Observation and study of $J/\psi\rightarrow\phi\eta\eta'$ at BESIII

We report the observation and study of $J/\psi\rightarrow\phi\eta\eta'$ decay using $1.3\times{10^9}$ $J/\psi$ events collected with the BESIII detector. Its branching fraction including all the possible intermediate states is measured to be $(2.32\pm0.06\pm0.16)\times{10^{-4}}$. A structure denoted as $X$ is observed in the $\phi\eta'$ mass spectrum in $2.0-2.1$ GeV/$c^2$ region. A simultaneous fit to $\phi\eta'$ mass spectra with two decay modes of $\eta'$ meson ($\gamma\pi^+\pi^-$ and $\eta\pi^+\pi^-$) is performed. Assuming the $J^P$ value of the structure as $1^-$, the significance of the structure is evaluated to be 5.3$\sigma$; the mass and width are determined to be $(2002.1 \pm 27.5 \pm 15.0)$ MeV/$c^2$ and $(129 \pm 17 \pm 7)$ MeV, respectively; the product branching fraction is measured to be $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.8 \pm 1.2 \pm 1.5)\times10^{-5}$. Assuming the $J^P$ value of the structure as $1^+$, the significance of the structure is evaluated to be 4.9$\sigma$; the mass and width are determined to be $(2062.8 \pm 13.1 \pm 4.2)$ MeV/$c^2$ and $(177 \pm 36 \pm 20)$ MeV, respectively; the product branching fraction is measured to be $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.6 \pm 1.4 \pm 1.6)\times10^{-5}$. The angular distribution is studied and the two assumptions could hardly be distinguished due to the limited statistics. In all measurements the first uncertainties are statistical and the second systematic.

We report the observation and study of J/ψ → φηη decay using 1.3 × 10 9 J/ψ events collected with the BESIII detector. Its branching fraction including all the possible intermediate states is measured to be (2.32 ± 0.06 ± 0.16) × 10 −4 . A structure denoted as X is observed in the φη mass spectrum in 2.0 − 2.1 GeV/c 2 region. A simultaneous fit to φη mass spectra with two decay modes of η meson (γπ + π − and ηπ + π − ) is performed. Assuming the J P value of the structure as 1 − , the significance of the structure is evaluated to be 5.3σ; the mass and width are determined to be (2002.1 ± 27.5 ± 15.0) MeV/c 2 and (129 ± 17 ± 7) MeV, respectively; the product branching fraction is measured to be B(J/ψ → ηX) × B(X → φη ) = (9.8 ± 1.2 ± 1.5) × 10 −5 . Assuming the J P value of the structure as 1 + , the significance of the structure is evaluated to be 4.9σ; the mass and width are determined to be (2062.8 ± 13.1 ± 4.2) MeV/c 2 and (177 ± 36 ± 20) MeV, respectively; the product branching fraction is measured to be B(J/ψ → ηX) × B(X → φη ) = (9.6 ± 1.4 ± 1.6) × 10 −5 . The angular distribution is studied and the two assumptions could hardly be distinguished due to the limited statistics. In all measurements the first uncertainties are statistical and the second systematic.

I. INTRODUCTION
The exotic hadrons, e.g., glueballs, hybrid states and multiquark states, are allowed in the framework of the Quantum Chromodynamics (QCD), but no conclusive evidence has been found yet. The decay of J/ψ → V P P , where V is a vector meson and P is a pseudoscalar meson, is an ideal environment to study the light hadron spectroscopy and to search for the new hadrons. There have been theoretical [1][2][3][4] and experimental [5][6][7][8][9][10] studies performed mainly focused on the V recoil system to search for the exotic hadrons. The P recoil system might also be utilized to search for the exotic hadrons. For example, the Y (2175), denoted as φ(2170) by the Particle Data Group (PDG) [11], was confirmed in J/ψ → ηY (2175), Y (2175) → φf 0 (980) decay by BESII [12] and BESIII [13]. Searching for its decay to φη state might provide valuable inputs for understanding its nature [14]. The decay of J/ψ → φηη has not been studied before, and investigating this process can help to understand J/ψ decay mechanism and offers an opportunity to study possible intermediate states.
In this article, we report the observation and study of J/ψ → φηη decay using (1310.6 ± 7.0) × 10 6 J/ψ events [15] collected with the BESIII detector. Its branching fraction including all the possible intermediate states is measured. A structure denoted as X is observed in the φη mass spectrum in 2.0−2.1 GeV/c 2 region. The mass and width of the structure, as well as the branching fraction B(J/ψ → ηX) × B(X → φη ), are measured. The φ meson is reconstructed through its K + K − decay mode, η through γγ, and η through both γπ + π − and ηπ + π − (with the η → γγ), denoted as mode I and mode II, respectively.

