Limits on anomalous WWγ and WWZ couplings from WW/WZâeνjj production

Abstract

Limits on anomalous WWγ and WWZ couplings are presented from a study of WW/WZâeνjj events produced in pp(bar sign) collisions at â(s)=1.8 TeV. Results from the analysis of data collected using the DOe detector during the 1993-1995 Tevatron collider run at Fermilab are combined with those of an earlier study from the 1992-1993 run. A fit to the transverse momentum spectrum of the W boson yields direct limits on anomalous WWγ and WWZ couplings. With the assumption that the WWγ and WWZ couplings are equal, we obtain -0.34

Full text

arXiv:hep-ex/9912033v2 7 Jun 2000
Limits on Anomalous W W γ and W W Z Couplings from
W W/W Z → eνjj Production
B. Abbott,
47
M. Abolins,
44
V. Abramov,
19
B.S. Acharya,
13
D.L. Adams,
54
M. Adams,
30
S. Ahn,
29
V. Akimov,
17
G.A. Alves,
2
N. Amos,
43
E.W. Anderson,
36
M.M. Baarmand,
49
V.V. Babintsev,
19
L. Babukhadia,
49
A. Baden,
40
B. Baldin,
29
S. Banerjee,
13
J. Bantly,
53
E. Barberis,
22
P. Baringer,
37
J.F. Bartlett,
29
U. Bassler,
9
A. Belyaev,
18
S.B. Beri,
11
G. Bernardi,
9
I. Bertram,
20
V.A. Bezzubov,
19
P.C. Bhat,
29
V. Bhatnagar,
11
M. Bhattacharjee,
49
G. Blazey,
31
S. Blessing,
27
A. Boehnlein,
29
N.I. Bojko,
19
F. Borcherding,
29
A. Brandt,
54
R. Breedon,
23
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3
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H. Evans,
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V.N. Evdokimov,
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T. Fahland,
25
S. Feher,
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21
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H.E. Fisk,
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31
K.C. Fra me,
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S. Fuess,
29
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A.N. Galyaev,
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V. Gavrilov,
17
R.J. Genik I I,
20
K. Genser,
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C.E. Gerber,
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48
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5
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J.L. Gonz´alez Sol´ıs,
15
H. Gordon,
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L.T. Goss,
55
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A. Goussiou,
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N. Graf,
50
P.D. Grannis,
49
D.R. Green,
29
J.A. Green,
36
H. Greenlee,
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S. Grinstein,
1
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29
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A. Gupta,
13
S.N. Gurzhiev,
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G. Gutierrez,
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N.J. Hadley,
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27
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27
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24
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26
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6
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A.S. Ito,
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K. Johns,
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M. Johnson,
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S.Y. Jun,
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D. Karmanov,
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D. Zieminska,
33
A. Zieminski,
33
V. Zutshi,
48
E.G. Zverev,
18
and A. Zylberstejn
10
(DØ Collaboration)
1
Universidad de Buenos Aires, Buenos Aires, Argentina
2
LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil
3
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
4
Institute of High Energy Physics, Beiji ng , People’s Republic of China
5
Universidad de los Andes, Bogot´a, Colombia
6
Universidad San Francisco de Quito, Quito, Ecuador
7
Institut des Sciences Nu cl´eaires, IN2P3-CNRS, U niversite de Grenoble 1, Grenoble, France
8
Centre de Physique des Particules de Marseille, IN2P3-CN RS, Marseille, France
9
LPNHE, Univ ersit´es Paris VI and VII, IN2P3-CNRS, Paris, France
10
DAPNIA/Service de Physique des Particules, CEA, Saclay, France
11
Panjab University, Chandigarh, India
12
Delhi University, Delhi, India
13
Tata Institute of Fundamental Research, Mumbai, India
14
Seoul National University, Seoul, Korea
15
CINVESTAV, Mexico City, Mexico
16
Institute of N uclear Physics, Krak´ow, Poland
17
Institute for Theoretical and Experimental Physics, Moscow, Russia
18
Moscow State University, M oscow, Russia
19
Institute for High Energy Physics, Protvino, Russia
20
Lancaster University, Lancaster, United Ki ng dom
2

21
University of Arizona, Tucson, Arizona 85721
22
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720
23
University of California, Davis, California 95616
24
California State University, Fresno, California 93740
25
University of California, Irvine, California 92697
26
University of California, Riverside, California 92521
27
Florida State University, Tallahassee, Florida 32306
28
University of Hawaii, Honolulu, Hawaii 96822
29
Fermi National Accelerator Laboratory, Batavia, Illinois 60510
30
University of Illinois at Chicago, Chicago, Illinois 60607
31
Northern Illinois University, DeKalb, Illinois 60115
32
Northwestern University, Evanston, Illinois 60208
33
Indiana University, Bloomington, Indiana 47405
34
University of Notre Dame, Notre Dame, Indiana 46556
35
Purdue University, West Lafayette, Indiana 47907
36
Iowa State University, Ames, Iowa 50011
37
University of Kansas, Lawrence, Kansas 66045
38
Kansas State University, Manhattan, Kansas 66506
39
Louisiana Tech University, Ruston, Louisiana 71272
40
University of Maryland, College Park, Maryland 20742
41
Boston University, Boston, Massachusetts 02215
42
Northeastern University, Boston, Massachusetts 02115
43
University of Michigan, Ann Arbor, Michigan 48109
44
Michigan State University, East Lansing, Michigan 48824
45
University of Nebraska, Lincoln, Nebraska 68588
46
Columbia University, New York, New York 10027
47
New York Unive rsity, New York, New York 10003
48
University of Rochester, Rochester, New York 14627
49
State University of New York, Stony Brook, New York 11794
50
Brookhaven National Laboratory, Upton, New York 11973
51
Langston University, Langston, Oklahoma 73050
52
University of Oklahoma, Norman, Oklahoma 73019
53
Brown University, Providence, Rhode Island 02912
54
University of Texas, Arlington, Texas 76019
55
Texas A&M University, College Station, Texas 77843
56
Rice University, Houston, Texas 77005
57
University of Washington, Seattle, Washington 98195
Abstract
Limits on anomalous W Wγ and W W Z couplings are presented from a study
of W W/W Z → eνjj events produced in p¯p collisions at
√
s = 1.8 TeV. Results
from the analysis of data collected using the DØ detector during the 1993–
3

1995 Tevatron collider run at Fermilab are combined with those of an earlier
study from the 1992–1993 run. A fit to the transverse momentum spectrum of
the W boson yields direct limits on anomalous W W γ and W W Z couplings.
With the assumption th at the W W γ and W W Z couplings are equal, we
obtain −0.34 < λ < 0.36 (with ∆κ = 0) and −0.43 < ∆κ < 0.59 (with λ = 0)
at the 95% confidence level for a f orm-factor scale Λ = 2.0 TeV.
Typeset using REVT
E
X
4

I. INTRODUCTIO N
The Tevatron p¯p collider at Fermilab offers one of the best opportunities to test trilinear
gauge boson couplings [1–3], which are a direct consequence of the non-Abelian SU(2 ) ×
U(1 ) gauge structure of the standard model ( SM). The trilinear gauge boson couplings can
be measured directly fro m g auge boson pair (diboson) production. Production of W W
and W Z pairs in p¯p collisions at
√
s = 1.8 TeV can proceed through s-channel boson
intermediaries, o r a t- or u-channel quark exchange processes as shown in Fig. 1. There are
important cancellations between the t- or u-diagrams, which involve o nly couplings of t he
bosons to fermions, and the s-channel diagrams which contain three-boson couplings. These
cancellations are essential for making calculations of SM diboson production unitary and
renormalizable. Since the fermionic couplings of the γ and W and Z bosons have been well
tested [4], we may regard diboson production as primarily a test of the three-boson vertex.
Production of W W pairs is sensitive to both W W γ and W W Z couplings; W Z production
is sensitive only to W W Z couplings.
FIG. 1. Feynman diagrams for W W and W Z production at leading order. a) and c): t- and
u-channel quark exchange d iagrams; b) and d): s-channel diagrams with three-boson couplings.
A generalized effective La grangian has been developed to describe the couplings of three
gauge bosons [5]. The Lo r entz-invariant effective Lagrangian for t he gauge boson self-
interactions contains fourteen dimensionless coupling parameters, λ
V
, κ
V
, g
V
1
,
˜
λ
V
, ˜κ
V
, g
V
4
,
and g
V
5
(V = Z or γ), seven for W W Z interactions and another seven for W W γ interac-
tions, and two overall couplings, g
W W γ
= −e and g
W W Z
= −e cot θ
W
, where e and θ
W
are
the positron char ge and the weak mixing angle. The couplings λ
V
and κ
V
conserve charge
C and parity P . The couplings g
V
4
are odd under CP and C, g
V
5
are odd under C and P ,
5

