1. Investigation of QCD Evolution through Jets with the ZEUS Detector at HERA
Preliminary Examination
Tom Danielson
University of Wisconsin
13 December 2004
Main point: Title page

2. Outline Framework for QCD Methods for investigation Present Status
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
Main point: Structure for talk to follow

3. Classification 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
Notes: Hadrons are particles that undergo strong interaction. Quarks come from SU(3) classification of particles. According to QPM, hadrons are composed only of quark bound states.
Important to mention: Missing from quark properties is “color,” which we get to later on. Important to say something like, “Initially, the important quark properties were thought to be…”

4. Size of proton ~ 1 fm HERA can probe to ~ 0.001 fm
Parton 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 probe
Q: related to momentum of probe
Main point: Study aims to improve on parton studies
Notes: Higher Q translates to shorter wavelength, allows probing to smaller distances (leading in to DIS)
probe
lepton
Size of proton ~ 1 fm HERA can probe to ~ fm

5. DIS Kinematics
Main point: these are the Lorentz invariant variables most important to DIS studies

6. DIS 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
Main point: DIS cross section depends both on proton structure and kinematic variables

7. Quark-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
Main point: with only valence quarks, proton structure should not depend on Q-squared
Note: PDF’s extracted using full QCD fits and evolution, not just part of the parton model.

8. QCD and Colored Gluons Problems with Quark-Parton Model
Statistics for Fermion D++
D++ 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
D++ quark composition: uRuBuG
Mediator of strong force → gluon
Gluons carry roughly half proton momentum
Observed particles “colorless” → color conservation
Isolated quarks not observed → Confinement
Main point: Experimental observation of 2+ charged particle just one example of why QPM thought to be naïve.
Notes: Be sure to mention why this particle is seen as a violation.

9. QCD 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
Main point: Evidence for QCD is seen in scaling violation at HERA
Notes: it’s important to know why this inflection point is crucial for QCD

10. 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 as
Methods of summation: next slide
Main point: with inclusion of gluons, structure functions gain Q-squared dependence S 
photon
quark
lepton
gluon

11. BFKL 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
Splitting Functions
Main Point: DGLAP gives prediction of PDF’s, but makes approximations that might be invalid for certain kinematic regions
Notes:
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi = DGLAP
Balidsky-Fadin-Kuraev-Lipatov = BFKL
Evolution with this approximation valid only where diagrams not summed over provide negligible contributions.
g and q are the PDF’s f_i previously mentioned.

12. BFKL-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
Main point: Approximations made by the two different evolutions limit their range of applicability to certain kinematic regions
Non-perturbative region

13. Parton Energy and kT 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
Main point: A convenient way to test the applicability of these two evolutions is to make use of the fact that they make different predictions of the energy and kt ordering of the jets.
Important point to express: k_t = transverse momentum w.r.t. the proton trajectory

14. Jets 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
Main point: Hard scattered partons for jets that deposit particle showers in detector

15. HERA Collider at DESY 920 GeV protons 27.5 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 H1
ZEUS
Main Point: HERA sufficient for study
Synchrotron radiation is lin. pol. in plane of acceleration.
Fixed target: ECM=S=2E1m2
Colliding Beam: ECM = S=4E1E2
Sigma_BH = Bethe-Heitler cross section (cross section for ep->ep gamma)
DESY
Hamburg, Germany

16. HERA Luminosity 1992 – 2000 total integrated luminosity: 193 pb-1
Main point: Luminosity achieved at HERA gives good statistics for study
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

17. ZEUS Detector
Main point: This is the detector

18. ZEUS Calorimeter
Main point: The calorimeter gives good angular coverage. Energy resolutions affect uncertainties.
How it works: Particles interact with DU, resulting particles picked up by scintillator, light from scintillator goes through WLS’s and light guides to PMT’s
Pseudorapidity rocks because changes in eta are invariant under Lorentz boosts along the beam direction.
Pseudorapidity  Rapidity if we can neglect the mass
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 < h< 4.0)

