# Measurement of $e^{+}e^{-}\to\omega\eta^{\prime}$ cross sections at
$\sqrt{s}=$ 2.000 to 3.080 GeV

###### Abstract

The Born cross sections for the process $e^{+}e^{-}\to\omega\eta^{\prime}$ are
measured at 22 center-of-mass energies from 2.000 to 3.080 GeV using data
collected with the BESIII detector at the BEPCII collider. A resonant
structure is observed with a statistical significance of 9.6$\sigma$. A Breit-
Wigner fit determines its mass to be $M_{R}=(2153\pm 30\pm
31)~{}{\rm{MeV}}/c^{2}$ and its width to be $\Gamma_{R}=(167\pm 77\pm
7)~{}\rm{MeV}$, where the first uncertainties are statistical and the second
are systematic.

###### Keywords:

$e^{+}e^{-}$ Experiments, Particle and Resonance Production, Spectroscopy

††arxiv: ….

##  1 Introduction

Hadron spectroscopy offers valuable insights into the non-perturbative
dynamics of the strong interaction. According to the Particle Data Group (PDG)
PDG , there are several vector states of the $\omega$ family, i.e.
$J^{PC}=1^{--}$ isoscalar states, with masses around 2.2 GeV, $\omega(2205)$,
$\omega(2290)$ and $\omega(2330)$, which need to be confirmed. It is
noteworthy that the measured widths are usually at least twice as wide as the
theoretical calculations omega2205 ; omega2290 ; omega2330 ; regge_pang ;
jiecheng ; pang2022 .

The BaBar Collaboration has studied the process
$e^{+}e^{-}\to\omega\pi^{+}\pi^{-}$ using the initial state radiation (ISR)
method. The cross section line shape shows evidence for an isoscalar resonance
structure near 2.25 GeV with a significance of 2.6$\sigma$ babar_omegapipi ;
babar_fit . The BESIII Collaboration has studied the processes
$e^{+}e^{-}\to\omega\eta$ bes_omegaeta , $e^{+}e^{-}\to\omega\pi^{0}\pi^{0}$
bes_omegapi0pi0  and $e^{+}e^{-}\to\omega\pi^{+}\pi^{-}$ bes_omegapippim  at
center-of-mass (c.m.) energies ($\sqrt{s}$) from 2.000 to 3.080 GeV. Two
structures around 2.2 GeV are observed with resonance parameters
$M_{1}=2176\pm 24$ ${\rm{MeV}}/c^{2}$, $\Gamma_{1}=89\pm 50$ $\rm{MeV}$ and
$M_{2}=2232\pm 19$ ${\rm{MeV}}/c^{2}$, $\Gamma_{2}=93\pm 53$ $\rm{MeV}$,
respectively. The authors in reference qinsong  introduced the $\omega(4S)$
and $\omega(3D)$ to represent the behavior of these enhancements in the cross
section, and claimed that these two structures are caused by the interference
of $\omega(4S)$ and $\omega(3D)$. To establish higher excited $\omega$ states,
more theoretical and experimental efforts are desirable.

In this paper, we present a measurement of the Born cross sections for the
process $e^{+}e^{-}\to\omega\eta^{\prime}$ at $\sqrt{s}$ from 2.000 to 3.080
GeV based on 22 data samples corresponding to an integrated luminosity of 650
$\rm{pb}^{-1}$ collected by the BESIII experiment.

##  2 BESIII detector and Monte Carlo simulation

The BESIII detector besiii  records symmetric $e^{+}e^{-}$ collisions provided
by the BEPCII storage ring bepcii  in the range of $\sqrt{s}$ from 2.0 to 4.95
GeV, with a peak luminosity of $1\times 10^{33}~{}{\rm{cm}}^{-2}{\rm{s}}^{-1}$
achieved at $\sqrt{s}=3.77$ GeV. BESIII has collected large data samples in
this energy region BESIIIDATA . The cylindrical core of the BESIII detector
covers 93% of the full solid angle and consists of a helium-based multilayer
drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a
CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a
superconducting solenoidal magnet providing a 1.0 T (0.9 T in 2012) magnetic
field. The solenoid is supported by an octagonal flux-return yoke with
resistive plate counter muon identification modules interleaved with steel.
The charged-particle momentum resolution at 1 GeV$/c$ is 0.5%, and the
specific ionization energy loss (d$E$/d$x$) resolution is 6% for electrons
from Bhabha scattering. The EMC measures photon energies with a resolution of
2.5% (5%) at 1 GeV in the barrel (end cap) region. The time resolution in the
TOF barrel region is 68 ps, while that in the end cap region is 110 ps.

Monte Carlo (MC) simulated data samples produced with a GEANT4-based bes_g4
software package, which includes the geometric description detvis  of the
BESIII detector and the detector response, are used to optimize the event
selection criteria, estimate background processes, and determine the detection
efficiency. The signal MC samples for the process
$e^{+}e^{-}\to\omega\eta^{\prime}$ are generated by ConExc bes_conexc  so that
the contribution of the P-wave amplitude between the vector and pseudoscalar
mesons in the final state is taken into account. The decay of the
$\eta^{\prime}$ and $\omega$ are described by the observed amplitude patterns
in $\eta^{\prime}\to\gamma\pi^{+}\pi^{-}$ and
$\omega\to\pi^{+}\pi^{-}\pi^{0}$, respectively besiii_etapDA ; besiii_omegaDA
. For background studies, MC samples of inclusive hadronic events are
generated with a hybrid generator that integrates ConExc bes_conexc , LUARLW
bes_luarlw  and PHOKHARA bes_phokhara . Exclusive MC samples of
$e^{+}e^{-}\to\omega\pi^{+}\pi^{-}$ and $e^{+}e^{-}\to
2(\pi^{+}\pi^{-}\pi^{0})$ are generated by ConExc bes_conexc  according to
published results of BESIII and BaBar bes_omegapippim ; babar_6pi .

##  3 Event selection and background analysis

The signal process $e^{+}e^{-}\to\omega\eta^{\prime}$ is reconstructed using
the decays $\omega\to\pi^{+}\pi^{-}\pi^{0}$, $\pi^{0}\to\gamma\gamma$ and
$\eta^{\prime}\to\gamma\pi^{+}\pi^{-}$. The signal candidates are required to
contain four charged pions with zero net charge and at least three photon
candidates.

Charged tracks detected in the MDC are required to be within a polar angle
($\theta$) range of $|\\!\cos\theta|<0.93$, where $\theta$ is defined with
respect to the $z$ axis, defined as the symmetry axis of the MDC. For each
charged track, the distance of closest approach to the interaction point (IP)
is required to be within 10 cm in the beam direction and within 1 cm in the
plane perpendicular to the beam direction. Particle identification (PID) for
charged tracks combines measurements of the d$E$/d$x$ in the MDC and the
flight time in the TOF to form likelihoods $\mathcal{L}(h)(h=p,K,\pi)$ for
each hadron $h$ hypothesis. Charged tracks are identified as pions when the
pion hypothesis has the greatest likelihood [$\mathcal{L}(\pi)>\mathcal{L}(K)$
and $\mathcal{L}(\pi)>\mathcal{L}(p)$].

Photon candidates are identified using isolated showers in the EMC. The
deposited energy of each shower must be more than 25 MeV in the barrel region
($|\\!\cos\theta|<0.80$) and more than 50 MeV in the end cap region
($0.86<|\\!\cos\theta|<0.92$). To exclude showers that originate from charged
tracks, the angle subtended by the EMC shower and the position of the closest
charged track at the EMC must be greater than $10^{\circ}$ as measured from
IP. To suppress electronic noise and showers unrelated to the event, the
difference between the EMC time and the event start time of the photon
candidate is required to be within [0,700] ns.

