Observation of $e^+ e^- \to \eta Y(2175)$ at center-of-mass energies above 3.7$\sim$GeV

The state $Y(2175)$ is observed in the process $e^+ e^- \to \eta Y(2175)$ at center-of-mass energies between 3.7 and 4.6$\sim$GeV with a statistical significance larger than $10\sigma$ using data collected with the BESIII detector operating at the BEPCII storage ring. This is the first observation of the $Y(2175)$ in this process. The mass and width of the $Y(2175)$ are determined to be ($2135\pm 8\pm 9$)~MeV/$c^2$ and ($104\pm 24\pm 12$)~MeV, respectively, and the production cross section of $e^+ e^- \to \eta Y(2175)\to \eta\phi f_{0}(980)\to \eta\phi \pi^+ \pi^-$ is at a several hundred femtobarn level. No significant signal for the process $e^+ e^- \to \eta' Y(2175)$ is observed and the upper limit on $\sigma(e^+ e^- \to \eta' Y(2175))/\sigma(e^+ e^- \to \eta Y(2175))$ is estimated to be 0.43 at the 90\% confidence level. We also search for $\psi(3686) \to \eta Y(2175)$. No significant signal is observed, indicating a strong suppression relative to the corresponding $J/\psi$ decay, in violation of the"12\% rule."

(Dated: March 12, 2018) The state Y (2175) is observed in the process e + e − → ηY (2175) at center-of-mass energies between 3.7 and 4.6 GeV with a statistical significance larger than 10σ using data collected with the BESIII detector operating at the BEPCII storage ring. This is the first observation of the Y (2175) in this process. The mass and width of the Y (2175) are determined to be (2135 ± 8 ± 9) MeV/c 2 and (104 ± 24 ± 12) MeV, respectively, and the production cross section of e + e − → ηY (2175) → ηφf0(980) → ηφπ + π − is at a several hundred femtobarn level. No significant signal for the process e + e − → η ′ Y (2175) is observed and the upper limit on σ(e + e − → η ′ Y (2175))/σ(e + e − → ηY (2175)) is estimated to be 0.43 at the 90% confidence level. We also search for ψ(3686) → ηY (2175). No significant signal is observed, indicating a strong suppression relative to the corresponding J/ψ decay, in violation of the "12% rule."

I. INTRODUCTION
The Y (2175) was first observed in 2006 by the BaBar collaboration [1] via the initial-state-radiation (ISR) process e + e − → γ ISR φf 0 (980) with a mass of (2175 ± 10 ± 15) MeV/c 2 and a width of (58 ± 16 ± 20) MeV. It was subsequently confirmed by the Belle collaboration in the same process [2] and by the BESII and BESIII collaborations [3,4] in J/ψ hadronic decays. The BaBar collaboration updated their analysis in 2012 with improved statistics [5].
Behaving similarly to the Y (4260) in the charm sector and the Υ(10860) in the bottom sector, the Y (2175) is regarded as a candidate for a tetraquark state [6,7], a strangeonium hybrid state [8], or a conventional ss state [9,10]. The quark model [11][12][13] predicts two conventional ss states near 2175 MeV/c 2 , 3 3 S 1 and 2 3 D 1 , but both of them are significantly broader than the Y (2175), which makes the Y (2175) more mysterious.
Despite all previous experimental and theoretical effort, our knowledge of the Y (2175) is still very poor. Its observed production mechanisms are so far limited to direct e + e − annihilation and J/ψ → ηY (2175) decay. Furthermore, there are inconsistencies in previous mass and width measurements [2,4,5].
