Observation of a resonant structure in e + e − → ωη and another in e + e − → ωπ 0 at center-of-mass energies between 2 . 00 and 3 . 08 GeV

M. Ablikim a, M.N. Achasov j,4, P. Adlarson bs, S. Ahmed o, M. Albrecht d, A. Amoroso bp,br, Q. An bm,ax, Y. Bai aw, O. Bakina ae, R. Baldini Ferroli w, I. Balossino y, Y. Ban an,12, K. Begzsuren ab, J.V. Bennett e, N. Berger ad, M. Bertani w, D. Bettoni y, F. Bianchi bp,br, J. Biernat bs, J. Bloms bj, A. Bortone bp,br, I. Boyko ae, R.A. Briere e, H. Cai bt, X. Cai a,ax, A. Calcaterra w, G.F. Cao a,be, N. Cao a,be, S.A. Cetin bb, J.F. Chang a,ax, W.L. Chang a,be, G. Chelkov ae,2,3, D.Y. Chen f, G. Chen a, H.S. Chen a,be, M.L. Chen a,ax, S.J. Chen al, X.R. Chen aa, Y.B. Chen a,ax, W. Cheng br, G. Cibinetto y, F. Cossio br, X.F. Cui am, H.L. Dai a,ax, J.P. Dai ar,8, X.C. Dai a,be, A. Dbeyssi o, R.B. de Boer d, D. Dedovich ae, Z.Y. Deng a, A. Denig ad, I. Denysenko ae, M. Destefanis bp,br, F. De Mori bp,br, Y. Ding aj, C. Dong am, J. Dong a,ax, L.Y. Dong a,be, M.Y. Dong a,ax,be, S.X. Du bw, J. Fang a,ax, S.S. Fang a,be, Y. Fang a, R. Farinelli y,z, L. Fava bq,br, F. Feldbauer d, G. Felici w, C.Q. Feng bm,ax, M. Fritsch d, C.D. Fu a, Y. Fu a, X.L. Gao bm,ax, Y. Gao bn, Y. Gao an,12, Y.G. Gao f, I. Garzia y,z, E.M. Gersabeck bh, A. Gilman bi, K. Goetzen k, L. Gong am, W.X. Gong a,ax, W. Gradl ad, M. Greco bp,br, L.M. Gu al, M.H. Gu a,ax, S. Gu b, Y.T. Gu m, C.Y. Guan a,be, A.Q. Guo v, L.B. Guo ak, R.P. Guo ap, Y.P. Guo ad, Y.P. Guo i,9, A. Guskov ae, S. Han bt, T.T. Han aq, T.Z. Han i,9, X.Q. Hao p, F.A. Harris bf, K.L. He a,be, F.H. Heinsius d, T. Held d, Y.K. Heng a,ax,be, M. Himmelreich k,7, T. Holtmann d, Y.R. Hou be, Z.L. Hou a, H.M. Hu a,be, J.F. Hu ar,8, T. Hu a,ax,be, Y. Hu a, G.S. Huang bm,ax, L.Q. Huang bn, X.T. Huang aq, Z. Huang an,12, N. Huesken bj, T. Hussain bo, W. Ikegami Andersson bs, W. Imoehl v, M. Irshad bm,ax, S. Jaeger d, S. Janchiv ab,11, Q. Ji a, Q.P. Ji p, X.B. Ji a,be, X.L. Ji a,ax, H.B. Jiang aq, X.S. Jiang a,ax,be, X.Y. Jiang am, J.B. Jiao aq, Z. Jiao r, S. Jin al, Y. Jin bg, T. Johansson bs, N. Kalantar-Nayestanaki ag, X.S. Kang aj, R. Kappert ag, M. Kavatsyuk ag, B.C. Ke as,a, I.K. Keshk d, A. Khoukaz bj, P. Kiese ad, R. Kiuchi a, R. Kliemt k, L. Koch af, O.B. Kolcu bb,6, B. Kopf d, M. Kuemmel d, M. Kuessner d, A. Kupsc bs, M.G. Kurth a,be, W. Kühn af, J.J. Lane bh, J.S. Lange af, P. Larin o, A. Lavania u, L. Lavezzi br, H. Leithoff ad,


Keywords: BESIII φ(2170)
Excited ω states Excited ρ states are consistent with the φ(2170). In the e + e − → ωπ 0 cross sections, a resonance denoted Y (2040) is observed with a significance of more than 10σ . Its mass and width are determined to be (2034 ± 13 ± 9) MeV/c 2 and (234 ± 30 ± 25) MeV, respectively, where the first uncertainties are statistical and the second ones are systematic.

