Measurements of the cross section for e(+)e(-) --> hadrons at center-of-mass energies from 2 to 5 GeV.

Abstract

We report values of R = sigma(e(+)e(-)-->hadrons)/sigma(e(+)e(-)-->mu(+)mu(-)) for 85 center-of-mass energies between 2 and 5 GeV measured with the upgraded Beijing Spectrometer at the Beijing Electron-Positron Collider.

Full text

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arXiv:hep-ex/0102003v3 12 Mar 2002
Measurements of the Cross Section for e+e−→ hadrons at Center-of-Mass Energies
from 2 to 5 GeV
J. Z. Bai1, Y. Ban10, J. G. Bian1, A. D. Chen1, H. F. Chen16, H. S. Chen1, J. C. Chen1, X. D. Chen1, Y. B. Chen1,
B. S. Cheng1, S. P. Chi1, Y. P. Chu1, J. B. Choi3, X. Z. Cui1, Y. S. Dai19, L. Y. Dong1, Z. Z. Du1,
W. Dunwoodie14, H. Y. Fu1, L. P. Fu7, C. S. Gao1, S. D. Gu1, Y. N. Guo1, Z. J. Guo2, S. W. Han1, Y. Han1,
F. A. Harris15, J. He1, J. T. He1, K. L. He1, M. He11, X. He1, T. Hong1, Y. K. Heng1, G. Y. Hu1, H. M. Hu1,
Q. H. Hu1, T. Hu1, G. S. Huang2, X. P. Huang1, Y. Z. Huang1, J. M. Izen17, X. B. Ji11, C. H. Jiang1, Y. Jin1,
B. D. Jones17, J. S. Kang8, Z. J. Ke1, H. J. Kim13, S. K. Kim13, T. Y. Kim13, D. Kong15, Y. F. Lai1, D. Li1,
H. B. Li1, H. H. Li6, J. Li1, J. C. Li1, P. Q. Li1, Q. J. Li1, R. Y. Li1, W. Li1, W. G. Li1, X. N. Li1, X. Q. Li9,
B. Liu1, F. Liu6, Feng Liu1, H. M. Liu1, J. Liu1, J. P. Liu18, T. R. Liu1, R. G. Liu1, Y. Liu1, Z. X. Liu1,
X. C. Lou17, G. R. Lu5, F. Lu1, J. G. Lu1, Z. J. Lu1, X. L. Luo1, E. C. Ma1, J. M. Ma1, R. Malchow4, H. S. Mao1,
Z. P. Mao1, X. C. Meng1, X. H. Mo1, J. Nie1, Z. D. Nie1, S. L. Olsen15, D. Paluselli15, H. Park8, N. D. Qi1,
X. R. Qi1, C. D. Qian12, J. F. Qiu1, Y. K. Que1, G. Rong1, Y. Y. Shao1, B. W. Shen1, D. L. Shen1, H. Shen1,
X. Y. Shen1, H. Y. Sheng1, F. Shi1, H. Z. Shi1, X. F. Song1, J. Y. Suh8, H. S. Sun1, L. F. Sun1, Y. Z. Sun1,
S. Q. Tang1, W. Toki4, G. L. Tong1, G. S. Varner15, J. Wang1, J. Z. Wang1, L. Wang1, L. S. Wang1, P. Wang1,
P. L. Wang1, S. M. Wang1, Y. Y. Wang1, Z. Y. Wang1, C. L. Wei1, N. Wu1, D. M. Xi1, X. M. Xia1, X. X. Xie1,
G. F. Xu1, Y. Xu1, S. T. Xue1, W. B. Yan1, W. G. Yan1, C. M. Yang1, C. Y. Yang1, G. A. Yang1, H. X. Yang1, W.
Yang4, X. F. Yang1, M. H. Ye2, S. W. Ye16, Y. X. Ye16, C. S. Yu1, C. X. Yu1, G. W. Yu1, Y. Yuan1, B. Y. Zhang1,
C. Zhang1, C. C. Zhang1, D. H. Zhang1, H. L. Zhang1, H. Y. Zhang1, J. Zhang1, J. W. Zhang1, L. Zhang1,
L. S. Zhang1, P. Zhang1, Q. J. Zhang1, S. Q. Zhang1, X. Y. Zhang11, Y. Y. Zhang1, Z. P. Zhang16, D. X. Zhao1,
H. W. Zhao1, Jiawei Zhao16, J. W. Zhao1, M. Zhao1, P. P. Zhao1, W. R. Zhao1, Y. B. Zhao1, Z. G. Zhao1,
J. P. Zheng1, L. S. Zheng1, Z. P. Zheng1, B. Q. Zhou1, G. M. Zhou1, L. Zhou1, K. J. Zhu1, Q. M. Zhu1, Y. C. Zhu1,
Y. S. Zhu1, Z. A. Zhu1, B. A. Zhuang1, and B. S. Zou1.
(BES Collaboration)