and ˜κ
V
and
˜
λ
V
are odd under CP and P . To first order in the SM (tree level), all of the
couplings vanish except g
V
1
and κ
V
(g
γ
1
= g
Z
1
= κ
γ
= κ
Z
= 1). For real photons, gauge
invariance in electromagnetic interactions does not allow deviations o f g
γ
1
, g
γ
4
, and g
γ
5
from
their SM values of 1, 0, and 0, respectively. The CP -violating W W γ couplings
˜
λ
γ
and ˜κ
γ
are tightly constrained by measurements of the neutron electric dipole moment [6 ]. In the
present study, we assume C, P and CP symmetries are conserved, reducing the independent
coupling parameters to κ
γ
, κ
Z
, λ
γ
, λ
Z
and g
Z
1
.
Cross sections for gauge boson pair production increase for couplings with non-SM values,
because the cancellation between the t- and u- channel diagrams and the s-channel diagrams
is destroyed. This can yield larg e cross sections at high energies, eventually violating tree-
level unitarity. A consistent description therefore requires anomalous couplings with a form
factor that causes them to vanish at very high energies. We will use dipo le form factors,
e.g., λ
V
(ˆs) = λ
V
/(1 + ˆs/Λ
2
)
2
, where ˆs is the square of the invariant mass of the ga uge-boson
pair. Given a form-factor scale Λ, the anomalous-coupling parameters are restricted by S-
matrix unitarity. Assuming t hat the independent coupling parameters are κ = κ
γ
= κ
Z
and
λ = λ
γ
= λ
Z
, tree-level unitarity is satisfied if Λ ≤ [6.88/((κ −1)
2
+ 2λ
2
]
1/4
TeV [2,7]. The
experimental limits on anomalous couplings can be compared with the bounds derived from
S-matrix unitarity, and constrain the trilinear gauge-boson couplings only if the limits are
more stringent than the bounds from unitarity f or any given value of Λ.
For both W W and W Z production processes, the effect of anomalous values of λ
V
on
the helicity amplitudes is enhanced for lar ge ˆs. On the other hand, terms containing ∆κ
V
(= κ
V
− 1) grow as
√
ˆs in the W Z production process, and as ˆs in the W W production
process. Limits on ∆κ
V
from the study of W W production are therefore expected to be
tighter than those from W Z production.
Since anomalous couplings contribute only via s-channel photon or W or Z boson in-
termediaries, their effects are expected mainly in the region of small vector boson rapidi-
ties, a nd the transverse momentum distribution of the vector boson is therefore partic-
ularly sensitive to anomalous trilinear gauge-boson couplings. This is demonstrated in
Fig. 2, which shows t he distribution of the W boson tr ansverse momentum p
W
T
in simu-
lated p¯p → W W + X → eνjj + X events for anomalous trilinear gauge boson couplings,
using a dipole form factor with a scale Λ = 1.5 TeV, and with the couplings for W W γ and
W W Z assumed to be equal.
Trilinear gauge-boson couplings can therefore be measured by comparing the shapes of
the p
T
distributions of the final state gauge bosons with theoretical predictions. Even if
the background is much larger than the expected gauge-boson pair production signal as is
the case for the W W/W Z → eνjj process, limits on anomalous couplings can still be set
using a kinematic region where the effects of anomalous tr ilinear gauge boson couplings are
expected to dominate.
Trilinear gauge-boson couplings have been studied in several experiments. W W γ cou-
plings have been studied in p¯p collisions by the UA2 [8], CDF [9], and DØ [10,11] collabo-
rations using W γ events. The UA2 results are based on data taken during the 1988–1990
CERN p¯p collider run at
√
s = 630 GeV with an integrated luminosity of 13 pb
−1
and the
CDF and DØ data are from the 1992–1993 and 1993–1995 Fermilab p¯p runs at
√
s = 1.8
6

10
-3
10
-2
10
-1
0 50 100 150 200 250 300
λ= 0.0, ∆κ= 0.0
λ= 0.0, ∆κ= -0.5
λ= 0.0, ∆κ= 1.0
p
W
T
GeV/c
dσ/dp
W
T
, pb/(10 GeV/c)
FIG. 2. The p
W
T
spectrum of generated p¯p → W W → eνjj events with SM couplings and two
examples of anomalous couplings.
TeV. W W Z couplings together with the W W γ couplings have been studied by the CDF
and DØ collaborations using W boson pair production in the dilepton decay modes [11 –13]
and W W /W Z production in the single-lepton modes [11,14–16]. Experiments at the CERN
LEP Collider have recently reported results of similar studies [17].
In this report, we present a detailed description of previously summarized work [18] on
W W and W Z production with one W boson decaying into an electron (or a positron) and
an antineutrino (or a neutrino) and a second W or Z boson decaying into two jets [19].
Due to the limitation in jet-energy resolution, the hadronic decay of a W boson can not be
differentiated from that of a Z boson. This analysis is based on the data collected during
the 1993–1995 Tevatron collider run at Fermilab. From the observed candidate events and
background estimates, 95% confidence level (C.L.) limits are set on the anomalous trilinear
gauge b oson couplings. The results are combined with those from the 1992–1993 data to
provide the final limits on the couplings from the DØ analysis.
Brief summaries o f the detector and the multilevel trigger and data acquisition systems
are presented in Sections II and III. Sections IV, V and VI describ e o ur particle identification
methods, the data sample, and event selection criteria. Sections VII and VIII are devoted
to detection efficiency and background estimates. Results and conclusions are presented in
Sections IX and X.
II. THE DØ DETECTOR
The DØ detector [20], illustrated in Fig. 3, is a general-purpose detector designed for the
study of proton-antiproton collisions at
√
s = 1.8 TeV and is located at the DØ interaction
region of the Tevatron ring at Fermilab.
The innermost part o f the detector consists of a set of tracking chambers that surround
7

D0 Detector
Muon Chambers
Calorimeters Tracking Chambers
FIG. 3. Cutaway view of the DØ detector
the beam pipe. There is no central magnetic field and jets are measured using a compact
set of calor imeters positioned o utside the tracking volume. To identify muons, an additional
set of tracking cha mbers is located outside the calorimeter, with a measurement of muon
momentum provided through magnetized iron toroids placed between the first two muon-
tracking layers.
The full detector is about 13 m high × 1 1 m wide × 17 m long, with a tot al weight of
about 5500 tons. The Tevatron beam pipe passes through the center of the detector, while
the Main Ring beam pipe passes through the upper portion of the calorimetry, approximately
2 m above the Teva t ron beam pipe. The coordinate system used in DØ is right-handed,
with the z-axis pointing along the direction of the proton beam (southward) and the y-axis
pointing up. The polar angle θ = 0 is along the proton beam direction, and the azimuthal
angle φ = 0 along the eastward direction. Instead of θ, we often use the pseudorapidity, η =
−ln[tan(θ/2)]. This quantity approximates the true rapidity y = 1/2 ln[(E + p
z
)/(E −p
z
)],
when the rest mass is much smaller than the total energy.
A. Central Detector
The tracking chambers and a transition radiation detector make up the central detector
(CD). The main purpose of the CD is t o measure the trajectories of charged particles and
determine the z position of the interaction vertex. This information can be used to determine
whether an electromagnetic energy cluster in the calorimeter is caused by an electron or by
a photon. Additional informatio n such as the number of tracks and the ionization energy
8

along the track (dE/dx) can be used to determine whether a track is caused by one or several
closely spaced charged particles, such as a photon conversion.
The CD consists of fo ur separate subsystems: the vertex drift chamber (VTX), the
transition radiation detector (TRD), the central drift chamber (CDC), and two forward
drift chambers (FDC). The full set of CD detectors fits within the inner cylindrical aperture
of the calorimeters in a volume of radius r = 78 cm and length l = 270 cm. The system
provides charged-particle tracking over the region |η| < 3.2. The trajectories of charged
particles are measured with a resolution of 2.5 mrad in φ and 28 mrad in θ. From these
measurements, the position of the interaction vertex along the z direction is determined
with a r esolution of 6 mm.
The VTX is the innermost tracking chamber in t he DØ detector, occupying the region
r = 3.7 cm to 16.2 cm. It is made of three mechanically independent concentric layers of
cells parallel to the beam pipe. The innermost layer has sixteen cells while the outer two
layers have thirty-two cells each.
The TRD occupies the space between the VTX and the CDC; it extends from r = 1 7 .5
cm to 49 cm. The TRD consists of three separate units, each containing a radiator (393 foils
of 18 µm thick polypropylene in a volume filled with nitro gen gas) a nd an X-ray detection
cha mber filled with Xe gas. The TRD information is not used in this a nalysis.
The CDC is a cylindrical drift chamber, 184 cm alo ng z, located between r = 49.5 and
r = 74.5 cm, and provides coverage for |η| < 1.2. It is made up of four concentric rings of 32
azimuthal cells per ring. Each cell contains seven sense wires (staggered by 20 0 µm relative
to each other to help resolve left-right ambiguities), and two delay lines. The rφ position
of a hit is determined via t he drift time measured for the hit wire and the z position of a
hit is measured using inductive delay lines embedded in the module-walls of the sense wire
planes.
The FDC consists of two sets of drift chambers located at the ends of the CDC. They
perform the same function as the CDC, but for 1.4 < |η| < 3.1. Each FDC packag e consists
of three separate chambers: a Φ module, whose sense wires are radial and measure the
φ coordinate, sandwiched between a pair of Θ modules whose sense wires measure the θ
coordinate.
B. Calorimeters
The DØ calorimeters are sampling calorimeters, with liquid argon as the sensitive ioniza-
tion medium. The primary absorber material is depleted uranium, with copper and stainless
steel used in the outer regions. There are three separate units, each cont ained in separate
cryostats: the Central Calorimeter (CC), the North End Calorimeter (ECN), and the South
End Calorimeter (ECS). The readout cells are arranged in a pseudo-projective geometry
pointing to the interaction region.
The calorimeters are subdivided in depth into three distinct types of modules: electro-
magnetic sections (EM) with relatively thin uranium absorber plates, fine-hadronic sections
9

(FH) with thicker uranium plates, and coarse-hadronic sections (CH) with t hick copper or
stainless steel plates. There are f our separate layers for the EM modules in both the CC
and EC that are readout separately. The first two layers are 2 radiation lengths thick in
the CC and 0.3 and 2.6 radiation lengths thick in the EC, and measure the initial longi-
tudinal shower development, where photons and π
0
s differ somewhat on a statistical basis.
The third layer spans the region of maximum EM shower energy deposition and the fourth
completes the EM coverage of approximately 20 total radiation lengths. The fine-hadronic
modules are typically segmented into three or four layers. Typical transverse sizes of towers
in both EM and hadronic modules are ∆η = 0.1 and ∆φ = 2π/64 ≈ 0.1. The third section
of the EM modules is segmented twice as finely in both η and φ to provide more precise
determination of centroids of EM showers.
The CC has a length of 2 .6 m, covering the pseudorapidity r egion |η| < 1.2, and consists
of three concentric cylindrical rings. There are 32 EM modules in the inner ring, 16 FH
modules in the surrounding ring, and 16 CH modules in the outer ring. The EM, FH and
CH module boundaries are rotated with respect to each other so a s to prevent having more
than one intermodular gap intercepting a trajectory from the origin of the detector.
The two end calorimeters (ECN and ECS) are mirror-images, and contain four types of
modules. To avoid the dead spaces in a multi-module design, there is just a single large EM
module and one inner hadronic (IH) module. Outside the EM and IH, there are concentric
rings of 1 6 middle and outer hadronic modules (MH and OH). The azimuthal boundaries
of the MH and OH modules are a lso offset to prevent cracks through which particles could
penetrate the calorimeter. This makes t he DØ detector almost completely hermetic and pro-
vides an accurate measurement of missing transverse energy. Due to increase in background
and loss of tracking efficiency for |η| > 2.5, electron and photon candidates are restricted t o
1.5 < |η| < 2.5 in the EC.
In the transition region between the CC and EC (0.8 ≤ |η| ≤ 1.4), there is a large
amount o f uninstrumented material in the form of cryostat walls, stiffening rings, and module
endplates. To correct for energy deposited in the uninstrumented material, we use two
segmented (0.1 × 0.1 in η ×φ) arrays of scintillation counters, called intercryostat detectors.
In addition, separate single-cell structures called “massless gaps” are mounted on the end
plates of the CC-FH modules and on the front plates of EC-MH and EC-OH modules, and
are used to correct showers in this region of the detector.
The Main Ring beam pipe passes through the outer layers o f the CC, ECN and ECS.
Beam losses from the Main-Ring cause energy deposition in the calor imeter t hat can bias
the energy measurement. The data acquisition system either stops recording data during
periods of Main-Ring activity near the DØ detector, or flags such events.
C. Muon Detectors
The DØ muon detector is designed to identify muons and to determine their trajectories
and momenta. It is located outside of the calorimeter, and is divided in two subsystems:
the Wide Angle Muon Spectrometer and the Small Angle Muon Spectrometer. Since the
10