Since the process J/ψ → ηY (2175) has been observed [3,4], it is natural to expect the production of ηY (2175) in ψ(3686) decays as well as in direct e + e − annihilation in the non-resonant energy region. The η is a mixture of the pseudoscalar SU(3) octet and singlet states, therefore the other mixture partner, η ′ , is also expected to accompany the production of the Y (2175) when the center-of-mass (c.m.) energy ( √ s) of e + e − annihilation is above the production threshold. BESIII has accumulated the world's largest data samples at the ψ(3686) peak and at higher energies up to 4.6 GeV, which gives us a good opportunity to search for these processes. I: Summary of the data samples and the cross section measurements of e + e − → ηY (2175) → ηφf0(980) → ηφπ + π − . Here √ s is the c.m. energy, Lint is the integrated luminosity, N obs is the number of observed signal events from the simultaneous fit, (1 + δ) · ǫ is the product of the ISR correction factor and efficiency. The correction factors of vacuum polarization, 1 + δ vac , are listed except for √ s = 3.686 GeV since the contribution of vacuum polarization is included in the parameters of the ψ(3686). Born cross sections σ B are listed with statistical (first) and systematic (second) uncertainties. The last column is the corresponding statistical significance for each data sample. Recently, several charged quarkonium-like states Z c [16][17][18][19] and Z b [20] have been observed through decays of the Y (4260), Υ(10860) or other charmonium-like or bottomonium-like states. One may expect similar charged strangeonium-like states produced in Y (2175) → φπ + π − decays, considering the similarity of the Y (2175), Y (4260), and Υ(10860). Ref. [21] predicts the existence of a sharp peaking structure (Z s1 ) close to the KK * threshold and a broad structure (Z s2 ) close to the K * K * threshold in the πφ mass spectrum. These can be searched for using the decays of the Y (2175) produced in e + e − → ηY (2175) and η ′ Y (2175).
In this article, we present the first observation of e + e − → ηY (2175) and measurement of its production cross sections, a search for e + e − → η ′ Y (2175) and an estimation of the upper limit of the production rate, and the search for ψ(3686) → ηY (2175) and determination of the upper limit on the branching fraction at the c.m. energies [14] from 3.686 to 4.6 GeV, as listed in Table I with the corresponding integrated luminosities L [15].
The remainder of this paper is organized as follows: in Sec. II, the BESIII detector and the data samples are described; in Sec. III, the event selections for e + e − → ηY (2175) are listed; Section IV presents the determination of the signal yield and the cross section measurement, as well as the measurement of the resonance parameters of the Y (2175) in e + e − → ηY (2175); while Secs. V and VI show the search for the Z s and ψ(3686) → ηY (2175). Section VII shows the search for e + e − → η ′ Y (2175), Sec. VIII lists the estimation of the systematic uncertainties. A summary of all results is given in Sec. IX.

II. BESIII DETECTOR AND DATA SAMPLES
The BESIII detector, described in detail in Ref. [22], has a geometrical acceptance of 93% of 4π. A small-cell helium-based main drift chamber (MDC) provides a charged particle momentum resolution of 0.5% at 1 GeV/c in a 1 T magnetic field, and supplies energy loss (dE/dx) measurements with a resolution better than 6% for electrons from Bhabha scattering. The electromagnetic calorimeter (EMC) measures photon energies with a resolution of 2.5% (5%) at 1.0 GeV in the barrel (endcaps). Particle identification (PID) is provided by a time-of-flight system (TOF) with a time resolution of 80 ps (110 ps) for the barrel (endcaps). The muon system, located in the iron flux return yoke of the magnet, provides 2 cm position resolution and detects muon tracks with momentum greater than 0.5 GeV/c.
The data used in this analysis are listed in Table I, where the data sample at √ s = 3.686 GeV corresponds to the ψ(3686) data samples of (106.8 ± 0.8) × The GEANT4-based [25] Monte Carlo (MC) simulation software BOOST [26] includes the geometric description of the BESIII detector and a simulation of the detector response. It is used to optimize event selection criteria, estimate backgrounds and evaluate the detection efficiency. For each energy point, signal MC samples of e + e − → ηY (2175) with Y (2175) → φf 0 (980) → φπ + π − , φ → K + K − and η → γγ are generated, and ηY (2175) is generated with an angular distribution of 1 + cos 2 θ in the e + e − c.m. frame. For the decays of intermediate states, both the Y (2175) → φf 0 (980) and η → γγ are generated evenly in phase space, and the φ → K + K − is generated using a VSS model in EVTGEN [27,28]. The resonant parameters of the Y (2175) are taken from the measurement in this analysis, and the f 0 (980) is parameterized with the Flatté formula [29], with parameters determined from the BESII experiment [30]. The ISR is simulated with KKMC [31], and the final state radiation (FSR) is handled with PHOTOS [32]. The process e + e − → η ′ Y (2175) is simulated at each energy point with a similar procedure, and the decay η ′ → γπ + π − is generated as η ′ → γρ 0 with ρ 0 → π + π − [33].