1Institute of High Energy Physics, Beijing 100039, People’s Republic of China
2China Center of Advanced Science and Technology, Beijing 100080, People’s Republic of China
3Chonbuk National University, Chonju 561-756, Korea
4Colorado State University, Fort Collins, Colorado 80523
5Henan Normal University, Xinxiang 453002, People’s Republic of China
6Huazhong Normal University, Wuhan 430079, People’s Republic of China
7Hunan University, Changsha 410082, People’s Republic of China
8Korea University, Seoul 136-701, Korea
9Nankai University, Tianjin 300071, People’s Republic of China
10Peking University, Beijing 100871, People’s Republic of China
11Shandong University, Jinan 250100, People’s Republic of China
12Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China
13Seoul National University, Seoul 151-742, Korea
14Stanford Linear Accelerator Center, Stanford, California 94309
15University of Hawaii, Honolulu, Hawaii 96822
16University of Science and Technology of China, Hefei 230026, People’s Republic of China
17University of Texas at Dallas, Richardson, Texas 75083-0688
18Wuhan University, Wuhan 430072, People’s Republic of China
19Zhejiang University, Hangzhou 310028, People’s Republic of China
(February 7, 2008)
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We report values of R = σ(e+e−→ hadrons)/σ(e+e−→ µ+µ−) for 85 center-of-mass energies
between 2 and 5 GeV measured with the upgraded Beijing Spectrometer at the Beijing Electron-
Positron Collider.
In precision tests of the Standard Model (SM) [1], the
quantities α(M2
Z), the QED running coupling constant
evaluated at the Z pole, and aµ= (g −2)/2, the anoma-
lous magnetic moment of the muon, are of fundamental
importance. The dominant uncertainties in both α(M2
and aSM
µ
are due to the effects of hadronic vacuum po-
larization, which cannot be reliably calculated in the low
energy region. Instead, with the application of dispersion
relations, experimentally measured R values are used to
determine the vacuum polarization, where R is the lowest
order cross section for e+e−→ γ∗→ hadrons in units of
the lowest-order QED cross section for e+e−→ µ+µ−,
namely R = σ(e+e−→ hadrons)/σ(e+e−→ µ+µ−),
where σ(e+e−→ µ+µ−) = σ0
Values of R in the center-of-mass (c.m.) energy (Ecm)
range below 5 GeV were measured about 20 years ago
with a precision of 15 − 20% [2–4]. In this paper, we
report measurements of R at 85 c.m. energies between
2 and 4.8 GeV, with an average precision of 6.6% [5].
The measurements were carried out with the upgraded
Beijing Spectrometer (BESII) [6] at the Beijing Electron-
Positron Collider (BEPC).
Experimentally, the value of R is determined from the
number of observed hadronic events, Nobs
tion
Z)
µµ= 4πα2(0)/3s.
had, by the rela-
R =Nobs
had− Nbg−?