II. BESIII EXPERIMENT AND MONTE CARLO SIMULATION
The BESIII detector is a magnetic spectrometer [16] located at the Beijing Electron Position Collider (BEPCII) [17]. 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 (0.9 T in 2012) 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.
Simulated samples produced with the geant4based [18] Monte Carlo (MC) package which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiency and to estimate the backgrounds. The simulation includes the beam energy spread and initial state radiation (ISR) in the e + e − annihilations modelled with the generator kkmc [19]. The inclusive MC sample con-sists of the production of the J/ψ resonance, and the continuum processes incorporated in kkmc [19]. The known decay modes are modelled with evtgen [20] using branching fractions taken from the PDG [11], and the remaining unknown decays from the charmonium states with lundcharm [21]. The final state radiations (FSR) from charged final state particles are incorporated with the photos package [22].

III. EVENT SELECTION AND DATA ANALYSIS
Charged tracks are reconstructed from hits in the MDC. We select four charged tracks with net charge zero in the polar angle range | cos θ| < 0.93, and require their points of closest approach to the e + e − interaction point to be within ±10 cm in the beam direction and 1 cm in the plane perpendicular to the beam direction. The dE/dx and TOF measurements are combined to form particle identification (PID) confidence levels for the π, K and p hypotheses. We require that one K + K − pair and one π + π − pair are identified. A vertex fit that assumes the π + π − K + K − tracks all come from a common vertex is applied.
Photons are reconstructed from electromagnetic showers in the EMC. At least three photons are required for mode I and four for mode II. The minimum energy for showers to be identified as photons in the barrel region (| cos θ| < 0.8) is 25 MeV, and in the end caps (0.86 < | cos θ| < 0.92) 50 MeV. Showers out of the above regions are poorly reconstructed and not used in this analysis. To suppress showers from charged particles, a photon must be separated by at least 10 degrees from the nearest charged track. EMC cluster timing requirements suppress electronic noise and energy deposits unrelated to this event.
Four-constraint (4C) kinematic fits are applied to all combinations of photons, and only the combination with the smallest χ 2 4C is kept, and we only keep those events with χ 2 4C ≤ 40 for mode I and χ 2 4C ≤ 80 for mode II. To suppress background events containing π 0 's, those events with the invariant mass of any photon pair within a π 0 mass window (0.12 ≤ M (γγ) ≤ 0.15 GeV/c 2 ) are rejected. For mode I, the combination with the smallest value of is used to assign photons to the η and η . Here m η and m η are the nominal η and η masses [11], respectively; σ η and σ η are the mass resolutions determined from signal MC simulation. Mass windows for the η, φ and η mesons are (in GeV/c 2 ): 0.522 ≤ M (γγ) ≤ 0.573, 1.010 ≤ M (K + K − ) ≤ 1.030 and 0.936 ≤ M (γπ + π − ) ≤ 0.979. M (π + π − ) is required to be less than 0.87 GeV/c 2 to suppress the background from the J/ψ → ηφf 0 (980) process as shown in Fig. 1. For mode II, we use the combination with the smallest The background inferred from the η sidebands is negligible according to the study of data and inclusive J/ψ decays, and the non-φ and/or nonη backgrounds are determined from the 2D sidebands of the φ and η mesons, following the similar procedure in Ref. [23]. The φ and η meson signals are clearly shown in both modes in the figure. The three body decay process of J/ψ → φηη is thus established, which is the first observation of this decay.
The branching fraction of J/ψ → φηη final state including all possible intermediate states is measured. Following the same procedure in Ref. [24], the regions of M 2 (φη ) versus M 2 (φη) are divided into 40 × 40 areas (each area is tagged with i and j) and the numbers of data (n ij data ), non-φ and/or non-η background (n ij bkg ) and efficiency ( ij ) are obtained individually in each area.
where N corr is the signal number after efficiency correction and it is calculated by N corr = Σ ij [(n ij data −n ij bkg )/ ij ]; N J/ψ [15] is the total number of J/ψ events; B means the branching fractions from PDG [11], in which B η is B(η → γπ + π − ) for mode I and for mode II, where the uncertainties are statistical only. The weighted average [25] of the results for the two η decay modes is (2.32 ± 0.06 ± 0.16) × 10 −4 , after taking into account the correlations between the uncertainties from the two modes as denoted with asterisks in Table I. The systematic uncertainties in B(J/ψ → φηη ) measurements are shown in Table I. The uncertainties from MDC tracking and PID efficiencies are established to be 1.0% per pion/kaon in Refs. [26,27]. The uncertainty related to photon detection is determined to be 0.6% per photon in Ref. [28]. The uncertainties associated with the 4C kinematic fit are studied with the track parameter correction method [29] and the differences between the efficiencies with and without corrections are regarded as uncertainties; the influence of χ 2 4C requirement is also considered in the uncertainty determination. The sideband regions of φ and η mesons are varied by 1σ (the width of signal region corresponds to 3σ), and the effects on the branching fraction measurements are assigned as uncertainties. The uncertainties from mass windows are determined by smearing the mass spectra from phase space (PHSP) MC samples to compensate for the differences between the resolutions from data and MC simulation; the differences between efficiencies before and after smearing are taken as uncertainties. The influences of finite MC statistics are taken into account. The uncertainties due to quoted branching fractions and number of J/ψ events are from the PDG [11] and Ref. [15], respectively. The uncertainties from 2D binning are obtained by changing the numbers of areas in B(J/ψ → φηη ) determination. The total systematic uncertainties are obtained by summing all individual contributions in quadrature, assuming they are independent.