For background studies, two inclusive MC samples with integrated luminosities equivalent to those of data are generated at √ s = 3.686 and 3.773 GeV. In these samples the ψ(3686) and ψ(3770) are allowed to decay generically, with the main known decay channels being generated using EVTGEN [27] with branching fractions set to world average values [34]. The remaining events associated with charmonium decays are generated with LUNDCHARM [35] while continuum hadronic events are generated with PYTHIA [36]. For the QED events, e + e − → τ + τ − is generated with KKMC [31], and other events are generated with BABAYAGA [37].

III. EVENT SELECTIONS
For the study of e + e − → ηY (2175), we expect four charged particles with zero net charge and two photons in the final state.
Each charged track is required to have its point of closest approach to the beamline within 1 cm in the radial direction and within 10 cm from the interaction point along the beam direction, and to lie within the polar angle coverage of the MDC, | cos θ| < 0.93 in the laboratory frame. PID for charged tracks is based on combining the dE/dx and TOF information. The confidence levels Prob PID (i) are calculated for each charged track for each particle hypothesis i =(pion, kaon, or proton). If Prob PID (K) > Prob PID (π) and Prob PID (K) is larger than 0.001, the track is regarded as a kaon, otherwise it is taken as a pion. Two identified kaons with opposite charge are required.
Photons are reconstructed from isolated showers in the EMC which are at least 10 degrees away from the charged tracks. A good photon is required to have an energy of at least 25 MeV in the barrel (| cos θ| < 0.80) or 50 MeV in the end-caps (0.86 < | cos θ| < 0.92). In order to suppress electronic noise and energy deposits unrelated to the event, the EMC time t of the photon candidate must be in coincidence with the event start time in the range 0 ≤ t ≤ 700 ns. The η candidate is reconstructed using the two most energetic photons.
A four-constraint (4C) kinematic fit, which constrains the four-momentum of all particles in the final state to be that of the initial e + e − system, is performed for the γγπ + π − K + K − system to get a better resolution and background suppression. The χ 2 of the kinematic fit is required to be less than 60.
After all the above selection criteria are applied, we use mass windows around the η and φ, numerically [0.513, 0.578] GeV/c 2 and [1.009, 1.031] GeV/c 2 , respectively, to select signal events. The π + π − system in Y (2175) → φπ + π − decays tends to have J P C = 0 ++ and is dominated by f 0 (980). Figure 1 shows the scatter plot of M (π + π − ) versus M (φπ + π − ) for the sum of the data samples with The invariant mass distribution of φf 0 (980) for the seven data samples with √ s >3.7 GeV is shown in Fig. 2, individually. The Y (2175) signal can be observed over a smooth background level, especially for data sample at 3.773 GeV, where the integrated luminosity is the largest. The invariant mass distribution of φf 0 (980) summing over the seven data samples with √ s >3.7 GeV is also shown in Fig. 2. We leave the analysis of data at 3.686 GeV to Sec. VI and focus on energy points with √ s >3.7 GeV here. The inclusive MC sample at 3.773 GeV is used to check for possible backgrounds. No peaking background is found and the main background is the non-Y (2175) process e + e − → ηK + K − π + π − , including both the ηφπ + π − and ηK + K − f 0 (980) processes. There are almost no other backgrounds around the Y (2175) peak area. Exclusive MC samples of non-Y (2175) processes are generated, and the shapes are used to describe the background in the fit to the invariant mass distributions. Events in the sideband regions of the f 0 (980) and φ are used to check for the presence of peaking background, and the corresponding distributions are shown in Fig. 2.

