1. Three-jet Production in Neutral Current Deep Inelastic Scattering with ZEUS Detector at HERA
Preliminary Examination
HERA, ZEUS data(intended 96-00, current 96-97)
100GeV<Q2<10000GeV
e+ energy 27.5GeV
p energy 920Gev
Introduction:
SM QCD Various Methods to Determine αs
DIS Structure Function PDF
Feynman Diagrams (1,2,3 jets)
The ratio of the three-jet to the dijet cross section R3/2 and αs
Jet Algorithms Breit Frame Lab Frame
MC Models NLO
Experimental Context
Liang Li
University of Wisconsin
Nov 27,2001

2. HERA • 820/920 GeV proton • 27.5 GeV electrons or positrons
• 300/318 GeV center of mass energy
• bunches 96 ns crossing time
• Instantaneous luminosity 1.8 x 1031 cm-2s-1
• Currents:
~90mA protons
~40mA positrons

3. HERA Luminosity . 820 GeV protons through 1997 920 GeV since 1998
. ZEUS integrated luminosity since 1992: ~185 pb-1
. Expect 1fb-1 by end of 2005
The Standard Model (SM) of particle physics describes the subnuclear world in the framework of renormalizable quantum field theories with a certain group structure re the nature of the forces that are governing this regime. The SM interprets interactions between pointlike fundamental particles, the quarks and leptons, as mediated by the exchange of virtual gauge bosons, the photon (electromagnetic interaction), the Z and W±(weak interaction), and the gluons g (strong interaction). These particles are listed in Table

4. HERA Kinematic Range Extended kinematic region
not accessible by fixed target experiments, with some overlap.
H1 and ZEUS: DESY e-p
HERMES: DESY e-A
E665: Fermilab -A
BCDMS: CERN -A
CCFR: Fermilab -A
SLAC: many experiments e-A
NMC: CERN -A
•BPC and BPT
–electron detectors near the rear beam pipe to accept very low Q 2

5. Deep Inelastic Scattering
=pq/M virtual photon energy in the lab
Q2=2M=2pq (x= Q2/2M=1 ) for elastic scattering, the nucleus recoils as a whole( coherent scattering) (b.c. W2=(p+q)2=p2 in this case)
1-y=p•k’/p•k~(1+cos)/2,  is the scattering angle in the positron-quark center of mass frame (angular dependence)
1-y=fraction of positron energy remained
s=318 GeV
• Deep Inelastic Scattering is the scattering of a
lepton from constituents of nucleons at high
momentum transfer
• The electron-proton interaction is mediated by the exchange
of a single vector boson (a photon, W ± or Z o force carrier)
• W ± and Z collisions are rare at ZEUS energies
• The photon is virtual - it can be polarized transversely or
longitudinally.
• Jets - clusters of hadrons formed by scattered quarks and
radiated gluons
The initial state positron with four-momentum k and initial state proton with
four-momentum P exchange a virtual photon with four-momentum q. The
final state positron has four-momentum k’. The proton breaks up into a system
of particles with large invariant mass.
s is the square of the ep center-of-mass energy.
Q2 is the negative square of the four-momentum, q, exchanged between the
positron and proton.
W=invariant mass of the
final hadronic system
W2 = (p+q)2

6. e+p DIS Event at HERA
The principal advantage of determining αs from R in e+e– annihilation is that there is no dependence on fragmentation models, jet algorithms, etc.
While this method has small theoretical uncertainties from QCD itself, it relies
sensitively on the electroweak couplings of the Z to quarks. However, this method gives the excellent agreement of many measurements at Z and very good precision for αs .
High-energy hadron collisons
Higher-order QCD calculations of the jet rates and shapes are in impressive agreement with data . This agreement has led to the proposal that these data could be used to provide a determination of αs. However, this method uses an indirect way and the precision of this method is not very good.