Introduction
In low-energy e + e − collision experiments, the vector mesons ρ, ω, and φ and their low lying excited states can be produced abundantly. The Particle Data Group (PDG) [1] has tabulated experimental results for these states. However, some of the higher lying excitations are not fully identified yet. It is especially in the region around 2 GeV where further experimental insight is needed to resolve the situation involving resonances such as the ρ(2000), ρ(2150) and φ(2170) states.
These models differ in their predictions of the branching fractions of the φ(2170) to decay channels such as φη or K ( * )K ( * ) as certain decay modes can either be suppressed or favored depending on its nature [2,4,[19][20][21]. It is therefore of great importance to measure the branching fractions for a variety of different decay channels in order to help in discriminating between different models.
In contrast to the e + e − → ωη process, the reaction e + e − → ωπ 0 allows the study of the isovector vector mesons and their excited states. Generally, the excited ρ states around 2 GeV/c 2 are not well understood. Although there are two results on the so-called ρ(2000) [33,34], its existence is not well-established. Furthermore, several experiments have claimed the observation of the ρ(2150) state with mass and width lying in the range of 1.990 to 2.254 GeV/c 2 and 70 to 389 MeV, respectively [35][36][37][38][39].
In an approach based on the quark-pair-creation model, the ρ(2150) state is identified as a candidate for the 4 3 S 1 state [40,41]. The Born cross section of e + e − → ωπ 0 in the energy region below 2 GeV has been measured by several experiments [42][43][44][45][46][47][48][49], while the data above 2 GeV is rather scarce. Thus, more measurements of e + e − → ωπ 0 above 2 GeV are of high interest to study the properties of excited ρ states.

Detector and data sample
The BESIII detector is a magnetic spectrometer [50] located at the Beijing Electron Position Collider (BEPCII) [51]. The cylindrical core of the BESIII detector 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 magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel. The acceptance of charged particles and photons is 93% over 4π solid angle. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for the 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 of the TOF barrel part is 68 ps, while that of the end cap part is 110 ps.
The data samples used in this letter have been collected with the BESIII detector at 22 center-of-mass (c.m.) energies from 2.000 to 3.080 GeV, corresponding to a total integrated luminosity of 651 pb −1 .
The geant4 based [52] simulation software boost [53] is used to produce Monte Carlo (MC) simulation samples. Events are generated using the ConExc generator [54] with ISR and vacuum polarization (VP) taken into account. Inclusive hadron production of the type e + e − → hadrons is simulated to estimate possible background processes and to optimize event selection criteria. Exclusive MC samples are generated to determine the detection efficiencies of the signal processes. Since the beam energy spread of BEPCII is less than 1 MeV at √ s < 3 GeV, it is much smaller than the experimental resolution of the BESIII detector and can thus be ignored in the simulation.

