VOLUME
82, NUMBER 12 PHYSICAL REVIEW LETTERS 22M
ARCH
1999
Inclusive Jet Cross Section in pp Collisions at
p
pp
s 5 1.8 TeV
B. Abbott,
40
M. Abolins,
37
V. Abramov,
15
B. S. Acharya,
8
I. Adam,
39
D.L. Adams,
48
M. Adams,
24
S. Ahn,
23
H. Aihara,
17
H. Alves,
2
N. Amos,
36
E. W. Anderson,
30
R. Astur,
42
M. M. Baarmand,
42
V.V. Babintsev,
15
L. Babukhadia,
16
A. Baden,
33
V. Balamurali,
28
B. Baldin,
23
S. Banerjee,
8
J. Bantly,
45
E. Barberis,
17
P. Baringer,
31
J.F. Bartlett,
23
A. Belyaev,
14
S. B. Beri,
6
I. Bertram,
26
V.A. Bezzubov,
15
P.C. Bhat,
23
V. Bhatnagar,
6
M. Bhattacharjee,
42
N. Biswas,
28
G. Blazey,
25
S. Blessing,
21
P. Bloom,
18
A. Boehnlein,
23
N.I. Bojko,
15
F. Borcherding,
23
C. Boswell,
20
A. Brandt,
23
R. Breedon,
18
R. Brock,
37
A. Bross,
23
D. Buchholz,
26
V.S. Burtovoi,
15
J.M. Butler,
34
W. Carvalho,
2
D. Casey,
37
Z. Casilum,
42
H. Castilla-Valdez,
11
D. Chakraborty,
42
S.-M. Chang,
35
S.V. Chekulaev,
15
L.-P. Chen,
17
W. Chen,
42
S. Choi,
10
S. Chopra,
36
B. C. Choudhary,
20
J. H. Christenson,
23
M. Chung,
24
D. Claes,
38
A.R. Clark,
17
W. G. Cobau,
33
J. Cochran,
20
L. Coney,
28
W.E. Cooper,
23
C. Cretsinger,
41
D. Cullen-Vidal,
45
M.A. C. Cummings,
25
D. Cutts,
45
O.I. Dahl,
17
K. Davis,
16
K. De,
46
K. Del Signore,
36
M. Demarteau,
23
D. Denisov,
23
S.P. Denisov,
15
H. T. Diehl,
23
M. Diesburg,
23
G. Di Loreto,
37
P. Draper,
46
Y. Ducros,
5
L.V. Dudko,
14
S.R. Dugad,
8
A. Dyshkant,
15
D. Edmunds,
37
J. Ellison,
20
V.D. Elvira,
42
R. Engelmann,
42
S. Eno,
33
G. Eppley,
48
P. Ermolov,
14
O.V. Eroshin,
15
V.N. Evdokimov,
15
T. Fahland,
19
M.K. Fatyga,
41
S. Feher,
23
D. Fein,
16
T. Ferbel,
41
G. Finocchiaro,
42
H.E. Fisk,
23
Y. Fisyak,
43
E. Flattum,
23
G.E. Forden,
16
M. Fortner,
25
K. C. Frame,
37
S. Fuess,
23
E. Gallas,
46
A.N. Galyaeav,
15
P. Gartung,
20
V. Gavrilov,
13
T. L. Geld,
37
R. J. Genik II,
37
K. Genser,
23
C. E. Gerber,
23
Y. Gershtein,
13
B. Gibbard,
43
B. Gobbi,
26
B. Gómez,
4
G. Gómez,
33
P. I. Goncharov,
15
J. L. González Solı
´
s,
11
H. Gordon,
43
L.T. Goss,
47
K. Gounder,
20
A. Goussiou,
42
N. Graf,
43
P. D. Grannis,
42
D. R. Green,
23
H. Greenlee,
23
S. Grinstein,
1
P. Grudberg,
17
S. Grünendahl,
23
G. Guglielmo,
44
J. A. Guida,
16
J. M. Guida,
45
A. Gupta,
8
S.N. Gurzhiev,
15
G. Gutierrez,
23
P. Gutierrez,
44
N.J. Hadley,
33
H. Haggerty,
23
S. Hagopian,
21
V. Hagopian,
21
K.S. Hahn,
41
R. E. Hall,
19
P. Hanlet,
35
S. Hansen,
23
J.M. Hauptman,
30
D. Hedin,
25
A.P. Heinson,
20
U. Heintz,
23
R. Hernández-Montoya,
11
T. Heuring,
21
R. Hirosky,
24
J. D. Hobbs,
42
B. Hoeneisen,
4,
* J. S. Hoftun,
45
F. Hsieh,
36
Ting Hu,
42
Tong Hu,
27
T. Huehn,
20
A.S. Ito,
23
E. James,
16
J. Jaques,
28
S.A. Jerger,
37
R. Jesik,
27
T. Joffe-Minor,
26
K. Johns,
16
M. Johnson,
23
A. Jonckheere,
23
M. Jones,
22
H. Jöstlein,
23
S.Y. Jun,
26
C. K. Jung,
42
S. Kahn,
43
G. Kalbfleisch,
44
D. Karmanov,
14