calorimeter is thick enough to absorb most of the debris from electromagnetic and hadronic
showers, muons can be identified with great confidence. The muon system is not used in
this analysis, and is therefore not discussed any further.
III. MULTILEVEL TRIGGER AND DATA ACQUISITION SYSTEMS
The DØ trigger system is a multilayer hierarchical system. Increasingly complex tests
are applied to the data at each successive stage to reduce background.
The first stage, called Level 0 (L0), consists of two scintillator arrays mounted on the front
surfaces o f the EC cryostats, perpendicular to the beam direction. Each array covers a partial
region of pseudorapidity for 1.9 < |η| < 4.3, with nearly complete coverage over the range
2.2 < |η| < 3.9. The L0 system is used to detect the occurrence of an inelastic p¯p collision,
and serves as the luminosity monitor for the experiment. In addition, it provides fast
information on the z-coordinate of the primary collision vertex, by measuring the difference
in arrival time between particles hitting the north and south L0 arrays; this is used in making
preliminary trigger decisions. A slower, more accurate measurement of the position of the
interaction vertex, and an indication of the possible occurrence of multiple interactions, are
also made available for subsequent trigger decisions. The L0 trigger is ≈ 99% efficient for
non-diffractive inelastic collisions. The output rate from L0 is on the order of 150 kHz at a
typical luminosity of 1.6 × 10
31
cm
−2
s
−1
.
The next stage of the trigger is called Level 1 (L1). It combines the results from individual
L1 components into a set of global decisions that command t he readout of the digitization
crates. It also interacts with the Level 2 trigger (L2). Most of the L1 components, such as
the calorimeter triggers and the muon triggers, operate within the 3 .5 µs interval between
beam crossings, so that all events are examined. However, other components, such as the
TRD trigger and several components of the calorimeter and muon triggers, called Level 1.5
trigger (L1.5), can require more time. The goal o f the L1 trigger is to r educe the event rate
to 100–200 Hz. The primary input for the L1 trigger consists of 256 trigger terms, each of
which corresponds to a single bit, indicating that some specific requirement is met. These
256 terms are reduced to a set of 32 L1 trigger bits by a two-dimensional AND-OR logic
network. An event is said to pass L1 if at least one of these 32 bits is set. The L1 trigger also
uses info r matio n based on Main Ring activity. To prevent saturation of the trigger system
by processes with large cross sections, such as QCD multijet production, any particular
contributor to the L1 trigger can be prescaled.
The L1 calorimeter trigger covers the region up to |η| < 4.0 in tr ig ger towers of 0.2 × 0.2
in η−φ space. These towers are subdivided longitudinally into electromagnetic and hadronic
trigger sectors. The output of the L1 calorimeter trigger corresponds to the transverse energy
deposited in t hese sectors and towers.
For the 1993–1995 collider run, an L1.5 trigger for the calorimeter was implemented
using the L1 calorimeter trigger da ta and filters based on neighbor sums and ratios o f the
EM and total transverse energies.
When an event satisfies the L1 t r ig ger, the data are passed on the DØ data acquisition
11

pathways to a farm o f 48 parallel microprocessors, which serve as event builders as well as
the L2 trigger system. The L2 system collects the digitized data from a ll elements of the
detector a nd trigger blocks for events that successfully pass Level 1. It applies sophisticated
algorithms to the data to reduce the event rate to about 2 Hz before passing the accepted
events on to the host computer for monitoring and recording. The data for a specific event
are sent over parallel paths to memory modules in specific selected nodes. The accepted
data are collected and formatted in final form in the nodes, and the L2 filter algorithms are
then executed.
The L2 filtering process in each node is built around a series of filter tools. Each tool
has a specific function related to the ident ification of a type o f particle or event character-
istic. There are tools to recognize jets, muons, calorimeter EM clusters, tracks associated
with calorimeter clusters,
P
E
T
(sum of transverse energies of jets), and /E
T
(imbalance in
transverse energy). Other tools recognize specific noise or background conditions. There are
128 L2 filters available. If all of t he L2 requirements (for at least one of these 128 filters)
are satisfied, the event is said to pass L2 and it is temporarily stored on disk before being
transferred t o an 8 mm magnetic tape.
Once an event is passed by an L2 node, it is tr ansmitted to the host cluster, where it is
received by the data logger, a program running on one of the host computers. This program
and o t hers associated with it are responsible for receiving data fr om the L2 system and
copying it to magnetic tape, while performing all necessary bookkeeping tasks (e.g., time
stamping, recording t he run number, an event number, etc.). Part of the data is sent to an
event pool for online monitoring.
A. Electron Trigger
To trigger on electrons, L1 requires the transverse energy in the EM section of a trigger
tower to be above a progra mmable threshold. The L2 electron algorithm then uses the full
segmentation of the EM calorimeter to identify electron showers. Using the t rigger towers
that are above threshold at L1 as seeds, the algorithm forms clusters that include all cells in
the four EM layers and the first FH layer in a region of ∆η × ∆φ = 0.3 × 0.3, centered on
the tower with the highest E
T
. The longitudinal and transverse energy profile of the cluster
must satisfy the following requirements: ( i) the fraction of the cluster energy in the EM
section (the EM fraction) must be above a threshold, which depends on energy and detector
position; and (ii) the difference between the energy depositions in two regions of the third
EM layer, covering ∆η × ∆φ = 0.25 × 0.25 and 0.15 × 0.15, and centered on the cell with
the highest E
T
, must be within a window that depends on the total cluster energy.
B. Jet Trigger
The L1 jet triggers require the sum of the transverse energy in the EM and FH sections
of a trigger tower (∆η × ∆φ = 0.2 × 0.2) to be above a programmable threshold. The L2
12

jet algorithm begins with an E
T
-ordered list of t owers that are above threshold at L1. At
L2, a jet is f ormed by placing a cone of given radius R, where R =
√
∆η
2
+ ∆φ
2
, around
the seed tower from L1. If another seed tower lies within the jet cone, it is passed over and
not allowed to seed a new jet. The summed E
T
in all of the towers included in the jet cone
defines the jet E
T
. If any two jets overlap, then the towers in the overlap region are added
into the jet candidate that is formed first. To filter out events, requirements on quantities
such as the minimum transverse energy of a jet, the minimum transverse size of a jet, the
minimum number of jets, and the pseudorapidity of jets, can be imposed at this point.
C. Missing Transverse Energy Trigger
Rare and interesting physics pro cesses often involve production of weakly interacting
particles such as neutrinos. These particles usually can not be detected directly. However,
assuming momentum conservation in a collision allows the moment a of such particles to be
inferred from the vector sum of the momenta of the observed particles. Since the energy
flow near the beamline is largely undetected, such calculations are realistic only in the plane
transverse to the beam. The negative of the vector sum of the momenta of the detected
particles is referred to as missing E
T
and denoted by /E
T
; it is used as an indicator of the
presence of weakly interacting particles. At L2, /E
T
is computed using the vector sum of
all calorimeter and intercryostat detector cell energies with respect to the z position of t he
interaction vertex, which is determined from the timing of the hits in the L0 counters.
IV. PARTICLE IDENTIFICATION
A. Electron
Electrons and photons are identified by the properties of the shower in the calorimeter.
The algorithm loops over all EM towers (∆η × ∆φ = 0.1 × 0.1) with energy E > 50 MeV,
and connects the neighboring tower with the next highest energy. The cluster energy is then
defined as the sum of the energies of the EM towers and the energies in the corresponding first
FH layer. The ratio of the energy in the EM cluster to the total energy (EM energy summed
with the corresponding hadronic layers), defined as the EM fraction, is used to discriminate
electrons and photons from hadronic showers. A cluster must pass the fo llowing criteria to
be an electron/photon candidate: (i) the EM fraction must be greater than 90% and (ii)
at least 40% of the energy must be contained in a single 0.1 × 0.1 tower. To distinguish
electrons from photons, we search for a track in the central detector that extrapolates to
the EM cluster f rom t he primary interaction vertex within a window of |∆η| ≤ 0.1, and
|∆φ| ≤ 0.1. If one or more tracks are found, the object is classified as an electron candidate.
Otherwise, it is classified as a photon candidate.
13

1. Selection Requirements
The spatial development of EM showers is quite different from that of hadro nic showers
and the shower shap e information can be used to differentiate electrons and photons from
hadrons. The f ollowing variables are used for final electron selection:
(i) Electromagnetic energy fra ction. This quantity is based on the observation that electrons
deposit almost all of their energy in the EM section o f the calorimeter, while hadron jets
are far more penetrating (typically only 10% of their energy is deposited in the EM section
of the calorimeter). It is defined as the ratio of EM energy to the total shower energy.
Electrons are required to have at least 95% of their total energy in the EM calorimeter.
This requirement loses only about 1% of all electrons.
(ii) Covariance matrix (H-matrix) χ
2
. The shape of any shower can be characterized by the
fraction of the cluster energy deposited in each layer and tower of the calorimeter. These
fractions are correlated, i.e., an electron shower deposits energies according to the expected
transverse and longitudinal shapes of an EM shower and a hadron shower following the
typical development of a hadronic shower. To obtain good discrimination against hadrons,
we use a covariance matrix technique. The observables in this method are the f r actional
energies in Layers 1, 2, and 4 of the EM sector and the fractional energy in each cell of a 6×6
array of cells in Layer 3 centered on the most energetic tower in the EM cluster. To take
account of the dependence o f the shower shape on energy a nd on the position of the primary
interaction vertex, we use the logarithm of the shower energy and the z-position of the event
vertex as the remaining input o bservables. The event vertex is determined by extrapolating
CDC tracks to the z axis, and for more than one possibility, the vertex associated with the
highest number of tracks is chosen as the event vertex. Using these 41 variables, covariance
matrices are constructed fo r each of the 37 detector towers (at different values of η) based
on Monte Carlo generated electrons. The Monte Carlo showers are tuned t o make them
agree with our test beam measurements of the shower shapes. The 41 o bservables for any
given shower can be compared with the parameters of the appropriate cova r ia nce matrix to
define a χ
2
, which is to be be less than 100 for electron candidates in the CC and less than
200 for the EC. This requirement loses about 5% of all true electrons.
(iii) Isolation. The decay electron from a W boson should not be close to any other object in
the event. This is quantified by the isolation fraction. If E(0.4) is the energy deposited in all
calorimeter cells within the cone R < 0.4 around the direction of the electron, and EM(0.2)
is the energy deposited in only the EM calorimeter in the cone R < 0.2, the isolation variable
is then defined as the ratio I = [E(0.4) − EM(0.2)]/EM(0.2). The requirement I < 0.1
loses only 3% of the electrons from W boson decays.
(iv) Track-match significance. An imp ortant source of background for electrons is the photon
from the decay of π
0
or η mesons. Such photons do not produce tracks, but their trajecto-
ries can overlap with those of nearby charged particles, thereby simulating electrons. This
background can be reduced by demanding a good spatial match between the energy cluster
in the calorimeter and nearby charged tracks. The significance S of the mismatch between
these quantities is given by S = [(∆φ/δ
∆φ
)
2
+ (∆z/δ
∆z
)
2
]
1/2
, where ∆φ is the azimuthal
mismatch, ∆z the mismatch along the beam axis, and the δ ar e the resolutions of these vari-
14