7. DIS Cross Section
F2 (x,Q2): Interaction between transversely polarized photons & spin 1/2 partons ; Charge weighted sum of the quark distributions
FL (x,Q2): Interaction between longitudinally polarized photons & the partons with transverse momentum.
F3 (x,Q2): Parity-violating structure function from Z 0 exchange.
e+p cross section can be written in terms of dimension-less structure functions
(matrix element)
* is longitudinally or transversely polarized
FL:
(Important at high y).
F3:
(Contribution small for Q2 << MZ2 = 8100 GeV2).
F2,FL,xF3…
FL is 0 in leading order QCD, and F2=2xF1

8. Naïve Quark Parton Model
· Partons are point-like objects
· No interaction between the partons
· Structure function independent of Q2
Bjorken Scaling (x) dependence:
Photon-proton interaction can be expressed as sum of incoherent scattering from
Point-like quark(parton) 
F2(x,Q2) = eq2(Q2) ·(xq(x,Q2) +xq(x,Q2))
quarks
F2(x,Q2)  F2(x), FL= 0

9. QCD Parton Parton interactions, mediated by gluons
Physics picture: presence of gluons
Parton Parton interactions,
mediated by gluons
Generate parton transverse momentum
Non zero FL
The structure functions gain
a Q2 dependence
Scaling Violation
Transverse momentum -> FL not equal 0
Parton distribution functions q(x,Q2) , q(x,Q2) are the average numbers of partons with momentum fraction between x and x+dx inside the proton.
Quantum Chromodynamics(QCD), the gauge field theory which describes the strong interactions of colored quarks and gluons, emerged as the result of many theoretical ideas and experimental results in 1970s. It is nowadays regarded as one of the cornerstones of the Standard Model of elementary particles and their interactions.
In QCD, hadrons are color-singlet bound states of quarks, anti-quarks and gluons. A quark of specific flavor comes in three colors; gluons, the gauge bosons carriers of the color interaction, come in eight colors.
The Lagrangian describing the interactions of quarks and gluons is given above(up to gauge-fixing terms).F is the gluon field strength tensor, T are the SU(3) representation matrices and the f abc are the structure constants of SU(3). The
ψiq (x) are the 4-component dirac spinors associated with each quark field of color
i and q, and the Aaμ are the Yang-Mills (gluon) fields. The sum on q is over the six
different quarks.
At the classical level, and in the limit in which quark-mass effects can be negleted, the QCD Lagrangian depends on a single dimensionless parameter: this is the gauge coupling constant gs, which determines the strength of the interaction between colored quanta. The strong coupling constant is defined, in analogy with the fine structure constant of QED, as αs= gs2/4π

10. Scaling Violation .High x, F2 falls with Q2
--valance quarks contribution falls
--gluon small at high x
.Low x, F2 rises strongly with Q2
--Strong gluon ­> sea quark contribution

11. Parton Distribution Functions
PDFs are not calculable, must be derived from the experiment
Derived from the experiment

12. DGLAP Evolution
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations describe
evolution of parton densities to higher Q2 — QCD prediction
Listed only leading order splitting functions
The relevant strong interactions are given by splitting functions,
which are related to the probabilities that
(a) a gluon splits into a quark-antiquark pair
(b) a quark radiates a gluon
(c) a gluon splits into a pair of gluons
s is the strong coupling constant.

13. Single Jet Dijet Trijet
b) Boson-Gluon Fusion
a) QCD Compton
Dijet
Single Jet
Trijet
What about alternative splitting ways? see “splitting functions”
Single Jet is Leading Order DIS
O()
Dijet
O( s)
Trijet
O( ss)