D. Karmgard,
21
R. Kehoe,
28
M. L. Kelly,
28
S.K. Kim,
10
B. Klima,
23
C. Klopfenstein,
18
W. Ko,
18
J. M. Kohli,
6
D. Koltick,
29
A.V. Kostritskiy,
15
J. Kotcher,
43
A.V. Kotwal,
39
A.V. Kozelov,
15
E. A. Kozlovsky,
15
J. Krane,
38
M.R. Krishnaswamy,
8
S. Krzywdzinski,
23
S. Kuleshov,
13
S. Kunori,
33
F. Landry,
37
G. Landsberg,
45
B. Lauer,
30
A. Leflat,
14
J. Li,
46
Q. Z. Li-Demarteau,
23
J.G.R. Lima,
3
D. Lincoln,
23
S.L. Linn,
21
J. Linnemann,
37
R. Lipton,
23
F. Lobkowicz,
41
S. C. Loken,
17
A. Lucotte,
42
L. Lueking,
23
A.L. Lyon,
33
A.K.A. Maciel,
2
R. J. Madaras,
17
R. Madden,
21
L. Magaña-Mendoza,
11
V. Manankov,
14
S. Mani,
18
H.S. Mao,
23,
†
R. Markeloff,
25
T. Marshall,
27
M.I. Martin,
23
K.M. Mauritz,
30
B. May,
26
A.A. Mayorov,
15
R. McCarthy,
42
J. McDonald,
21
T. McKibben,
24
J. McKinley,
37
T. McMahon,
44
H.L. Melanson,
23
M. Merkin,
14
K. W. Merritt,
23
C. Miao,
45
H. Miettinen,
48
A. Mincer,
40
C. S. Mishra,
23
N. Mokhov,
23
N.K. Mondal,
8
H. E. Montgomery,
23
P. Mooney,
4
M. Mostafa,
1
H. da Motta,
2
C. Murphy,
24
F. Nang,
16
M. Narain,
23
V. S. Narasimham,
8
A. Narayanan,
16
H. A. Neal,
36
J. P. Negret,
4
P. Nemethy,
40
D. Norman,
47
L. Oesch,
36
V. Oguri,
3
E. Oliveira,
2
E. Oltman,
17
N. Oshima,
23
D. Owen,
37
P. Padley,
48
A. Para,
23
Y.M. Park,
9
R. Partridge,
45
N. Parua,
8
M. Paterno,
41
B. Pawlik,
12
J. Perkins,
46
M. Peters,
22
R. Piegaia,
1
H. Piekarz,
21
Y. Pischalnikov,
29
B. G. Pope,
37
H.B. Prosper,
21
S. Protopopescu,
43
J. Qian,
36
P.Z. Quintas,
23
R. Raja,
23
S. Rajagopalan,
43
O. Ramirez,
24
S. Reucroft,
35
M. Rijssenbeek,
42
T. Rockwell,
37
M. Roco,
23
P. Rubinov,
26
R. Ruchti,
28
J. Rutherfoord,
16
A. Sánchez-Hernández,
11
A. Santoro,
2
L. Sawyer,
32
R. D. Schamberger,
42
H. Schellman,
26
J. Sculli,
40
E. Shabalina,
14
C. Shaffer,
21
H.C. Shankar,
8
R. K. Shivpuri,
7
M. Shupe,
16
H. Singh,
20
J. B. Singh,
6
V. Sirotenko,
25
E. Smith,
44
R. P. Smith,
23
R. Snihur,
26
G.R. Snow,
38
J. Snow,
44
S. Snyder,
43
J. Solomon,
24
M. Sosebee,
46
N. Sotnikova,
14
M. Souza,
2
A.L. Spadafora,
17
G. Steinbrück,
44
R. W. Stephens,
46
M.L. Stevenson,
17
D. Stewart,
36
F. Stichelbaut,
42
D. Stoker,
19
V. Stolin,
13
D. A. Stoyanova,
15
M. Strauss,
44
K. Streets,
40
M. Strovink,
17
A. Sznajder,
2
P. Tamburello,
33
J. Tarazi,
19
M. Tartaglia,
23
T. L.T. Thomas,
26
J. Thompson,
33
T. G. Trippe,
17
P. M. Tuts,
39
V. Vaniev,
15
N. Varelas,
24
E. W. Varnes,
17
D. Vititoe,
16
A.A. Volkov,
15
A. P. Vorobiev,
15
H.D. Wahl,
21
G. Wang,
21
J. Warchol,
28
G. Watts,
45
M. Wayne,
28
H. Weerts,
37
A. White,
46
J.T. White,
47
J. A. Wightman,
30
S. Willis,
25
S.J. Wimpenny,
20
J. V. D. Wirjawan,
47
J. Womersley,
23
E. Won,
41
D. R. Wood,
35
Z. Wu,
23,
†
H. Xu,
45
R. Yamada,
23
P. Yamin,
43
T. Yasuda,
35
P. Yepes,
48
K. Yip,
23
C. Yoshikawa,
22
S. Youssef,
21
J. Yu,
23
Y. Yu,
10
B. Zhang,
23,
†
Y. Zhou,
23,
†
Z. Zhou,
30