ables. This form fo r S is appropriate for the central calorimeter. For the end calorimeter, r
replaces z. Requiring S < 5 accepts 95(78)% of the CC(EC) electrons reconstructed in the
central tracker.
(v) Track-in-road. All electrons from W → eν decays ar e required to have a partially
reconstructed track along the trajectory between the energy cluster in the calorimeter and
the interaction vertex. This requirement is found to reject 16(14)% of CC(EC) electrons
from W boson decay.
In our analysis, we combine the above quantities to form the electron identification
criteria. A summary of the selection requirements and their acceptance efficiencies is listed
in Table I (See SectVII).
TABLE I. Electron selection requir ements and their acceptance efficiencies for W → eν events.
Selection CC EC
requirement
ε ε
H-matrix χ
2
< 100 0.946±0.005 < 200 0.950±0.008
EM fraction > 0.95 0.991±0.003 > 0.95 0.987±0.006
Isolation < 0.10 0.970±0.004 < 0.10 0.976±0.007
Track match < 5 0.948±0.005 < 5 0.776±0.012
Track-in-road 0.835±0.009 0.858±0.006
2. Electromagnetic Energy Corrections
The energy scales of the calorimeters were originally set through calibration in a test-
beam. However, due to differences in conditions between the test beam and the DØ envi-
ronment, additional corrections had to be implemented.
The EM energy scales for the calorimeters were determined by comparing the measured
masses of π
0
→ γγ, J/ψ → ee, and Z → ee to their known values. If the electron energy
measured in the calorimeter and the true energy are related by E
meas
= αE
true
+ δ, the
measured and true mass values are, to first order, related by m
meas
= αm
true
+ δf, where
the calculable variable f reflects the topology of the decay. To determine α and δ, we fit the
Mont e Carlo prediction to the observed resonances, with α and δ as free parameters [21].
The va lues of α and δ are found to be α = 0.9533 ±0.0008 and δ = −0.16
+0.03
−0.21
GeV f or the
CC and α = 0.952 ± 0.002 and δ = −0.1 ± 0.7 GeV for the EC.
3. Energy Resolution
The relative energy resolution for electrons and photons in the CC is expressed by the
empirical relation

σ
E

2
= C
2
+
S
2
E
T
+
N
2
E
2
, where E and E
T
are the energy and transverse energy
15

of the incident electron/photon, C is a constant term from uncertainties in calibration, S
reflects the sampling fluctuation of the liquid argo n calor imeter, and N corresponds to a
contribution from noise. For the EC, the E
T
in the relation is replaced by E. The sampling
and noise terms are based on results from the test beam. The noise t erm measured at the
test beam agrees with the one obtained in the collider environment (based on the width of
pedestal distributions). The constant term is tuned to match the mass resolution o f both
observed and simulated Z → ee events. Table II lists these parameters.
TABLE II. Parameters for describing the energy resolution of electrons and photons.
Quantity CC EC
C 0.017 0.009
S (
√
GeV) 0.14 0.157
N (GeV) 0.49 1.140
B. Jets
In our analysis, jets are reconstructed using a fixed-cone algorithm with radius R =
√
∆η
2
+ ∆φ
2
= 0.5. The algorithm forms preclusters of cont ig uous cells using a radius of
R
precluster
= 0.3 centered on the tower with highest E
T
. O nly towers with E
T
> 1 GeV are
included in preclusters. These preclusters serve as the starting points for jet reconstruction.
An E
T
-weighted cent er of gravity is then formed using the E
T
of all towers within a radius
R of the center of the cluster, and the process is repeated until the jet becomes stable. A
jet must have E
T
> 8 GeV. If two jets share energy, they are combined or split, based on
the fraction of overlapping energy relative to the E
T
of the lesser jet. If this shared fraction
exceeds 50%, the jets are combined.
Although the R = 0.3 cone algorithm is more efficient for jet finding than our larger
cone size, which leads to undesired merging of jets f or high-p
T
W or Z bosons, the relatively
large uncertainties in the measurement o f jet-energy for the R = 0.3 cones negate their
advantage, and we therefore choose to use the R = 0.5 cone alg orithm for our studies.
1. Selection Requirements
To remove jets produced by cosmic rays, calorimeter noise, and interactions in the Main
Ring, we developed a set of requirements based on Monte Carlo studies of jets in such
environments and on data on noise taken with and without colliding beams. The variables
used are:
(i) Electromagnetic energy fraction (emf). As for electrons, this quantity is defined as the
fraction of the total energy deposited in the electromagnetic section of the calorimeter. A
16

requirement on this quantity removes electrons, photons and false jets from the jet sample.
Electrons and photons typically have a high EM fraction. False jets are caused mainly
by backgro und from the Main Ring or by noisy or “hot” cells, and therefore generally
do not contain energy in the EM section, thereby yielding very low EM fractions. Jets
with 0.05 < emf < 0.95 are defined as acceptable in this analysis. The efficiency of this
requirement is 99.9% at E
T
= 20 GeV and decreases to 99.6% at 100 GeV.
(ii) Hot cell energy fraction (hcf). The hcf is defined as the ratio of the energy in the cell
of second highest E
T
to that of the cell with highest E
T
within a jet. A requirement on
this quantity is imposed to remove event s with a large amount of noise in the calorimeter.
Hot cells can appear when a discharge occurs between electrodes within a cell; often this
does not affect neighboring cells. In this case, hcf is small, which signals a problem, since
the hcf for a jet should not be small because the energy is expected to be distributed over
cells. If most of the energy is concentrated in a single cell, it is very likely to be a false jet
reconstructed from discharge noise. For good jets, hcf is found to be greater than 0.1 . The
efficiency of this requirement is 97.3% at E
T
= 20 GeV and decreases to 96.9% at 100 GeV.
(iii) Coarse hadronic energy fraction (chf). This quantity is defined as the fraction of jet
energy deposited in the coarse hadronic section of t he calorimeter. The Main Ring at DØ
passes through the CH modules, and any energy deposition related to the Main Ring will
be concentrated in this section of the calorimeter. Such jets tend to have more t han 40% of
their energy in the CH region, while standard jets have less than 10% of their energy in this
section of the calorimeter. All acceptable jets are therefore required to have chf < 0.4. The
efficiency of this requirement is 99.6% at E
T
= 20 GeV and decreases to 99.3% at 100 GeV.
2. Hadronic Energy Corrections
Since t he measured jet energy is usually not equal to the energy of the original parton
that formed the jet, corrections are needed t o minimize any systematic bias. Jet energy
response affected by non-uniformities in the calorimeter, non- linearities in the response to
hadrons, emission of particles outside of the R = 0.5 cone (often referred to as out-of-cone
showering), noise due to the r adioactivity of uranium, and energy overlap from the products
of soft interactions of spectator partons within the proton and the a ntiproton (“underlying
event”). The first two effects are estimated using a method called Missing-E
T
Projection
Fraction (MPF) [22].
The MPF method is based o n events that contain a single isolated EM cluster (due
to a photon or a jet that f r agmented mostly into neutral mesons), and one hadronic jet
located opposite in φ, and no other objects in the event. It is assumed that such events
do not have energetic neutrinos so that any missing transverse energy can be attributed
to a mismeasurement of the hadronic jet. The EM-cluster energy is corrected using the
electromagnetic energy corrections described above. Projecting the corrected /E
T
along the
jet axis determines corrections to the jet energy. This correction is averaged over many
events in the sample to obtain a correction as a function of jet E
T
, η, and electromagnetic
content of t he jet. The ha dronic energy correction is 20% at E = 2 0 GeV and 15% at
17

E = 100 GeV, and gradually approaches 10 % at high E.
The impact of out-of -cone showering is estimated using Monte Carlo jet events. Effects
due to the underlying events and uranium noise are determined in separate studies using
minimum-bias event data. (Minimum-bias data corresponds to inclusive inelastic collisions
collected using only the L0 trigger.)
3. Energy Resolution
The jet energy resolution has been studied by examining momentum balance in dijet
events [23]. The fo r mula used for parametrizing the relative jet energy resolution is

σ
E

2
=
C
2
+
S
2
E
+
N
2
E
2
. Table III shows the values of the parameters for different η regions of the
calorimeter.
TABLE III. Jet energy resolution for different regions of the calorimeter.
η Region C S (
√
GeV) N (GeV)
|η| < 0.5 0.00±0.01 0.81±0.02 7.07±0.09
0.5 < |η| < 1.0 0.00±0.01 0.91±0.02 6.92±0.09
1.0 < |η| < 1.5 0.05±0.01 1.45±0.02 0.00±1.40
1.5 < |η| < 2.0 0.00±0.01 0.48±0.07 8.15±0.21
2.0 < |η| < 3.0 0.01±0.58 1.64±0.13 3.15±2.50
C. Neutrinos: Missing Transverse Energy
The presence of neutrinos in an event is inferred from the /E
T
. In this analysis we assume
that the /E
T
in each candidate event corresponds to the neutrino from the decay W → eν.
1. Missing E
T
The missing transverse energy in the calorimeter is defined as /E
T
= ( /E
T
2
x
+ /E
T
2
y
)
1/2
, where
/E
T
x
= −
P
i
E
i
sin(θ
i
) cos(φ
i
) −
P
j
∆E
j
x
and /E
T
y
= −
P
i
E
i
sin(θ
i
) sin(φ
i
) −
P
j
∆E
j
y
. The
first sum (over i) is over all cells in the calorimeters, intercryostat detectors and massless
gaps (see Sec. II B). The second sum (over j) is over the E
T
corrections applied to all
electrons and jets in the event. This can be used to estimate the transverse momentum of
any neutrinos in an event that does not contain muons, which deposit only a small portion
of their energy in the calorimeter. The total missing E
T
is missing E
T
from the calorimeter
corrected for the transverse momenta of any observed muon tracks. Since this analysis does
not use muons, we will refer to the /E
T
based o n the calorimeters as t he tr ue /E
T
.
18