IV. SIGNAL YIELDS AND BORN CROSS SECTIONS
We use an unbinned maximum likelihood method to fit the φf 0 (980) invariant mass spectra in order to extract the yields of signal events and the Y (2175) resonant parameters. A simultaneous fit is applied to all the data samples with √ s >3.7 GeV. The same signal shape is used to describe the signal at different energy points, which is where M and Γ are the mass and width of the Y (2175), respectively, G is a Gaussian function with a mean fixed to zero and a free standard deviation σ to describe the mass resolution, ǫ(m) is the mass-dependent efficiency determined from MC simulation. Φ(m) = ( |p| √ s ) 3 is the two-body phase space factor for a P -wave system, where p is the momentum of Y (2175) in the e + e − rest frame. The background shape is taken from MC simulation of the non-resonant process.  Table I. The Born cross section of e + e − → ηY (2175) → ηφf 0 (980) → ηφπ + π − is calculated using where σ obs is the observed cross section including the branching fraction B(Y (2175) → φf 0 (980) → φπ + π − ), N obs is the number of signal events, L int is the integrated luminosity, B is the product of branching fractions of η → γγ and φ → K + K − , ǫ is the detection efficiency, and (1 + δ) is the ISR correction factor, including ISR, e + e − self-energy and initial vertex correction; and the vacuum polarization factor (1 + δ vac ), including leptonic and hadronic contributions, is taken from Ref. [38].
The vector-pseudoscalar (VP) processes e + e − → V P are predicted to have Born cross sections that vary as 1/s n [39] in the absence of contributions from charmonium(-like) resonances. In calculating the ISR correction factors [40], the Born cross section of e + e − → ηY (2175) from threshold to the c.m. energy under study is needed as input. We assume the ηY (2175) comes from a QED process without the contribution from any charmonium(-like) resonances, and the line-shape is parameterized as Here n is a parameter describing the energy-dependent form factor of e + e − → ηY (2175), which is obtained from a fit to the measured Born cross sections in this analysis. We use an iterative procedure to measure the Born cross sections and determine the ISR correction factors together with the efficiencies.
The resultant Born cross section and all the numbers used in the calculation are listed in Table I and shown in Fig. 3. The fit to the final Born cross sections with Eq. (3) results in n = 2.65 ± 0.86, as shown in Fig. 3, and the goodness of fit is χ 2 /ndf = 2.52/5.

V. SEARCH FOR Zs STATES
Since we have observed a distinct Y (2175) signal, possible charged Z s states in the φπ ± invariant mass spectrum can be searched for in the Y (2175) decays. In the cross section measurement, the candidate events are required to be within the f 0 (980) mass window to suppress background. This requirement is released to include the non-f 0 (980) decay of Y in the search for the Z s states. The events in the Y (2175) signal region, [1.989, 2.272] GeV/c 2 , are selected and the Dalitz plot of Y (2175) → φπ + π − events for the sum of data samples above 3.7 GeV is shown in Fig. 4 (left). A clear f 0 (980) band in the horizental direction is observed which dominates the Y (2175) → φπ + π − decays. Figure 4 (right) shows the projection on M (φπ ± ) for data and MC simulations of the non-Z s process, which covers all the energy points and is normalized according to the luminosity and the fit result in Fig. 3.  From the theoretical calculation [21], which assumes the Z s states being KK * and K * K * molecular states, the masses of Z s states are expected at around 1.4 and 1.7 GeV/c 2 . No significant vertical bands can be seen at the expected positions. We do not try to give quantitative results on the Z s production due to the limited statistics and the not well-defined masses and widths of these states.

Energy (GeV
It is worth noting that the Y (2175) signal produced in e + e − → ηY (2175) at c.m. energies above 3.7 GeV has a much lower background level compared with those in the other two known production processes, i.e., e + e − annihilation around the Y (2175) peak [1, 2, 5] and J/ψ → ηY (2175) [3,4], though the signal yield is not comparable to the later two processes at BESIII. With more data accumulated above 3.7 GeV, the Z s states could be searched for with high sensitivity via e + e − → ηY (2175).

