of 9
Measurement of the total cross section for
e
1
e
2
ò
hadrons at
A
s
5
10.52 GeV
R. Ammar, P. Baringer, A. Bean, D. Besson, D. Coppage, C. Darling, R. Davis, N. Hancock, S. Kotov, I. Kravchenko,
and N. Kwak
University of Kansas, Lawrence, Kansas 66045
S. Anderson, Y. Kubota, M. Lattery, S. J. Lee, J. J. O’Neill, S. Patton, R. Poling, T. Riehle, V. Savinov, and A. Smith
University of Minnesota, Minneapolis, Minnesota 55455
M. S. Alam, S. B. Athar, Z. Ling, A. H. Mahmood, H. Severini, S. Timm, and F. Wappler
State University of New York at Albany, Albany, New York 12222
A. Anastassov, S. Blinov,
*
J. E. Duboscq, K. D. Fisher, D. Fujino,
K. K. Gan, T. Hart, K. Honscheid, H. Kagan, R. Kass,
J. Lee, M. B. Spencer, M. Sung, A. Undrus,
*
R. Wanke, A. Wolf, and M. M. Zoeller
Ohio State University, Columbus, Ohio 43210
B. Nemati, S. J. Richichi, W. R. Ross, P. Skubic, and M. Wood
University of Oklahoma, Norman, Oklahoma 73019
M. Bishai, J. Fast, E. Gerndt, J. W. Hinson, N. Menon, D. H. Miller, E. I. Shibata, I. P. J. Shipsey, and M. Yurko
Purdue University, West Lafayette, Indiana 47907
L. Gibbons, S. Glenn, S. D. Johnson, Y. Kwon, S. Roberts, and E. H. Thorndike
University of Rochester, Rochester, New York 14627
C. P. Jessop, K. Lingel, H. Marsiske, M. L. Perl, D. Ugolini, R. Wang, and X. Zhou
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309
T. E. Coan, V. Fadeyev, I. Korolkov, Y. Maravin, I. Narsky, V. Shelkov, J. Staeck, R. Stroynowski, I. Volobouev,
and J. Ye
Southern Methodist University, Dallas, Texas 75275
M. Artuso, A. Efimov, F. Frasconi, M. Gao, M. Goldberg, D. He, S. Kopp, G. C. Moneti, R. Mountain, S. Schuh,
T. Skwarnicki, S. Stone, G. Viehhauser, and X. Xing
Syracuse University, Syracuse, New York 13244
J. Bartelt, S. E. Csorna, V. Jain, and S. Marka
Vanderbilt University, Nashville, Tennessee 37235
R. Godang, K. Kinoshita, I. C. Lai, P. Pomianowski, and S. Schrenk
Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
G. Bonvicini, D. Cinabro, R. Greene, L. P. Perera, and G. J. Zhou
Wayne State University, Detroit, Michigan 48202
B. Barish, M. Chadha, S. Chan, G. Eigen, J. S. Miller, C. O’Grady, M. Schmidtler, J. Urheim, A. J. Weinstein,
and F. Wu
̈
rthwein
California Institute of Technology, Pasadena, California 91125
D. M. Asner, D. W. Bliss, W. S. Brower, G. Masek, H. P. Paar, S. Prell, M. Sivertz, and V. Sharma
University of California, San Diego, La Jolla, California 92093
J. Gronberg, T. S. Hill, R. Kutschke, D. J. Lange, S. Menary, R. J. Morrison, H. N. Nelson, T. K. Nelson, C. Qiao,
J. D. Richman, D. Roberts, A. Ryd, and M. S. Witherell
University of California, Santa Barbara, California 93106
R. Balest, B. H. Behrens, K. Cho, W. T. Ford, H. Park, P. Rankin, J. Roy, and J. G. Smith
University of Colorado, Boulder, Colorado 80309-0390
PHYSICAL REVIEW D
1 FEBRUARY 1998
VOLUME 57, NUMBER 3
57
0556-2821/98/57
~
3
!
/1350
~
9
!