19. Central Tracking Detector (CTD)p
View Along Beam Pipe
Side View
Drift chamber inside 1.43 T solenoid
Measures event vertex
Vertex resolution
longitudinal (z): 4mm
transverse (x-y): 1mm
Main point: CTD gives good vertex finding resolution

20. 10 MHz crossing rate, 100 kHz Background rate, 10Hz physics rate
ZEUS Trigger
10 MHz crossing rate, 100 kHz Background rate, 10Hz physics rate
First level: Use data subset: 10 MHz → 500 Hz
Dedicated custom hardware
Pipelined without deadtime
Global and regional energy sums
Isolated m 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
Main point: ZEUS trigger essential for eliminating background events
Important feature: all events in the detector are passed in to the FLT, so there’s in principle no event that doesn’t go through the triggers.

21. ZEUS DIS Event
Main point: features of DIS observable in detectors. Jets show up as a spray of particles

22. Kinematic Reconstruction
Four measured quantities: EH, gH, E‘e, qe
Three reconstruction methods used: Double angle, Electron method, Jaquet-Blondel
Methods have different resolutions over different kinematic regions gH qe
Variable
Double angle method (gH,qe)
Electron method (E’e,qe)
Jaquet-Blondel (EH,gH) Q2 x y
Main point: Many different ways to reconstruct the important variables
Note: although I use all three, I don’t necessarily use all three for each variable, but overall, I use them all.

23. ZEUS 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
Main point: different methods for reconstructing kinematic variables are appropriate for different phase space regions.
Notes: The plots here are reconstructed data vs. the hadron “true” values of MC

24. Single Jets and Dijets Leading order: one hard scattered parton Dijets
Single jet event
Leading order diagrams O(a0s)
Dijets
Leading-Order diagrams O(a1s)
Direct coupling to gluon
Boson-Gluon Fusion (BGF)
QCD Compton
Main point: Dijets provide direct examination of QCD effects.
Notes: The primary advantage of using events with at least two jets is that quark-gluon coupling carries a factor of alpha_s. Multijets then allow for examination at higher orders of alpha_s, which is crucial for this study, as both BFKL and DGLAP are perturbative expansions in alpha_s.

25. Multiple Jets Trijet: Advantages of using multiple jets
Radiated gluons from dijets
Correction to leading-order dijet
Leading Order: O(a2s)
Advantages of using multiple jets
Account for corrections beyond leading order dijet
Further in pQCD perturbation series

26. Jet 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 – s → ∞ as seed threshold → 0
For the jet:
Notes: Important to say for IR unsafe: sigma = Cross section calculated at NNLO (but since NLO not introduced, just say “at higher orders in pQCD”) R

27. Jet Finding – kt Algorithm
kt: In ep transverse momentum with respect to beam line
For every object i and every pair of objects i, j calculate
di = (ET,i)2 → Distance to beam line in momentum space
dij = min{E2T,i,E2T,j}[(Dh)2 + (Df)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
Main point: the kt algorithm provides the best method for finding jets because there are no issues with seeds or overlapping jets, and it’s IR safe

28. Dijet Event at ZEUS jet jet remnant e jet jet Two “back to back” jets
Main point: Visual aid for seeing dijet in detector
jet
jet
Two “back to back” jets

29. Breit 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
“Brick wall” frame
similar to ee→qq
Main point: Breit frame is the best frame for finding jets in a multijet study
Commonly referred to as the “Brick wall” frame

30. Leading Order Monte Carlo
Simulate events to leading order (O(as) for dijets)
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
Main point: LO MC’s exhibiting both BFKL and DGLAP-like behavior are available
MEPS

31. Next-to-Leading-Order (NLO) Calculations
Programs for DIS
DISENT
MEPJET
DISASTER++
NLOJET
Soft gluon
emission
One loop
correction
Inclusion of single gluon emission in dijet final state
Only terms of up to O(a2s) 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 as
Indicates size of contributions from higher order diagrams.
Factorization scale: scale at which parton densities are evaluated
Main point: Calculations available for higher orders in alpha-s
Notes: In order for this to be complete, I need to be ready to explain two things:
1. How we compare to data, given that corrections do not include parton showering or hadronization
2. How the programs for DIS differ from each other