VI. SEARCH FOR ψ(3686) → ηY (2175)
With the same selections as those described in Sec. III, the φf 0 (980) invariant mass distribution at c.m. energy 3.686 GeV is shown in Fig. 5. In contrast to the distributions at √ s > 3.7 GeV, no significant Y (2175) signal is observed. The background level is much higher than that at other energies, considering the difference in integrated luminosities, indicating that ψ(3686) decays are the main background. The inclusive MC sample at 3.686 GeV is used to check for possible backgrounds. No peaking background is found and the main background is the non-Y (2175) process ψ(3686) → ηK + K − π + π − (as well as a small fraction of e + e − → ηK + K − π + π − through continuum production), including both the ηφπ + π − and ηK + K − f 0 (980) processes, and there are no other kinds of background around the Y (2175) peak area. Exclusive MC samples of non-Y (2175) processes are generated and the shapes are used to describe the background in the fit to the invariant mass distribution as in the analysis of data with higher energy.
The same fit functions for signal and background as in the fit to the data with higher energy (Sec. IV) are used to determine the signal yield of Y (2175). Since the signal yield of Y (2175) is very small, we fix the mass and width of the Y (2175) to the values obtained in the previous fit. The fit returns 19.0 ± 9.0 events of Y (2175) signal with a statistical significance of 1.5σ. The fit curve is shown in Fig. 5. The Born cross section and all other numbers used to calculate the Born cross section are listed in Table I and are shown in Fig. 3. The cross section does not show any peaking structure, within the large experimental uncertainties. We therefore assume that the Y (2175) signal is due to continuum production only.
As the process J/ψ → ηY (2175) has been observed [3,4], we expect the production of ψ(3686) → ηY (2175) to occur as well, although there is no guideline for a prediction of the decay branching fraction. This branching fraction can be obtained by combining the measured Born cross sections at 3.686 GeV and those at higher energies which serve to estimate the continuum cross section at 3.686 GeV.
For e + e − → η ′ Y (2175), the analysis is similar to that of e + e − → ηY (2175). The difference occurs in the reconstruction of the η ′ . We use the decay mode γπ + π − to reconstruct η ′ , and use the same final state to reconstruct the Y (2175) as in the e + e − → ηY (2175) case. There are four charged pions and two charged kaons in the final state. To classify these particles, we first use PID to separate kaons from pions, and use a kinematic fit to identify the π + π − from η ′ decays. The fit enforces energy-momentum conservation and the invariant mass of γπ + π − is constrained to the nominal η ′ mass. We loop over all the π + π − combinations, and the one with the smallest χ 2 is retained. In order to use the information of the η ′ sideband for further study, the η ′ mass constraint is released after the π + π − from η ′ decays is identified and the χ 2 of the 4C kinematic fit is required to be less than 60. Mass windows of η ′ ([0.943,0.971] GeV/c 2 ), f 0 (980), and φ are used to select signal events.
Due to the low integrated luminosity and the relatively large background level, the data sample at 3.686 GeV is not used to study e + e − → η ′ Y (2175). After all the above event selections are applied, the distribution of the φf 0 (980) invariant mass for the sum of data samples with c.m. energies greater than 3.7 GeV is shown in Fig. 6, together with the distributions of the events in η ′ , f 0 (980) and φ sideband regions. There are only a few events and no significant Y (2175) or any other structure is observed. Events from the sidebands can describe the events in the signal regions reasonably well. The inclusive MC sample at 3.773 GeV is used to check the background and no peaking background is found. An unbinned maximum likelihood fit is applied to the sum of the φf 0 (980) invariant mass distributions to determine the signal yields for these data samples. We use the shape from an exclusive MC simulation to describe the signal, and use a second-order polynomial function for the background shape. The resonant parameters for the Y (2175) are taken from our measured values in the previous study of e + e − → ηY (2175). The Bayesian method is used to estimate the upper limit as described in Ref. [42], and an upper limit of 27.6 events is obtained at the 90% C.L. after considering the systematic uncertainty.