Z.H. Zhu,
41
M. Zielinski,
41
D. Zieminska,
27
A. Zieminski,
27
E.G. Zverev,
14
and A. Zylberstejn
5
0031-9007y99y82(12)y2451(6)$15.00 © 1999 The American Physical Society 2451
VOLUME
82, NUMBER 12 PHYSICAL REVIEW LETTERS 22M
ARCH
1999
(D0 Collaboration)
1
Universidad de Buenos Aires, Buenos Aires, Argentina
2
LAFEX, Centro Brasileiro de Pesquisas Fı
´
sicas, Rio de Janeiro, Brazil
3
Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
4
Universidad de los Andes, Bogotá, Colombia
5
DAPNIA/Service de Physique des Particules, CEA, Saclay, France
6
Panjab University, Chandigarh, India
7
Delhi University, Delhi, India
8
Tata Institute of Fundamental Research, Mumbai, India
9
Kyungsung University, Pusan, Korea
10
Seoul National University, Seoul, Korea
11
CINVESTAV, Mexico City, Mexico
12
Institute of Nuclear Physics, Kraków, Poland
13
Institute for Theoretical and Experimental Physics, Moscow, Russia
14
Moscow State University, Moscow, Russia
15
Institute for High Energy Physics, Protvino, Russia
16
University of Arizona, Tucson, Arizona 85721
17
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720
18
University of California, Davis, California 95616
19
University of California, Irvine, California 92697
20
University of California, Riverside, California 92521
21
Florida State University, Tallahassee, Florida 32306
22
University of Hawaii, Honolulu, Hawaii 96822
23
Fermi National Accelerator Laboratory, Batavia, Illinois 60510
24
University of Illinois at Chicago, Chicago, Illinois 60607
25
Northern Illinois University, DeKalb, Illinois 60115
26
Northwestern University, Evanston, Illinois 60208
27
Indiana University, Bloomington, Indiana 47405
28
University of Notre Dame, Notre Dame, Indiana 46556
29
Purdue University, West Lafayette, Indiana 47907
30
Iowa State University, Ames, Iowa 50011
31
University of Kansas, Lawrence, Kansas 66045
32
Louisiana Tech University, Ruston, Louisiana 71272
33
University of Maryland, College Park, Maryland 20742
34
Boston University, Boston, Massachusetts 02215
35
Northeastern University, Boston, Massachusetts 02115
36
University of Michigan, Ann Arbor, Michigan 48109
37
Michigan State University, East Lansing, Michigan 48824
38
University of Nebraska, Lincoln, Nebraska 68588
39
Columbia University, New York, New York 10027
40
New York University, New York, New York 10003
41
University of Rochester, Rochester, New York 14627
42
State University of New York, Stony Brook, New York 11794
43
Brookhaven National Laboratory, Upton, New York 11973
44
University of Oklahoma, Norman, Oklahoma 73019
45
Brown University, Providence, Rhode Island 02912
46
University of Texas, Arlington, Texas 76019
47
Texas A&M University, College Station, Texas 77843
48
Rice University, Houston, Texas 77005
(
Received 17 July 1998)
We have made a precise measurement of the central inclusive jet cross section at
p
s 1.8 TeV.