2. Re solution in /E
T
For a n ideal calorimeter, the magnitude of the components of the /E
T
vector would
sum to zero for events with no true source of /E
T
. However, detector noise and energy
resolution in the measurement of jets, photons, and electrons contribute to the /E
T
. In
addition, non-uniform response in the detector also results in /E
T
. The /E
T
resolution for our
candidate events is parameterized as σ = 1.08GeV +0.019(
P
E
T
), and is based on studies of
minimum-bias data [23]. The
P
E
T
used in the parameterization is quite reasonable because
the greater the total amount of transverse energy in t he event, the la rger the possibility for
its mismeasurement.
V. DATA SAMPLE
The analysis of t he W W/W Z → eνjj process is based on data taken during the 1993–
1995 Tevatron Collider run (called Run 1b). The L0 trigger is used to check the presence of
an inelastic collision, but is not included in the trigger conditions for W - boson data. This
was done to allow studies of diffractive W -boson production. Our analysis uses the collected
W → eν data sample, with the L0 trigger requirement imposed offline. The L1 trigger used
in this analysis (called the EM1
1 HIGH tr ig ger) requires the presence of an electromagnetic
trigger tower with E
T
> 10 GeV. The L1.5 trig ger then requires the L1 tr ig ger tower to have
E
T
> 15 GeV and checks that the electromagnetic fraction is greater tha n 85%. The L 2
component of the trigger (called the EM1
EISTRKCC MS trigger) requires an isolated electron
candidate with E
T
> 20 GeV that has a shower shape consistent with that of an electron
and /E
T
> 15 GeV.
Additional conditions are imposed on the data to further reduce background. Triggers
that occur at the times when a proton bunch in the Main Ring passes through the detector
are not used in this analysis. Similarly, triggers that occur during the first 0.4 seconds of the
2.4-second antiproton production cycle are rejected. Data taken during periods when the
data acquisition system o r the detector sub-systems malfunctioned are also discarded. With
these trigger requirements, the integrated luminosity of the data sample is estimated to be
82.3 ±4.4 pb
−1
[24]. The efficiency and turn-on of the L2 trigg er are described in Ref. [25].
The trigger efficiency for signal is (98.1 ± 1.9)%.
Data samples that satisfy two other L2 triggers, the EM1
ELE MON and ELE 1 MON trigg ers,
are used for ba ckground studies. These trig gers select events that have a n electron candidate
with E
T
> 20 GeV and E
T
> 16 GeV, respectively. The electron candidates in these samples
must pass the standard shower-shape requirements, but not the isolation requirement. These
triggers use the same L1 and L1.5 conditions as the trigger used for signal.
19

VI. EVENT SELECTION
W W/W Z → eνjj candidates are selected by searching for events with an isolated high-
E
T
electron, large /E
T
, and at least two high-E
T
jets. Electrons in the candidate sample
must be in the |η| < 1.1 region but away from the boundaries between calorimeter modules
in φ (∆φ > 0 .0 1), or within the region 1.5 < | η| < 2.5. Jets in the candidate sample must
be in the region |η| < 2.5.
The W → eν decay is defined through the presence of only a single isolated electron
with E
e
T
> 25 GeV and /E
T
> 25 GeV in the event. The transverse mass of the electron a nd
neutrino ( /E
T
) system is required to be M
T
> 40 GeV/c
2
, where M
T
= {2E
e
T
/E
T
[1 −cos(φ
e
−
φ
ν
)]}
1/2
. The requirement on the electron E
T
is sufficiently high to provide an efficiency
that is independent of E
T
(the hardware threshold of 20 GeV). Requiring only one electron
reduces background from Z → ee production. The requirements on /E
T
and M
T
reduce the
background contribution from misidentified electrons.
The W/Z → jj decay is defined by requiring at least two jets with E
j
T
> 20 GeV and an
invariant mass of the two-jet system consistent with that of the W or Z boson (50 < M
jj
<
110 GeV/c
2
). The dijet invariant mass (M
jj
) is calculated via M
jj
= {2E
j1
T
E
j2
T
[cosh(η
j1
−
η
j2
) −cos(φ
j1
−φ
j2
)]}
1/2
. If there are more than two jets in the event, the two jets with the
highest dijet invariant mass are chosen to represent the W (or Z) decay.
The difference between the p
T
values of the eν and the two-jet systems is used to reduce
backgrounds. For W W or W Z production, the p
T
(eν) − p
T
(jj) distribution should be
peaked near zero and have a symmetric Gaussian shape, with the width of the Gaussian
distribution determined primarily by the jet energy resolution. On the other hand, for
background such as t
¯
t production (see Sec. VIII), the distribution should be broader and
asymmetric (shifted to positive values) due to additional b-quark jets in the events. Our
analysis therefore requires |p
T
(eν) − p
T
(jj)| < 40 GeV/c.
The data satisfying t he above selection criteria yield 399 event s. Figure 4a shows a scatter
plot of p
T
(eν) vs p
T
(jj) for candidate events that satisfy the two-jet mass requirement. The
width of the band reflects both the resolution and the true spread in the p
T
values. Figure 4b
shows a scatter plot of p
T
(eν) vs M
jj
without the imposition of the two-jet mass requirement.
VII. DETECTION EFFICIENCY
A. Electron Selection Efficiency
The efficiency of electron selection is studied using the Z → ee event sample from the
1993–1995 Tevatro n collider run using the EM2
EIS HI trigger. Z → ee events were selected
at L1 and L1.5 by requiring two EM towers with E
T
> 7 GeV at L1, and at least one tower
with E
T
> 12 GeV with more than 85% o f its energy in the EM section o f the calorimeter. At
L2, the trigger required two electron candidates with E
T
> 20 GeV that satisfied electron
shower-shape a nd isolation requirements. To select an unbiased sample of electrons, we
20

(a)
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120 140 160 180 200
p
T
(jj) GeV/c
p
T
(eν) GeV/c
(b)
0
20
40
60
80
100
120
140
160
180
200
0 50 100 150 200 250 300 350 400
M
jj
GeV/c
2
p
T
(eν) GeV/c
FIG. 4. Scatter plots of (a) p
T
(eν) vs p
T
(jj) and (b) p
T
(eν) vs M
jj
.
use events in which one of the electrons passes the tag quality requirements: EM fraction
> 0.90, Isolation < 0.15, H-matrix χ
2
< 100(200) for CC(EC), and track-match significance
< 10 . The second electron in the event is then assumed to be unbiased. If both electrons
pass t he tag requirements, the event contributes twice to the sample. The efficiency of a
selection requirement for electrons is given by ε = (ε
s
− ε
b
f
b
)/(1 − f
b
), where ε
s
is the
efficiency measured in the signal region, ε
b
is the efficiency measured in the background
region, and f
b
is the ratio of the number of background events in the signal region to the
total number of events in the signal region. The signal region is defined as the region of
the Z mass peak (86 < m
ee
< 96 GeV/c
2
), and the background regions are defined as
61 < m
ee
< 71 GeV/c
2
and 1 11 < m
ee
< 121 GeV/c
2
. We determine f
b
in the region
of the signal using an average of the number of events in the background regions. The
systematic uncertainties on the efficiencies are estimated from a comparison with efficiencies
obtained using an alternative method that fits the invariant mass spectrum of two electrons
to the sum of a Breit-Wigner form convoluted with a Gaussian and a linear dependence for
the background. Efficiencies from the two methods agree within their uncertainties. The
track-in-road efficiency is estimated in a similar manner, except that EM clusters with no
matching track are included as unbiased electrons in the sample. Table I summarizes the
electron efficiencies. Although these efficiencies are based mainly o n Z events with few jets,
the corrections for ≥ 2 jets are small.
21

B. W/Z → jj Selection Efficiency
The W/Z → jj selection efficiency is estimated using Monte Carlo W W/W Z → eνjj
events generated with the isajet [26] and pythia [27] programs, followed by a detailed
simulation of the DØ detector, and parametrized as a function of p
W
T
. Figure 5 shows
the W/Z → jj detection efficiency ǫ(W → jj) calculated as the ratio of events a fter the
imposition of the two-jet selection requirements relative to the initial number of events. At
low p
T
, the detection efficiency is artificially elevated due to the presence of additional jets
from initial- and final-state g luon radiation (ISR/FSR) that are mislabeled as being decays
of W or Z bosons. The decrease in the efficiency at high p
T
is due to the merging of the
two j ets from a W or a Z boson. The results o bta ined from isajet are used to estimate the
efficiencies for identifying the W W/W Z process.
0
0.2
0.4
0.6
0.8
0 50 100 150 200 250 300 350 400 450 500
ISAJET
PYTHIA
P
T
(W→ jj) GeV/c
Efficiency(W→ jj)
FIG. 5. Efficiency for W → jj selection as a function of p
W
T
. T he decrease in the efficiency at
high p
T
is due to the merging of the two j ets from the decay of a W boson.
The estimated W/Z → jj efficiency is affected by the jet energy scale, the a ccuracy
of the ISR/F SR simulation, the accuracy of the parton fragmentation mechanism, and the
statistics of the Monte Carlo samples.
The energy-scale correction has an uncertainty that decreases from 5% at jet E
T
= 20
GeV to 2% at 80 GeV, and then increases to 5% at 350 GeV. The effect of this uncertainty
has been studied by recalculating the efficiency with the jet energy scale changed by one
standard deviation. The largest relative change in the accepted number of events is found
to be 3%.
To estimate the uncertainty due to the accuracy of the ISR/FSR simulation and of the
parton fragmentation mechanism, we use the W/Z → jj efficiency based on Monte Carlo
samples generated with pythia. The efficiency obtained using isajet is lower than that f or
pythia, but by less than 10%. We use the efficiencies from isajet because they provide
smaller yields of W W/W Z event s and therefore weaker limits on anomalous couplings. We
define one-half of the largest difference in isajet/pythia efficiency estimations (5%) as the
systematic uncertainty attributable to the choice of event generator.
C. Overall Selection Efficiency
The overall detection efficiency for W W/W Z → eνjj events assuming SM couplings is
calculated using two MC methods, coupled with electron-selection a nd trig ger efficiencies
22