The upper limit on the ratio of the cross sections R = σ η ′ Y (2175) /σ ηY (2175) is determined by assuming this ratio is the same at different c.m. energy points, that is, Here N obs is the number of observed ηY (2175) (95.0 ± 12.1) or η ′ Y (2175) events from the sum of the seven data samples; B η and B η ′ are the branching fractions of η → γγ and η ′ → γπ + π − [34], respectively; σ i ηY (2175) and L i are the Born cross section for e + e − → ηY (2175) and the integrated luminosity for the i-th data sample, and the numbers are listed in Table I; ǫ i is the reconstruction efficiency from MC simulation. With the numbers obtained above, the upper limit on the ratio R is estimated to be 0.43 at the 90% C.L., where the systematic uncertainties, which will be detailed later, are included.

VIII. SYSTEMATIC UNCERTAINTIES
A. Cross section measurement of e + e − → ηY (2175) Systematic uncertainties for the cross section measurement of e + e − → ηY (2175) are summarized in Table II and are discussed below.  The luminosity is measured using large-angle Bhabha scattering with an uncertainty less than 1.0% [15]. The difference in detection efficiency between data and MC simulation in tracking is 1.0% per track, and that due to PID is taken as 1.0% per track [42]. The uncertainty in the reconstruction efficiency for a photon is determined to be less than 1.0% by studying a sample of J/ψ → ρπ events.
The branching fractions of the η and φ decays are taken from the world average values in the PDG [34], and the corresponding uncertainties are taken as a systematic uncertainty. For the η and φ mass windows, the nominal values are taken to be ±1.5·FWHM; the efficiency difference due to any mass resolution difference between data and MC simulation is very small and can be neglected compared to other sources of uncertainties.
Since statistics are limited, the line shape of e + e − → ηY (2175) cannot be measured precisely. We assume there is no contribution from charmonium(-like) states above 3.7 GeV and parameterize the line shape to be proportional to 1/s n . While we take the mean value of n from a fit to the data by an iterative process, we vary n by one standard deviation and regenerate MC samples. The difference in (1 + δ) · ǫ is taken as a systematic uncertainty.
To estimate the uncertainties introduced by the kinematic fit, we use the same method described in Refs. [43,44], i.e., correct the track helix parameters in the MC sample and take half the difference between results obtained with and without corrections as systematic uncertainty (around 0.4% for the all the data samples). The MC sample with track parameter correction is used by default in the nominal analysis.
In the nominal fit, the shape from simulation of the non-Y (2175) process e + e − → ηK + K − π + π − is taken to describe the background. We change the shape of background to be a second order polynomial function for data with √ s > 3.7 GeV and to a shape from inclusive MC sample at 3.686 GeV, and take the difference in signal yields as the systematic uncertainties. The uncertainty due to signal parametrization, which is obtained by altering the signal shape into a Breit-Winger function with a mass-dependent width, is found to be negligible compared with that from the background shape. The systematic uncertainty associated with the fit range is studied by changing fit range with 100 MeV/c 2 , the resultant value is 0.5% only and is neglected. The Flatté formula [29] is used to model the f 0 (980) lineshape in MC generation, where the parameters of f 0 (980) are from the BESII experiment [30]. To estimate the corresponding systematic uncertainty, we vary the parameters by one standard deviation from the central values and the resultant difference in efficiency is taken as the systematic uncertainty.
Assuming all the sources of uncertainty are independent, the total uncertainty is obtained by summing all the individual uncertainties in quadrature, and is summarized in Table II. B. Mass and width of the Y (2175) The systematic uncertainties for the mass and width of the Y (2175) include those from the mass calibration, signal shape of the Y (2175), background shape and the c.m. energy.
A kinematic fit is performed with energy-momentum conservation, so we can use the mass of η to calibrate the mass of the Y (2175). A simultaneous fit is performed on M (γγ) for all the data samples. The difference between the fitted mass and the nominal mass [34], 2.1 MeV/c 2 , is taken as the systematic uncertainty.