The measurement is based on an integrated luminosity of 92 pb
21
collected at the Fermilab Tevatron
pp Collider with the D0 detector. The cross section, reported as a function of jet transverse energy
sE
T
$ 60 GeVd in the pseudorapidity interval jhj # 0.5, is in good agreement with predictions from
next-to-leading order quantum chromodynamics. [S0031-9007(99)08800-6]
PACS numbers: 13.87.Ce, 12.38.Qk
Within the framework of quantum chromodynamics
(QCD), inelastic scattering between a proton and an an-
tiproton can be described as an elastic collision between
a single proton constituent and a single antiproton con-
stituent. These constituents are often referred to as par-
tons. After the collision, the outgoing partons manifest
2452
VOLUME
82, NUMBER 12 PHYSICAL REVIEW LETTERS 22M
ARCH
1999
themselves as localized streams of particles or “jets.” Pre-
dictions for the inclusive jet cross section are given by
the folding of parton scattering cross sections with experi-
mentally determined parton distribution functions (pdf’s).
These predictions have recently improved with next-to-
leading order (NLO) QCD scattering calculations [1–3]
and new, accurately measured pdf’s [4,5]. We measure
the cross section for the production of jets as a function
of the jet energy in the plane transverse to the incident
beams, E
T
. The measurement is based on an integrated
luminosity of 92 pb
21
[6] of
pp collisions collected with
the D0 detector [7] at the Fermilab Tevatron Collider.
Measurements of inclusive jet production with smaller in-
tegrated luminosity have been performed previously by
the UA2 and CDF Collaborations [8,9]. The cross sec-
tion measurement presented here allows a stringent test of
QCD, with a total uncertainty substantially reduced rela-
tive to previous results.
Jet detection in the D0 detector utilizes primarily the
uranium-liquid argon calorimeters which have full cov-
erage for pseudorapidity jhj # 4.1 (h 2lnftansuy2dg,
where u is the polar angle relative to the proton beam).
Initial event selection occurred in two hardware trigger
stages and a software stage. The first hardware trigger
selected an inelastic
pp collision—indicated by signals
from the trigger hodoscopes located near the beams on ei-
ther side of the interaction region. The next stage required
transverse energy above a preset threshold in calorime-
ter trigger tiles of Dh 3 Df 0.8 3 1.6, where f is
the azimuthal angle. Selected events were digitized and
sent to an array of processors. Jet candidates were then
reconstructed with a cone algorithm and the entire event
recorded if any jet E
T
exceeded a specified threshold. For
software jet thresholds of 30, 50, 85, and 115 GeV, inte-
grated luminosities of 0.34, 4.6, 55, and 92 pb
21
, respec-
tively, were accumulated in a 1994–1995 data run.
Jets were reconstructed off-line using an iterative fixed-
cone algorithm with a cone radius of R 0.7 in h-f
space [10]. Background from isolated noisy calorime-
ter cells and accelerator beam losses which mimicked
jets were eliminated with quality cuts [11]. Background
events from cosmic ray bremsstrahlung or misvertexed
events were eliminated by requiring the missing trans-
verse energy in each event to be less than the larger of
30 GeV or 0.3E
max
T
, where E
max
T
is the E
T
of the leading
jet. Residual jet contamination is less than 1% at all E
T
,
based on event simulations with superimposed calorime-
ter noise distributions and on visual scanning of jet can-
didates with E
T
greater than 350 GeV. The jet selection
efficiency for jhj # 0.7 has been measured as a function
of jet E
T
and found to be s97 6 1d% below 250 GeV and
decreasing smoothly to s95 6 2d% at 400 GeV.