σ0
lNll− Nγγ
µµ· L · ǫtrg· ¯ ǫhad· (1 + δ),(1)
where Nbgis the number of beam-associated background
events;?
lNll, (l = e,µ,τ) are the numbers of lepton-
pair events from one-photon processes and Nγγthe num-
ber of two-photon process events that are misidentified as
hadronic events; L is the integrated luminosity; δ is the
effective initial state radiative (ISR) correction; ¯ ǫhad is
the average detection efficiency for hadronic events; and
ǫtrg is the trigger efficiency. The triggers and the inte-
grated luminosity measurement were the same as those
used in a preliminary scan that measured R at 6 energy
points between 2.6 and 5 GeV [7].
The hadronic event selection is similar with that used
in the first R scan [7] but with improvements that in-
clude: for good track selection, the distance of closest ap-
proach requirement (< 18cm) of a track to the interaction
point along the beam axis is not imposed; for event-level
selection, the selected tracks must not all point into the
forward (cosθ > 0) or the backward (cosθ < 0) hemi-
sphere. Some distributions comparing data and Monte
Carlo data are shown in Figs. 1 (a)-(c). The cuts used for
selecting hadronic events were varied over a wide range,
e.g. |cosθ| from 0.75 to 0.90, Esum from 0.24Ebeam to
0.32Ebeam (Esum is the total deposited energy, Ebeam
the beam energy) to estimate the systematic error arising
from the event selection; this is the dominant component
of the systematic error as indicated in Table II.
0
100
200
300
400
500
600
700
0 0.51 1.52
0
50
100
150
200
250
-1-0.500.51
0
20
40
60
80
100
120
140
160
180
0123
(a)
p(GeV/c)
Entries/0.033GeV
cosθ
Entries/0.05
(b)
Esum(GeV)
Entries/0.05GeV
(c)
z(cm)
Events/cm
(d)
1
10
102
103
-40 -200 2040
FIG. 1. Distributions for Ecm=3.0 GeV of (a) track mo-
mentum; (b) track cosθ; (c) total energy deposited in the
BSC; and (d) event vertex position along the beam (z) axis.
Histograms and dots in (a)-(c) represent Monte Carlo and real
data, respectively; the beam associated background in (c) has
been removed by sideband subtraction.
The numbers of hadronic events and beam-associated
background events are determined by fitting the distri-
bution of event vertices along the beam direction with
a Gaussian to describe the hadronic events and a poly-
nomial of degree one to three for the beam-associated
background. This background varies from 3 to 10% of
the selected hadronic event candidates, depending on the
energy. The fit using a second degree polynomial, shown
in Fig. 1 (d), turned out to be the best. The difference
between using a polynomial of degree one or three to
that of degree two is about 1%, which is included in the
systematic error in the event selection.
A special joint effort was made by the Lund group and
the BES collaboration to develop the LUARLW gener-
ator, which uses a formalism based on the Lund Model
Area Law, but without the extreme-high-energy approx-
imations used in JETSET’s string fragmentation algo-
rithm [8]. The final states simulated in LUARLW are
exclusive, in contrast to JETSET, where they are inclu-
sive. Above 3.77 GeV, the production of D, D∗, Ds, and
2

Page 3

D∗
Model [9]. A Monte Carlo event generator has been de-
veloped to handle decays of the resonances in the radia-
tive return processes e+e−→ γJ/ψ or γψ(2S) [10].
The parameters in LUARLW are tuned to reproduce
14 distributions of kinematic variables over the entire en-
ergy region covered by the scan [11]. We find that one
set of parameter values is required for the c.m. energy
region below open charm threshold, and that a second
set is required for higher energies. In an alternative ap-
proach, the parameter values were tuned point-by-point
throughout the entire energy range. The detection ef-
ficiencies determined using individually tuned parame-
ters are consistent with those determined with globally
tuned parameters to within 2%. This difference is in-
cluded in the systematic errors. The detection efficien-
cies were also determined using JETSET74 for the ener-
gies above 3 GeV. The difference between the JETSET74
and LUARLW results is about 1%, and is also taken into
account in estimating the systematic uncertainty. Fig-
ure 2 (a) shows the variation of the detection efficiency
as a function of c.m. energy.
