Measurement of the Forward-Backward Charge Asymmetry and Extraction
of sin
2
eff
W
in p
p ! Z=
þ X ! e
þ
e
þ X Events Produced at
ffiffiffi
s
p
¼ 1:96 TeV
V. M. Abazov,
36
B. Abbott,
75
M. Abolins,
65
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29
M. Adams,
51
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49
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*
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PHYSICAL REVIEW LETTERS
week ending
7 NOVEMBER 2008
0031-9007=08=101(19)=191801(7) 191801-1 Ó 2008 The American Physical Society
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**
L. Zivkovic,
70
V. Zutshi,
52
and E. G. Zverev
38
(The 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
Universidade Federal do ABC, Santo Andre
´
, Brazil
5
Instituto de Fı
´
sica Teo
´
rica, Universidade Estadual Paulista, Sa
˜
o Paulo, Brazil
6
University of Alberta, Edmonton, Alberta, Canada,
Simon Fraser University, Burnaby, British Columbia, Canada,
York University, Toronto, Ontario, Canada,
and McGill University, Montreal, Quebec, Canada
7
University of Science and Technology of China, Hefei, People’s Republic of China
8
Universidad de los Andes, Bogota
´
, Colombia
9
Center for Particle Physics, Charles University, Prague, Czech Republic
10
Czech Technical University, Prague, Czech Republic
11
Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic
12
Universidad San Francisco de Quito, Quito, Ecuador
13
LPC, Univ Blaise Pascal, CNRS/IN2P3, Clermont, France
14
LPSC, Universite
´
Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, France
15
CPPM, Aix-Marseille Universite
´
, CNRS/IN2P3, Marseille, France
16
LAL, Univ Paris-Sud, IN2P3/CNRS, Orsay, France
17
LPNHE, IN2P3/CNRS, Universite
´
s Paris VI and VII, Paris, France
18
DAPNIA/Service de Physique des Particules, CEA, Saclay, France
19
IPHC, Universite
´
Louis Pasteur et Universite
´
de Haute Alsace, CNRS/IN2P3, Strasbourg, France
20
IPNL, Universite
´
Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universite
´
de Lyon, Lyon, France
21
III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany
22
Physikalisches Institut, Universita
¨
t Bonn, Bonn, Germany
23
Physikalisches Institut, Universita
¨
t Freiburg, Freiburg, Germany
24
Institut fu
¨
r Physik, Universita
¨
t Mainz, Mainz, Germany
25
Ludwig-Maximilians-Universita
¨
tMu
¨
nchen, Mu
¨
nchen, Germany
26
Fachbereich Physik, University of Wuppertal, Wuppertal, Germany
27
Panjab University, Chandigarh, India
28
Delhi University, Delhi, India
29
Tata Institute of Fundamental Research, Mumbai, India
30
University College Dublin, Dublin, Ireland
31
Korea Detector Laboratory, Korea University, Seoul, Korea
32
SungKyunKwan University, Suwon, Korea
33
CINVESTAV, Mexico City, Mexico
PRL 101, 191801 (2008)
PHYSICAL REVIEW LETTERS
week ending
7 NOVEMBER 2008
191801-2
34
FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands
35
Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands
36
Joint Institute for Nuclear Research, Dubna, Russia
37
Institute for Theoretical and Experimental Physics, Moscow, Russia
38
Moscow State University, Moscow, Russia
39
Institute for High Energy Physics, Protvino, Russia
40
Petersburg Nuclear Physics Institute, St. Petersburg, Russia
41
Lund University, Lund, Sweden,
Royal Institute of Technology and Stockholm University, Stockholm, Sweden,
and Uppsala University, Uppsala, Sweden
42
Lancaster University, Lancaster, United Kingdom
43
Imperial College, London, United Kingdom
44
University of Manchester, Manchester, United Kingdom
45
University of Arizona, Tucson, Arizona 85721, USA
46
Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA
47
California State University, Fresno, California 93740, USA
48
University of California, Riverside, California 92521, USA
49
Florida State University, Tallahassee, Florida 32306, USA
50
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
51
University of Illinois at Chicago, Chicago, Illinois 60607, USA
52
Northern Illinois University, DeKalb, Illinois 60115, USA