32. Present 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
Trijet
Dijet
Main point: In general, DGLAP-based NLO jet cross-section predictions describe the data well.
Notes: Differential cross sections plotted as function of Q^2

33. ZEUS 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
Main point: Disagreement between data and NLO cross sections evident at low Bjorken-x
Notes:
Differential cross section plotted as a function of x for inclusive sample (i.e. selection QPM suppression and multijets not applied).
One thing that might be asked: if we do see a departure from DGLAP, does that mean the issue is settled? The answer is no, for a few reasons. First, when selection for QPM suppression and multijets was applied, the agreement between data and DISENT actually improved, when it was expected to worsen. Second, the uncertainty scale of the DISENT calculation became larger with higher eta and lower x, thus obscuring any results.
Hadronization correction factor taken from Ariadne

34. BFKL/DGLAP vs. Jet Angles
Examine jet f 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 f
kt ordering of scattered partons: jets with highest ET should have similar h
BFKL: Jet ET and angles not strongly correlated
More jets with high ET expected in forward region than with DGLAP
Main point: Well-defined strategy for studying BFKL begins with revisit of H1 measurement, but also includes jet pseudorapidity studies.

35. H1 Inclusive Dijet Events
f correlation of two most energetic jets in multijet events
H1 data: Jet ET > 7 GeV
Compare to DGLAP for NLO O(as2) and NLO O(as3)
O(as2): Data not described
O(as3): Agreement at high xBj Still excess at low Q2 and xBj
Excess events with small f separation of highest ET jets
Main Point: Studies examining the phi correlation of the two highest energetic jets in a multijet event show kinematic range where DGLAP might not be applicable.
Notes: S is the ratio of events where the phi separation of the two most energetic jets is less than 120 degrees to the total number of events
NLO: O(as3)
DESY–03–160 October 2003
NLO: O(as2)

36. Data: 1998-2000 electron and positron: 82.2 pb-1
ZEUS DIS Data Sample
Data: 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 DIS
10 < Q2DA < 5000 GeV2
Improve precision
yjb > 0.04
Requires minimum hadron energy
yel < 0.6
Electron energy > 10 GeV
cos(gh) < 0.7
Breit Frame jet finding
(E – pz)e < 54 GeV
Electron E, p conservation
hmax > 2.5
Eliminate diffractive events
Notes: 82.2 is non-prescaled luminosity. For prescale, it’s about inverse picobarns
Gamma_h cut due to low number of forward cells in Breit frame

37. Dijet and BFKL Analysis Sample
Inclusive dijets
E1,2T,Breit > 5 GeV
Well-resolved jets
-1 < hLab < 2.5
Jet h 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
Notes: Invariant mass of dijet system implemented as an attempt to reproduce Liang, Nils’ control plots. Probably not going to be used in the final analysis.

38. Dijet Data vs. LEPTO MC First look: Inclusive dijets
ET in Breit Frame of 2 highest ET jets
Ordered in ET
Area normalized
h in lab frame of 2 highest ET jets
Ordered in h
Reasonable agreement overall
Events
Events
ET2Bre
ET1Bre
Main point: For non-BFKL kinematic range, LEPTO describes the data well
Events
Events
h2Lab
h1Lab

39. Dijet Data vs. ARIADNE MC
First look: inclusive dijets
ET in Breit Frame of 2 highest ET jets
Ordered in ET
Area normalized
h in lab frame of 2 highest ET jets
Ordered in h
Need to investigate discrepancies with ARIADNE
Events
Events
ET2Bre
ET1Bre
Main point: Although previously observed, the disagreement between ARIADNE and data needs investigation. (Private note: removing the requirement for the invariant mass of the dijet system removes this discrepancy)
Events
Events
h2Lab
h1Lab

40. Summary 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 inclusive dijet sample and LEPTO
Disagreement between ZEUS inclusive dijet sample and ARIADNE needs investigation
Main point: I’ve got the lumi, the data well in hand, new angles of attack, and some initial data-MC comparisons.

41. Plans
Examine f 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
Main point:
We can improve on the H1 measurement from a luminosity standpoint, but more importantly, we can add a new angle by examining jet pseudorapidities