/$15.00
1350
© 1998 The American Physical Society
J. P. Alexander, C. Bebek, B. E. Berger, K. Berkelman, K. Bloom, D. G. Cassel, H. A. Cho, D. M. Coffman,
D. S. Crowcroft, M. Dickson, P. S. Drell, K. M. Ecklund, R. Ehrlich, R. Elia, A. D. Foland, P. Gaidarev, R. S. Galik,
B. Gittelman, S. W. Gray, D. L. Hartill, B. K. Heltsley, P. I. Hopman, J. Kandaswamy, P. C. Kim, D. L. Kreinick, T. Lee,
Y. Liu, G. S. Ludwig, J. Masui, J. Mevissen, N. B. Mistry, C. R. Ng, E. Nordberg, M. Ogg,
J. R. Patterson,
D. Peterson, D. Riley, A. Soffer, B. Valant-Spaight, and C. Ward
Cornell University, Ithaca, New York 14853
M. Athanas, P. Avery, C. D. Jones, M. Lohner, C. Prescott, J. Yelton, and J. Zheng
University of Florida, Gainesville, Florida 32611
G. Brandenburg, R. A. Briere, Y. S. Gao, D. Y.-J. Kim, R. Wilson, and H. Yamamoto
Harvard University, Cambridge, Massachusetts 02138
T. E. Browder, F. Li, Y. Li, and J. L. Rodriguez
University of Hawaii at Manoa, Honolulu, Hawaii 96822
T. Bergfeld, B. I. Eisenstein, J. Ernst, G. E. Gladding, G. D. Gollin, R. M. Hans, E. Johnson, I. Karliner, M. A. Marsh,
M. Palmer, M. Selen, and J. J. Thaler
University of Illinois, Champaign-Urbana, Illinois 61801
K. W. Edwards
Carleton University, Ottawa, Ontario, Canada K1S 5B6
and the Institute of Particle Physics, Canada
A. Bellerive, R. Janicek, D. B. MacFarlane, K. W. McLean, and P. M. Patel
McGill University, Montre
́
al, Que
́
bec, Canada H3A 2T8
and the Institute of Particle Physics, Canada
A. J. Sadoff
Ithaca College, Ithaca, New York 14850
~
CLEO Collaboration
!
~
Received 7 July 1997; published 13 January 1998
!
Using the CLEO detector at the Cornell Electron Storage Ring, we have made a measurement of
R
[
s
(
e
1
e
2
!
hadrons) /
s
(
e
1
e
2
!
m
1
m
2
)
5
3.56
6
0.01
6
0.07 at
A
s
5
10.52 GeV. This implies a value for the
strong
coupling
constant
of
a
s
( 10.52 GeV)
5
0.20
6
0.01
6
0.06,
or
a
s
(
M
Z
)
5
0.13
6
0.005
6
0.03.
@
S0556-2821
~
98
!
05703-8
#
PACS number
~
s
!
: 12.38.Aw, 12.38.Qk, 13.60.Hb, 13.85.Lg
I. INTRODUCTION
The measurement of the hadronic production cross sec-
tion in
e
1
e
2
annihilation is perhaps the most fundamental
experimentally accessible quantity in quantum chromody-
namics
~
QCD
!
due to its insensitivity to the fragmentation
process. The measured hadronic cross section is generally
expressed in terms of its ratio
R
to the point cross section for
m
1
m
2
production. In QCD,
R
is directly proportional to the
number of colors, depends on quark charges, and varies with
energy, both discretely as quark mass thresholds are crossed
and gradually as the strong coupling constant
a
s
‘‘runs.’’
R
measurements have been valuable in verifying quark thresh-
olds, charges, color counting, and the existence of the gluon.
The theoretical prediction for
R
, expressed as an expan-
sion in powers of
a
s
/
p
,is
R
5
R
~
0
!
@
1
1
a
s
/
p
1
C
2
~
a
s
/
p
!
2
1
C
3
~
a
s
/
p
!
3
#
.
~
1
!
R
(0)
is the lowest-order prediction for this ratio, given by
R
(0)
5
N
c
S
i
q
i
2
, where
N
c
is the number of quark colors; the
sum runs over the kinematically allowed quark flavors. Just
below the
Y~
4S
!
resonance, where bb
̄
production is kine-
matically forbidden, the lowest-order prediction is therefore
obtained by summing over
udcs
quarks, yielding
R
(0)
5
10/3.
The
a
s
corrections contribute an additional
;
15% to this
value. A calculation appropriate at CERN
e
1
e
2
collider
LEP energies obtained
C
2
5
1.411 and
C
3
52
12.68
@
1
#
for
five active flavors, in the limit of massless quarks. A recent
calculation, applicable to the
Y
mass region
~
four active fla-
vors
!
, has included corrections due to the effects of quark
masses and QED radiation to obtain
C
2
5
1.5245 and
C
3
52
11.52 at
A
s
5
10 GeV
@
2
#
. The effect of including
these additional corrections is a difference of approximately
*
Permanent address: BINP, RU-630090 Novosibirsk, Russia.