53
Northwestern University, Evanston, Illinois 60208, USA
54
Indiana University, Bloomington, Indiana 47405, USA
55
University of Notre Dame, Notre Dame, Indiana 46556, USA
56
Purdue University Calumet, Hammond, Indiana 46323, USA
57
Iowa State University, Ames, Iowa 50011, USA
58
University of Kansas, Lawrence, Kansas 66045, USA
59
Kansas State University, Manhattan, Kansas 66506, USA
60
Louisiana Tech University, Ruston, Louisiana 71272, USA
61
University of Maryland, College Park, Maryland 20742, USA
62
Boston University, Boston, Massachusetts 02215, USA
63
Northeastern University, Boston, Massachusetts 02115, USA
64
University of Michigan, Ann Arbor, Michigan 48109, USA
65
Michigan State University, East Lansing, Michigan 48824, USA
66
University of Mississippi, University, Mississippi 38677, USA
67
University of Nebraska, Lincoln, Nebraska 68588, USA
68
Princeton University, Princeton, New Jersey 08544, USA
69
State University of New York, Buffalo, New York 14260, USA
70
Columbia University, New York, New York 10027, USA
71
University of Rochester, Rochester, New York 14627, USA
72
State University of New York, Stony Brook, New York 11794, USA
73
Brookhaven National Laboratory, Upton, New York 11973, USA
74
Langston University, Langston, Oklahoma 73050, USA
75
University of Oklahoma, Norman, Oklahoma 73019, USA
76
Oklahoma State University, Stillwater, Oklahoma 74078, USA
77
Brown University, Providence, Rhode Island 02912, USA
78
University of Texas, Arlington, Texas 76019, USA
79
Southern Methodist University, Dallas, Texas 75275, USA
80
Rice University, Houston, Texas 77005, USA
81
University of Virginia, Charlottesville, Virginia 22901, USA
82
University of Washington, Seattle, Washington 98195, USA
(Received 20 April 2008; published 6 November 2008)
We present a measurement of the forward-backward charge asymmetry (A
FB
)inp
p ! Z=
þ X !
e
þ
e
þ X events at a center-of-mass energy of 1.96 TeV using 1:1fb
1
of data collected with the D0
detector at the Fermilab Tevatron collider. A
FB
is measured as a function of the invariant mass of the
electron-positron pair, and found to be consistent with the standard model prediction. We use the A
FB
measurement to extract the effective weak mixing angle sin
2
eff
W
¼ 0:2326 0:0018ðstatÞ0:0006ðsystÞ.
DOI: 10.1103/PhysRevLett.101.191801 PACS numbers: 12.15.Ji, 12.15.Mm, 13.38.Dg, 13.85.t
PRL 101, 191801 (2008)
PHYSICAL REVIEW LETTERS
week ending
7 NOVEMBER 2008
191801-3
In the standard model (SM), the neutral-current cou-
plings of the Z bosons to fermions (f) at tree level are
defined as
i
g
2 cos
W
f
ðg
f
V
g
f
A
5
ÞfZ
(1)
where
W
is the weak mixing angle, and g
f
V
and g
f
A
are the
vector and axial-vector couplings with g
f
V
¼ I
f
3
2Q
f
sin
2
W
and g
f
A
¼ I
f
3
. Here, I
f
3
is the weak isospin
component of the fermion and Q
f
its charge. The presence
of both vector and axial-vector couplings in q
q ! Z=
!
‘
þ
‘
gives rise to an asymmetry in the polar angle ()of
the negatively charged lepton momentum relative to the
incoming quark momentum in the rest frame of the lepton
pair. The angular differential cross section can be written as
d
d cos
¼ Að1 þ cos
2
ÞþB cos; (2)
where A and B are functions dependent on I
f
3
, Q
f
, and
sin
2
W
. Events with cos>0 are called forward events,
and those with cos<0 are called backward events.
The forward-backward charge asymmetry, A
FB
, is de-
fined as
A
FB
¼
F
B
F
þ
B
; (3)
where
F=B
is the integral cross section in the forward or
backward configuration. We measure A
FB
as a function of
the invariant mass of the lepton pair. To minimize the effect
of the unknown transverse momenta of the incoming
quarks in the measurement of the forward and backward
cross sections, we use calculated in the Collins-Soper
reference frame [1]. In this frame, the polar axis is defined
as the bisector of the proton beam momentum and the
negative of the antiproton beam momentum when they
are boosted into the rest frame of the lepton pair.