Analysis of e + e − → ωη
For e + e − → ωη (with subsequent ω → π + π − π 0 , π 0 → γ γ and η → γ γ decays), candidate events are required to have at least two reconstructed charged tracks and at least four reconstructed photons. Each charged track is required to be located within the MDC acceptance, | cos θ| < 0.93, where θ is the polar angle of the charged track, and to originate from a cylinder around the interaction point of 1 cm radius and extending ±10 cm  π + π − π 0 invariant mass versus the two-photon invariant mass. The area marked in red corresponds to the signal region. (b) Fit to the M(γ γ ) distribution, where the (black) dots with error bars are data, the (blue) solid curve is the total fit result, the (green) dashed curve indicates background described by a second order Chebychev polynomial, the (red) dotted curve is the η → γ γ signal shape described by a Voigt function and the (green) histogram is the e + e − → ωπ 0 π 0 MC sample scaled to the integral of the background function in the fit. The vertical lines indicate the signal (red) and sideband regions (blue). (c) and (d) represent the M(π + π − π 0 ) invariant mass distributions in the η signal and sideband region, respectively. The dots with error bars are data, the solid curves are the total fit results, the dashed curves indicate the background described by a second order Chebychev polynomial and the dotted curves are the ω signal shapes determined from MC simulations convolved with a Gaussian accounting for a potential difference in resolution between data and MC simulation. along the detector axis. Information from TOF and dE/dx measurements is combined to form particle identification (PID) likelihoods for the π , K , and p hypotheses. Each track is assigned a particle type corresponding to the hypothesis with the highest PID likelihood. Exactly two oppositely charged pions are required in each event. Photon candidates are reconstructed using clusters of energy deposited in the EMC crystals. The energy is required to be larger than 25 MeV in the barrel region (| cos θ| < 0.80) and larger than 50 MeV in the end cap region (0.86 < | cos θ| < 0.92). The energy deposited in nearby TOF counters is included to improve the reconstruction efficiency and energy resolution. The difference of the EMC time from the event start time is required to be within [0,700] ns to suppress electronic noise and showers unrelated to the event.
To improve the momentum and energy resolution and to suppress background events, a four-constraint (4C) kinematic fit imposing four-momentum conservation is performed under the hypothesis e + e − → π + π − 4γ . For the goodness of the kinematic fit, χ 2 4C < 70 is required. For events with more than four photon candidates, the combination with the smallest χ 2 4C is retained. In addition, a kinematic fit for the alternative hypothesis e + e − → π + π − 5γ is performed and only those events that satisfy χ 2 4C (π + π − 4γ ) < χ 2 4C (π + π − 5γ ) are retained in order to suppress backgrounds from e + e − → ωπ 0 π 0 events. Two photon pairs corresponding to the best π 0 η, π 0 π 0 and ηη candidates are selected separately by choosing the combination with the smallest value 34 , where α and β represent either π 0 or η, and the mass resolution σ 12 (34) in the invariant mass region of the π 0 or η meson is obtained from MC simulations. Only combinations with χ 2 π 0 η < χ 2 π 0 π 0 and χ 2 π 0 η < χ 2 ηη are retained. The π 0 and η candidates are selected by requiring |M(γ 1 γ 2 ) − m π 0 | < 0.02 GeV/c 2 and |M(γ 3 γ 4 ) − m η | < 0.03 GeV/c 2 , corresponding to about 3σ intervals around the respective nominal masses of π 0 and η, m π 0 and m η [1]. Events with |E γ 3 − E γ 4 |/p η > 0.9, where p η is the momentum of the η meson in the laboratory system, are rejected to suppress background events from the e + e − → ωγ ISR and e + e − → ωπ 0 π 0 processes. The distribution of the π + π − π 0 invariant mass versus the two-photon invariant mass of the selected events at GeV is shown as an example in Fig. 1(a), where an ω signal around the nominal ω meson mass is visible. Potential background reactions to the e + e − → ωη process are studied using both inclusive e + e − → hadrons and exclusive MC samples. Simulated events are subject to the same selection procedure as that applied to the experimental data. According to MC simulations, the dominant background stems from e + e − → π + π − π 0 η, which contains the same final state particles as the signal reaction. The e + e − → ωπ 0 π 0 and e + e − → ωγ ISR processes form a peaking background contribution in the π + π − π 0 invariant mass distribution. The total peaking background from e + e − → ωγ ISR is estimated by MC simulations normalized to the experimental luminosity and is found to be negligible. The peaking background from e + e − → ωπ 0 π 0 is inferred from the η sidebands, which are defined as 0.400 < M(γ 3 γ 4 ) < 0.508 GeV/c 2 and 0.588 < M(γ 3 γ 4 ) < 0.700 GeV/c 2 as shown in Fig. 1 To determine the signal yield of the e + e − → ωη process, a simultaneous unbinned maximum likelihood fit is performed to the M(π + π − π 0 ) spectra in both the η signal and sideband regions at each energy, where the shapes of signal and background are shared. Fig. 1 (c) and (d) show the fit results in signal and sideband regions at 2.125 GeV. The signal is modeled with the peak shape obtained from MC simulation convolved with a Gaussian function allowing for a potential resolution difference between data Table 1 The Born cross sections of the e + e − → ωη process. In addition, upper limits are given at 90% confidence level. All symbols defined are the same as those in Eq. (1). In the column of Born cross section σ , the first uncertainty is statistical, and the second one is systematic. Sig. is the significance of the observed signal. VP lists the vacuum polarization factor.