We changed the fractions of D, D∗, Ds, and D∗
duction by 50% and find that the detection efficiency
varies less than 1%. We also varied the fraction of the
continuum under the broad resonances by 20%, and find
the change of the detection efficiency is about 1%. These
variations are included in the systematic errors.
sis included in the generator according to the Eichten
spro-
0.4
2.5
0.6
0.8
1
1.5
2
ε(0)
(a)
1+δobs
(b)
Ecm (GeV)
ε(0)(1+δobs)
(c)
0.5
1
1.5
2 2.533.544.55
FIG. 2. (a) The c.m. energy dependence of the detection
efficiency for hadronic events estimated using the LUARLW
generator. The error bars are the total systematic errors. (b)
The calculated radiative correction, and (c) the product of
(a) and (b).
Different schemes for the initial state radiative cor-
rections were compared [12–15], as reported in ref. [7].
Below charm threshold, the four different schemes agree
with each other to within 1%, while above charm thresh-
old, where resonances are important, the agreement is
within 1 to 3%. The radiative correction used in this
analysis is based on ref. [15], and the differences with
the other schemes are included in the systematic error
[16]. In practice, the radiative effects in the detection
efficiency were moved into radiative correction factor by
making the replacement ¯ ǫhad(1 + δ) → ǫ(0)(1 + δobs),
where ǫ(k) is the efficiency for events with a radiative
photon of energy k, and δobscontains a modification of
the bremsstrahlung term to reflect the k-dependence of
the hadronic acceptance.
To calculate δobs, a cutoff in s′, the effective c.m. en-
ergy after ISR to produce hadrons, has to be made.
In our calculation, the mimimum value of s′should be
the threshold for producing two pions, corresponding to
kmax = 1 − s′/s = (0.9805 − 0.9969) in the 2-5 GeV
range. Our criteria to select hadronic events is such that
ǫ approaches zero when k is close to 0.90, which makes
us insensitive to events with high ISR photon energy.
In calculating the radiative correction for the narrow
resonances J/ψ and ψ(2S), the theoretical cross section
is convoluted with the energy distribution of the collid-
ing beams, which is treated as a Gaussian with a rel-
ative beam energy spread of 1.32 × 10−4Ecm (Ecm in
GeV). For the broad resonances at 3770, 4040, 4160, and
4416 MeV, the interferences and the energy-dependence
of total widths were taken into consideration. Initially
the resonance parameters from PDG2000 [17] were used;
then the parameters were allowed to vary and were de-
termined from our fit. The calculation converged after a
few iterations.
We varied the input parameters (masses and widths)
of the J/ψ, ψ(2S), and the broad resonances used in the
radiative correction determination by one standard devi-
ation from the values quoted in ref. [17], and find that the
changes in the R value are less than 1% for most points.
Points close to the resonance at 4.0 GeV have errors from
1 to 1.7%. Figure 2 (b) shows the radiative correction as
a function of c.m. energy, where the structure at higher
energy is related to the radiative tail of the ψ(2S) and
the broad resonances in this energy region. Tables I and
II list some of the values used in the determination of R
and the contributions to the uncertainty in the value of
R at a few typical energy points in the scanned energy
range, respectively.
TABLE I. Some values used in the determination of R at
a few typical energy points.
Ecm
(GeV)
2.000 1155.4 19.5
3.000 2055.4 24.3
4.000768.7
4.800 1215.3 92.6
Nobs
had
Nll+
Nγγ (nb−1) (%)
47.3
135.9
58.0 48.9
84.4
Lǫ(0) 1 + δobs
R
Stat. Sys.
error error
2.18 0.07
2.21 0.05
3.16 0.14
3.66 0.14
49.50
67.55
80.34
86.79
1.024
1.038
1.055
1.113
0.18
0.11
0.15
0.19
Table III lists the values of R from this experiment.