To suppress the background and improve the resolution of kinematic quantities,
a four-constraint (4C) kinematic fit imposing energy-momentum conservation is
carried out under the hypothesis of $e^{+}e^{-}\to 2(\pi^{+}\pi^{-})3\gamma$.
If there are more than three photon candidates in one event, the combination
with the minimum $\chi_{{\rm{4C}}}^{2}$ is retained for further analysis. The
candidate events are required to satisfy $\chi_{{\rm{4C}}}^{2}<60$. To
suppress the contamination from the processes $e^{+}e^{-}\to
2(\pi^{+}\pi^{-})\pi^{0}$ or $e^{+}e^{-}\to 2(\pi^{+}\pi^{-}\pi^{0})$, two
additional 4C kinematic fits under the hypotheses of $e^{+}e^{-}\to
2(\pi^{+}\pi^{-}\gamma)$ and $e^{+}e^{-}\to 2(\pi^{+}\pi^{-}2\gamma)$ are
independently performed. Only those events which satisfy
$\chi^{2}_{{\rm{4C}}}<\chi^{2}_{{\rm{4C}}}(2(\pi^{+}\pi^{-}\gamma))$ and
$\chi^{2}_{{\rm{4C}}}<\chi^{2}_{{\rm{4C}}}(2(\pi^{+}\pi^{-}2\gamma))$ are
retained. The photon combination with the smallest value of
$|M(\gamma\gamma)-M_{\pi^{0}}|$ is used to form the $\pi^{0}$ candidate, where
$M_{\pi^{0}}$ is the known $\pi^{0}$ mass PDG . The distribution of the
$\gamma\gamma$ invariant mass, $M(\gamma\gamma)$, at $\sqrt{s}=2.125$ GeV is
shown in Fig. LABEL:fig:2125signal(a). The $\omega$ candidate is taken to be
the $\pi^{+}\pi^{-}\pi^{0}$ combination with the smallest value of
$|M(\pi^{+}\pi^{-}\pi^{0})-M_{\omega}|$, where $M_{\omega}$ is the nominal
$\omega$ mass PDG . The distribution of the $\pi^{+}\pi^{-}\pi^{0}$ invariant
mass, $M(\pi^{+}\pi^{-}\pi^{0})$, at $\sqrt{s}=2.125$ GeV is shown in Fig.
LABEL:fig:2125signal(b). The distribution of the invariant mass of the
remaining photon and $\pi^{+}\pi^{-}$, $M(\gamma\pi^{+}\pi^{-})$, at
$\sqrt{s}=2.125$ GeV is shown in Fig. LABEL:fig:2125signal(c), where an
$\eta^{\prime}$ signal is visible with the
$|M(\gamma\gamma)-M_{\pi^{0}}|<0.015$ GeV/$c^{2}$ and
$|M(\pi^{+}\pi^{-}\pi^{0})-M_{\omega}|<0.029$ GeV/$c^{2}$ requirements,
corresponding to about 3$\sigma$ in the mass resolutions. The signal region of
the $\eta^{\prime}$ is defined as
$|M(\gamma\pi^{+}\pi^{-})-M_{\eta^{{}^{\prime}}}|<0.025$ ${\rm{GeV}}/c^{2}$,
where $M_{\eta^{\prime}}$ is the nominal $\eta^{\prime}$ mass PDG . The
sideband region of the $\eta^{\prime}$ is defined as
$0.05<|M(\gamma\pi^{+}\pi^{-})-M_{\eta^{{}^{\prime}}}|<0.10$
${\rm{GeV}}/c^{2}$.

\begin{overpic}[width=208.13574pt]{figure/2125pi0.pdf} \put(75.0,60.0){(a)}
\end{overpic}\begin{overpic}[width=208.13574pt]{figure/2125omega3.pdf}
\put(75.0,60.0){(b)}
\end{overpic}\begin{overpic}[width=208.13574pt]{figure/2125.pdf}
\put(75.0,60.0){(c)} \end{overpic}

Potential background sources are studied by analyzing inclusive
$e^{+}e^{-}\to$ hadrons and exclusive MC samples. Exclusive MC samples for
$e^{+}e^{-}\to\omega\pi^{+}\pi^{-}$ and $e^{+}e^{-}\to
2(\pi^{+}\pi^{-}\pi^{0})$ are generated by ConExc bes_conexc  with an
amplitude model introduced in ref. bes_omegapippim  for the process
$e^{+}e^{-}\to\omega\pi^{+}\pi^{-}$ and a phase-space model for the process
$e^{+}e^{-}\to 2(\pi^{+}\pi^{-}\pi^{0})$ taking into account the cross
sections measured by BaBar babar_6pi . Simulated events are subject to the
same selection procedure as the signal process. Those non-$\eta^{\prime}$
events, e.g., $e^{+}e^{-}\to\omega\pi^{+}\pi^{-}$, form a peaking background
in the $M(\pi^{+}\pi^{-}\pi^{0})$ distribution, as shown in figure
LABEL:fig:2125signal(b) and are estimated using the $\eta^{\prime}$ sideband.
The background in the $M(\gamma\pi^{+}\pi^{-})$ distribution, determined from
exclusive MC samples and the inclusive hadronic MC sample, is flat. Therefore,
the number of signal is determined by fitting the $M(\gamma\pi^{+}\pi^{-})$
spectrum. The dominant background stems from the $e^{+}e^{-}\to
2(\pi^{+}\pi^{-}\pi^{0})$ process. The background distribution obtained from
the inclusive hadronic MC sample, which has been normalized to the integrated
experimental luminosity, is shown in figure LABEL:fig:2125signal(c).

The signal yields of the $e^{+}e^{-}\to\omega\eta^{\prime}$ process are
obtained by performing an unbinned maximum likelihood fit to the
$M(\gamma\pi^{+}\pi^{-})$ spectrum. The signal is described by the signal MC-
simulated shape convolved with a Gaussian function that describes the
difference between data and MC simulation. The background function is
parametrized by a second-order Chebychev function. The corresponding fit
result for data taken at $\sqrt{s}=2.125$ GeV is shown in Fig.
LABEL:fig:2125signal(c). The same event selection criteria and fit procedure
are applied for all data samples at the other c.m. energies. The obtained
signal yields are listed in table 1.

##  4 Born cross section and systematic uncertainty

The Born cross section for $e^{+}e^{-}\to\omega\eta^{\prime}$ is calculated by

$\sigma(\sqrt{s})=\frac{N_{\rm{sig}}}{\mathcal{L}\cdot\epsilon\cdot\mathcal{B}\cdot\frac{1}{|1-\Pi|^{2}}\cdot(1+\delta)},$
(1)

where $N_{\rm{sig}}$ is the number of signal events, $\mathcal{L}$ is the
integrated luminosity, $\epsilon$ is the selection efficiency, $\mathcal{B}$
is the product of subleading branching fractions,
$\mathcal{B}=\mathcal{B}_{\omega\to\pi^{+}\pi^{-}\pi^{0}}\cdot\mathcal{B}_{\eta^{\prime}\to\gamma\pi^{+}\pi^{-}}\cdot\mathcal{B}_{\pi^{0}\to\gamma\gamma}=26.0\%$,
taken from the PDG PDG , $\frac{1}{|1-\Pi|^{2}}$ is the vacuum polarization
factor (VP) VP , and $1+\delta$ is the ISR correction factor, which is
obtained by a QED calculation isr_calculate  that takes the line shape of the
Born cross section into account. Both $\epsilon$ and $1+\delta$ depend on the
line shape of the cross sections and are determined via an iterative procedure
jingmq ; bes_kskl . The $\epsilon$ and $1+\delta$ are calculated according to
the fit curve and are taken as input for the next iteration. The procedure is
repeated until the difference between the final measured Born cross sections
and the last one less than 0.1%. The statistical significance of the signal
for each energy point is estimated by considering the change of likelihood
$\Delta(L)$ and the number of degrees of freedom in fits that include or do
not include the signal function. For energy points where the significance of
the signal is less than or close to $3\sigma$, the upper limits for the number
of signal events ($N_{\rm{sig}}^{\rm{up}}$) and the cross section
($\sigma^{\rm{up}}$) are obtained by performing a profile-likelihood method
upper . The Born cross sections and upper limits at the 90% confidence level
for all 22 energy points are summarized in table 1.