and MC simulation. The background is described with a secondorder Chebychev polynomial. In the fit, peaking background is automatically subtracted by constructing the number of ω events in the η signal region as N obs = N sig + f scale · N bkg , where N sig is the number of ωη signal events, N bkg is the number of ω events in the η sideband region, and f scale is the normalization is the number of background events falling into the signal (sideband) region as shown in Fig. 1 The Born cross section of the e + e − → ωη process is calculated where L is the integrated luminosity of the individual dataset, (1 + δ) is the radiative correction factor accounting for both ISR and VP, and ε is the product of geometrical acceptance and selection efficiency obtained from MC simulation. The total branching fraction B is the product of the branching fractions for the decays The Born cross sections as well as upper limits at the 90% confidence level are given for all 22 energy points together with all values used in the calculation in Table 1. VP factors are also listed for the convenience of calculating dressed cross sections. The results are consistent with previous measurements [55][56][57] but with improved precision. A comparison to the previous results is shown in Fig. 2(a). Various sources of systematic uncertainties concerning the measurement of the Born cross sections are investigated, including integrated luminosity, branching fractions, ISR and VP correction factors, event selection criteria, the fit procedure of the signal, and the contributions from peaking background processes.
The integrated luminosity at each energy point is measured using large angle Bhabha events with an uncertainty of 1% following the method in Ref. [58]. The uncertainties associated with the branching fractions of intermediate states are taken from the PDG [1]. The uncertainty of the ISR and VP correction factors is obtained from the accuracy of radiation function, which is about 0.5% [54], and has an additional contribution from the cross section lineshape, which is estimated by varying the model parameters of the fit to the cross sections. All parameters are randomly varied within their uncertainties and the resulting parametrization of the lineshape is used to recalculate (1 + δ), ε and the corresponding cross sections. This procedure is repeated 1000 times and the standard deviation of the resulting cross sections is taken as a systematic uncertainty. Differences between the data and MC simulation for the tracking efficiency and PID of charged pions are investigated using the high-purity control sample of e + e − → K + K − π + π − [28,59]. The photon detection efficiency is studied with a sample of e + e − → K + K − π + π − π 0 with similar method for tracking uncertainty [59]. The result shows that the difference in detection efficiency between data and MC simulation is 1% per photon. The uncertainties associated with the kinematic fit are studied with the track helix parameter correction method, as described in Ref. [60].
Due to large statistical fluctuations in the data, toy MC samples are used to estimate the systematic uncertainties stemming from the description of the signal and background shape as well as from  [42,44] (green filled crosses and brown filled triangles), BaBar [49] (blue filled X crosses), DM2 [48] (magenta open stars) and ND [45] (cyan filled downward triangles) experiments.