The forward-backward asymmetry is sensitive to
sin
2
eff
W
, which is an effective parameter that includes
higher order corrections. The current world average value
of sin
2
eff
W
at the Z-pole is 0:23149 0:00013 [2]. Two
sin
2
eff
W
measurements are more than 2 standard deviations
from the world average value: that from the charge asym-
metry for b quark production (A
0;b
FB
) from the LEP and SLD
collaborations [3] and that from neutrino and antineutrino
cross sections from the NuTeV collaboration [4]. The A
0;b
FB
measurement is sensitive to the couplings of b quarks to the
Z boson, and the NuTeV measurement is sensitive to the
couplings of u and d quarks to the Z boson, as is the
measurement presented here. Previous direct measure-
ments of u and d quark couplings to the Z are of limited
precision [5,6]. Thus, modifications to the SM that would
affect only u and d couplings are poorly constrained. In
addition, A
FB
measurements at the Tevatron can be per-
formed up to values of the dilepton mass exceeding those
achieved at LEP and SLC, therefore becoming sensitive to
possible new physics effects [7,8]. Although direct
searches for these new phenomena in the Z=
! ‘
þ
‘
final state have been recently performed by the CDF and
D0 collaborations [9], charge asymmetry measurements
are sensitive to different combination of couplings, and
can provide complementary information [10].
The CDF collaboration measured A
FB
using 108 pb
1
of
data in Run I [11] and 72 pb
1
of data in Run II [ 5]. This
analysis uses 1066 65 pb
1
of data [12] collected with
the D0 detector [13] at the Fermilab Tevatron collider at a
center-of-mass energy of 1.96 TeV to measure the A
FB
distribution and extract sin
2
eff
W
.
To select Z=
events, we require two isolated electro-
magnetic (EM) clusters that have shower shapes consistent
with that of an electron. EM candidates are required to
have transverse momentum p
T
> 25 GeV. The dielectron
pair must have a reconstructed invariant mass 50 <M
ee
<
500 GeV. If an event has both its EM candidates in the
central calorimeter (CC events), each must be spatially
matched to a reconstructed track in the tracking system.
Because the tracking efficiency decreases with magnitude
of the rapidity in the end calorimeter, events with one
candidate in the central and one candidate in the end
calorimeter (CE events) are required to have a matching
track only for that in the central calorimeter. For CC events,
the two candidates are further required to have opposite
charges. For CE events, the determination of forward or
backward is made according to the charge of the EM
candidate in the central calorimeter. A total of 35 626
events remain after application of all selection criteria,
with 16 736 CC events and 18 890 CE events. The selection
efficiencies are measured using Z=
! ee data with the
tag-probe method [14], and no differences between for-
ward and backward events are observed.
The asymmetry is measured in 14 M
ee
bins within the
50 <M
ee
< 500 GeV range. The bin widths are deter-
mined by the mass resolution, of order (3–4)%, and event
statistics.
Monte Carlo (MC) samples for the Z=
! e
þ
e
pro-
cess are generated using the
PYTHIA event generator [15]
using the CTEQ6L1 parton distribution functions (PDFs)
[16], followed by a detailed
GEANT-based simulation of the
D0 detector [17]. To improve the agreement between data
and simulation, selection efficiencies determined by the
MC calculations are corrected to corresponding values
measured in the data. Furthermore, the simulation is tuned
to reproduce the calorimeter energy scale and resolution, as
well as the distributions of the instantaneous luminosity
and z position of the event primary vertex observed in data.
Next-to-leading order (NLO) quantum chromodynamics
(QCD) corrections for Z=
boson production [18,19]
are applied by reweighting the Z=
boson transverse
momentum, rapidity, and invariant mass distributions
from
PYTHIA.