V. STUDY OF THE INTERMEDIATE STATE IN
φη MASS SPECTRUM Figure 3 shows the Dalitz plots for modes I and II, both of which have concentrations of events with There are also diagonal bands in both modes corresponding to J/ψ → φf 0 (1500), f 0 (1500) → ηη process based on MC study. Apart from these, no other structures are evident.

A. Simultaneous fit
With the assumption that there is an X structure in the φη mass spectrum in 2.0 − 2.1 GeV/c 2 region, corresponding to the clusters near 4.5 (GeV/c 2 ) 2 visible in Fig. 3, a simultaneous fit is performed on the φη mass spectra for modes I and II. Since the spin-parity value (J P ) of the structure could affect the relative orbital angular momenta between the decay products of J/ψ → ηX and X → φη , the fits with two different assumptions on the J P value are both performed. However, due to the limited statistics, they could hardly be distinguished. In the simultaneous fits, the interference between the structure and the direct decay of J/ψ → φηη is not considered.
Assuming the J P value of the structure as 1 − , the signal component is parametrized by where m is the reconstructed mass of φη system; M and Γ are the mass and width of the structure in the constant-width relativistic Breit-Wigner (BW) function; the P-wave PHSP factor (pq) 3 is considered in the partial width, where p is the φ momentum in the φη rest frame, and q is the η momentum in the J/ψ rest frame; denotes the efficiency and R is the double-Gaussian resolution function, both of which are determined from signal MC simulation. The mass and width of the BW function are allowed to float but are constrained to be the same for both modes; the signal ratio of the two modes is fixed based on PDG η branching fractions [11] and MC-determined efficiencies. The total signal yield of the two modes is allowed to float in the fit. The background components consist of nonresonant φηη , J/ψ → φf 0 (1500), f 0 (1500) → ηη and non-φ and/or non-η processes. For the non-resonant φηη process, the line shapes are derived from J/ψ → φηη PHSP MC simulation, and the ratio of background numbers for the two modes is fixed, similar to the signal case. For J/ψ → φf 0 (1500), f 0 (1500) → ηη background, whose influence on the observation of the structure is small, the shapes are from MC simulation; B(J/ψ → φf 0 (1500)) × B(f 0 (1500) → ππ) and B(J/ψ → φf 0 (1500)) × B(f 0 (1500) → KK) from BESII [9], together with B(f 0 (1500) → ππ), B(f 0 (1500) → KK) and B(f 0 (1500) → ηη ) from PDG [11], are used to obtain the expected f 0 (1500) number in this analysis, and the background number is fixed to the expected value. The non-φ and/or non-η backgrounds are determined from the 2D sidebands of the φ and η mesons as shown in Fig. 2.  (Table III), the significance is evaluated to be 5.3σ. Many checks are made to make sure that none of the possible background contributions could produce peaking backgrounds in 2.0 − 2.1 GeV/c 2 region in the φη mass spectrum. Comparison between data and MC also indicates no significant structures in the φη mass spectrum.
Assuming the J P value of the structure as 1 + , the simultaneous fit with the S-wave PHSP factor pq in the partial width is performed as shown in Fig. 5. The mass and width of the structure are determined to be (2062.8±13.1) MeV/c 2 and (177±36) MeV, respectively. The log-likelihood value is 15595.9, with a goodness-offit value of χ 2 /d.o.f. to be 16.68/26 = 0.64 for mode I and 24.36/26 = 0.94 for mode II. The significance of the structure after considering the systematic uncertainties (Table IV) is evaluated to be 4.9σ.