$\sqrt{s}$ (GeV) | $N_{\rm{sig}}$ | $N_{\rm{sig}}^{\rm{up}}$ |  $\mathcal{L}$ (pb-1) | $\epsilon\cdot(1+\delta)$ | VP |  $\sigma$ (pb) |  $\sigma^{\rm{up}}$(pb) | Significance ($\sigma$)
---|---|---|---|---|---|---|---|---
2.0000 | $10.9\pm 5.6$ | <23.1 | 10.1 | 0.0988 | 1.037 | $40.63\pm 20.87\pm 2.56$ | <86.13 | 1.9
2.0500 | $10.5\pm 4.1$ | - | 3.3 | 0.0986 | 1.038 | $118.40\pm 46.22\pm 7.46$ | - | 3.6
2.1000 | $23.7\pm 6.8$ | - | 12.2 | 0.0987 | 1.039 | $72.43\pm 20.78\pm 4.56$ | - | 4.4
2.1250 | $273.7\pm 22.6$ | - | 108.5 | 0.1000 | 1.039 | $93.71\pm 7.74\pm 5.90$ | - | 15.6
2.1500 | $8.8^{+4.3}_{-3.5}$ | <16.6 | 2.8 | 0.1016 | 1.040 | $113.00^{+55.22}_{-44.95}\pm 7.12$ | <213.23 | 3.1
2.1750 | $13.8\pm 4.3$ | <22.5 | 10.6 | 0.1045 | 1.040 | $46.02\pm 14.34\pm 2.90$ | <75.05 | 3.4
2.2000 | $26.2\pm 8.0$ | - | 13.7 | 0.1046 | 1.040 | $67.40\pm 20.58\pm 4.25$ | - | 4.8
2.2324 | $8.4^{+5.0}_{-4.3}$ | <16.5 | 11.9 | 0.1046 | 1.041 | $24.84^{+14.79}_{-12.72}\pm 1.56$ | <48.80 | 2.2
2.3094 | $0.4^{+4.1}_{-3.3}$ | <8.4 | 21.1 | 0.1036 | 1.041 | $0.67^{+6.91}_{-5.56}\pm 0.04$ | <14.15 | 0.1
2.3864 | $0.0^{+4.4}_{-3.6}$ | <8.4 | 22.5 | 0.1063 | 1.041 | $0.03^{+6.82}_{-5.58}\pm 0.00$ | <13.02 | 0.0
2.3960 | $3.6^{+6.6}_{-5.8}$ | <16.5 | 66.9 | 0.1066 | 1.041 | $1.85^{+3.40}_{-2.99}\pm 0.12$ | <8.50 | 0.8
2.5000 | $0.4^{+1.6}_{-0.0}$ | <4.7 | 1.1 | 0.1127 | 1.041 | $11.84^{+47.36}_{-79.91}\pm 0.85$ | <139.11 | 0.1
2.6444 | $9.5^{+4.5}_{-3.8}$ | <16.4 | 33.7 | 0.1146 | 1.039 | $9.08^{+4.30}_{-3.63}\pm 0.57$ | <15.67 | 3.0
2.6464 | $1.2^{+3.0}_{-2.3}$ | <6.9 | 34.0 | 0.1151 | 1.039 | $1.14^{+2.86}_{-2.19}\pm 0.07$ | <6.57 | 0.5
2.7000 | $0.0^{+0.6}_{-0.0}$ | <3.9 | 1.0 | 0.1188 | 1.039 | $0.00^{+18.63}_{-0.00}\pm 0.00$ | <121.12 | 0.0
2.8000 | $0.0^{+0.5}_{-0.0}$ | <2.5 | 1.0 | 0.1185 | 1.037 | $0.00^{+15.53}_{-0.00}\pm 0.00$ | <77.64 | 0.0
2.9000 | $1.5^{+3.8}_{-2.9}$ | <8.7 | 105.3 | 0.1238 | 1.033 | $0.43^{+1.10}_{-0.84}\pm 0.03$ | <2.51 | 0.5
2.9500 | $1.6^{+2.3}_{-1.6}$ | <6.5 | 15.9 | 0.1208 | 1.029 | $3.08^{+4.43}_{-3.08}\pm 0.19$ | <12.51 | 1.6
2.9810 | $3.4^{+2.9}_{-2.1}$ | <8.5 | 16.1 | 0.1266 | 1.025 | $6.30^{+5.38}_{-3.89}\pm 0.40$ | <15.76 | 1.9
3.0000 | $0.0^{+1.1}_{-2.1}$ | <3.2 | 15.9 | 0.1270 | 1.021 | $0.00^{+2.07}_{-3.95}\pm 0.00$ | <6.02 | 0.0
3.0200 | $0.3^{+1.5}_{-0.8}$ | <3.2 | 17.3 | 0.1262 | 1.014 | $0.52^{+2.60}_{-1.39}\pm 0.03$ | <5.55 | 0.3
3.0800 | $0.9^{+3.0}_{-2.1}$ | <6.5 | 126.2 | 0.1298 | 0.915 | $0.24^{+0.79}_{-0.55}\pm 0.02$ | <1.70 | 0.4

Table 1: The Born cross sections for $e^{+}e^{-}\to\omega\eta^{\prime}$. All
definitions of symbols are the same as those in eq. (1). Upper limits are
given at the 90% confidence level. For the Born cross section $\sigma$, the
first uncertainty is statistical and the second is systematic. The VP column
lists the vacuum polarization correction factor.

Various sources of systematic uncertainties concerning the measurement of the
Born cross sections are investigated; these include the integrated luminosity,
the charged track efficiency, the photon reconstruction efficiency, the PID
efficiency, the kinematic fit, the requirement on $M(\pi^{+}\pi^{-}\pi^{0})$,
ISR and VP correction factors, input branching fractions, and the fit to the
$M(\gamma\pi^{+}\pi^{-})$ distribution. These sources are described as
follows.

  * •

The uncertainty associated with the integrated luminosity is $1\%$, which is
estimated by using large angle Bhabha events in ref. besiii_lumin .

  * •

The uncertainties related to the tracking and PID efficiencies of charged
pions are investigated using a control sample of $e^{+}e^{-}\to
K^{+}K^{-}\pi^{+}\pi^{-}$ besiii_kk ; bes_kskl . The uncertainties on the
tracking and PID efficiencies are estimated to be 1% per charged pion track.

  * •

The uncertainty concerning the photon detection efficiency is studied with a
control sample of $e^{+}e^{-}\to K^{+}K^{-}\pi^{+}\pi^{-}\pi^{0}$ besiii_pi0 .
The result shows that the difference in detection efficiency between data and
MC simulation is 1% per photon.

  * •

The uncertainties arising from the $\chi^{2}_{\rm{4C}}$ requirement in the
kinematic fit and the $\omega$ invariant mass requirement are evaluated from a
control sample $J/\psi\to\omega\eta^{\prime}$. The averaged difference between
the data and MC simulation of $J/\psi\to\omega\eta^{\prime}$ by using each
requirement or not is taken as the systematic uncertainty.

  * •

The uncertainty of the VP and ISR correction factors is obtained with the
accuracy of the radiation function, which is about 0.5% VP , and has an
additional contribution from the cross section line shape, which is estimated
by varying the model parameters of the fit to the cross section. Considering
correlations among the parameters, all parameters are randomly generated using
a correlated multi-variable Gaussian function and the resulting
parametrization of the line shape is used to recalculate $(1+\delta)\epsilon$
and the corresponding cross section. This procedure is repeated one thousand
times and the standard deviation of the resulting cross section is considered.
The systematic uncertainty associated with the VP and ISR correction factors
is assigned as their quadratic sum besiii_kk .

  * •

The uncertainty associated with the quoted branching fractions from the PDG
PDG  is $1.5\%$, including the effects of
$\mathcal{B}_{\omega\to\pi^{+}\pi^{-}\pi^{0}}=(89.2\pm 0.7)\%$,
$\mathcal{B}_{\pi^{0}\to\gamma\gamma}=(98.823\pm 0.034)\%$ and
$\mathcal{B}_{\eta^{\prime}\to\gamma\pi^{+}\pi^{-}}=(29.5\pm 0.4)\%$.

  * •

The uncertainty caused by the fit to the $M(\gamma\pi^{+}\pi^{-})$
distribution includes the descriptions of the signal shape, background shape
and fit range and is estimated by the control sample
$J/\psi\to\omega\eta^{\prime}$. The nominal MC-simulated shape convolved with
a Gaussian function is replaced by a pure MC-simulated shape, and the
difference is taken as the uncertainty. Replacing the nominal background shape
by a first-order Chebychev function, the deviation from the nominal result is
taken as the uncertainty. The fit range is varied by $\pm 10$ MeV$/c^{2}$ at
both boundaries, and the largest difference is taken as the uncertainty. The
uncertainties from these three sources are added in quadrature and taken as
the total uncertainty from the $M(\gamma\pi^{+}\pi^{-})$ fit.

Table 2 summarizes all the systematic uncertainties related to the Born cross
section for each energy point, where the sources of the uncertainties tagged
with ‘*’ are assumed to be 100% correlated among c.m. energies. The total
systematic uncertainty for each energy point is calculated as the quadratic
sum of the individual uncertainties, assuming they are independent.