At high instantaneous luminosity, more than one inter-
action in a single beam crossing is probable (,20% for
this data set). The event vertex was reconstructed using
data from the central tracking system. For events with
multiple vertices, the two vertices with the largest number
of tracks were retained. Because of the fluctuations of jet
charged-particle multiplicity, an additional parameter was
used to select the vertex. If an event had more than one
vertex, the quantity S
T
jS
$
E
jet
T
j was calculated for both
vertices. The vertex with the smaller S
T
was selected as
the event vertex and used to calculate jet E
T
and h. The
selected vertex was required to be within 50 cm of the de-
tector center. This last requirement retained s90 6 1d%
of the events, independent of jet E
T
.
The transverse energy of each jet was corrected for
the underlying event, additional interactions, noise from
uranium decay, the fraction of particle energy showered
outside of the reconstruction cone, detector uniformity,
and detector hadronic response. A complete discussion
of the jet energy scale calibration can be found in
Ref. [12]. For jhj # 0.5, the mean total correction factor
for jet E
T
is 1.154 6 0.017 f1.118 6 0.023g at 100 GeV
[400 GeV].
The inclusive jet cross section was computed in con-
tiguous E
T
ranges using data from the four trigger sets.
The spectrum includes data from the 30 GeV trigger be-
tween 60 and 90 GeV, from the 50 GeV E
T
trigger
between 90 and 130 GeV, from the 85 GeV trigger be-
tween 130 and 170 GeV, and above 170 GeV from the
115 GeV trigger. A single interaction (per beam cross-
ing) requirement on the two lowest-E
T
triggers introduced
an inefficiency corrected by matching the 50 GeV trigger
cross section to the 85 GeV trigger cross section above
130 GeV, where both triggers are fully efficient. This
introduces an additional 1.1% luminosity uncertainty to
the 50 GeV trigger set. A similar matching between the
lowest-E
T
trigger and the 50 GeV trigger introduces an-
other 1.4% uncertainty for the lower set, which is added
in quadrature to the 1.1% matching uncertainty.
The steep E
T
spectrum is distorted by jet energy reso-
lution. At all E
T
, the resolution (measured by balancing
E
T
in jet events) is well described by a Gaussian distri-
bution; at 100 GeV the standard deviation is 7 GeV. The
distortion was corrected by assuming an ansatz function
sAE
2B
T
ds1 2 2E
T
y
p
sd
C
, smearing it with the measured
resolution and comparing the smeared result with the mea-
sured cross section. The procedure was repeated by vary-
ing parameters A, B, and C until the best fit was found
between the observed cross section and the smeared trial
spectrum. The ratio of the initial ansatz to the smeared
ansatz was used to correct the cross section on a bin-by-
bin basis [13]. The resolution correction reduces the ob-
served cross section by s13 6 3d% fs8 6 2d%g at 60 GeV
[400 GeV].
The resulting inclusive jet cross section for jhj #
0.5, shown in Fig. 1, has been averaged over each E
T
bin sDE
T
d and over the central unit of rapidity sDh
1d. This bin-averaged double differential cross section,
kd
2
sysdE
T
dhdl, was calculated as NCysDE
T
DheLd
where N is the total number of jets observed in a bin,
2453
VOLUME
82, NUMBER 12 PHYSICAL REVIEW LETTERS 22M
ARCH
1999
FIG. 1. The jhj # 0.5 inclusive cross section. Statistical
uncertainties are invisible on this scale. The solid curves
represent the 61s systematic uncertainty band on the data.
C the smearing correction, e the selection efficiency, and
L the integrated luminosity associated with the trigger
set. The cross section is consistent with a preliminary
measurement from a smaller 1992–1993 data set [11].
Figure 1 also shows a theoretical prediction for the
cross section from the NLO event generator
JETRAD [3].
There is good agreement over 7 orders of magnitude.
Inputs to the NLO calculation are the renormalization
scale m (equal to the factorization scale), the pdf, and the
parton clustering algorithm. For the calculation shown
here, m 0.5E
max
T
and the pdf is CTEQ3M [4]. Partons
separated by less than R
sep
1.3R were clustered if
they were also within R 0.7 of their E
T
-weighted h-f
centroid. This choice of R
sep
is discussed in Ref. [10].
Variations in the predicted cross section due to the input
choices are about 30% [14].