Permanent address: Lawrence Livermore National Laboratory,
Livermore, CA 94551.
Permanent address: University of Texas, Austin, TX 78712.
57
1351
MEASUREMENT OF THE TOTAL CROSS SECTION FOR . . .
0.3% in the prediction for
R
at this energy. In this article we
present a measurement of
R
using the CLEO detector oper-
ating at the Cornell Electron Storage Ring
~
CESR
!
at a
center-of-mass energy
A
s
5
10.52 GeV.
II. APPARATUS AND EVENT SELECTION
The CLEO II detector is a general purpose solenoidal
magnet spectrometer and calorimeter
@
3
#
. The detector was
designed to trigger efficiently on two-photon, tau-pair, and
hadronic events. As a result, although hadronic event recon-
struction efficiencies are high, lower-multiplicity nonhad-
ronic backgrounds require careful consideration in this
analysis. Good background rejection is afforded by the high-
precision electromagnetic calorimetry and excellent charged-
particle-tracking capabilities. Charged particle momenta are
measured with three nested coaxial drift chambers with 6,
10, and 51 layers, respectively. These chambers fill the vol-
ume from
r
5
3cmto
r
5
100 cm, where
r
is the radial coor-
dinate relative to the beam (
z
) axis, and have good efficiency
for charged particle tracking for polar angles
u
cos
u
u
,
0.94,
with
u
measured relative to the positron beam direction
(
1
z
ˆ
) . This system achieves a momentum resolution of
(
d
p
/
p
)
2
5
( 0.0015
p
)
2
1
( 0.005)
2
, where
p
is the momentum
in GeV/
c
. Pulse height measurements in the main drift cham-
ber provide a specific ionization resolution of 6.5% for
Bhabha events, giving good
K
/
p
separation for tracks with
momenta up to 700 MeV/
c
and approximately two standard
deviation resolution in the relativistic rise region. Outside the
central tracking chambers are plastic scintillation counters
that are used as fast elements in the trigger system and also
provide particle identification information from time-of-
flight measurements. Beyond the time-of-flight system is the
electromagnetic calorimeter, consisting of 7800 thallium-
doped cesium iodide crystals. The central ‘‘barrel’’ region of
the calorimeter covers about 75% of the solid angle and has
an energy resolution of about 4% at 100 MeV and 1.2% at 5
GeV. Two end cap regions of the crystal calorimeter extend
solid angle coverage to about 98% of 4
p
, although with
somewhat worse energy resolution than the barrel region.
The tracking system, time-of-flight counters, and calorimeter
are all contained within a 1.5 T superconducting coil.
To suppress
tt
,
gg
, low-multiplicity QED, and other
backgrounds while maintaining relatively high qq
̄
event re-
construction efficiency, we impose several requirements to
enrich our hadronic event sample. To suppress events origi-
nating as collisions of
e
6
beam particles with gas or the
vacuum chamber walls, we require that the reconstructed
event vertex
~
defined as
z
vrtx
) be within 6 cm in
z
(
z
ˆ
defined
above as the
e
1
beam direction
!
and 2 cm in cylindrical
radius of the nominal interaction point. Figure 1 displays the
distribution in the
z
coordinate. Single-beam backgrounds
are expected to be flat in this distribution; hadronic events
peak at
z
5
0 with a resolution of approximately 2 cm. Other
event selection criteria are imposed on various kinematic
quantities. To illustrate the effect of these selection require-
ments, we show below distributions from data; Monte Carlo
comparisons are also shown. Simulated hadronic events are
produced using the
JETSET
7.3 qq
̄
event generator
@
4
#
run
through a full
GEANT
-based
@
5
#
CLEO-II detector simulation.
Tau-pair events use the
KORALB
@
6
#
event generator in con-
junction with the same detector simulation.
1
We also use this
Monte Carlo event sample to determine the efficiency for qq
̄
and
tt
̄
events to pass the following hadronic event selection
requirements:
~
1
!
At least five detected, good quality,
charged tracks (
N
chrg
>
5, as shown in Fig. 2
!
;
~
2
!
the total
visible energy
E
vis
(
5
E
chrg
1
E
neutral
) should be greater than
the single beam energy,
E
vis
.
E
beam
~
Fig. 3
!
;
~
3
!
The
z
com-
ponent of the missing momentum must satisfy
u
P
z
miss
u
/
E
vis
,
0.3
~
Fig. 4
!
.
In addition to these primary requirements, additional cri-
teria are imposed to remove backgrounds remaining at the
;
1% level, as well as to suppress events with hard initial
state radiation, for which theoretical uncertainties are large.