$\sqrt{s}$ (GeV) | $\mathcal{L}^{*}$ | $\rm{Track}^{*}$ | $\rm{Pho.}^{*}$ | $\rm{PID}^{*}$ | $\rm{Kin.}^{*}$ | $\omega~{}\rm{Mass}^{*}$ | $\rm{Rad.}$ | $\rm{Br}^{*}$ | Fit∗ | Sum
---|---|---|---|---|---|---|---|---|---|---
2.0000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.1
2.0500 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.7 | 1.5 | 2.4 | 7.2
2.1000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 1.5 | 1.5 | 2.4 | 7.3
2.1250 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 1.5 | 1.5 | 2.4 | 7.3
2.1500 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 1.1 | 1.5 | 2.4 | 7.2
2.1750 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.8 | 1.5 | 2.4 | 7.2
2.2000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.7 | 1.5 | 2.4 | 7.2
2.2324 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.2
2.3094 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.2
2.3864 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.2
2.3960 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.2
2.5000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.2
2.6444 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
2.6464 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.2
2.7000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.6 | 1.5 | 2.4 | 7.2
2.8000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
2.9000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
2.9500 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
2.9810 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
3.0000 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
3.0200 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
3.0800 | 1.0 | 4.0 | 3.0 | 4.0 | 0.2 | 0.9 | 0.5 | 1.5 | 2.4 | 7.2
Table 2: Systematic uncertainties (in %) in the Born cross section of
$e^{+}e^{-}\to\omega\eta^{\prime}$ at each energy point. These represent the
uncertainties in the estimated effects of the integrated luminosity
($\mathcal{L}$), tracking efficiency ($\rm{Track}$), photon reconstruction
efficiency ($\rm{Pho.}$), PID efficiency ($\rm{PID}$), kinematic fit
($\rm{Kin.}$), $\omega$ mass window ($\omega~{}\rm{Mass}$), VP and ISR
correction factor ($\rm{Rad.}$), branching fraction ($\rm{Br}$) and
$M(\gamma\pi^{+}\pi^{-})$ fit ($\rm{Fit}$). The total uncertainty (Sum) is
obtained by summing the individual contributions in quadrature.

##  5 Fit to the line shape

The measured Born cross sections are shown in figure LABEL:fig:fitresult,
where a clear structure is visible around 2.2 GeV. A $\chi^{2}$ fit,
incorporating the correlated and uncorrelated uncertainties among different
energy points, is performed to extract resonance parameters. The fit
probability density function is a coherent sum of a continuum component
$f_{1}$ and a resonant component $f_{2}$. The cross section is modeled as

$\sigma=\frac{12\pi}{s^{3/2}}|f_{1}+e^{i\phi}f_{2}|^{2}PS(\sqrt{s}),$ (2)

where $\phi$ is the relative phase between these two components, and
$PS(\sqrt{s})$ is the phase-space factor bes_omegaeta  given by
$PS(\sqrt{s})=q^{3}$, where $q$ is the $\omega$ momentum in the $e^{+}e^{-}$
c.m. frame calculated for the mass value $M_{\omega}=0.78265$ GeV/$c^{2}$ PDG
. The contribution from lower-mass vector states is considered in the
description of $f_{1}$ as

$f_{1}=C_{0}\cdot e^{-p_{0}(\sqrt{s}-M_{\rm{th}})},$ (3)

where $C_{0}$ and $p_{0}$ are free parameters, and $M_{\rm{th}}=1.7404$
GeV/$c^{2}$ is the mass threshold for $\omega\eta^{\prime}$ production PDG ;
besiii_kkpi . The resonant amplitude $f_{2}$ is described by a Breit-Wigner
(BW) function:

$f_{2}=\sqrt{\frac{\Gamma_{R}^{e^{+}e^{-}}\cdot
B_{R}^{\omega\eta^{\prime}}}{PS(m_{R})}}\frac{m_{R}^{3/2}\sqrt{\Gamma_{R}}}{s-m_{R}^{2}+i\sqrt{s}\Gamma_{R}},$
(4)

where $m_{R}$ and $\Gamma_{R}$ are the mass and width of the resonant
structure, $\Gamma_{R}^{e^{+}e^{-}}$ is its partial width to $e^{+}e^{-}$, and
$B_{R}$ is the branching fraction of $R\to\omega\eta^{\prime}$.

In total, there are six free parameters in the fit:
$\phi,C_{0},p_{0},m_{R},\Gamma_{R}$ and the product of
$\Gamma_{R}^{e^{+}e^{-}}B_{R}$. The fit results are shown in figure
LABEL:fig:fitresult, and resonance parameters are listed in table 3. The fit
has two solutions with identical mass and width for the resonance. The two
solutions for the phase $\phi$ and $\Gamma_{R}^{e^{+}e^{-}}B_{R}$ are
consistent with each other considering their uncertainties. The fit quality is
$\chi^{2}/\rm{ndf}=13.5/16$, where ndf is the number of degrees of freedom.
The mass and width of the resonance are $M_{R}=(2153\pm 30)~{}\rm{MeV}/c^{2}$
and $\Gamma_{R}=(167\pm 77)~{}\rm{MeV}$, respectively, where the uncertainties
are statistical only. The significance of the resonance is determined to be
$9.6\sigma$ by comparing the change of the $\chi^{2}$ in fits with and without
the resonance and considering the change in ndf. The uncertainties
(statistical and systematic) of the measured Born cross sections have been
considered when fitting the line shape, extracting the resonance parameters
and estimating the significance of the resonance.

\begin{overpic}[width=195.12767pt]{figure/so1_more.pdf} \put(87.0,63.0){(a)}
\end{overpic}\begin{overpic}[width=195.12767pt]{figure/so2_more.pdf}
\put(87.0,63.0){(b)} \end{overpic}

Parameter | Solution 1 | Solution 2
---|---|---
$M_{R}$ (MeV/$c^{2}$) | $2153\pm 30(\rm{stat.})\pm 31(\rm{syst.})$
$\Gamma_{R}$ (MeV) | $167\pm 77(\rm{stat.})\pm 7(\rm{syst.})$
$\phi$ (rad) | $3.78\pm 0.24(\rm{stat.})\pm 0.12(\rm{syst.})$ | $3.16\pm 0.4(\rm{stat.})\pm 0.2(\rm{syst.})$
$\Gamma^{e^{+}e^{-}}_{R}\cal{B}_{R}^{\omega\eta^{\prime}}$ (eV) | $5.72\pm 1.68(\rm{stat.})\pm 1.5(\rm{syst.})$ | $2.99\pm 1.68(\rm{stat.})\pm 1.2(\rm{syst.})$
Significance | $9.6\sigma$
Table 3: The obtained resonance parameters.

The systematic uncertainties of the resonant parameters are due to the c.m.
energy from BEPCII and the formula used in the fit procedure. The uncertainty
of the c.m. energy calibration is estimated as $0.1\%$. It is ignored in the
determination of the resonance parameters besiii_lumin . To evaluate the
systematic uncertainty associated with the fit formula, the continuum term
$C_{0}\cdot e^{-p_{0}(\sqrt{s}-M_{\rm{th}})}$ is replaced with an exponential
function of the form $c_{1}/s^{c_{2}}$, where $c_{1}$ and $c_{2}$ are free
parameters and the width $\Gamma_{R}$ is replaced with an energy-dependent
width of the form
$\Gamma_{R}(\sqrt{s})=\Gamma_{R}\cdot\frac{PS(\sqrt{s})}{PS(M_{R})}$
besiii_kkpi . The deviation of the obtained parameters from the nominal
results are taken as the systematic uncertainties. The resonance parameters,
which have been considered systematically, are listed in table 3.

##  6 Summary

In summary, the Born cross sections of the process
$e^{+}e^{-}\to\omega\eta^{\prime}$ are measured at center-of-mass energies
from 2.000 to 3.080 GeV using 22 data samples corresponding to a total
integrated luminosity of 650 $\rm{pb}^{-1}$ collected by the BESIII detector.
By analyzing the energy dependence of the cross sections, a structure is
observed with a statistical significance of 9.6$\sigma$ with mass
$M_{R}=(2153\pm 30\pm 31)~{}{\rm{MeV}}/c^{2}$ and width $\Gamma_{R}=(167\pm
77\pm 7)~{}\rm{MeV}$, where the first and second uncertainties are statistical
and systematic, respectively.

Compared to the resonance parameters for structures around 2.2 GeV obtained
from the previous BESIII measurements via $e^{+}e^{-}\to\omega\eta$
bes_omegaeta , $e^{+}e^{-}\to\omega\pi^{0}\pi^{0}$ bes_omegapi0pi0  and
$e^{+}e^{-}\to\omega\pi^{+}\pi^{-}$ bes_omegapippim , $M_{1}=2176\pm 24$
${\rm{MeV}}/c^{2}$, $\Gamma_{1}=89\pm 50$ $\rm{MeV}$ and $M_{2}=2232\pm 19$
${\rm{MeV}}/c^{2}$, $\Gamma_{2}=93\pm 53$ $\rm{MeV}$, respectively, the
parameters obtained in this work are in agreement with them within $3\sigma$.