Table 2
Summary of relative systematic uncertainties (in %) associated with the luminosity (L), the tracking efficiency (Track), the photon detection efficiency (Photon), PID, Branching fraction (Br), χ 2 requirement, 4C kinematic fit (4C), |E γ3 − E γ4 |/p η < 0.9 (Angle), background shape (Bkg), signal shape (Sig), fit range (Range), η and π 0 mass windows (m(η) and m(π 0 )), peaking background (Peak), the initial state radiation and the vacuum polarization correction factor (1 + δ) in the measurement of the Born cross section of the e + e − → ωη process.  the fit range when determining N obs . A total of 500 sets of toy MC samples are generated according to the final fit result shown in Fig. 1(c) with the same statistics as in data. For each toy MC sample, the following procedure is performed: the ω signal shape is changed to a Breit-Wigner function convolved with a Gaussian, the background shape is varied from a second to a third order Chebychev polynomial and the fit range is varied by ±10 MeV/c 2 . The mean value of the differences of the signal yield between the nominal and the alternative fits is taken as the systematic uncertainty. The uncertainty of peaking background is related to the uncertainty of N bkg and f scale . We estimate uncertainty of N bkg with the same method for N obs , and that of f scale by considering the fit uncertainty of the non-η background at 2.125 GeV. Since the statistics are quite low at several energy points, the uncertainties related to the fit of peaking background and the signal are quoted from nearby energy points when the signal significance is lower than 2σ . The total systematic uncertainty for the Born cross section measurement is determined to be 12% for the e + e − → ωη process at √ s = 2.125 GeV. The uncertainties at the other c.m. energies are determined accordingly and are summarized in Table 2.

Analysis of e + e − → ωπ 0
The event selection criteria for the e + e − → ωπ 0 process are mostly the same as described in Sec. 3.1. The π 0 π 0 candidate pairs are selected by minimizing χ 2 2 34 . These π 0 candidates are required to be in a mass window of (m π 0 − 0.02 GeV/c 2 , m π 0 + 0.02 GeV/c 2 ). Since there are two π 0 candidates, the π + π − π 0 combination whose invariant mass is closest to m ω is retained as the ω candidate, where the π 0 is denoted as π 0 ω to distinguish it from the bachelor pion π 0 bach . Using the above selection criteria, the distribution of the invariant mass of π + π − π 0 ω versus the two-photon invariant mass for π 0 bach candidates is depicted in Fig. 3(a). The ω signal is clearly evident.
A method similar to that described in Sec. 3.1 is used to study possible background contributions. According to the study, the dominant background stems from the four body process e + e − → π + π − π 0 π 0 , which has the same final state particles as the signal channel. In a similar way as in the e + e − → ωη case, possible peaking background contributions are inferred from the π 0 bach sideband regions defined as 0.055 < |M(γ 1 γ 2 ) − m π 0 | < 0.095 GeV/c 2 (as illustrated in Fig. 3(b)). Note that due to mis-combination of photons, a large fraction of the π 0 sideband is composed of signal reactions. Still, while a peaking sideband contribution is found, its fraction is negligible (and would still have to be scaled down in a similar procedure as described for the ωη process) compared to the signal region as shown in Fig. 3 (c) and (d).
The signal yield is determined using the M(π + π − π 0 ω ) mass spectra (as shown in Fig. 3(c)) with a similar method as described in Sec. 3.1, with the difference being that peaking backgrounds are neglected, so that the fit reduces to a one-dimensional unbinned likelihood fit. The fit yields N sig = 22627 ± 180 events.
The Born cross section of the e + e − → ωπ 0 process is calculated using Eq. (1), with the product of the branching fractions determined by B = B(ω → π + π − π 0 ) · B 2 (π 0 → γ γ ) = 87.1%. The values used in the calculation of the Born cross section of the e + e − → ωπ 0 process are listed in Table 3, together with the results at all c.m. energies. The results are consistent with most of the previous measurements [42][43][44][45][46][47][48] but with improved precision, however, there exists a small difference with the BaBar measurement [49] at center-of-mass energies around 2.1 GeV. A comparison is shown in Fig. 2(b).