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TABLE II. Contributions to systematic errors: experimen-
tal selection of hadronic events, luminosity determination,
theoretical modeling of hadronic events, trigger efficiency, ra-
diative corrections and total systematic error. All errors are
in percentages (%).
Ecm
(GeV) selection
2.000
3.000
4.000
4.800
hadron
L
M.C.
modeling
2.62
2.66
2.25
3.05
triggerradiative
correction
1.06
1.32
1.82
1.02
total
7.07
3.30
2.64
3.58
2.81
2.30
2.43
1.74
0.5
0.5
0.5
0.5
8.13
5.02
4.64
5.14
They are displayed in Fig. 3, together with BESII val-
ues from ref. [7] and those measured by MarkI, γγ2, and
Pluto [2–4]. The R values from BESII have an aver-
age uncertainty of about 6.6%, which represents a factor
of two to three improvement in precision in the 2 to 5
GeV energy region. Of this error, 3.3% is common to
all points. These improved measurements have a signifi-
cant impact on the global fit to the electroweak data and
the determination of the SM prediction for the mass of
the Higgs particle [18]. In addition, they are expected to
provide an improvement in the precision of the calculated
value of aSM
µ
[19,20], and test the QCD sum rules down
to 2 GeV [21,22].
1
2
3
4
5
6
2345
(a)
Ecm (GeV)
R Value
Gamma2
MarkI
pluto
BESII (1998)
BESII (1999)
2
3
4
5
3.84 4.24.4
Ecm (GeV)
4.6
(b)
R Value
FIG. 3. (a) A compilation of measurements of R in the
c.m. energy range from 1.4 to 5 GeV. (b) R values from this
experiment in the resonance region between 3.7 and 4.6 GeV.
We would like to thank the staff of the BEPC Accelera-
tor Center and IHEP Computing Center for their efforts.
We thank B. Andersson for helping in the development
of the LUARLW generator. We also wish to acknowl-
edge useful discussions with M. Davier, B. Pietrzyk, T.
Sj¨ ostrand, A. D. Martin and M. L. Swartz. We especially
thank M. Tigner for major contributions not only to BES
but also to the operation of the BEPC during the R scan.
This work is supported in part by the National Nat-
ural Science Foundation of China under Contract Nos.
19991480, 19805009 and 19825116; the Chinese Academy
of Sciences under contract Nos.
01 (IHEP); and by the Department of Energy under
Contract Nos.DE-FG03-93ER40788 (Colorado State
University), DE-AC03-76SF00515 (SLAC), DE-FG03-
94ER40833 (U Hawaii), DE-FG03-95ER40925 (UT Dal-
las), and by the Ministry of Science and Technology of
Korea under Contract KISTEP I-03-037(Korea).
KJ95T-03, and E-
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4

Page 5

TABLE III. Values of R from this experiment; the first error is statistical, the second systematic (Ecm in GeV).