Supposing the resonances around 2.2 GeV observed in $R\to\omega\eta$ and
$R\to\omega\eta^{\prime}$ are the same, and $R$ only contains $u\bar{u}$ and
$d\bar{d}$ quarks, the ratio between branching fractions of $R\to\omega\eta$
and $R\to\omega\eta^{\prime}$ can be written as

$\frac{B_{R}^{\omega\eta^{\prime}}}{B_{R}^{\omega\eta}}=\left|\frac{\cos(\Theta_{0}-\Theta)}{\sin(\Theta_{0}-\Theta)}\right|^{2}\frac{\Omega_{\eta^{\prime}}}{\Omega_{\eta}},$
(5)

where $\Theta_{0}=35.3^{\circ}$ is the ideal mixing angle between pure
$s\bar{s}$ and $u\bar{u}-d\bar{d}$, and
$\Omega_{\eta^{\prime}}(\Omega_{\eta})$ is the phase-space factor including
the P-wave effect in the decay Zhukai ; Zhukai2 . Based on the suggested
mixing angle $\Theta=-14.1\pm 2.8^{\circ}$ calculated by lattice QCD PDG ;
LQCD_mix , the ratio between
$\Gamma^{e^{+}e^{-}}_{R}\cal{B}_{R}^{\omega\eta^{\prime}}$ and
$\Gamma^{e^{+}e^{-}}_{R}\cal{B}_{R}^{\omega\eta}$ is $0.34\pm 0.07$. Combining
our results with the previous BESIII measurements of the
$e^{+}e^{-}\to\omega\eta$ process bes_omegaeta , and taking into account the
mutiple solutions for the resonance parameters, these ratios are measured to
be $13.30\pm 6.06\pm 3.61$, $2.39\pm 1.63\pm 1.01$, $4.58\pm 2.21\pm 1.34$ and
$6.95\pm 4.60\pm 2.83$, where the first and second uncertainties are
statistical and systematic, respectively. All of them are greater than
$0.34\pm 0.07$ based on the $\eta-\eta^{\prime}$ mixing angle given by lattice
QCD. Future experimental and theoretical studies will be helpful to improve
the knowledge of excited $\omega$ states around 2.2 GeV.

###### Acknowledgements.

The BESIII Collaboration thanks the staff of BEPCII, the IHEP computing center
and the supercomputing center of USTC for their strong support. This work is
supported in part by National Key R&D Program of China under Contracts Nos.
2020YFA0406400, 2020YFA0406300; National Natural Science Foundation of China
(NSFC) under Contracts Nos. 11635010, 11735014, 11835012, 11935015, 11935016,
11935018, 11961141012, 12022510, 12025502, 12035009, 12035013, 12192260,
12192261, 12192262, 12192263, 12192264, 12192265, 12275320, 11625523,
11705192, 11950410506, 12061131003, 12105276, 12122509; the Chinese Academy of
Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for
Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility
Funds of the NSFC and CAS under Contracts Nos. U1832207, U1732263, U1832103,
U2032111; CAS Key Research Program of Frontier Sciences under Contracts Nos.
QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100 Talents Program of CAS; The Institute
of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for
Particle Physics and Cosmology; ERC under Contract No. 758462; European
Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-
Curie grant agreement under Contract No. 894790; German Research Foundation
DFG under Contracts Nos. 443159800, 455635585, Collaborative Research Center
CRC 1044, FOR5327, GRK 2149; Istituto Nazionale di Fisica Nucleare, Italy;
Ministry of Development of Turkey under Contract No. DPT2006K-120470; National
Research Foundation of Korea under Contract No. NRF-2022R1A2C1092335; National
Science and Technology fund; National Science Research and Innovation Fund
(NSRF) via the Program Management Unit for Human Resources & Institutional
Development, Research and Innovation under Contract No. B16F640076; Polish
National Science Centre under Contract No. 2019/35/O/ST2/02907; The Royal
Society, UK under Contracts Nos. DH140054, DH160214; The Swedish Research
Council; U. S. Department of Energy under Contract No. DE-FG02-05ER41374.

## References

  * (1) Particle Data Group collaboration, _Review of Particle Physics_ , _PTEP_ 2022 (2022) 083C01.
  * (2) A.V. Anisovich et al., _$I=0,C=-1$ mesons from 1940 to 2410 MeV_, _Phys. Lett. B_ 542 (2002) 19 [1109.5817].
  * (3) D.V. Bugg, _Partial wave analysis of $\bar{p}p\to\bar{\Lambda}\Lambda$_, _Eur. Phys. J. C_ 36 (2004) 161 [hep-ph/0406292].
  * (4) Omega Photon collaboration, _Photon diffractive dissociation to $\rho\rho\pi$ and $\rho\pi\pi\pi$ states_, _Z. Phys. C_ 38 (1988) 535.
  * (5) C.-Q. Pang, Y.-R. Wang, J.-F. Hu, T.-J. Zhang and X. Liu, _Study of the $\omega$ meson family and newly observed $\omega$-like state $X(2240)$_, _Phys. Rev. D_ 101 (2020) 074022 [1910.12408].
  * (6) J.-C. Feng, X.-W. Kang, Q.-F. Lü and F.-S. Zhang, _Possible assignment of excited light ${}^{3}S_{1}$ vector mesons_, _Phys. Rev. D_ 104 (2021) 054027 [2104.01339].
  * (7) Y.-R. Wang, T.-Y. Li, Z.-Y. Fang, H. Chen and C.-Q. Pang, _Study of the $\omega$ and $\omega$3, $\rho$ and $\rho$3, and the newly observed $\omega$-like state X(2220)_, _Phys. Rev. D_ 106 (2022) 114024 [2208.10329].
  * (8) BaBar collaboration, _The $e^{+}e^{-}$ $\to$ $2(\pi^{+}\pi^{-})\pi^{0},2(\pi^{+}\pi^{-})\eta,K^{+}K^{-}\pi^{+}\pi^{-}\pi^{0}$ and $K^{+}K^{-}\pi^{+}\pi^{-}\eta$ Cross Sections Measured with Initial-State Radiation_, _Phys. Rev. D_ 76 (2007) 092005 [0708.2461].
  * (9) BaBar collaboration, _Resonances in $e^{+}e^{-}$ annihilation near 2.2 GeV_, _Phys. Rev. D_ 101 (2020) 012011 [1912.04512].
  * (10) BESIII collaboration, _Observation of a resonant structure in $e^{+}e^{-}\to\omega\eta$ and another in $e^{+}e^{-}\to\omega\pi^{0}$ at center-of-mass energies between 2.00 and 3.08 GeV_, _Phys. Lett. B_ 813 (2021) 136059 [2009.08099].
  * (11) BESIII collaboration, _Measurement of the $e^{+}e^{-}\rightarrow\omega\pi^{0}\pi^{0}$ cross section at center-of-mass energies from 2.0 to 3.08 GeV_, _Phys. Rev. D_ 105 (2022) 032005 [2112.15076].
  * (12) BESIII collaboration, _Measurement of $e^{+}e^{-}\rightarrow\omega\pi^{+}\pi^{-}$ cross section at $\sqrt{s}=$ 2.000 to 3.080 GeV_, 2208.04507.
  * (13) Q.-S. Zhou, J.-Z. Wang and X. Liu, _Role of the $\omega$(4S) and $\omega$(3D) states in mediating the $e^{+}e^{-}$→$\omega$$\eta$ and $\omega$$\pi$0$\pi$0 processes_, _Phys. Rev. D_ 106 (2022) 034010 [2207.00276].
  * (14) BESIII collaboration, _Design and construction of the BESIII detector_ , _Nucl. Instrum. Meth. A_ 614 (2010) 345 [0911.4960].
  * (15) C. Yu et al., _BEPCII Performance and Beam Dynamics Studies on Luminosity_ , in _Proc. of International Particle Accelerator Conference (IPAC’16), Busan, Korea, May 8-13, 2016_ , no. 7 in International Particle Accelerator Conference, (Geneva, Switzerland), pp. 1014–1018, JACoW, June, 2016, DOI.
  * (16) BESIII collaboration, _Future physics programme of BESIII_ , _Chin. Phys. C_ 44 (2020) 040001 [1912.05983].
  * (17) GEANT4 collaboration, _Geant4–a simulation toolkit_ , _Nucl. Instrum. Meth. A_ 506 (2003) 250.
  * (18) K.-X. Huang, Z.-J. Li, Z. Qian, J. Zhu, H.-Y. Li, Y.-M. Zhang et al., _Method for detector description transformation to Unity and application in BESIII_ , _Nucl. Sci. Tech._ 33 (2022) 142 [2206.10117].
  * (19) R.-G. Ping, _An exclusive event generator for $e^{+}e^{-}$ scan experiments_, _Chin. Phys. C_ 38 (2014) 083001 [1309.3932].
  * (20) BESIII collaboration, _Precision Study of $\eta^{\prime}\rightarrow\gamma\pi^{+}\pi^{-}$ Decay Dynamics_, _Phys. Rev. Lett._ 120 (2018) 242003 [1712.01525].
  * (21) BESIII collaboration, _Dalitz Plot Analysis of the Decay $\omega\rightarrow\pi^{+}\pi^{-}\pi^{0}$_, _Phys. Rev. D_ 98 (2018) 112007 [1811.03817].
  * (22) B. Andersson and H.-M. Hu, _Few body states in Lund string fragmentation model_ , hep-ph/9910285.
  * (23) H. Czyż, P. Kisza and S. Tracz, _Modeling interactions of photons with pseudoscalar and vector mesons_ , _Phys. Rev. D_ 97 (2018) 016006 [1711.00820].
  * (24) BaBar collaboration, _The $e^{+}e^{-}\to 3(\pi^{+}\pi^{-}),2(\pi^{+}\pi^{-}\pi^{0})$ and $K^{+}K^{-}2(\pi^{+}\pi^{-})$ cross sections at center-of-mass energies from production threshold to 4.5-GeV measured with initial-state radiation_, _Phys. Rev. D_ 73 (2006) 052003 [hep-ex/0602006].
  * (25) Working Group on Radiative Corrections, Monte Carlo Generators for Low Energies collaboration, _Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data_ , _Eur. Phys. J. C_ 66 (2010) 585 [0912.0749].
  * (26) E.A. Kuraev and V.S. Fadin, _On Radiative Corrections to $e^{+}e^{-}$ Single Photon Annihilation at High-Energy_, _Sov. J. Nucl. Phys._ 41 (1985) 466.
  * (27) W. Sun, T. Liu, M. Jing, L. Wang, B. Zhong and W. Song, _An iterative weighting method to apply ISR correction to $e^{+}e^{-}$ hadronic cross section measurements_, _Front. Phys. (Beijing)_ 16 (2021) 64501 [2011.07889].
  * (28) BESIII collaboration, _Cross section measurement of $e^{+}e^{-}\to K_{S}^{0}K_{L}^{0}$ at $\sqrt{s}=2.00-3.08~{}{GeV}$_, _Phys. Rev. D_ 104 (2021) 092014 [2105.13597].
  * (29) J. Lundberg, J. Conrad, W. Rolke and A. Lopez, _Limits, discovery and cut optimization for a Poisson process with uncertainty in background and signal efficiency: TRolke 2.0_ , _Comput. Phys. Commun._ 181 (2010) 683 [0907.3450].
  * (30) BESIII collaboration, _Luminosity measurements for the R scan experiment at BESIII_ , _Chin. Phys. C_ 41 (2017) 063001 [1702.04977].
  * (31) BESIII collaboration, _Measurement of $e^{+}e^{-}\rightarrow K^{+}K^{-}$ cross section at $\sqrt{s}=2.00-3.08$ GeV_, _Phys. Rev. D_ 99 (2019) 032001 [1811.08742].
  * (32) W.-L. Yuan, X.-C. Ai, X.-B. Ji, S.-J. Chen, Y. Zhang, L.-H. Wu et al., _Study of tracking efficiency and its systematic uncertainty from $J/\psi\to p\overline{p}\pi^{+}\pi^{-}$ at BESIII_, _Chin. Phys. C_ 40 (2016) 026201 [1507.03453].
  * (33) BESIII collaboration, _Measurement of $e^{+}e^{-}\to K^{+}K^{-}\pi^{0}$ cross section and observation of a resonant structure_, _JHEP_ 07 (2022) 045 [2202.06447].
  * (34) K. Zhu, _Selecting the physical solution via $\eta$-$\eta$’ mixing_, _Phys. Rev. D_ 105 (2022) L031506 [2109.01367].
  * (35) R. Sinha and S. Okubo, _Analysis of $\psi/J\to p\bar{p}\pi^{0}$, $\eta$, and $\eta^{\prime}$ Decays_, _Phys. Rev. D_ 30 (1984) 2333.
  * (36) N.H. Christ, C. Dawson, T. Izubuchi, C. Jung, Q. Liu, R.D. Mawhinney et al., _The $\eta$ and $\eta^{\prime}$ mesons from Lattice QCD_, _Phys. Rev. Lett._ 105 (2010) 241601 [1002.2999].

