional energy sums• Isolated and e+ recognition• Track and vertex information
Second level: Use all data: 500 Hz → 100 Hz• Calorimeter timing cuts• E – pz < 55 GeV
• Energy, momentum conservation• Vertex information• Simple physics filters• Commodity transputers
Third level: Use full reconstruction information: 100 Hz → < 10 Hz
• Processor farm• Full event information• Refined jet and electron finding• Complete tracking algorithms• Advanced physics filters
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 21
ZEUS DIS EventZEUS DIS EventZEUS DIS EventZEUS DIS Event
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 22
Kinematic ReconstructionKinematic ReconstructionKinematic ReconstructionKinematic Reconstruction
Four measured quantities: EH, , E‘e, e
Three reconstruction methods used: Double angle, Electron method, Jaquet-Blondel
Variable Double angle method (H,e)
Electron method (E’
e,e)Jaquet-Blondel
(EH,H)
Q2
x
y
H e
sxyQ 2
JB
Ht
y
p
1
2,
e
H HzH
E
pE
2
)( , JB
JB
sy
Q2
)cos1(2 'eeeEE
)cos1(2
1'
ee
e
E
E
pel
ee Ey
E2
cos1' )sin(sinsin
)cos1(sin4 2
eHeH
eHeE
)sin(sinsin
sin)cos1(4 2
eHeH
HeeE
DA
DA
sy
Q2
Methods have different resolutions over different kinematic regions
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 23
ZEUS Data ReconstructionZEUS Data ReconstructionZEUS Data ReconstructionZEUS Data Reconstruction
• Use reconstruction methods that minimize resolution and systematic errors in different kinematic regions
• Double Angle (DA) method
• Resolution worse than electron method at low xBj, Q2
• Resolution comparable to electron method at higher xBj, Q2
• Electron (EL) method
• Good resolution in general
• Underestimates slightly at higher xBj, Q2
DA DA
EL EL
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 24
Boson-Gluon Fusion (BGF) QCD Compton
Leading order: one hard scattered parton
• Single jet event
• Leading order diagrams O(0
s)
Dijets• Leading-Order
diagrams O(1s)
• Direct coupling to gluon
Single Jets and DijetsSingle Jets and DijetsSingle Jets and DijetsSingle Jets and Dijets
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 25
Multiple JetsMultiple JetsMultiple JetsMultiple Jets
Trijet:• Radiated gluons from dijets
• Correction to leading-order dijet• Leading Order: O(2
s)
• Advantages of using multiple jets• Account for corrections beyond leading order dijet
• Further in pQCD perturbation series
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 26
Jet Finding: Cone AlgorithmJet Finding: Cone AlgorithmJet Finding: Cone AlgorithmJet Finding: Cone Algorithm
Maximize ET of hadrons in cone of fixed size• Construct seeds from energy deposits in cells
• Move cone until stable position found
• Decide whether to merge overlapping cones
• Issues• Overlapping
• Seed – Energy threshold
• Infrared unsafe – → ∞ as seed threshold → 0
For the jet: R
22 )()( R
j jTT EE ,
j jjT
T
EE
,
1 j jjT
T
EE
,
1
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 27
Jet Finding – Jet Finding – kktt Algorithm AlgorithmJet Finding – Jet Finding – kktt Algorithm Algorithm
kt: In ep transverse momentum with respect to beam lineFor every object i and every pair of objects i, j calculate
• di = (ET,i)2 → Distance to beam line in momentum space• dij = min{E2
T,i,E2T,j}[()2 + ()2] → Distance between objects
• Combine all di, dij into set
Calculate min{di,dij} for each object and pair of objects• If minimum of set corresponds to di → Object for di taken as jet• If minimum of set corresponds to dij → Combine objects i and j
Advantages• No seed required and no overlapping jets• Suitable for beyond-NLO pQCD calculations
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 28
Dijet Event at ZEUSDijet Event at ZEUSDijet Event at ZEUSDijet Event at ZEUS
jet
jet
e
jet
jet
remnant
Two “back to back” jets
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 29
Breit FrameBreit FrameBreit FrameBreit Frame
Select a frame to optimize jet finding
Single jet event • Struck quark rebounds with
equal and opposite momentum
• Zero transverse energy (ET)
Dijet event• Jets balanced in ET
Requiring minimum jet ET, Breit selects multijet events
02 pq x
“Brick wall” framesimilar to ee→qq
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 30
Leading Order Monte CarloLeading Order Monte CarloLeading Order Monte CarloLeading Order Monte Carlo
• Leading Order Matrix elements• Parton showering• Hadronization
ARIADNE v4.08• Color Dipole Model (CDM)
• Gluons emitted from color field between quark-antiquark pairs
• Gluons not necessarily kt ordered (BFKL-like)
• Supplemented with boson-gluon fusion processes
LEPTO v6.5.1• Matrix Element + Parton Shower (MEPS)
• Parton cascade: approximate higher orders in LO calc
• Decreasing virtuality (q2) as cascade progresses
• Radiated gluons kt-ordered (DGLAP-based)
Both use Lund String Model to simulate hadronization
CDM
MEPS
Simulate events to leading order (O(s) for dijets)
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 31
Next-to-Leading-Order (NLO) Next-to-Leading-Order (NLO) CalculationsCalculations
Next-to-Leading-Order (NLO) Next-to-Leading-Order (NLO) CalculationsCalculations
Inclusion of single gluon emission in dijet final state• Only terms of up to O(2