measured fro m data. The first MC method uses t he isajet event generator followed by a
detailed simulation of the DØ detector. The second MC method uses the event generator of
Ref. [2] and a fast simulation program to characterize the response of the detector. isajet
used the CTEQ2L [28] parton distribution functions to simulate 2500 W W → eνjj events
and 1000 W Z → eνjj events with SM couplings. The event selection efficiency for for
the W W → eνjj signal is estimated as ǫ
W W
= (13.4 ± 0.8)%, a nd ǫ
W Z
= (15.7 ± 1.4)%
for the W Z → eνjj signal, where the errors are statistical. The combined efficiency for
W W/W Z → eνjj is given by [ǫ
W W
· σ · B(W W → eνjj) + ǫ
W Z
· σ · B(W Z → eνjj)]/[σ ·
B(W W → eνjj) + σ ·B(W Z → eνjj)] = (13.7 ±0.7)%, where the theoretical cross sections
of 9.5 pb for W W and 2.5 pb for W Z production [29], and the W and Z boson branching
fractions from the Particle Data Gro up [4], are used in the calculation (σ·B(W W → eνjj) =
1.38 ± 0.05 pb and σ · B(WZ → eνjj) = 0.188 ± 0.006 pb).
For the fast simulation, we generated over 30,000 events, with approximately four times
more for W W production than WZ production, reflecting the sizes of their expected produc-
tion cross sections. The overall detection efficiencies for the SM couplings were calculated
as [14.7 ± 0.2(stat) ± 1.2(sys)]% fo r W W → eνjj and [14.6 ± 0.4(stat) ± 1.1(sys)]% for
W Z → eνjj. The 7.8% systematic uncertainty includes statistics of the fast MC (1%),
efficiency of trigger and electron identification (1%), /E
T
smearing and modeling of the p
T
of
the W W/W Z system (5%), difference in W → jj detection efficiencies from the two event
generators (5%), and the effect of the jet energy scale (3%). The combined efficiency is
[14.7 ± 0.2(stat) ± 1.2(sys)]%. The combined efficiency estimated using the fast simulation
is consistent with the value obtained using isajet.
D. Expected Number of Signal Events
Using the fast detector simulation and the cross section times branching ratio from the
event generator of Ref. [2] (σ · B(W W → eνjj) = 1.26 ± 0.18 pb, a nd σ · B(W Z → eνjj)
= 0.18 ± 0.03 pb), we estimate the number of expected W W/W Z → eνjj events to be
17.5 ± 3.0 (15 .3 ± 3.0 W W events and 2.2 ± 0.5 W Z events), with the uncertainty (17.1%)
given by the sum in quadrature of the uncertainty in the efficiency, the uncertainty in the
luminosity (5.4%), and that in the NLO calculation (14%).
VIII. BACKGROUND
The sources o f background to the W W/W Z → eνjj process can be divided into two
categories. The first is instrumental background due to misidentified or mismeasured parti-
cles, and the other is inherent irreducible background consisting of physical processes with
the same signature as the events of interest.
23

A. Instrumental Background
The major source of instrumental background is QCD multijet production in which one
of the jets showers (mainly) in the electromagnetic calorimeter and is misidentified as an
electron, and the energies of the remaining jets fluctuate to produce /E
T
. Although the
probability f or a jet to be misidentified as an electron is small, the large cross section for
QCD multijet events makes this background significant.
This background is estimated using samples of “good” and “bad” electrons. A “good”
electron has the quality requirements described in Sec. IV A 1, while a “bad” electron has an
EM cluster with EM fraction > 0.95, Isolation ≤0.15, and either H-matrix χ
2
≥ 250 or track-
match significance ≥ 10. We a ssume that the shape of the /E
T
spectrum of the events with a
bad electron is identical to the /E
T
spectrum of the QCD multijet background. Furthermore,
with the assumption that the contribution of signal events at low /E
T
is negligible, the bad-
electron sample can be normalized to the good-electron data in the low- /E
T
region and the
/E
T
distribution of the bad-electron events can then be extrapolated to the signal region of
the good-electron sample.
To estimate the multijet background, we use triggers that do not require /E
T
. Several
L2 triggers in Run 1b meet this requirement, in particular the trigg ers EM1
ELE MON and
ELE 1 MON described in Sec. V. To avoid biases, we a dd a condition that the EM object in
these trigg ers pass the same L2 requirements as the signal. We then extract two samples
from these data, based on the electron quality. The /E
T
distribution for the bad-electron
sample is then normalized to agree with the /E
T
distribution for the good-electron sample at
low /E
T
( /E
T
< 15 GeV). Figure 6 shows these two distributions. The normalization factor
N
F
is calculated as the ratio of the number of bad-electron events to the number of good-
electron events with 0 ≤ /E
T
≤ 15 GeV. After imposing the jet selection requirements o n
the events, we find N
F
= 1.8 70 ± 0.060 (stat) ± 0.003 (sys). The systematic uncertainty on
the normalization factor is obtained by varying the range of /E
T
used for the normalization
procedure fro m 0–12 GeV to 0–18 GeV.
Missing E
T
1
10
10
2
10
3
10
4
0 10 20 30 40 50 60 70 80 90 100
Good electron sample
Bad electron sample
GeV
Nevts / (2 GeV)
FIG. 6. /E
T
distributions for the go od-electron (histogram) and bad-electron (solid circles)
samples selected from data taken w ith th e EM1
ELE MON and ELE 1 MON triggers (see text). The
bad-electron sample is normalized to the goo d electron sample for /E
T
< 15 GeV.
In the next step, we select two samples from the data taken with the trigger for signal
events, one containing background and signal (“good” electrons obtained through our se-
24

lection procedure) and the other containing only background events (“bad” electrons). The
normalization factor N
F
is then applied to the background sample. Figure 7 shows the
distributions of /E
T
for the candidates and the estimated QCD multijet background based
on the bad-electron events after the imposition of jet requirements.
Missing E
T
0
20
40
60
80
0 10 20 30 40 50 60 70 80 90 100
GeV
Nevt/ 2 GeV
Good electron sample
Bad electron sample
FIG. 7. Distributions of /E
T
of the good-electron (sum of signal and background) and
bad-electron (background only) samples selected from data taken with the trigger used for sig-
nal events.
From the above procedure, we estimate 1 04.3 ± 8.2 (stat) ± 9.1 (sys) background events
for /E
T
> 25 GeV. The systematic uncertainty (8.7%) includes the uncertainty on the nor-
malization factor (1%), the difference when an alternative method is used to estimate the
multijet background (5.2%), and the difference for events with /E
T
> 25 GeV when the /E
T
region 15–25 GeV is used for normalization (6.9%). In the alternative method, the probabil-
ity of a jet to be misidentified as an electron is multiplied by the number of multijet events
that satisfy selection criteria when one of the jets in the event is treated as an electron.
When more than one jet in an event satisfies the kinematic requirements, all are considered
in estimating the background from multijet production.
B. Inherent Background
The background contribution from processes with similar event topology (i.e., with final-
state objects identical to those of the signal) is estimated using Monte Carlo events.
1. W + ≥ 2 jets
W + ≥ 2 jets production is the dominant background to t he W W and W Z sig-
nals. This background is estimated using the Monte Carlo program vecbos [30], fol-
lowed by herwig [31] for the hadronization of the pa rt ons generated in vecbos and
then by the detailed simulation of the DØ detector. The cross section from vecbos has
a large uncertainty, and the generated W + ≥ 2 jets sample is therefore normalized to
the candidate event sample a fter subtraction of the QCD multijet background. To avoid
the inclusion of W W a nd W Z events in this normalization procedure, we use only the
events whose two-jet invariant mass lies outside of the mass peak of the W boson (i.e.,
25

M
jj
> 50 or M
jj
> 110 GeV/c
2
). Figure 8 shows the two- jet invariant mass distribu-
tions fo r data and the estimated background. The normalization factor is found to be
N
V
= N
V B
/(N
cand
− N
QCD
/N
F
) = 3.41 ± 0.31(stat) ± 0.29(syst), where N
V B
= 879 cor-
resonds to the number of vecbos events, N
cand
= 392 is the number of candidate events
in the data, a nd N
QCD
= 251 is the number of QCD multijet events outside of the W
boson mass window. Using this normalization factor, we estimate 279.5 ± 27.2 (stat) ±
23.8 (sys) W + ≥ 2 jets events in the candidate sample. The systematic uncertainty is
due to the normalization of the multijet background (6.9%), uncertainty in the jet energy
scale (4%), and the difference observed when the range of excluded M
jj
is changed to 40–
120 or 60–100 GeV/c
2
(3%). The cross section multiplied by the branching fraction for
W + ≥ 2 jets production, with the W boson decaying to eν, determined with this method
is 38795/(3.4 × 82.3) = 138.6 ±14.3 pb (where 38795 is the number of vecbos events gen-
erated, 3.4 is the normalization factor N
V
, and 82.3 pb
−1
is the integrated luminosity of
the data sample), which is consistent with the value (135 pb) given by the vecbos pro-
gram. Figure 9 shows distributions in the difference p
T
(eν) − p
T
(jj) and in the separation
between jets ∆R(jj), which provide sensitive measures for how well background estimates
describe the jets in the data. The backgrounds from the W + ≥ 2 jets and QCD multijet
contributions are seen to agree well with the data.
M
jj
0
10
20
30
40
50
60
70
80
90
0 50 100 150 200 250 300 350 400 450 500
Data
W +≥ 2 j + multijets
GeV /c
2
Nevt / 10 GeV/c
2
FIG. 8. Dijet invariant mass distribution. The solid circles and the histogram are the candidate
events and the background events from W + ≥ 2 jet events and QCD multijet events with a false
electron, respectively.
2. t
t → W
+
W
−
bb → eνjjX
Since no limit on the number of jets is applied to retain high efficiency, tt → W
+
W
−
bb →
eνjjX events contribute to the candidate sample. A sample, simulated using isajet with
M
t
= 170 GeV/c
2
, is used to estimate this contribution. We find it to be small, 3.7 ± 0.3
(stat) ± 1 .3 (sys) events. The production cross section for t
¯
t events is taken from the DØ
measurement (5.2 ± 1.8 pb) [32]. The error in this measurement (35%) is included as a
systematic uncertainty in our analysis.
26