Since Y (2175) has J P C = 1 −− , we expect it decays to φf 0 (980) in a relative S-wave. An S-wave Breit-Winger function with mass-dependent width is used to parameterize the Y (2175) shape in the fit, yielding a mass difference of 2.5 MeV/c 2 and a width difference of 1.5 MeV. The mass resolution is about 4.5 MeV/c 2 , which is much smaller than the width of Y (2175), and the corresponding effect on width measurement is found to be negligible.
In the nominal fit, we use the shape from simulated non-resonant MC events to describe the background. To study the corresponding systematic uncertainty, we change the background shape to a second-order polynomial function and the resultant differences in fitted mass and width, 8.2 MeV/c 2 and 12.1 MeV, respectively, are taken as systematic uncertainties.
The c.m. energy of the e + e − system also affects the determination of the mass and width of the Y (2175) due to the kinematic constraint between initial and final states. An analysis [14] reveals that the uncertainty on c.m. energy of e + e − is less than 0.6 MeV. We change the c.m. energy by ±0.6 MeV in the kinematic fit and study the changes of mass and width, which are 0.2 MeV/c 2 and 0.4 MeV, respectively.
The quadratic sum of all the above uncertainties, 8.8 MeV/c 2 and 12.2 MeV for the mass and width, respectively, are taken as the total uncertainties. The sources of systematic uncertainties on the product of branching fractions B(ψ(3686) → ηY (2175)) · B(Y (2175) → φf 0 (980) → φπ + π − ) are the same as those in the cross section measurement. An additional uncertainty associated with the total number of ψ(3686) events [24], 0.66%, is also taken into account. The resultant systematic uncertainty for the branching fraction B(ψ(3686) → ηY (2175)) is 57.8%. D. Ratio R = σ(e + e − → η ′ Y (2175))/σ(e + e − → ηY (2175)) For the ratio R, the common systematic uncertainties between e + e − → ηY (2175) and η ′ Y (2175) cancel and the remaining uncertainties arise from the differences between η and η ′ reconstruction, where η is reconstructed from two photons and η ′ from one photon and two charged pions. The fraction of common systematic uncertainty introduced by the kinematic fit is hard to estimate. To be conservative, we assume they are independent and the quadratic sum of them is taken as the uncertainty of R. The systematic uncertainty due to the background shape, 48.7%, is obtained by varying the shape to that determined by the events in sideband regions of η ′ and φ. We assume that all the sources of systematic uncertainty are independent and obtain the total uncertainty in R as a quadratic sum of statistical and systematic uncertainties, which is 50.6%, and is considered in calculating the upper limit of R.

IX. SUMMARY
We observe clear Y (2175) signals in the process e + e − → ηY (2175) using data samples at √ s = 3.773, 4.008, 4.226, 4.258, 4.358, 4.416, and 4.600 GeV. In the measured c.m. energy dependent Born cross sections, no obvious peaks corresponding to decays of charmonium(-like) states to the final state ηY (2175) are seen. The mass and width of the Y (2175) are measured to be (2135 ± 8 ± 9) MeV/c 2 and (104 ± 24 ± 12) MeV, respectively, where the first uncertainties are statistical and the second systematic. The results are consistent with previous measurements [1][2][3][4][5], and the width tends to be larger but similar with the results of Belle and BESIII [2,4]. An examination of the Dalitz plot of the Y (2175) → φπ + π − indicates that φf 0 (980) is a dominant component, and no obvious signal of a potential charged strangeonium-like state Z s → φπ is observed.
The cross section of e + e − → ηY (2175) varies with c.m. energy as 1/s n with n = 2.65 ± 0.86, which can be compared with measurements of other vector-pseudoscalar final states and theoretical calculations [39,45]. The deviation from the behavior of final states with ordinary vector quarkonium states may reveal the nature of the Y (2175), where theoretical calculations are expected for different assumptions of the parton configuration of the Y (2175).