These are the following:
~
a
!
No more than two identified electrons are in the event.
~
b
!
The ratio
R
2
of the second to the zeroth Fox-Wolfram
moments
@
7
#
for the event should satisfy
R
2
,
0.9
~
Fig. 5
!
.As
can be seen from the figure, the separation between Monte
Carlo qq
̄
and
tt
events is quite good, and the inclusion of
the
tt
component significantly improves the fit.
2
~
c
!
The ratio of calorimeter energy contained in showers
that match to charged particles divided by the beam energy
(
E
calorimeter
charged tracks
/
E
beam
) must be less than 0.9
~
Fig. 6
!
.
~
d
!
We impose a requirement on the highest-energy pho-
ton in an event—the most energetic photon candidate de-
1
In the comparison plots, both the data and the ‘‘Monte Carlo
sum’’ have been normalized to unit area in the ‘‘good’’ acceptance
region. All remaining hadronic event selection requirements save
for the one being displayed have been imposed.
2
In fact, we can determine the qq
̄
and
tt
fractions by fitting the
R
2
distribution to the sum of the expected qq
̄
and
tt
R
2
shapes,
with only the relative normalizations floating. Such a fit gives a
value of the
tt
fraction which is consistent with that calculated
using the expected relative tau pair and qq
̄
production cross sec-
tions and efficiencies.
FIG. 1. Distribution of the
z
coordinate of the event vertex for
candidate hadronic events. Arrows indicate the location of cuts.
1352
57
R. AMMAR
et al.
tected in the event must have a measured energy less than
0.75 of the beam energy (
x
g
[
E
g
max
/
E
beam
,
0.75
!
, as shown
in Fig. 7. This requirement also reduces the uncertainty from
radiative corrections, as discussed later.
We note that, according to the Monte Carlo simulation,
the trigger inefficiency with the default event selection crite-
ria is less than 0.1%. This has been checked with the data by
counting the fraction of events classified as ‘‘hadronic’’
which trigger only a minimum bias, prescaled trigger line.
III. BACKGROUNDS
After imposition of the above hadronic event selection
criteria, we are left with a sample of 4.00
3
10
6
candidate
hadronic events. Agreement between data and Monte Carlo
simulations is, at this point, rather good, as illustrated in
Figs. 8, 9, and 10, which show the distributions in the
z
component of the missing momentum, the
z
component of
the event thrust axis, and the scaled event transverse momen-
tum, respectively. Nevertheless, small backgrounds still re-
main. These are enumerated as follows.
~
1
!
Backgrounds from
e
1
e
2
!
t
1
t
2
(
g
) events are sub-
tracted statistically using a large Monte Carlo sample of
KORALB
tau-pair events. These events comprise ( 1.3
6
0.1) %
~
statistical error only
!
of the sample passing the above event
selection criteria.
~
2
!
Contributions from the narrow
Y
resonances
@
the
~
1S
!
,
~
2S
!
, and
~
3S
!
states
#
are determined from a combination of
data and theoretical calculation. Backgrounds from radiative
production of the
Y~
3S
!
and
Y~
2S
!
resonances are assessed
using
e
1
e
2
!
g
Y
( 3S/2S) ,
Y
( 3S/2S)
!
p
1
p
2
Y
( 1S) ,
Y
( 1S)
!
l
1
l
2
events in data. These events are distinctive by
their characteristic topology of two low-momentum pions
accompanied by two very-high-momentum, back-to-back
leptons; the photon generally escapes undetected along the
beam axis. As shown in Fig. 11, we observe these events as
distinct peaks in the mass distribution recoiling against two
low-momentum pions in events also containing two high-
energy muons.
@
The recoil mass is calculated from
M
recoil
5
A
(2
E
beam
2
E
p
1
2
E
p
2
)
2
2
(
p
W
p
1
1
p
W
p
2
)
2
, and therefore ne-
glects the four-momentum of the initial state radiation pho-
ton. This calculated recoil mass is thus the sum of the
Y~
1S
!
and the undetected photon four-vectors.
#
Knowing the
branching fractions
@
8
#
for
Y~
2S
!
!
pp
Y~
1S
!
( 18.5
6
0.8%
!
and
Y~
3S
!
!
pp
Y~
1S
!
( 4.5
6
0.2%
!
, the leptonic branching
fraction for the
Y~
1S
!
( 2.5
6
0.1) %, and the reconstruction
FIG. 2. Normalized charged multiplicity distribution for data
~
solid line
!