Ecm
2.000
2.200
2.400
2.500
2.600
2.700
2.800
2.900
3.000
3.700
3.730
3.750
3.760
3.764
3.768
3.770
3.772
3.776
3.780
3.790
3.810
3.850
REcm
3.890
3.930
3.940
3.950
3.960
3.970
3.980
3.990
4.000
4.010
4.020
4.027
4.030
4.033
4.040
4.050
4.060
4.070
4.080
4.090
4.100
4.110
REcm
4.120
4.130
4.140
4.150
4.160
4.170
4.180
4.190
4.200
4.210
4.220
4.230
4.240
4.245
4.250
4.255
4.260
4.265
4.270
4.280
4.300
4.320
REcm
4.340
4.350
4.360
4.380
4.390
4.400
4.410
4.420
4.430
4.440
4.450
4.460
4.480
4.500
4.520
4.540
4.560
4.600
4.800
R
2.18 ± 0.07 ± 0.18
2.38 ± 0.07 ± 0.17
2.38 ± 0.07 ± 0.14
2.39 ± 0.08 ± 0.15
2.38 ± 0.06 ± 0.15
2.30 ± 0.07 ± 0.13
2.17 ± 0.06 ± 0.14
2.22 ± 0.07 ± 0.13
2.21 ± 0.05 ± 0.11
2.23 ± 0.08 ± 0.08
2.10 ± 0.08 ± 0.14
2.47 ± 0.09 ± 0.12
2.77 ± 0.11 ± 0.13
3.29 ± 0.27 ± 0.29
3.80 ± 0.33 ± 0.25
3.55 ± 0.14 ± 0.19
3.12 ± 0.24 ± 0.23
3.26 ± 0.26 ± 0.19
3.28 ± 0.12 ± 0.12
2.62 ± 0.11 ± 0.10
2.38 ± 0.10 ± 0.12
2.47 ± 0.11 ± 0.13
2.64 ± 0.11 ± 0.15
3.18 ± 0.14 ± 0.17
2.94 ± 0.13 ± 0.19
2.97 ± 0.13 ± 0.17
2.79 ± 0.12 ± 0.17
3.29 ± 0.13 ± 0.13
3.13 ± 0.14 ± 0.16
3.06 ± 0.15 ± 0.18
3.16 ± 0.14 ± 0.15
3.53 ± 0.16 ± 0.20
4.43 ± 0.16 ± 0.21
4.58 ± 0.18 ± 0.21
4.58 ± 0.20 ± 0.23
4.32 ± 0.17 ± 0.22
4.40 ± 0.17 ± 0.19
4.23 ± 0.17 ± 0.22
4.65 ± 0.19 ± 0.19
4.14 ± 0.20 ± 0.19
4.24 ± 0.21 ± 0.18
4.06 ± 0.17 ± 0.18
3.97 ± 0.16 ± 0.18
3.92 ± 0.16 ± 0.19
4.11 ± 0.24 ± 0.23
3.99 ± 0.15 ± 0.17
3.83 ± 0.15 ± 0.18
4.21 ± 0.18 ± 0.19
4.12 ± 0.15 ± 0.16
4.12 ± 0.15 ± 0.19
4.18 ± 0.17 ± 0.18
4.01 ± 0.14 ± 0.14
3.87 ± 0.16 ± 0.16
3.20 ± 0.16 ± 0.17
3.62 ± 0.15 ± 0.20
3.21 ± 0.13 ± 0.15
3.24 ± 0.12 ± 0.15
2.97 ± 0.11 ± 0.14
2.71 ± 0.12 ± 0.13
2.88 ± 0.11 ± 0.14
2.97 ± 0.11 ± 0.14
3.04 ± 0.13 ± 0.14
3.26 ± 0.12 ± 0.16
3.08 ± 0.12 ± 0.15
3.11 ± 0.12 ± 0.12
2.96 ± 0.12 ± 0.14
3.27 ± 0.15 ± 0.18
3.49 ± 0.14 ± 0.14
3.47 ± 0.13 ± 0.18
3.50 ± 0.15 ± 0.17
3.48 ± 0.16 ± 0.16
3.91 ± 0.16 ± 0.19
3.79 ± 0.15 ± 0.20
3.68 ± 0.14 ± 0.17
4.02 ± 0.16 ± 0.20
3.85 ± 0.17 ± 0.17
3.75 ± 0.15 ± 0.17
3.66 ± 0.17 ± 0.16
3.54 ± 0.17 ± 0.18
3.49 ± 0.14 ± 0.15
3.25 ± 0.13 ± 0.15
3.23 ± 0.14 ± 0.18
3.62 ± 0.13 ± 0.16
3.31 ± 0.11 ± 0.16
3.66 ± 0.14 ± 0.19
5