p
T
(eν)-p
T
(jj)
(a)
0
10
20
30
40
50
60
70
-100 -80 -60 -40 -20 0 20 40 60 80 100
Data
W+≥2j + multijets
GeV/c
Nevt/ 2 GeV/c
∆R(jj)
(b)
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10
Data
W+≥2j + multijets
Nevt/0.2
FIG. 9. (a) Distributions in p
T
(eν) −p
T
(jj) before imposition of the mass window on M
jj
. (b)
Distributions for the separation of two jets in η − φ space.
3. W W/W Z → τνjj → eννjj
Since the contribution from W W/W Z → τνjj → eννjj is small, and no separate
simulation of the signal is available, we treat it as background. We use the isajet event
generator and the detailed detector simulation program to estimate this source. The W W
and W Z production cross sections are assumed to be 9.5 pb and 2.5 pb, respectively. After
event selection, we find 0.15
+0.16
−0.08
(stat) ± 0.01 (sys) events. The systematic uncertainty on
the background estimate is assigned to have the larger value of the asymmetric errors on
the theoretical cross section (8.4%) [29].
4. ZX → e
+
e
−
X
The ZX → eeX processes can produce events that can be misidentified as signal. These
events can be included in the candidate sample if one electron goes through a boundary in
a calorimeter module and is measured as /E
T
in the event. From a sample of 10,000 isajet
ZX → e
+
e
−
X events generated, none survive the selection pro cedure. The background
from events of this type is therefore negligible.
27

5. ZX → τ
+
τ
−
X → eνjjX
The ZX → ττX processes can also produce events that can be mistaken for signal if ,
due to shower fluctuation, one or two jets from ISR or FSR are observed in the detector.
From a sample of 10,000 pythia-generated ZX → ττX events, none survive our selection.
The background from this source is therefore also negligible.
IX. RESULTS
A total of 399 candidate events remain after all selections. The number of events expected
from SM W W/W Z and from SM background processes are 17.5 ± 3.0 and 387.5 ± 38.1,
respectively. The transverse mass distribution of the candidate events is shown in Fig. 10,
along with the contributions from background and t he SM production of W W/W Z. The
distributions for data a gree well with expectations fr om background. Table IV summarizes
the number of candidate events, the estimated backgrounds, and SM predictions for the Run
1a and 1b data samples.
TABLE IV. Number of events for backgrounds , data and SM pr ed iction for Run 1a and Run 1b.
Run 1a [11] Run 1b
Luminosity 13.7 pb
−1
82.3 pb
−1
Background
QCD multijet 12.2± 2.6 104.3±12.3
W + ≥ 2 jets 62.2±13.0 279.5±36.0
t
¯
t → eνjj + X 0.87±0.12 3.7± 1.3
Total background 75.5±13.3 387.5±38.1
Data 84 399
W W +W Z (SM prediction) 3.2±0.6 17.5±3.0
Figure 11 shows the p
T
distributions of the eν system for data, background estimates,
and SM predictions. We do not observe a statistically significant signal above background.
Of the 399 events that satisfy the selection criteria, 18 events have p
T
(eν) > 100 GeV/c.
The numbers of background and SM events in this p
T
range are estimated as 18.5 ±1.8 and
3.2 ± 0.5, respectively. The absence of an excess of events with high p
T
(eν) excludes large
deviations from SM couplings.
A. Limits on Anomalous Couplings Using Minimum p
W
T
The W W/W Z production cross section increases, especially at high p
W
T
, as the coupling
parameters deviate from the SM values, as shown in Fig. 2. The p
W
T
distribution for back-
ground is softer than that of W W/W Z production with anomalous couplings. When events
28

M
T
(eν)
0
20
40
60
80
100
120
0 20 40 60 80 100 120 140 160 180 200
Data
W +≥ 2 j + multijets
ISAJET WW/WZ SMx10
GeV /c
2
Nevt / 5 GeV/c
2
FIG. 10. Transverse-mass distributions of the electron and ν ( /E
T
) system. The solid circles,
solid histogram, and dotted histogram are, respectively, the candidate events, the background from
QCD multijet events with false electrons and W + ≥ 2 jet events, and the expected SM production
of W W/W Z events scaled up by a factor of ten.
0
20
40
60
80
100
0 50 100 150 200 250
p
T
(W→eν) GeV/c
Nevts/10 GeV/c
FIG. 11. The p
T
distributions of the eν system from the 1993–1995 (Run 1b) data. The solid
circles are data. The light-shaded histogram is the SM prediction for the b ackground, including
the dark-shaded histogram, which represents the SM prediction for W W/W Z processes.
are selected with p
W
T
above some large minimum value, almost all background events are
rejected, but a good fraction of signal with anomalo us couplings remains, providing better
sensitivity to such couplings. This kind of selection eliminates most of SM production, and
therefore does not have sensitivity to the SM couplings. Moreover the 95% C.L. upper limit
on the number of signal events (N
95%C.L.
) can be obtained from the observed number of
candidate events and the expected background beyond some minimum p
W
T
cutoff, using the
method described in the report by the Par ticle Da t a Group [4]. To do this, Mont e Carlo
events ar e generated for pairs of anomalous couplings in grid points of ∆κ and λ. We as-
sume that the couplings for W W γ and W W Z are equal. The expected number of events
for each pair of anomalous couplings is calculated using the integrated luminosity of the
data sample, and entered into a two-dimensional density plot with ∆κ and λ as coordinate
axes. The results are fitted with a two-dimensional parabolic function, and limits on anoma-
lous couplings are calculated at the 95% C.L. from the intersection of the two-dimensional
parabolic surface for the predicted number of events with a plane of N
95%C.L.
values. The
resulting contour of constant probability is an ellipse in the ∆κ − λ plane. The numerical
values for the “one-dimensional” 95% C.L. limits (setting one of the coordinates to zero) are
29

summarized in Table V for different minimum values of p
W
T
.
TABLE V. Limits on λ and ∆κ at the 95% C.L. as a function of m inimum p
W
T
, for Λ = 1.5
TeV. The number of candidates (N
cand
), background (N
BG
), and the SM W W/W Z predictions
(N
SM
) are also listed.
p
W
T
(GeV/c) N
cand
N
BG
N
SM
λ ∆κ
events events events (∆κ = 0) (λ = 0)
150 4 2.8 1.9 (−0.66, 0.67) (−0.96, 1.08)
160 1 2.1 1.8 (−0.54, 0.54) (−0.79, 0.89)
170 0 1.5 0.9 (−0.52, 0.52) (−0.76, 0.86)
180 0 1.2 0.2 (−0.59, 0.58) (−0.87, 0.96)
190 0 0.7 0.1 (−0.64, 0.64) (−0.96, 1.05)
200 0 0.3 0.1 (−0.74, 0.73) (−1.13, 1.20)
B. Limits on Anomalous Couplings from the p
W
T
Spectrum
The limits obta ined for some cutoff minimum p
W
T
do not take into account information
that is available in the full p
W
T
spectrum, and depend on the chosen minimum p
T
value as
well as on the overall normalization factors f or background and predictions for signal. An
alternative way to proceed is to fit the shape of kinematical distributions that are sensitive
to anomalous couplings. This usually provides tighter limits, since it uses all the information
contained in the differential distributions, a nd it is also less sensitive to overall nor malization
factors.
As described in Sec. I, the differential distribution that is most sensitive to anomalous
couplings is the p
W (Z)
T
distribution. Our analysis relies on the p
T
(W → eν) spectrum rather
than p
T
(W → jj) or p
T
(Z → jj) because the resolution on p
T
(eν) (12.5 GeV/c) is better
than on p
T
(jj) (16.7 GeV/c). This is primarily due to the ambiguity in assigning jets to the
W (Z) boson.
The differential cross sections have been exploited by previous publications
[9–11,13–16,18,19] for extracting limits on trilinear gauge boson couplings. We use a mod-
ified fit to the binned p
W
T
distribution to obtain limits, with the modification consisting of
adding an extra bin in p
W
T
with no observed events, thereby improving the sensitivity to
anomalous couplings [33].
Based on the number of expected W W/W Z → eνjj events, we choose two 25 GeV/c
bins between 0 and 50 G eV/c, five 10 GeV/c bins from 50 to 100 GeV/c, two 20 GeV/c bins
from 100 to 140 GeV/c, one 30 GeV/c bin from 140 to 170 GeV/c, and a single bin from 170
GeV/c to 500 GeV/c. The cross section for p
W
T
> 500 GeV/c is negligible for any anomalous
couplings allowed by unitarity. For each bin i of p
W
T
, the probability P
i
for observing N
i
30

events is given by the Poisson distribution:
P
i
=
(b
i
+ Lǫ
i
σ
i
(λ, ∆κ))
N
i
N
i
!
e
−(b
i
+Lǫ
i
σ
i
(λ,∆κ))
,
where L is the luminosity, and b
i
, ǫ
i
, and and σ
i
are the expected background, the total
detection efficiency, and the cross section, respectively, for bin i. Our fast Monte Carlo is
used to calculate ǫ
i
σ
i
(λ, ∆κ). The joint probability for all p
W
T
bins is the product of the
individual probabilities P
i
, P =
Q
N
bin
i=1
P
i
. Since the values L, b
i
, and ǫ
i
are measured values
with their respective uncertainties, we assign them Gaussian prior distributions of mean
µ = 1 and standard deviation σ
x
:
P
′
=
Z
G
f
n
df
n
Z
G
f
b
df
b
N
bin
Y
i=1
e
f
n
n
i
+f
b
b
i
(f
n
n
i
+ f
b
b
i
)
N
i
N
i
!
,
where n
i
= Lǫ
i
σ
i
is the predicted number of signal events, and G
f
n
and G
f
b
are Gaussian
distributions for the fractions of signal and background events. The integrals are calculated
using 50 evenly spaced points between ±3 standard deviations. For convenience, the log of
the likelihood L = log P
′
is used in the fit and the set of couplings that best describes the
data is given by the point in the λ − ∆κ plane that maximizes the likelihood given in the
above equation.
It is conventional to quote the limits on one coupling when all the others are set to their
SM values. These “one-dimensional” limits a t the 95% C.L., assuming that the W W γ and
W W Z couplings are equal, are shown in Table VI. The limits are more stringent than those
obtained using the minimum p
W
T
method.
TABLE VI. Limits on anomalous trilinear gauge boson couplings at the 95% C.L. for three
values of Λ obtained using the fit to p
W
T
for data from the Run 1b.
Couplings Λ = 1.0 TeV Λ = 1.5 TeV Λ = 2.0 TeV
λ
γ
= λ
Z
(∆κ
γ
= ∆κ
Z
= 0) −0.50, 0.53 −0.42, 0.45 −0.39, 0.42
∆κ
γ
= ∆κ
Z
(λ
γ
= λ
Z
= 0) −0.66, 0.90 −0.56, 0.75 −0.52, 0.70
λ
γ
(HISZ) (∆κ
γ
= 0) −0.50, 0.53 −0.42, 0.45 −0.39, 0.42
∆κ
γ
(HISZ) (λ
γ
= 0) −0.78, 1.15 −0.68, 0.98 −0.63, 0.91
λ
γ
(SM W W Z) (∆κ
γ
= 0) −1.54, 1.58 −1.53, 1.56
∆κ
γ
(SM W W Z) (λ
γ
= 0) −2.03, 2.45 −1.79, 2.12
λ
Z
(SM W W γ) (∆κ
Z
= ∆g
Z
1
= 0) −0.58, 0.62 −0.49, 0.51 −0.45, 0.48
∆κ
Z
(SM W W γ) (λ
Z
= ∆g
Z
1
= 0) −0.86, 1.12 −0.72, 0.93 −0.67, 0.87
We have assumed thus far that the couplings ∆κ and λ for W W Z and W W γ are equal.
However, this is not the only possibility. Another common assumption leads to the HISZ
relations [34]. These relations specify λ
Z
, κ
Z
, and g
Z
1
in terms of the independent variables
λ
γ
and κ
γ
, thereby reducing the number of independent couplings from five to two: ∆κ
Z
=
31