,qq
̄
Monte Carlo simulations
~
dashed line
!
, and
tt
Monte Carlo simulations
~
dotted line
!
. Sum of qq
̄
plus
tt
Monte
Carlo simulations is shown as solid circles.
FIG. 3. Normalized visible energy distribution for data
~
solid
line
!
,qq
̄
Monte Carlo simulations
~
dashed line
!
, and
tt
Monte
Carlo simulations
~
dotted line
!
. Sum of qq
̄
plus
tt
Monte Carlo
simulations is shown as solid circles. The excess in the region
E
vis
/
E
beam
,
1 is attributed primarily to two-photon collisions.
FIG. 4. Ratio of
P
z
miss
/
E
visible
for data vs Monte Carlo simula-
tions. Two-photon collisions and beam-gas interactions tend to
populate the regions away from zero and towards
6
1 in this plot.
57
1353
MEASUREMENT OF THE TOTAL CROSS SECTION FOR . . .
efficiency for such events (
;
0.7
!
, we can determine the con-
tribution to the observed hadronic cross section from the
Y~
2S
!
and
Y~
3S
!
resonances directly, by simply measuring
the event yields in the peaks shown in Fig. 11, and correcting
by branching fractions and efficiency.
We have estimated the contribution from
g
Y~
1S
!
events
in two ways. First, we assume that the initial state photon
spectrum varies as
dN
/
dE
g
;
1/
E
g
, and that the production
of a given
Y
resonance is proportional to its dielectron width
G
ee
. This gives a fairly simple prediction for the cross sec-
tions expected for the three narrow
Y
resonances, since
E
g
;
( 10.52
2
M
Y
) GeV. We would expect that the production
cross section for
Y
g
in
e
1
e
2
annihilation therefore varies as
G
(
e
1
e
2
!
Y
g
)
}G
ee
Y
/
E
g
. This allows us to infer an ex-
pected production cross section for
g
Y
( 1S) based on our
measurements for
g
Y
( 2S) and
g
Y
( 3S) production. Theory
@
2
#
also prescribes what the magnitude of these corrections
should be. We compare our extrapolated cross section for
e
1
e
2
!
g
Y~
1S
!
through the simpleminded procedure out-
lined above with the theoretical calculation for this correc-
tion in order to estimate the total magnitude of this correc-
tion, and its associated error. We determine that the sum of
g
Y~
1S
!
,
g
Y~
2S
!
, and
g
Y~
3S
!
events comprise
~
1.8
6
0.6
!
%
of the observed hadronic cross section, where the error in-
cludes the uncertainties in the
Y
decay branching fractions
and detection efficiencies as well as the deviations between
the estimates from theoretical calculation and data.
FIG. 5. Ratio of Fox-Wolfram moments
R
2
5
H
2
/
H
0
for data vs
Monte Carlo calculation.
FIG. 6. Comparison of data vs Monte Carlo distribution of calo-
rimeter energy deposited by charged tracks relative to the beam
energy in an event.
FIG. 7. Comparison of data vs Monte Carlo spectrum of most
energetic photon observed in event.
FIG. 8. Distribution of the
z
component
~
i.e., direction cosine
!
of the missing momentum
P
z
miss
/
u
P
miss
u
for data vs Monte Carlo
simulations, after application of all hadronic event selection re-
quirements
~
this variable is not cut on
!
.
1354
57
R. AMMAR
et al.
~
3
!
Two-photon collisions, which produce hadrons in the
final state via
e
1
e
2
!
e
1
e
2
gg
!
e
1
e
2
1
hadrons, are deter-
mined by running final-state specific
gg
collision Monte
Carlo events, and also by determining the magnitude of pos-
sible excesses in the
E
visible
vs
P
transverse
plane for data over
qq
̄
Monte Carlo calculation. Figure 12 shows the visible
energy vs transverse momentum distribution for events
which are
e
1
e
2
!
gg
e
1
e
2
depleted
~
left, obtained by re-
quiring our default hadronic event selection requirements,
save for the requirement that the total visible energy exceed
the beam energy
!
and
e
1
e
2
!
gg
e
1
e
2
enriched
~
right, ob-
tained by requiring
u
P
z
miss
u
/
E
vis
.
0.3 and
N
chrg
5
3or4
!
.We
notice the presence of a prominent peak in the
gg
-enriched
sample at low values of the transverse momentum and small
visible energy. We can use the shape of this peak to estimate
the possible residual contamination from two-photon colli-
sions remaining in the
gg
-poor distribution after imposition
of all our hadronic event selection requirements. Two-photon
collisions are thus determined to comprise
~
0.8
6
0.4
!