## The BESIII collaboration

M. Ablikim1, M. N. Achasov5,b, P. Adlarson74, X. C. Ai80, R. Aliberti35, A.
Amoroso73A,73C, M. R. An39, Q. An70,57, Y. Bai56, O. Bakina36, I.
Balossino29A, Y. Ban46,g, V. Batozskaya1,44, K. Begzsuren32, N. Berger35, M.
Berlowski44, M. Bertani28A, D. Bettoni29A, F. Bianchi73A,73C, E.
Bianco73A,73C, A. Bortone73A,73C, I. Boyko36, R. A. Briere6, A. Brueggemann67,
H. Cai75, X. Cai1,57, A. Calcaterra28A, G. F. Cao1,62, N. Cao1,62, S. A.
Cetin61A, J. F. Chang1,57, T. T. Chang76, W. L. Chang1,62, G. R. Che43, G.
Chelkov36,a, C. Chen43, Chao Chen54, G. Chen1, H. S. Chen1,62, M. L.
Chen1,57,62, S. J. Chen42, S. M. Chen60, T. Chen1,62, X. R. Chen31,62, X. T.
Chen1,62, Y. B. Chen1,57, Y. Q. Chen34, Z. J. Chen25,h, W. S. Cheng73C, S. K.
Choi11A, X. Chu43, G. Cibinetto29A, S. C. Coen4, F. Cossio73C, J. J. Cui49, H.
L. Dai1,57, J. P. Dai78, A. Dbeyssi18, R. E. de Boer4, D. Dedovich36, Z. Y.
Deng1, A. Denig35, I. Denysenko36, M. Destefanis73A,73C, F. De Mori73A,73C, B.
Ding65,1, X. X. Ding46,g, Y. Ding40, Y. Ding34, J. Dong1,57, L. Y. Dong1,62,
M. Y. Dong1,57,62, X. Dong75, M. C. Du1, S. X. Du80, Z. H. Duan42, P.
Egorov36,a, Y.H. Y. Fan45, Y. L. Fan75, J. Fang1,57, S. S. Fang1,62, W. X.
Fang1, Y. Fang1, R. Farinelli29A, L. Fava73B,73C, F. Feldbauer4, G. Felici28A,
C. Q. Feng70,57, J. H. Feng58, K Fischer68, M. Fritsch4, C. Fritzsch67, C. D.
Fu1, J. L. Fu62, Y. W. Fu1, H. Gao62, Y. N. Gao46,g, Yang Gao70,57, S.
Garbolino73C, I. Garzia29A,29B, P. T. Ge75, Z. W. Ge42, C. Geng58, E. M.
Gersabeck66, A Gilman68, K. Goetzen14, L. Gong40, W. X. Gong1,57, W. Gradl35,
S. Gramigna29A,29B, M. Greco73A,73C, M. H. Gu1,57, C. Y Guan1,62, Z. L.
Guan22, A. Q. Guo31,62, L. B. Guo41, M. J. Guo49, R. P. Guo48, Y. P. Guo13,f,
A. Guskov36,a, T. T. Han49, W. Y. Han39, X. Q. Hao19, F. A. Harris64, K. K.
He54, K. L. He1,62, F. H H.. Heinsius4, C. H. Heinz35, Y. K. Heng1,57,62, C.
Herold59, T. Holtmann4, P. C. Hong13,f, G. Y. Hou1,62, X. T. Hou1,62, Y. R.
Hou62, Z. L. Hou1, H. M. Hu1,62, J. F. Hu55,i, T. Hu1,57,62, Y. Hu1, G. S.
Huang70,57, K. X. Huang58, L. Q. Huang31,62, X. T. Huang49, Y. P. Huang1, T.
Hussain72, N Hüsken27,35, W. Imoehl27, J. Jackson27, S. Jaeger4, S. Janchiv32,
J. H. Jeong11A, Q. Ji1, Q. P. Ji19, X. B. Ji1,62, X. L. Ji1,57, Y. Y. Ji49, X.
Q. Jia49, Z. K. Jia70,57, H. J. Jiang75, P. C. Jiang46,g, S. S. Jiang39, T. J.
Jiang16, X. S. Jiang1,57,62, Y. Jiang62, J. B. Jiao49, Z. Jiao23, S. Jin42, Y.
Jin65, M. Q. Jing1,62, T. Johansson74, X. K.1, S. Kabana33, N. Kalantar-
Nayestanaki63, X. L. Kang10, X. S. Kang40, R. Kappert63, M. Kavatsyuk63, B. C.
Ke80, A. Khoukaz67, R. Kiuchi1, R. Kliemt14, O. B. Kolcu61A, B. Kopf4, M.
Kuessner4, A. Kupsc44,74, W. Kühn37, J. J. Lane66, P. Larin18, A. Lavania26,
L. Lavezzi73A,73C, T. T. Lei70,k, Z. H. Lei70,57, H. Leithoff35, M.
Lellmann35, T. Lenz35, C. Li47, C. Li43, C. H. Li39, Cheng Li70,57, D. M.
Li80, F. Li1,57, G. Li1, H. Li70,57, H. B. Li1,62, H. J. Li19, H. N. Li55,i,
Hui Li43, J. R. Li60, J. S. Li58, J. W. Li49, K. L. Li19, Ke Li1, L. J Li1,62,
L. K. Li1, Lei Li3, M. H. Li43, P. R. Li38,j,k, Q. X. Li49, S. X. Li13, T.
Li49, W. D. Li1,62, W. G. Li1, X. H. Li70,57, X. L. Li49, Xiaoyu Li1,62, Y. G.
Li46,g, Z. J. Li58, C. Liang42, H. Liang1,62, H. Liang70,57, H. Liang34, Y. F.
Liang53, Y. T. Liang31,62, G. R. Liao15, L. Z. Liao49, Y. P. Liao1,62, J.
Libby26, A. Limphirat59, D. X. Lin31,62, T. Lin1, B. J. Liu1, B. X. Liu75, C.
Liu34, C. X. Liu1, F. H. Liu52, Fang Liu1, Feng Liu7, G. M. Liu55,i, H.
Liu38,j,k, H. M. Liu1,62, Huanhuan Liu1, Huihui Liu21, J. B. Liu70,57, J. L.
Liu71, J. Y. Liu1,62, K. Liu1, K. Y. Liu40, Ke Liu22, L. Liu70,57, L. C.
Liu43, Lu Liu43, M. H. Liu13,f, P. L. Liu1, Q. Liu62, S. B. Liu70,57, T.
Liu13,f, W. K. Liu43, W. M. Liu70,57, X. Liu38,j,k, Y. Liu38,j,k, Y. Liu80, Y.
B. Liu43, Z. A. Liu1,57,62, Z. Q. Liu49, X. C. Lou1,57,62, F. X. Lu58, H. J.
Lu23, J. G. Lu1,57, X. L. Lu1, Y. Lu8, Y. P. Lu1,57, Z. H. Lu1,62, C. L.
Luo41, M. X. Luo79, T. Luo13,f, X. L. Luo1,57, X. R. Lyu62, Y. F. Lyu43, F. C.
Ma40, H. L. Ma1, J. L. Ma1,62, L. L. Ma49, M. M. Ma1,62, Q. M. Ma1, R. Q.
Ma1,62, R. T. Ma62, X. Y. Ma1,57, Y. Ma46,g, Y. M. Ma31, F. E. Maas18, M.
Maggiora73A,73C, S. Malde68, Q. A. Malik72, A. Mangoni28B, Y. J. Mao46,g, Z.
P. Mao1, S. Marcello73A,73C, Z. X. Meng65, J. G. Messchendorp14,63, G.
Mezzadri29A, H. Miao1,62, T. J. Min42, R. E. Mitchell27, X. H. Mo1,57,62, N.
Yu. Muchnoi5,b, J. Muskalla35, Y. Nefedov36, F. Nerling18,d, I. B.
Nikolaev5,b, Z. Ning1,57, S. Nisar12,l, Y. Niu 49, S. L. Olsen62, Q.
Ouyang1,57,62, S. Pacetti28B,28C, X. Pan54, Y. Pan56, A. Pathak34, P.
Patteri28A, Y. P. Pei70,57, M. Pelizaeus4, H. P. Peng70,57, K. Peters14,d, J.
L. Ping41, R. G. Ping1,62, S. Plura35, S. Pogodin36, V. Prasad33, F. Z. Qi1,
H. Qi70,57, H. R. Qi60, M. Qi42, T. Y. Qi13,f, S. Qian1,57, W. B. Qian62, C.
F. Qiao62, J. J. Qin71, L. Q. Qin15, X. P. Qin13,f, X. S. Qin49, Z. H.
Qin1,57, J. F. Qiu1, S. Q. Qu60, C. F. Redmer35, K. J. Ren39, A. Rivetti73C,
V. Rodin63, M. Rolo73C, G. Rong1,62, Ch. Rosner18, S. N. Ruan43, N. Salone44,
A. Sarantsev36,c, Y. Schelhaas35, K. Schoenning74, M. Scodeggio29A,29B, K. Y.
Shan13,f, W. Shan24, X. Y. Shan70,57, J. F. Shangguan54, L. G. Shao1,62, M.
Shao70,57, C. P. Shen13,f, H. F. Shen1,62, W. H. Shen62, X. Y. Shen1,62, B. A.
Shi62, H. C. Shi70,57, J. L. Shi13, J. Y. Shi1, Q. Q. Shi54, R. S. Shi1,62, X.