1
2
∆κ
γ
(1 − tan
2
θ
W
), ∆g
Z
1
=
1
2
∆κ
γ
/ cos
2
θ
W
, and λ
Z
= λ
γ
. These one-dimensional limits at
the 95% C.L. are also shown in Table VI.
Since the W W Z and W W γ couplings are independent, it is interesting to find the limits
on one when the other is set to its SM values. Table VI includes the one-dimensional limits
at the 95% C.L. for both assumptions: limits on ∆κ
γ
and λ
γ
when the W W Z couplings
are assumed to be standard, and limits on ∆κ
Z
and λ
Z
when the W W γ couplings are
assumed to be standard. These results indicate that our analysis is more sensitive to W W Z
couplings, as should be expected fr om the la r ger overall SM couplings for W W Z than for
W W γ, and that our analysis is complementary to studies of the W γ production process
which is sensitive only to the W W γ couplings.
C. Combined Results for Run 1 on W W/W Z → eνjj
The limits on anomalous couplings presented in this paper are significantly tighter than
those in our previous publications [11,1 5]. The primary reason for this is the increase in the
amount of data (about a factor of six). We can obtain even stronger limits by combining
the results from R un 1a and 1b. The ana lysis based on the Run 1a data is described in
Refs [11,15]. A summary of the signal and backgrounds for the two analyses [18] is given in
Table IV.
The two analyses can be treated as different experiments. However, because both ex-
periments used the same detector, there are certain correlated uncertainties, such as the
uncertainties on the luminosity, lepton reconstruction and identification, and the theoretical
prediction. Also, the background estimate is common to each experiment. The uncertainty
on the W/Z → jj selection efficiency is assumed to be uncorrelated, since we use differ-
ent cone sizes for jet reconstruction in the two ana lyses. (This hypothesis does not affect
the results in any significant way.) The uncertainties for both analyses are summarized in
Tables VII and VIII. Each uncertainty is weighted by the integrated luminosity for the
respective data sample. Figure 12 shows the combined p
W
T
spectrum.
TABLE VII. Common sys tematic uncertainties for Run 1a and Run 1b analyses.
Source of Uncertainty
Luminosity 5.4%
QCD corrections 14%
Electron and trigger efficiency 1.2%
Statistics of fast MC 1%
/E
T
smearing 5.1%
Jet energy scale 3.4%
Total 16%
To set limits on anomalous couplings, we combine the results of the two analyses by calcu-
lating a combined likelihood function. The individual uncertainties on signal and background
32

TABLE VIII. Uncorrelated systematic uncertainties for Run 1a and Run 1b analyses.
Source of Uncertainty Run 1a Run 1b
isajet vs pythia 9% 4%
Stat. uncertainties of ǫ(W → jj) 4% 2%
Parametrization of ǫ
i
σ
i
(λ, ∆κ) 4% 5%
Total (added in quadrature) 11% 7%
Background 13% 7%
0
20
40
60
80
100
0 50 100 150 200 250
p
T
(W→eν) GeV/c
Nevts/10 GeV/c
FIG. 12. The p
W
T
spectrum f or eνjj candidates for the full Run 1 data sample. The solid circles
are data. The light-shaded histogram is the sum of predictions from the SM and b ackground, and
the dark-shaded histogram is the SM prediction for W W/W Z processes alone.
for each analysis are taken into account as in the previous section. Common systematic un-
certainties are taken into account by introducing a common Gaussian prior distribution for
the two data samples.
Combining results from Run 1a and Run 1b yields the 95% C.L. contours of constant
probability shown in Fig. 13. The one and two dimensional 95 % C.L. contour limits (corre-
sponding to log-likelihood values of 1.92 and 3.00 units below the maximum, respectively)
are shown as the inner contours, along with the unitarity limits from the S-matrix, shown
as the outermost contours. Figure 1 3(a) shows the contour limits when couplings for W W γ
are assumed to be equal to those for W W Z. Figure 13 ( b) shows contour limits a ssuming the
HISZ relations. In Figs. 13(c) and 13(d), SM W W γ couplings are assumed and the limits
are shown for W W Z couplings. Assuming SM W W γ couplings, the U(1) point that corre-
sponds to the condition in which there is no W W Z couplings (κ
Z
= 0, λ
Z
= 0, g
Z
1
= 0) is
excluded at the 99% C.L. This is direct evidence for the existence of W W Z couplings. These
limits are slightly stronger than those from the 1993–1995 data alone. The one-dimensional
95% C.L. limits for four assumptions on the relation between W W γ and W W Z couplings:
(i) ∆κ ≡ ∆κ
γ
= ∆κ
Z
, λ ≡ λ
γ
= λ
Z
, (ii) HISZ relations, (iii) SM W W γ couplings, and (iv)
SM W W Z couplings are listed in Table IX.
33

TABLE IX. Limits on anomalous trilinear gauge boson couplings at 95% C .L. from the com-
bined Run 1a and Run 1b data samples for these values of Λ.
Couplings Λ = 1.0 TeV Λ = 1.5 TeV Λ = 2.0 TeV
λ
γ
= λ
Z
(∆κ
γ
= ∆κ
Z
= 0) −0.42, 0.45 −0.36, 0.39 −0.34, 0.36
∆κ
γ
= ∆κ
Z
(λ
γ
= λ
Z
= 0) −0.55, 0.79 −0.47, 0.63 −0.43, 0.59
λ
γ
(HISZ) (∆κ
γ
= 0) −0.42, 0.45 −0.36, 0.39 −0.34, 0.36
∆κ
γ
(HISZ) (λ
γ
= 0) −0.69, 1.04 −0.56, 0.85 −0.53, 0.78
λ
γ
(SM W W Z) (∆κ
γ
= 0) −1.28, 1.33 −1.21, 1.25
∆κ
γ
(SM W W Z) (λ
γ
= 0) −1.60, 2.03 −1.38, 1.70
λ
Z
(SM W W γ) (∆κ
Z
= ∆g
Z
1
= 0) −0.47, 0.51 −0.40, 0.43 −0.37, 0.40
∆κ
Z
(SM W W γ) (λ
Z
= ∆g
Z
1
= 0) −0.74, 0.99 −0.60, 0.79 −0.54, 0.72
∆g
Z
1
(SM W W γ) (λ
Z
= ∆κ
Z
= 0) −0.75, 1.06 −0.64, 0.89 −0.60, 0.81
X. CONCLUSIONS
We have searched f or a no malous W W and W Z production in the eνjj decay mode at
√
s = 1.8 TeV. In a total of 82.3 pb
−1
of data from the 1993–1995 collider run at Fermilab,
we observe 399 candidate events with an expected background of 387.5±38.1 events. The
expected number of events from SM W W/W Z production is 17.5 ± 3.0 events fo r this
integrated luminosity. The sum of the SM prediction and the background estimates is
consistent with the observed number of events, indicating that no new physics phenomena is
seen. Comparing the p
W
T
distributions of the observed events with theoretical predictions, we
set limits on the W W γ and W W Z ano malous couplings. The limits on anomalous couplings
are significantly tighter than those using the 1992–1993 data sample. The two results are
combined to set even tighter limits on the anomalous couplings. With an assumption that
the W W γ and W W Z couplings are equal, we obtain −0.34 < λ < 0.36 (with ∆κ = 0) and
−0.43 < ∆κ < 0.59 (with λ = 0) at the 95% C.L. for a form factor scale Λ = 2.0 TeV [35].
XI. ACKNOWLEDGEMENTS
We thank the Fermilab and collaborating institution staffs for contributions to this work,
and acknowledge support from the Department of Energy and National Science Foundation
(USA), Commissariat `a L’Energie Atomique (France), Ministry for Science and Technol-
ogy and Ministry for Atomic Energy (Russia), CAPES and CNPq (Brazil), Departments
of Atomic Energy and Science and Education (India), Colciencias (Colombia), CONA-
CyT (Mexico), Ministry of Education and KOSEF (Korea), CONICET and UBACyT ( Ar-
gentina), A.P. Sloan Foundation, and the Humboldt Foundation.
34

-1
0
1
-1 0 1
SM
(a)
∆κ
λ
-1
0
1
-1 0 1
SM
(b)
∆κ
γ
λ
γ
-1
0
1
-1 0 1
SM
U(1)
(c)
∆κ
Z
λ
Z
-2
-1
0
1
2
-2 -1 0 1 2
SM
U(1)
(d)
∆κ
Z
∆g
Z
1
FIG. 13. Contour limits on anomalous couplings at the 95% C.L. (two inner curves) and un itary
constraints (outermost curves), assuming (a) ∆κ ≡ ∆κ
γ
= ∆κ
Z
, λ ≡ λ
γ
= λ
Z
; (b) HISZ relations;
(c) and (d) SM W W γ couplings. Λ = 1.5 TeV is used for all fou r cases. The U(1) point is the
expectation with no W W Z couplings.
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36

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37