Concerning the systematic uncertainties, the contribution stemming from the luminosity determination is common for the e + e − → ωη and e + e − → ωπ 0 reactions. Furthermore, for the uncertainties relating to the detection efficiencies, the radiative corrections, the fitting procedure and the branching fractions taken from the literature, the same method is applied as previously stated in Sec. 3.1. In addition, the uncertainty arising from the π 0 selection is obtained by varying the mass window requirements for both π 0 ω and π 0 bach and examining the changes in the resulting cross sections. The total systematic uncertainty of the determination of the Born cross section is determined to be 6.7% for Table 3 The Born cross sections of the e + e − → ωπ 0 process. The symbols are the same as those in Eq. (1). In the column of the Born cross section σ , the first uncertainty is statistical and the second one is systematic.  Table 4. Table 4 Summary of relative systematic uncertainties (in %) associated with the luminosity (L), the tracking efficiency (Track), the photon detection efficiency (Photon), PID, branching fraction (Br), 4C kinematic fit (4C), background shape (Bkg), signal shape (Sig), fit range (Range), π 0 mass windows (m(π 0 ) and m(π 0 ω )), the initial state radiation and the vacuum polarization correction factor (1 + δ) in the measurement of the Born cross section of the e + e − → ωπ 0 process.

Analysis of the e + e − → ωη process
To study possible resonant structures in e + e − → ωη, a maximum likelihood fit of the type used in Ref. [61] is performed to the dressed cross sections, which are the products of Born cross sections and VP factors. Previous results from the SND [55] and CMD3 [56] collaborations are also included to be able to describe the low-energy behavior of the cross section, while BaBar's result is not used due to their large uncertainties or non-observation without uncertainty. In the fit, a possible resonant amplitude is parameterized using a Breit-Wigner function with a massindependent width. The flat contribution in the c.m. energy region between 2 and 3 GeV dominantly stems from tails of the ω(1420) and ω(1650) (or φ(1680)) resonances. Following Ref. [55], the dressed cross section is modeled as  [55], since the significance of the ω(1420) resonance is not large enough at the given c.m. energies. In the fit, uncertainties from previous experiments are considered uncorrelated, while the uncertainties derived in this work are split into the uncorrelated and the correlated contributions. The former contributions include those stemming from the choice of signal and background shape as well as fit range and the treatment of peaking backgrounds whereas the latter include the remaining systematic uncertainties. Fig. 4 and Table 5 show the results from our fit. Two solutions are found with the same fit quality of χ 2 /ndf = 79/67, where ndf is the number of degrees of freedom. The significance of the third resonance is determined by comparing the change of the goodness (χ 2 ) in a fit without the third resonance and considering the change of the ndf. Solution I corresponds to constructive interference between the f 3 amplitude and the remaining f 1 − f 2 contribution, while solution II corresponds to the case of destructive interference. The two solutions share all parameters other than those given in Table 5. Among the other free parameters, the mass and width of f 2 are determined to be 1670 ± 4 MeV/c 2 and 124 ± 7 MeV, respectively, with ee · B ωη f 2 equal to 54 ± 2 eV.

Analysis of the e + e − → ωπ 0 process
A fit is performed to the dressed cross sections of e + e − → ωπ 0 using a similar method as described in Sec. 4.1. Previous results from the SND collaboration [43,44] are included in order to provide the low-energy contributions that will only appear as tails in the energy region under study. BaBar's result is not used since there is an obvious bias compared to the result in this work in the overlap region, and others are not used due to their large uncertainties.
Here, the fit model is parameterized as a coherent sum of four Breit-Wigner functions,  the average values as given by the PDG [1]. In the fit, a possible effect of omitting other data available in the literature on the results obtained in this work is studied and will be discussed in Sec. 4.3. Correlated and uncorrelated uncertainties of the present work are incorporated in the same way as described in Sec. 4.1, while the uncertainties of the previous experiments are considered uncorrelated.