%of
our total hadronic event sample.
~
4
!
Beam-wall, beam-gas, and cosmic ray events are ex-
pected to have a flat event vertex distribution in the interval
FIG. 10. Ratio of transverse momentum relative to beam energy,
after application of all hadronic event selection requirements
~
this
variable is not cut on
!
.
FIG. 11. Mass recoiling against two charged particles, assumed
to be pions, in events consistent with the kinematics for
e
1
e
2
!
g
Y
( 3S/2S) ,
Y
( 3S/2S)
!
Y
( 1S)
p
1
p
2
,
Y
( 1S)
!
l
1
l
2
. Two
peaks are evident; the leftmost peak corresponds to
Y
( 3S)
!
p
1
p
2
Y~
1S
!
transitions, the rightmost peak corresponds to
Y~
2S
!
!
p
1
p
2
Y~
1S
!
transitions. The calculated recoil mass differs
from the true
Y~
1S
!
mass due to our neglecting the
~
undetected
!
radiated photon in the recoil mass calculation.
FIG. 12. Distribution of transverse momentum vs visible energy
for event samples depleted
~
left
!
and enriched
~
right
!
in
e
1
e
2
!
gg
e
1
e
2
,
gg
!
hadrons events.
FIG. 9.
z
component of the thrust axis for data vs Monte Carlo
calculation, after application of all hadronic event selection require-
ments
~
this variable is not cut on
!
.
57
1355
MEASUREMENT OF THE TOTAL CROSS SECTION FOR . . .
u
z
vrtx
u
,
10 cm. Figure 1 shows the distribution in the
z
coor-
dinate of the event vertex for events passing the remainder of
our hadronic event selection requirements. The contribution
of such events is estimated by extrapolating the yield of
events having a vertex in the interval 6 cm
,
u
z
vrtx
u
,
10 cm
into the ‘‘good’’ acceptance region (
u
z
vrtx
u
,
6cm
!
. These
backgrounds are determined to comprise
;
( 0.2
6
0.1) % of
our hadronic sample.
~
5
!
Remaining QED backgrounds producing more than
two electrons or muons in the final state are assessed using a
high-statistics sample of Monte Carlo events
~
to 3
rd
order in
a
QED
) , and found to comprise
<
0.1% of the sample passing
the above hadronic event selection requirements.
Summing these estimates results in a net background frac-
tion
f
5
( 4.1
6
0.7) % . We note that, as this error is assessed
partly by examining the difference between Monte Carlo
hadronic event simulations and our data, this error also in-
cludes Monte Carlo modeling errors.
IV. EFFICIENCIES AND RADIATIVE CORRECTIONS
The computation of
R
is peformed with
R
5
N
had
~
1
2
f
!
L
e
had
~
1
1
d
!
s
mm
0
,
~
2
!
where
N
had
is the number of events classified as hadronic,
f
is the fraction of selected events attributable to all back-
ground processes,
e
had
is the efficiency for triggering and
selection of events,
d
is the fractional increase in hadronic
cross section due to electromagnetic radiative corrections,
s
mm
0
is the point cross section for muon pair production
@
86.86 nb/
E
c.m.
2
~
GeV
2
)
#
, and
L
is the measured integrated
luminosity. The luminosity is determined from wide angle
e
1
e
2
,
gg
, and
m
1
m
2
final states and is known to
6
1%
@
9
#
.
For the data analyzed here, the integrated luminosity
L
is
equal to ( 1.521
6
0.015) fb
2
1
.
To calculate
R
, we must therefore evaluate Eq.
~
2
!
.Ifthe
initial-state radiation corrections were known precisely, we
would be able to calculate the denominator term
e
(1
1
d
)
with very good precision. However, since the uncertainties
become very large as the center-of-mass energy approaches
the cc
̄
threshold (
A
s
;
4 GeV
!
, the preferred procedure is to
choose some explicit cutoff in the initial-state radiation
~
ISR
!
photon energy that makes us as insensitive as possible to the
corrections in this high-ISR-photon-energy–low-hadronic-
recoil-mass region. We therefore purposely design our selec-
tion criteria so that our acceptance for events with highly
energetic ISR photons approaches zero. By choosing cuts
that drive
e
to zero beyond some kinematic point, we ensure
that the product
e
3
(1
1
d
) is insensitive to whatever value
of
d
may be prescribed by theory beyond our cut. Thus,
although there is a large uncertainty in the magnitude of the
initial-state radiation correction for large values of radiated
photon momentum, we have minimized our sensitivity to this
theoretical uncertainty. Figure 13 displays our acceptance for
an
e
1
e
2
!
g
qq
̄
event to pass our hadronic event criteria as
a function of the scaled photon energy
x
g
[
E
g
/
E
beam
. Based
on the agreement between data and Monte Carlo simulations
shown in Fig. 7, we have applied a cut on the maximum
energy allowed for a single shower in an event:
x
g
,
0.75.