The data in Fig. 1 have an overall luminosity uncer-
tainty of 6.1%, and are plotted at the E
T
value for which
a smooth function describing the cross section is equal to
the average cross section in each bin. The band shows the
total systematic uncertainty as a function of E
T
. Listed
in Table I are the plotted values of E
T
, E
T
ranges, cross
section, and statistical and systematic uncertainty. The
systematic uncertainties include jet and event selection,
unsmearing, relative luminosity, and energy scale uncer-
tainties added in quadrature. The 6.1% luminosity uncer-
tainty is not included.
Figure 2 shows the various uncertainties for the jhj #
0.5 cross section. Each curve represents the average of
the nearly symmetric upper and lower uncertainties. The
energy scale uncertainty varies from 8% at low E
T
to
TABLE I. The jhj , 0.5 cross section (overall luminosity
uncertainty not included).
Plotted E
T
Bin range Cross sec. 6 stat. Syst.
(GeV) (GeV)
sfbyGeVd
Uncer. (%)
64.6 60–70
s6.59 6 0.04d 3 10
6
68
74.6 70–80
s2.89 6 0.03d 3 10
6
68
84.7 80–90
s1.41 6 0.02d 3 10
6
68
94.7 90–100
s7.07 6 0.04d 3 10
5
68
104.7 100–110
s3.88 6 0.03d 3 10
5
68
114.8 110–120
s2.21 6 0.02d 3 10
5
68
124.8 120–130
s1.27 6 0.02d 3 10
5
68
134.8 130–140
s7.70 6 0.04d 3 10
4
68
144.8 140–150
s4.86 6 0.03d 3 10
4
68
154.8 150–160
s3.07 6 0.02d 3 10
4
19, 28
164.8 160–170
s2.00 6 0.02d 3 10
4
69
174.8 170–180
s1.34 6 0.01d 3 10
4
69
184.8 180–190
s9.12 6 0.10d 3 10
3
69
194.8 190–200
s6.15 6 0.09d 3 10
3
110, 29
204.8 200–210
s4.29 6 0.07d 3 10
3
610
214.8 210–220
s2.93 6 0.06d 3 10
3
111, 210
224.8 220–230
s2.14 6 0.05d 3 10
3
111, 210
239.4 230–250
s1.30 6 0.03d 3 10
3
611
259.4 250–270
s6.54 6 0.20d 3 10
2
112, 211
279.5 270–290
s3.77 6 0.15d 3 10
2
113, 212
303.9 290–320
s1.79 6 0.08d 3 10
2
115, 213
333.9 320–350
s6.82 6 0.52d 3 10
1
117, 215
375.5 350–410
s1.89 6 0.19d 3 10
1
120, 217
461.1 410–560
s1.24 6 0.31d 3 10
0
130, 226
30% at 450 GeV. This contribution dominates all other
sources of uncertainty, except at low E
T
, where the 6.1%
luminosity uncertainty is of a comparable magnitude.
The jhj # 0.5 region provides our optimum test for
departures of data from NLO QCD. In this region, the
detector is uniformly thick (seven or more interaction
lengths with no gaps) and both jet resolution and cali-
bration are precise. Also, jet production from the scat-
tering of possible constituents within quarks is largest for
h 0, relative to standard QCD predictions [15]. For
comparison to Ref. [9], we have also carried out a similar
E
T
(GeV)
Cross Section Uncertainty (%)
Total Error
Energy Scale (partially correlated)
Overall Luminosity (fully correlated)
Relative Luminosity (partially correlated)
Resolution (fully correlated)
Jet Selection (fully correlated)
0
5
10
15
20
25
30
35
50 100 150 200 250 300 350 400 450
FIG. 2. Contributions to the jhj # 0.5 cross section uncer-
tainty plotted by component.
2454
VOLUME
82, NUMBER 12 PHYSICAL REVIEW LETTERS 22M
ARCH
1999
|η
jet
| < 0.5
CTEQ3M
(Data-Theory)/Theory
CTEQ4M
E
T
(GeV)
MRST
-0.25
0
0.25
-0.25
0
0.25
-0.25
0
0.25
0.5
50 100 150 200 250 300 350 400 450
FIG. 3. The difference between data and JETRAD QCD predic-
tions normalized to predictions. The bands represent the total
experimental uncertainty.
analysis for 0.1 # jhj # 0.7. Figure 3 shows the ratios
sD 2 T dyT for the data sDd and
JETRAD NLO theoretical
sTd predictions based on the CTEQ3M, CTEQ4M, and
MRST pdf’s [4,5] for jhj # 0.5. Given the experimental
and theoretical uncertainties, the predictions are in agree-
ment with the data; in particular, the data above 350 GeV
show no indication of an excess relative to QCD.