Shi1,57, J. J. Song19, T. Z. Song58, W. M. Song34,1, Y. J. Song13, Y. X.
Song46,g, S. Sosio73A,73C, S. Spataro73A,73C, F. Stieler35, Y. J. Su62, G. B.
Sun75, G. X. Sun1, H. Sun62, H. K. Sun1, J. F. Sun19, K. Sun60, L. Sun75, S.
S. Sun1,62, T. Sun1,62, W. Y. Sun34, Y. Sun10, Y. J. Sun70,57, Y. Z. Sun1, Z.
T. Sun49, Y. X. Tan70,57, C. J. Tang53, G. Y. Tang1, J. Tang58, Y. A. Tang75,
L. Y Tao71, Q. T. Tao25,h, M. Tat68, J. X. Teng70,57, V. Thoren74, W. H.
Tian58, W. H. Tian51, Y. Tian31,62, Z. F. Tian75, I. Uman61B, S. J. Wang 49,
B. Wang1, B. L. Wang62, Bo Wang70,57, C. W. Wang42, D. Y. Wang46,g, F. Wang71,
H. J. Wang38,j,k, H. P. Wang1,62, J. P. Wang 49, K. Wang1,57, L. L. Wang1, M.
Wang49, Meng Wang1,62, S. Wang13,f, S. Wang38,j,k, T. Wang13,f, T. J. Wang43,
W. Wang58, W. Wang71, W. P. Wang70,57, X. Wang46,g, X. F. Wang38,j,k, X. J.
Wang39, X. L. Wang13,f, Y. Wang60, Y. D. Wang45, Y. F. Wang1,57,62, Y. H.
Wang47, Y. N. Wang45, Y. Q. Wang1, Yaqian Wang17,1, Yi Wang60, Z. Wang1,57, Z.
L. Wang71, Z. Y. Wang1,62, Ziyi Wang62, D. Wei69, D. H. Wei15, F. Weidner67,
S. P. Wen1, C. W. Wenzel4, U. Wiedner4, G. Wilkinson68, M. Wolke74, L.
Wollenberg4, C. Wu39, J. F. Wu1,62, L. H. Wu1, L. J. Wu1,62, X. Wu13,f, X. H.
Wu34, Y. Wu70, Y. J. Wu31, Z. Wu1,57, L. Xia70,57, X. M. Xian39, T. Xiang46,g,
D. Xiao38,j,k, G. Y. Xiao42, S. Y. Xiao1, Y. L. Xiao13,f, Z. J. Xiao41, C.
Xie42, X. H. Xie46,g, Y. Xie49, Y. G. Xie1,57, Y. H. Xie7, Z. P. Xie70,57, T.
Y. Xing1,62, C. F. Xu1,62, C. J. Xu58, G. F. Xu1, H. Y. Xu65, Q. J. Xu16, Q.
N. Xu30, W. Xu1,62, W. L. Xu65, X. P. Xu54, Y. C. Xu77, Z. P. Xu42, Z. S.
Xu62, F. Yan13,f, L. Yan13,f, W. B. Yan70,57, W. C. Yan80, X. Q. Yan1, H. J.
Yang50,e, H. L. Yang34, H. X. Yang1, Tao Yang1, Y. Yang13,f, Y. F. Yang43, Y.
X. Yang1,62, Yifan Yang1,62, Z. W. Yang38,j,k, Z. P. Yao49, M. Ye1,57, M. H.
Ye9, J. H. Yin1, Z. Y. You58, B. X. Yu1,57,62, C. X. Yu43, G. Yu1,62, J. S.
Yu25,h, T. Yu71, X. D. Yu46,g, C. Z. Yuan1,62, L. Yuan2, S. C. Yuan1, X. Q.
Yuan1, Y. Yuan1,62, Z. Y. Yuan58, C. X. Yue39, A. A. Zafar72, F. R. Zeng49, X.
Zeng13,f, Y. Zeng25,h, Y. J. Zeng1,62, X. Y. Zhai34, Y. C. Zhai49, Y. H.
Zhan58, A. Q. Zhang1,62, B. L. Zhang1,62, B. X. Zhang1, D. H. Zhang43, G. Y.
Zhang19, H. Zhang70, H. H. Zhang58, H. H. Zhang34, H. Q. Zhang1,57,62, H. Y.
Zhang1,57, J. Zhang80, J. J. Zhang51, J. L. Zhang20, J. Q. Zhang41, J. W.
Zhang1,57,62, J. X. Zhang38,j,k, J. Y. Zhang1, J. Z. Zhang1,62, Jianyu
Zhang62, Jiawei Zhang1,62, L. M. Zhang60, L. Q. Zhang58, Lei Zhang42, P.
Zhang1,62, Q. Y. Zhang39,80, Shuihan Zhang1,62, Shulei Zhang25,h, X. D.
Zhang45, X. M. Zhang1, X. Y. Zhang49, Xuyan Zhang54, Y. Zhang71, Y. Zhang68,
Y. T. Zhang80, Y. H. Zhang1,57, Yan Zhang70,57, Yao Zhang1, Z. H. Zhang1, Z.
L. Zhang34, Z. Y. Zhang75, Z. Y. Zhang43, G. Zhao1, J. Zhao39, J. Y. Zhao1,62,
J. Z. Zhao1,57, Lei Zhao70,57, Ling Zhao1, M. G. Zhao43, S. J. Zhao80, Y. B.
Zhao1,57, Y. X. Zhao31,62, Z. G. Zhao70,57, A. Zhemchugov36,a, B. Zheng71, J.
P. Zheng1,57, W. J. Zheng1,62, Y. H. Zheng62, B. Zhong41, X. Zhong58, H.
Zhou49, L. P. Zhou1,62, X. Zhou75, X. K. Zhou7, X. R. Zhou70,57, X. Y. Zhou39,
Y. Z. Zhou13,f, J. Zhu43, K. Zhu1, K. J. Zhu1,57,62, L. Zhu34, L. X. Zhu62, S.
H. Zhu69, S. Q. Zhu42, T. J. Zhu13,f, W. J. Zhu13,f, Y. C. Zhu70,57, Z. A.
Zhu1,62, J. H. Zou1, J. Zu70,57
(BESIII Collaboration)
1 Institute of High Energy Physics, Beijing 100049, People’s Republic of China
2 Beihang University, Beijing 100191, People’s Republic of China
3 Beijing Institute of Petrochemical Technology, Beijing 102617, People’s
Republic of China
4 Bochum Ruhr-University, D-44780 Bochum, Germany
5 Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090,
Russia
6 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
7 Central China Normal University, Wuhan 430079, People’s Republic of China
8 Central South University, Changsha 410083, People’s Republic of China
9 China Center of Advanced Science and Technology, Beijing 100190, People’s
Republic of China
10 China University of Geosciences, Wuhan 430074, People’s Republic of China
11 Chung-Ang University, Seoul, 06974, Republic of Korea
12 COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind
Road, 54000 Lahore, Pakistan
13 Fudan University, Shanghai 200433, People’s Republic of China
14 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
15 Guangxi Normal University, Guilin 541004, People’s Republic of China
16 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
17 Hebei University, Baoding 071002, People’s Republic of China
18 Helmholtz Institute Mainz, Staudinger Weg 18, D-55099 Mainz, Germany
19 Henan Normal University, Xinxiang 453007, People’s Republic of China
20 Henan University, Kaifeng 475004, People’s Republic of China
21 Henan University of Science and Technology, Luoyang 471003, People’s
Republic of China
22 Henan University of Technology, Zhengzhou 450001, People’s Republic of
China
23 Huangshan College, Huangshan 245000, People’s Republic of China
24 Hunan Normal University, Changsha 410081, People’s Republic of China
25 Hunan University, Changsha 410082, People’s Republic of China
26 Indian Institute of Technology Madras, Chennai 600036, India
27 Indiana University, Bloomington, Indiana 47405, USA
28 INFN Laboratori Nazionali di Frascati , (A)INFN Laboratori Nazionali di