The fit shown in Fig. 5 finds a resonance with a mass of (2034 ± 13) MeV/c 2 , width of (234 ± 30) MeV and ee · B ωπ 0 of (34 ± 11) eV with a fit quality of χ 2 /ndf = 128/90. The significance of the Y (2040) contribution is found to be larger than 10σ .

Systematic uncertainties
The systematic uncertainties of the resonant parameters in the fit to the Born cross sections of e + e − → ωη include contributions from the determination of the c.m. energy and the energy spread, fixed parameters in the fit, and the data from other experiments that is included in the fit. The uncertainty of the c.m. energy from BEPCII is small and found to be negligible comparing to the statistic uncertainty in the determination of the resonance parameters.
The effect resulting from fixing the parameters of the ω(1420) resonance is studied by varying the mass and width within the uncertainties quoted in the PDG [1] and yields an uncertainty of m = 3 MeV/c 2 , = 5 MeV and ( ee · B ωη ) equal to 0.03 eV for solution I and 0.16 eV for solution II. We distinguish between two different types of systematic uncertainties, those that are uncorrelated between the different center-of-mass energies and those that are correlated. While the uncorrelated uncertainties are included in the fit to the cross section, the correlated uncertainties that are common for all centerof-mass energies (∼ 6%) only affect the ee · B ωη measurement and we find a resulting systematic uncertainty of 0.03 eV for solution I and 0.09 eV for solution II. Assuming all sources of systematic uncertainties are uncorrelated and thus adding them in quadrature, the total systematic uncertainty is 3 MeV/c 2 for the mass, 5 MeV for the width, 0.04 eV (solution I) or 0.18 eV (solution II) for ee · B ωη of the Y (2180).
For the systematic uncertainties of the resonant parameters of the Y (2040) in e + e − → ωπ 0 , the contribution introduced by taking the data points of other experiments into account in the fit is significant. It is investigated by including all available measurements [42][43][44][45][46][47][48][49] and comparing with the nominal fit result above. Other uncertainties are considered in the same way as stated before for the Y (2180) → ωη case. All sources of systematic uncertainties are added in quadrature, obtaining the total systematic uncertainty of 9 MeV/c 2 for the mass, 25 MeV for the width and 16 eV for ee · B ωπ 0 of the observed Y (2040). Since the resonances in e + e − → ωπ 0 line shape are from the excited ρ states, which are wider than those in the ωη line shape, the contribution from other resonances and the interferences lead to larger systematic uncertainties in the resonant parameters of the Y (2040) state.

Summary and discussion
The Born cross sections of the e + e − → ωη and e + e − → ωπ 0 processes have been measured at √ s from 2.000 to 3.080 GeV. They are consistent with most of previous measurements in the overlap region, but deviate with BaBar's results, especially in the ωπ 0 process. Two resonant structures are observed in the mea-sured line shapes. One resonant structure is observed with a significance of 6.2σ in the cross section of the e + e − → ωη process, with mass m = (2176 ± 24 ± 3) MeV/c 2 , width = (89 ± 50 ± 5) MeV, and ee · B ωη = (0.43 ± 0.15 ± 0.04) eV or (1.25 ± 0.48 ± 0.18) eV, depending on the choice between two ambiguous fit solutions. The observed structure agrees well with the properties of the φ(2170) resonance, which indicates the first observation of the decay φ(2170) → ωη.
Another structure is observed in the ωπ 0 cross section with a significance of more than 10σ and with a mass of m = (2034 ± 13 ± 9) MeV/c 2 , width of = (234 ± 30 ± 25) MeV and ee · B ωπ 0 of (34 ± 11 ± 16) eV. This structure could either be the ρ(2000) or the ρ(2150) state. However, the mass and width of the observed resonance is closer to the ρ(2000) resonance, which is suggested to be the 2 3 D 1 state [41].

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.