PRL 101, 191801 (2008)
PHYSICAL REVIEW LETTERS
week ending
7 NOVEMBER 2008
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The largest background arises from photon þ jets and
multijet final states in which photons or jets are misrecon-
structed as electrons. Smaller background contributions
arise from electroweak processes that produce two real
electrons in the final state. The multijet background is
estimated using collider data by fitting the electron isola-
tion distribution in data to the sum of the isolation distri-
butions from a pure electron sample and an EM-like jet
sample. The pure electron sample is obtained by enforcing
tighter track matching requirements on the two electrons
with 80 <M
ee
< 100 GeV. The EM-like jets sample is
obtained from a sample where only one good EM cluster
and one jet are back-to-back in azimuthal angle . The
contamination in the EM-like jets sample from W ! e
events is removed by requiring missing transverse energy
E6
T
< 10 GeV. The average multijet background fraction
over the entire mass region is found to be approximately
0.9%. Other SM backgrounds due to W þ , W þ jets,
WW, WZ, and t
t are estimated separately for forward
and backward events using
PYTHIA events passed through
the
GEANT simulation. Higher order corrections to the
PYTHIA leading order (LO) cross sections have been ap-
plied [ 19–21]. These SM backgrounds are found to be
negligible for almost all mass bins. The Z=
!
þ
contribution is similarly negligible.
In the SM, the A
FB
distribution is fully determined by
the value of sin
2
eff
W
in a LO prediction for the process
q
q ! Z=
! ‘
þ
‘
. The value of sin
2
eff
W
is extracted
from the data by comparing the background-subtracted
raw A
FB
distribution with templates corresponding to dif-
ferent input values of sin
2
eff
W
generated with PYTHIA and
GEANT-based MC simulation. Although sin
2
eff
W
varies over
the full mass range 50 <M
ee
< 500 GeV, it is nearly
constant over the range 70 <M
ee
< 130 GeV. Over this
region, we measure sin
2
eff
W
¼ 0:2321 0:0018ðstatÞ
0:0006ðsystÞ. The primary systematic uncertainties are
due to the PDFs (0.0005) and the EM energy scale and
resolution (0.0003). We include higher order QCD and
electroweak corrections using the
ZGRAD2 [22 ] program
with the generator-level Z=
boson p
T
distribution tuned
to match our measured distribution [23]. The effect of
higher order corrections results in a central value of
sin
2
eff
W
¼ 0:2326 [24].
Because of the detector resolution, events may be re-
constructed in a different mass bin than the one in which
they were generated. The CC and CE raw A
FB
distributions
are unfolded separately and then combined. The unfolding
(GeV)
ee
M
FB
A
-0.5
0
0.5
50 70 100 300 500
PYTHIA
ZGRAD2
Statistical uncertainty
Total uncertainty
/d.o.f. = 10.6/14
2
χ
DØ 1.1 fb
-1
FIG. 1 (color online). Comparison between the unfolded A
FB
(points) and the PYTHIA (solid curve) and ZGRAD2 (dashed line)
predictions. The inner (outer) vertical lines show the statistical
(total) uncertainty.
TABLE I. The first column shows the mass ranges used. The second column shows the cross
section weighted average of the invariant mass in each mass bin derived from
PYTHIA. The third
and fourth columns show the A
FB
predictions from PYTHIA and ZGRAD2. The last column is the
unfolded A
FB
; the first uncertainty is statistical, and the second is systematic.
M
ee
range hM
ee
i Predicted A
FB
Unfolded A
FB
(GeV) (GeV) PYTHIA ZGRAD2
50–60 54.5 0:293 0:307 0:262 0:066 0:072
60–70 64.9 0:426 0:431 0:434 0:039 0:040
70–75 72.6 0:449 0:452 0:386 0:032 0:031
75–81 78.3 0:354 0:354 0:342 0:022 0:022
81–86.5 84.4 0:174 0:166 0:176 0:012
0:014
86.5–89.5 88.4 0:033 0:031 0:034 0:007 0:008
89.5–92 90.9 0.051 0.052 0:048 0:006 0:005
92–97 93.4 0.127 0.129 0:122 0:006 0:007
97–105 99.9 0.289 0.296 0:301 0:013 0:015
105–115 109.1 0.427 0.429 0:416 0:030 0:022
115–130 121.3 0.526 0.530 0:543 0:039 0:028
130–180 147.9 0.593 0.603 0:617 0:046 0:013
180–250 206.4 0.613 0.600 0:594
0:085 0:016
250–500 310.5 0.616 0.615 0:320 0:150 0:018
PRL 101, 191801 (2008)
PHYSICAL REVIEW LETTERS
week ending
7 NOVEMBER 2008
191801-5