We note that for
x
g
.
0.75
~
corresponding to a
qq
̄
recoil
mass of
M
recoil
,
5.25 GeV/
c
2
) , our integrated event-finding
acceptance
e
had
,
1%. For
x
g
.
0.75, we have therefore mini-
mized our sensitivity to modeling uncertainties in this kine-
matic regime—increasing
~
theoretically
!
the initial-state ra-
diation contribution to this high-
x
g
region results in a
compensating loss of overall acceptance such that the prod-
uct of
e
(1
1
d
) remains relatively constant. Our event selec-
tion criteria thus corresponds to a value of
e
(1
1
d
)(
x
g
max
5
0.75)
5
0.90
6
0.01, where the error reflects the systematic
uncertainty in the radiative corrections.
After subtracting all backgrounds, dividing by the total
luminosity, and normalizing to the mu-pair point cross sec-
tion, we obtain a value of
R
5
3.56
6
0.01
~
statistical error
only, including statistical errors in data, Monte Carlo statis-
tics, and the statistics of the sample used to calculate our
luminosity
!
.
V. SYSTEMATIC ERRORS AND CONSISTENCY CHECKS
We have checked our results in several ways. Back-
grounds can be suppressed significantly by tightening the
minimum charged track multiplicity to
N
chrg
>
7, albeit at a
loss of
;
20% in the overall event-reconstruction efficiency.
Imposition of such a cut leads to only a
2
0.4% change in the
calculated value of
R
. Continuum data have been collected
over 17 distinct periods from 1990 to 1996, covering many
different trigger configurations and running conditions. We
find a 0.3% rms variation between the various data sets used
~
the statistical error on
R
within each data set is of order
0.1%
!
. We can check contributions due to the narrow
Y
resonances by calculating
R
using a small amount
~
5pb
2
1
)
of continuum data taken just below the
Y~
2S
!
resonance, at
E
beam
5
4.995 GeV. At this center-of-mass energy, we are
insensitive to corrections from
e
1
e
2
!
g
Y~
3S
!
and
e
1
e
2
!
g
Y~
2S
!
. We find that the value of
R
calculated using the
Y~
2S
!
continuum agrees with that calculated using the
Y~
4S
!
FIG. 13. Acceptance for
e
1
e
2
!
g
qq
̄
events as a function of
the scaled photon momentum
x
g
[
E
g
/
E
beam
.
1356
57
R. AMMAR
et al.
continuum to within one statistical error ( 1
s
stat
) . Systematic
errors are summarized in Table I.
VI. EXTRACTION OF
a
s
Using the expansion for
R
in powers of
a
s
/
p
given pre-
viously, with coefficients appropriate for this center-of-mass
energy
@
2
#
, we can evaluate the strong coupling constant,
using the prescription outlined by the Particle Data Group
@
8
#
. Using that expression, our value for
R
translates to
a
s
( 10.52 GeV
!
5
0.20
6
0.01
6
0.06.
To compare this
a
s
value with measurements at the
Z
0
,
we need to extrapolate our result to
A
s
5
90 GeV. The strong
coupling constant
a
s
can be written as a function of the basic
QCD parameter
L
MS
̄
, defined in the modified minimal sub-
traction scheme
@
8
#
as
a
s
~
m
!
5
4
p
b
0
x
H
1
2
2
b
1
b
0
2
ln
~
x
!
x
1
4
b
1
2
b
0
4
x
2
S
F
ln
~
x
!
2
1
2
G
2
1
b
2
b
0
8
b
1
2
2
5
4
D
J
,
~
3
!
where
b
0
5
(11
2
2
n
f
/3) ,
m
is the energy scale, in GeV, at
which
a
s
is being evaluated,
b
1
5
(51
2
19
n
f
)/3,
b
2
5
2857
2
5033
n
f
/9
1
325
n
f
2
/27,
x
5
ln(
m
2
/
L
MS
̄
2
) , and
n
f
is the num-
ber of light quark flavors which participate in the process. To
determine the value of
a
s
( 90 GeV
!
implied by our measure-
ment, we must evolve
a
s
across the discontinuity in
L
MS
̄
when the five-flavor threshold is crossed from the four-flavor
regime. We do so using the next-to-next-to-leading order
~
NNLO
!
prescription, as described in
@
8
#
:
~
a
!