The data and theory can be compared quantitatively
with a x
2
test incorporating the uncertainty covariance
matrix. The matrix elements are constructed from the sta-
tistical and systematic uncertainties and by analyzing the
mutual correlation of the uncertainties in Fig. 2 at each
pair of E
T
values. As indicated by the figure the over-
all systematic uncertainty is highly correlated from bin
to bin. Table II shows that the bin-to-bin correlations in
the full uncertainty for representative E
T
bins are greater
than 40% and positive. (The full matrix can be found in
Ref. [16].)
Table III lists x
2
values for several JETRAD predictions
incorporating various parton distribution functions [4,5].
Each comparison has 24 degrees of freedom. The
JETRAD
predictions have been fit to a smooth function of E
T
. All
five predictions describe the jhj # 0.5 cross section very
well (the probabilities for x
2
to exceed the listed values
are between 47% and 90%). The 0.1 # jhj # 0.7 cross
section is also well described (probabilities between 24%
and 72%). We have also made comparisons between the
jhj # 0.5 data and Ellis-Kunszt-Soper (EKS) [1] calcu-
lations using CTEQ3M, R
sep
1.3R, and with renor-
malization scales m 0.25E
max
T
, 0.50E
max
T
, and 1.00E
max
T
TABLE II. Cross section total uncertainty correlations.
E
T
sGeVd
64.6 104.7 204.8 303.9 461.1
64.6 1.00 0.96 0.85 0.71 0.40
104.7 0.96 1.00 0.92 0.79 0.46
204.8 0.85 0.92 1.00 0.91 0.61
303.9 0.71 0.79 0.91 1.00 0.67
461.1 0.40 0.46 0.61 0.67 1.00
TABLE III. x
2
comparisons between JETRAD and jhj # 0.5
and 0.1 # jhj # 0.7 data for m 0.5E
max
T
, R
sep
1.3R and
various pdfs. There are 24 degrees of freedom.
pdf
jhj # 0.5 0.1 # jhj # 0.7
CTEQ3M 23.9 28.4
CTEQ4M 17.6 23.3
CTEQ4HJ 15.7 20.5
MRSA
0
20.0 27.8
MRST 17.0 19.5
and m 0.25E
jet
T
, 0.50E
jet
T
, and 1.00E
jet
T
. These calcula-
tions also describe the data very well (better than 57%
probability) at all renormalization scales.
The top panel in Fig. 4 shows sD 2 T dyT for our
data in the 0.1 # jhj # 0.7 region relative to an EKS
calculation using the CTEQ3M pdf, m 0.5E
jet
T
, and
R
sep
2.0R. (The tabulated data can be found in
Ref. [16].) Also shown are the data of Ref. [9] relative
to the same EKS prediction. For this rapidity region,
we have carried out a x
2
comparison between our data
and the nominal curve describing the central values of
the data of Ref. [9]. Comparing our data to the nominal
curve, as though it were theory, we obtain a x
2
of 63.2 for
24 degrees of freedom (probability of 0.002%). Thus our
data cannot be described with this parametrization. As
illustrated in the bottom panel of Fig. 4, our data and the
curve differ at low and high E
T
; such differences cannot
be accommodated by the highly correlated uncertainties
of our data. If we include the systematic uncertainties of
the data of Ref. [9] in the covariance matrix, the x
2
is
reduced to 24.7 (probability of 42%).
In conclusion, we have made the most precise mea-
surement to date of the inclusive jet cross section for
E
T
$ 60 GeV. QCD predictions are in good agreement
with the observed cross section for standard parton dis-
tribution functions and different renormalization scales.
This is consistent with our previous measurements of
dijet angular distributions [15], which are also in good
FIG. 4. Top: Comparisons of our data to EKS and of the data
in Ref. [9] to EKS. See text for details. Bottom: Our data
minus smoothed results of Ref. [9] divided by the latter. The
band represents the uncertainty on our data.
2455