14. Why Trijet? Adding a gluon radiation to dijet  A direct test of QCD.
Recent important advance in understanding QCD
in dijets makes it an ideal laboratory for studying
added gluon radiation.
Measure s at a wide range of Q2
In the the ratio of R3/2 = trijet/dijet = O(s),
there is a cancellation of some experimental and
theoretical uncertainties
=xbj(1+Mjjj2/Q2)
Mjjj2 is the invariant mass squared of the trijet system
The trijet cross section in DIS is already proportional to O(αs2) in leading order in pQCD.
Unlike e+e– Annihilation measurements, the ones in ep scattering are not at a fixed value of Q2.
Take the ratio of R3/2 = trijet/dijet = O(s), reduce uncertainty
fq(x,2 ) and g(x, 2 ) are the densities of the quarks and gluons respectively. fq(x,2) comes from other experiments
trijet is the inclusive trijet cross section. q and g are the partonic cross sections for processes initiated by the quarks and gluons respectively (calculated by theory).
 Is the momentum fraction of the struck parton
NLO
(x)->(x,2) NLO calculations reduce dependency on the factorization scale.
The principle of “asymptotic freedom” determines that the renormalized QCD coupling is small only at high energies, and it is only in the domain that high-precision tests can be performed using perturbation theory(pQCD). The strong coupling constant is the only parameter relevant to the high-energy regime of QCD that needs to be determined, as, in principle, everything else can be calculated
from first principles. The strong coupling is one of the fundamental `constants' of nature, and, as such, there is no limit to the accuracy with which we would like to know its value. Beside setting the overall precision of any fixed-order perturbative QCD (pQCD) calculation, an accurate knowledge of αs is, for example, necessary to extract electroweak parameters from precise e+e– data, as well as to see all forces of nature are unified at some large energy scale.
Because the measurement of αs is so important, people would like to use as many ways to measure it as possible. The most frequently used ones are: e+e– Annihilation, High-energy hadron collisons and ep collisions.

15. Jet Algorithms
Jets defined by inclusive–kT–Algorithm in Breit Frame

16. Breit Frame
Single jet event in Breit Frame
q + 2xp=0
In single jet events, struck quark rebounds with equal and opposite
momentum, the resulting jet has zero ET (transverse energy)
similar to e+e-
In multi-jet events, the outgoing jets
are balanced in ET
  4-momentum only has a z component
 -proton axis is the common axis
The proton and exchanged photon collide on a common axis,
with the z-direction chosen to be the proton direction.

17. Leading Order MC Choose Factorization scale: hadronization begins!
LO matrix element
ARIADNE, LEPTO and HERWIG use the Feynman
inspired calculation of the matrix element
Parton Showers
LEPTO, HERWIG use parton showers that evolve
according to the DGLAP Equation
ARIADNE uses the color dipole model, in which each
pair of partons is treated as an independent radiating dipole.
Hadronization
LEPTO, ARIADNE use the Lund String Model
HERWIG uses Cluster Fragmentation
Choose

18. Next Leading Order MC
Use LO MC models to estimate non-perturbative hadronization effects
Apply corrections from LO MC model esitmates to NLO calculations
NLO calculations do not include hadronization models

19. MC Scales Factorization scale
fq(x,2f), scale f at which the parton densities are
evaluated and where the hadronization begins
Renormalization scale
s(2r), scale r at which the constant s is evaluated
NLO reduces renormalization scale dependence
with respect to LO MC
Renormalization scale uncertainty is the largest
contribution to NLO theoretical uncertainty

20. ZEUS Detector Luminosity Monitor
Background Rejection (Veto Wall, C5, SRTD)

21. Central Tracking Detector
Tracking info can be used to check Cal energies

22. ZEUS Uranium Calorimeter
• The ZEUS calorimeter is made of alternating
layers of scintillator and depleted uranium
• Uranium is dense - Calorimeter is compact
• Layers are designed so the Calorimeter has a linear
response to hadrons and electrons to ±3%
• Calorimeter has energy resolution of 35%/.E ±1% for
hadrons and 17%/.E ±1% for electrons
• ZEUS Calorimeter covers 99.7% of the solid angle
• Angular resolution of 10 mrad
• Timing resolution is 1 ns << 96 ns crossing time
US groups, including Wisconsin are responsible for barrel calorimeter

23. ZEUS Trigger Wisconsin group is responsible for Level 1CAL trigger
• Pipeline all events
• Discard background events
• Select DIS and photoproduction events
• Loose cuts at FLT are tightened at SLT and TLT
• The Calorimeter First Level Trigger(CFLT) has
the primary responsibility for getting the First
Level Trigger below 500Hz.
The Calorimeter First Level Trigger calculates regional and
global total energy, Etot , and the missing transverse energy
ETmiss from Ex and Ey .
Wisconsin group
is responsible for
Level 1CAL trigger