We substitute
a
s
~
10.52
!
into Eq.
~
3
!
to determine a value for
L
MS
̄
in the
four-flavor continuum
@
obtaining
L
MS
̄
(
udcs
)
5
498 MeV
#
.
~
b
!
With that value of
L
MS
̄
, we can now again use Eq.
~
3
!
to
determine the value of
a
s
at the five-flavor threshold when
the
b
-quark pole mass
~
we use
m
b
, pole
5
4.7 GeV
!
is crossed,
and then use that value of
a
s
, as well as
n
f
5
5 in Eq.
~
3
!
to
determine
L
MS
̄
appropriate for the five-flavor continuum.
~
c
!
Assuming that this value of
L
MS
̄
is constant in the entire
five-flavor energy region, we can now evolve
a
s
up to the
Z
pole, to obtain
a
s
(
M
Z
)
5
0.13
6
0.005
6
0.03, in good agree-
ment with the world average
a
s
(
M
Z
)
5
0.118
6
0.003
@
8
#
.
VII. SUMMARY
Near
A
s
5
10 GeV,
R
has been measured by many experi-
ments, as shown in Table II. The measurement of
R
de-
scribed here is the most precise below the
Z
0
. Our
R
value is
in good agreement with the previous world average, includ-
ing a recent determination by the MD-1 Collaboration
@
18
#
.
Our implied value of
a
s
is in agreement with higher-energy
determinations of this quantity. Theoretical uncertainties in
QED radiative corrections
Ñ
in the acceptance
@
e
3
(1
1
d
)
#
and luminosity
@
9
#
Ö
contribute about the same amount to the
systematic error as do backgrounds and efficiencies. Sub-
stantial improvements in this measurement will require
progress on radiative corrections as well as on experimental
techniques.
ACKNOWLEDGMENTS
We gratefully acknowledge the effort of the CESR staff in
providing us with excellent luminosity and running condi-
tions. J.P.A., J.R.P., and I.P.J.S. thank the NYI program of
the NSF, M.S. thanks the PFF program of the NSF, G.E.
thanks the Heisenberg Foundation, K.K.G., M.S., H.N.N.,
T.S., and H.Y. thank the OJI program of DOE, J.R.P., K.H.,
M.S., and V.S. thank the A.P. Sloan Foundation, R.W.
thanks the Alexander von Humboldt Stiftung, and M.S.
thanks Research Corporation for support. This work was
supported by the National Science Foundation, the U.S. De-
partment of Energy, and the Natural Sciences and Engineer-
ing Research Council of Canada.
@
1
#
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, 144
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Rev. Lett.
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, 560
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!
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2
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̈
hn, and T. Teubner, Phys. Rev. D
56
,
3011
~
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!
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̈
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!
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3
#
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et al.
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TABLE I. Systematic errors in
R
analysis.
Source
Error
e
3
(1
1
d
)1%
L
1%
Background uncertainty/hadronic
event modeling uncertainty
0.7%
Data-set–to–data-set variation
0.3%
Total
1.8%
TABLE II. Summary of inclusive cross section measurements.
Experiment
A
s
~
GeV
!
R
PLUTO
@
10
#
9.4
3.67
6
0.23
6
0.29
DASPII
@
11
#
9.4
3.37
6
0.16
6
0.28
DESY-Heidelberg
@
12
#
9.4
3.80
6
0.27
6
0.42
LENA
@
13
#
9.1-9.4
3.34
6
0.09
6
0.18
LENA
@
13
#
7.4-9.4
3.37
6
0.06
6
0.23
CUSB
@
14
#
10.5
3.54
6
0.05
6
0.40
CLEO 83
@
15
#
10.5
3.77
6
0.06
6
0.24
Crystal Ball
@
16
#
9.4
3.48
6
0.04
6
0.16
ARGUS
@
17
#
9.36
3.46
6
0.03
6
0.13
MD-1
@
18
#
7.25-10.34
3.58
6
0.02
6
0.14
Previous experiments,
weighted average
'
9.5
3.58
6
0.07
CLEO 97
~
this work
!
10.5
3.56
6
0.01
6
0.07
57
1357
MEASUREMENT OF THE TOTAL CROSS SECTION FOR . . .
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@
4
#
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5
#
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