s) included for dijet calculations• Exact calculation: does not include approx. for higher orders
NLO calculations include• One-loop corrections for virtual particles• Correction for 3rd parton in final state (soft/collinear gluon emissions)
Corrections do not include• Parton showering• Hadronization• Corrections taken from Leading Order MC
Uncertainties• Renormalization scale: scale for evaluating s
• Indicates size of contributions from higher order diagrams.• Factorization scale: scale at which parton densities are evaluated
Programs for DIS DISENT MEPJET DISASTER++ NLOJET
Soft gluonemission
One loopcorrection
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 32
Present ZEUS Multijet ResultsPresent ZEUS Multijet ResultsPresent ZEUS Multijet ResultsPresent ZEUS Multijet Results
ZEUS inclusive dijet and trijet measurements well understood and modeled
• Multijet cross sections vs. NLO calculations
• Dijet: UW PhD student D. Chapin (2001)
• Trijet: UW PhD student L. Li, defends Jan 12, 2005
• DGLAP NLO dijet and trijet calculations describe data well in general
• Examine if agreement extends to “BFKL” kinematic regions
DijetTrijet
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 33
ZEUS Inclusive JetsZEUS Inclusive JetsZEUS Inclusive JetsZEUS Inclusive Jets
• Start with event cross section where at least one jet required
• Former UW PhD student S. Lammers, graduated 2004
• Low xBj disagreement between data and DISENT
• Examine low xBj contribution from multijet events
Hadronization correction factor taken from Ariadne
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 34
BFKL/DGLAP vs. Jet AnglesBFKL/DGLAP vs. Jet AnglesBFKL/DGLAP vs. Jet AnglesBFKL/DGLAP vs. Jet Angles
• Examine jet and ET at low xBj and low Q2
• xBj < 10-2
• Q2 < 150 GeV2
• DGLAP: Jet ET and angles strongly correlated
• “Back to back” in • kt ordering of scattered partons: jets with highest ET
should have similar • BFKL: Jet ET and angles not strongly correlated
• More jets with high ET expected in forward region than with DGLAP
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 35
H1 Inclusive Dijet EventsH1 Inclusive Dijet EventsH1 Inclusive Dijet EventsH1 Inclusive Dijet Events
correlation of two most energetic jets in multijet events
• 1996-1997 H1 data: Jet ET > 7 GeV
• Compare to DGLAP for NLO O(s2)
and NLO O(s3)
• O(s2): Data not described
• O(s3): Agreement at high xBj Still
excess at low Q2 and xBj
• Excess events with small separation of highest ET jets
Dijet
Dijet
N
NS
)120(
NLO: O(s2)
NLO: O(s3)DESY–03–160
October 2003
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 36
ZEUS DIS Data SampleZEUS DIS Data SampleZEUS DIS Data SampleZEUS DIS Data Sample
Data: 1998-2000 electron and positron: 82.2 pb-1
Remove background|z vertex| < 50 cm Eliminate beam gas events
40 < E – pz < 60 GeV Eliminate cosmic, beam gas events
Select DIS10 < Q2
DA < 5000 GeV2
Improve precisionyjb > 0.04 Requires minimum hadron energy
yel < 0.6 Electron energy > 10 GeV
cos(h) < 0.7 Breit Frame jet finding
(E – pz)e < 54 GeV Electron E, p conservation
max > 2.5 Eliminate diffractive events
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 37
Dijet and BFKL Analysis SampleDijet and BFKL Analysis SampleDijet and BFKL Analysis SampleDijet and BFKL Analysis Sample
Inclusive dijetsE1,2
T,Breit > 5 GeV Well-resolved jets
-1 < Lab < 2.5 Jet in well-understood region
Mass dijet system > 25 GeV NLO calculations
Above plus BFKL Dijets: Low x, Q2
Q2DA < 150 GeV2
10-4 < xDA < 10-2
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 38
Dijet Data vs. LEPTO MCDijet Data vs. LEPTO MCDijet Data vs. LEPTO MCDijet Data vs. LEPTO MC
First look: Inclusive dijets
ET in Breit Frame of 2 highest ET jets
• Ordered in ET
• Area normalized
in lab frame of 2 highest ET jets
• Ordered in
Reasonable agreement overall
ET1
BreET
2Bre
1Lab
2Lab
Eve
nts
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 39
Dijet Data vs. ARIADNE MCDijet Data vs. ARIADNE MCDijet Data vs. ARIADNE MCDijet Data vs. ARIADNE MC
ET1
BreET
2Bre
1Lab
2Lab
First look: inclusive dijets
ET in Breit Frame of 2 highest ET jets
• Ordered in ET
• Area normalized
in lab frame of 2 highest ET jets
• Ordered in
Need to investigate discrepancies with ARIADNE
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 40
SummarySummarySummarySummary
QCD evolution studies with ZEUS at HERA• Good understanding of inclusive multijet events at
ZEUS
• DGLAP NLO discrepancy with event cross sections with at least one jet, jet azimuthal separation at low xBj, Q2
• Reasonable agreement between ZEUS 98-00 inclusive dijet sample and LEPTO
• Disagreement between ZEUS 98-00 inclusive dijet sample and ARIADNE needs investigation
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Multijets in DIS study, Tom Danielson, U. Wisconsin Preliminary Examination, 13 December 2004 - 41
PlansPlansPlansPlans
• Examine separation of two most energetic jets in multijet events, compare to DGLAP NLO, other calculations
• See if H1 result consistent with higher statistics and other models
• H1 luminosity 21 pb-1 from 96/97
• ZEUS 98-00: 82.2 pb-1
• Examine kinematics and variables that enhance differences between BFKL and DGLAP.
• Focus on jet pseudorapidities