Frascati, I-00044, Frascati, Italy; (B)INFN Sezione di Perugia, I-06100,
Perugia, Italy; (C)University of Perugia, I-06100, Perugia, Italy
29 INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara,
Italy; (B)University of Ferrara, I-44122, Ferrara, Italy
30 Inner Mongolia University, Hohhot 010021, People’s Republic of China
31 Institute of Modern Physics, Lanzhou 730000, People’s Republic of China
32 Institute of Physics and Technology, Peace Avenue 54B, Ulaanbaatar 13330,
Mongolia
33 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica
1000000, Chile
34 Jilin University, Changchun 130012, People’s Republic of China
35 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45,
D-55099 Mainz, Germany
36 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
37 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-
Buff-Ring 16, D-35392 Giessen, Germany
38 Lanzhou University, Lanzhou 730000, People’s Republic of China
39 Liaoning Normal University, Dalian 116029, People’s Republic of China
40 Liaoning University, Shenyang 110036, People’s Republic of China
41 Nanjing Normal University, Nanjing 210023, People’s Republic of China
42 Nanjing University, Nanjing 210093, People’s Republic of China
43 Nankai University, Tianjin 300071, People’s Republic of China
44 National Centre for Nuclear Research, Warsaw 02-093, Poland
45 North China Electric Power University, Beijing 102206, People’s Republic of
China
46 Peking University, Beijing 100871, People’s Republic of China
47 Qufu Normal University, Qufu 273165, People’s Republic of China
48 Shandong Normal University, Jinan 250014, People’s Republic of China
49 Shandong University, Jinan 250100, People’s Republic of China
50 Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
51 Shanxi Normal University, Linfen 041004, People’s Republic of China
52 Shanxi University, Taiyuan 030006, People’s Republic of China
53 Sichuan University, Chengdu 610064, People’s Republic of China
54 Soochow University, Suzhou 215006, People’s Republic of China
55 South China Normal University, Guangzhou 510006, People’s Republic of China
56 Southeast University, Nanjing 211100, People’s Republic of China
57 State Key Laboratory of Particle Detection and Electronics, Beijing 100049,
Hefei 230026, People’s Republic of China
58 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
59 Suranaree University of Technology, University Avenue 111, Nakhon
Ratchasima 30000, Thailand
60 Tsinghua University, Beijing 100084, People’s Republic of China
61 Turkish Accelerator Center Particle Factory Group, (A)Istinye University,
34010, Istanbul, Turkey; (B)Near East University, Nicosia, North Cyprus,
99138, Mersin 10, Turkey
62 University of Chinese Academy of Sciences, Beijing 100049, People’s
Republic of China
63 University of Groningen, NL-9747 AA Groningen, The Netherlands
64 University of Hawaii, Honolulu, Hawaii 96822, USA
65 University of Jinan, Jinan 250022, People’s Republic of China
66 University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
67 University of Muenster, Wilhelm-Klemm-Strasse 9, 48149 Muenster, Germany
68 University of Oxford, Keble Road, Oxford OX13RH, United Kingdom
69 University of Science and Technology Liaoning, Anshan 114051, People’s
Republic of China
70 University of Science and Technology of China, Hefei 230026, People’s
Republic of China
71 University of South China, Hengyang 421001, People’s Republic of China
72 University of the Punjab, Lahore-54590, Pakistan
73 University of Turin and INFN, (A)University of Turin, I-10125, Turin,
Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy;
(C)INFN, I-10125, Turin, Italy
74 Uppsala University, Box 516, SE-75120 Uppsala, Sweden
75 Wuhan University, Wuhan 430072, People’s Republic of China
76 Xinyang Normal University, Xinyang 464000, People’s Republic of China
77 Yantai University, Yantai 264005, People’s Republic of China
78 Yunnan University, Kunming 650500, People’s Republic of China
79 Zhejiang University, Hangzhou 310027, People’s Republic of China
80 Zhengzhou University, Zhengzhou 450001, People’s Republic of China

a Also at the Moscow Institute of Physics and Technology, Moscow 141700,
Russia
b Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
c Also at the NRC "Kurchatov Institute", PNPI, 188300, Gatchina, Russia
d Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany
e Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology,
Ministry of Education; Shanghai Key Laboratory for Particle Physics and
Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240,
People’s Republic of China
f Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and
Institute of Modern Physics, Fudan University, Shanghai 200443, People’s
Republic of China
g Also at State Key Laboratory of Nuclear Physics and Technology, Peking
University, Beijing 100871, People’s Republic of China
h Also at School of Physics and Electronics, Hunan University, Changsha
410082, China
i Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of
Quantum Matter, South China Normal University, Guangzhou 510006, China
j Also at Frontiers Science Center for Rare Isotopes, Lanzhou University,
Lanzhou 730000, People’s Republic of China
k Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou
730000, People’s Republic of China
l Also at the Department of Mathematical Sciences, IBA, Karachi 75270,
Pakistan