24. Background Rejection: Timing
• Backgrounds at ZEUS are
beam-gas interactions (100 kHz),
cosmic rays (1 kHz) and electronic
noise (> 0.1 kHz).
Energy deposit in RCAL mimics electron
FCAL deposit mimics current jet

25. Background Rejection: E-Pz

26. Event Reconstruction  Track finding and the event vertex
 Require good track.
 Use good track to find event vertex
 Electron finding
 Find electrons by looking for isolated EM
energy deposits in Calorimeter cells.
 The ZEUS primary electron finder is > 95%
efficient for electron energy > 10 GeV.
Cell energies recalibration/correction.
If the energy in a Calorimeter cell is above a threshold and HAC/EMC < 0.25, an isolated electron trigger bit is set.
improvements can be made using additional components: Small Rear Tracking Detector and the RCAL Presampler
Isolated electron trigger allows us to set lower electron energy threshold.
The isolated electron trigger is essential for measuring structure functions
And the frame boosting.
Track Finding Vertex Reconstruction and Electron Finding
Hadronic Reconstruction
Kinematic Reconstruction Q2 X Y
Jet Quantities ET η θ
Offline Event Selection
MC Event Selection

27. Kinematic Reconstruction
Two Kinematic Variables: x Q2
Four Measured Quantities: Ee’ e Eh h
Electron Method
Use scattered electron energy, electron angle
Good resolution in x and Q2, best at low Q2
Sensitive to miscalibrations (energy scale uncertainties)
Double Angle Method
Use electron angle and hadronic jet angle
Depends only on ratios of energies
Better mean resolution in x and Q2
Weakly affected by miscalibrations
Q2 = 2EE´(1+cosqe)
Gives an accurate determination of y for small values of y.
In this Analysis, yJB is used exclusively to measure y.
Jacquet-Blondel Method
Use hadronic energy and hadronic jet angle
Gives an accurate determination of y for small values of y

28. Data Offline Cuts
• Detector Acceptance and Efficiency yJB > positron found with E > 10 GeV vertex cut: -50cm < z < 50cm positron position cut: |X| > 14 cm or |Y| > 14 cm
• Signal Selection
38 GeV < E-Pz < 65 GeV A well found track with p > 5 GeV & DCA < 15 cm yEL < 0.95
• Physics and Kinematic Requirement GeV2 < Q2 < GeV Three jets found using KTCLUS algorithm
|| < 2.0
ETLAB > 5 GeV
Give reasons here:
Asymmetric cut, MC calculation requirement
ET,1BRT > 8 GeV, ET,2BRT > 5 GeV , ET,3BRT > 5 GeV

29. First Comparison of Data and MC DIS Trijets at ZEUS
HERA running period
ZEUS data sample: integrated luminosity 38.4pb-1
510 DIS trijets passed offline cuts in a sample of
39576 DIS events
MC:
Use leading order MC program Ariadne
568 DIS trijets selected from MC
 No Adjustment, run with default ZEUS settings

30. DIS Trijets  A First Look
ReconstructedQ2, y, x by
Double Angle method
Use Ariadne
for all MC
OK agreement
between
data and MC

31. DIS Trijets  A First Look
Reconstructed
Q2, y, x by
Electron method
Better agreement
between
data and MC
Pick Electron
method
Control Plots
Possible Data Corrections and Systematic Uncertainty Estimate

32. DIS jet ET in the Lab Frame
ET Ordered:
First Jet
Second Jet
Third Jet
Reasonable
agreement

33. DIS jet ET in the Breit Frame
ET Ordered:
First Jet
Second Jet
Third Jet
Reasonable
agreement

34. DIS jet  in the Lab Frame
ET Ordered:
First Jet
Second Jet
Third Jet
Reasonable
agreement

35. DIS jet  in the Lab Frame
 Ordered:
First Jet
Second Jet
Third Jet
Reasonable
agreement

36. Conclusions and Expectations
First look at DIS Trijets at ZEUS, reasonable agreement
Ariadne used as it is, a good starting point
Need to calculate cross sections and compare in detail with other QCD calculations and different MC programs
Add new data (99-00) to have more statistics
Explore systematic uncertainties
Hadron and Parton Level Comparison?