B. Angular distribution
The J P assignment for the observed structure is investigated by examining the distribution of |cosθ|, where θ is the η polar angle in the J/ψ rest frame. If J P = 1 − , the decay of J/ψ → ηX takes place through a P wave, neglecting the higher orbital angular momenta due to the closeness of the threshold, and the |cosθ| is expected to follow 1+cos 2 θ distribution. If J P = 1 + , the above decay takes place through an S wave, and the |cosθ| distribution is expected to be flat.
The data is divided into four intervals of |cosθ|, and the total signal yield in each interval is obtained with the same method of simultaneous fit with 1 + assumption as described above. After efficiency correction and normalization, the |cosθ| distribution of data is shown in Fig. 6, together with the fitting results with the 1 − and 1 + assumptions. The 1 − assumption determines that the f. value is 10.55/3 = 3.52 and the 1 + assumption determines that the value is 4.41/3 = 1.47. Although the χ 2 /d.o.f. value favors the 1 + assumption, hardly could these two assumptions be distinguished due to the limited statistics. The 0 + assumption is ruled out for it violates the law of J P conservation, and the 0 − assumption could be rejected at 99.5% confidence level from the Pearson χ 2 test. The results of simultaneous fit with 1 − assumption are consistent with those from 1 + .

C. Measurement of product branching fraction
The product branching fraction of ηφη final state through the observed structure is calculated by where N sig is the total signal yield from the two modes in the simultaneous fit;¯ is B(η → γπ + π − ) I + B(η → ηπ + π − )B(η → 2γ) II , where I and II are the detection efficiencies determined from signal MC simulation after considering the J P value of the structure and the angular distributions of the η, φ and η particles; other variables have been defined before. The measured N sig and B(J/ψ → ηX) × B(X → φη ) with 1 − and 1 + assumptions are summarized in Table II, where the uncertainties are statistical only.  The crosses are experimental data. The dashed curve is the fitting result with the 1 − assumption, and the solid curve is that with the 1 + assumption. Table III and Table IV summarise the systematic uncertainties in the measurements of mass and width of the observed structure, as well as B(J/ψ → ηX) × B(X → φη ) with 1 − and 1 + assumptions, respectively. In case there are differences between the uncertainties from two modes, the more conservative values are used. The signal parametrization is changed from a constantwidth BW function to a BW function with massdependent width. The impact on the signal yield is taken as the uncertainty of B(J/ψ → ηX) × B(X → φη ). The pole mass (m pole ) and pole width (Γ pole ) are obtained by solving for the complex equation P = m pole −iΓ pole /2 for which the BW denominator is zero, and the differences between the mass and width from nominal fit and m pole and Γ pole are considered as the uncertainties of mass and width, respectively. To obtain the uncertainties associated with the f 0 (1500) component of the data, the levels of the background that are included in the simultaneous fit are varied by 1σ [9,11], where σ denotes the uncertainty on the determined number of the f 0 (1500), and the maximum changes in the fit results are regarded as uncertainties. The sideband regions of φ and η mesons are varied by 1σ (the width of signal region corresponds to 3σ), and the effects on the results of the simultaneous fit are assigned as uncertainties. We vary the range of the simultaneous fit by 5% and take the largest deviations of the fitting results as uncertainties. To obtain the uncertainties due to the M (π + π − ) requirement for mode I, it is relaxed from 0.87 to 0.90 GeV/c 2 and the effects on the fitting results are considered as uncertainties. The two possible extra structures around 2.3 GeV/c 2 in Figs. 4 (b) and 5 (b) are considered. Following the same procedure in Ref. [13], we use a BW function convolved with a resolution function to describe them and the corresponding significances are determined to be less than 1.1σ. In that case, they are not considered in the nominal result. However, their impacts on the fitting results are taken as systematic uncertainties. The difference between the fitted η mass and that from PDG [11] is taken as uncertainty due to momentum calibration. The descriptions of other items could refer to Table I. The total systematic uncertainties are obtained by summing all individual contributions in quadrature, assuming they are independent.

VI. SUMMARY AND DISCUSSION
In summary, using (1310.6 ± 7.0) × 10 6 J/ψ events collected with the BESIII detector, we report the observation and study of the J/ψ → φηη process. Its branching fraction including all possible intermediate states is determined to be (2.32 ± 0.06 ± 0.16) × 10 −4 . A structure denoted as X is observed in the φη mass spectra in two dominant η decay modes, and a simultaneous fit is performed. Assuming the J P value of the structure as 1 − , the significance of the structure is evaluated to be 5.3σ; the mass and width are determined to be (2002.1 ± 27.5 ± 15.0) MeV/c 2 and (129 ± 17 ± 7) MeV, respectively; the product branching fraction B(J/ψ → ηX) × B(X → φη ) is measured to be (9.8 ± 1.2 ± 1.5) × 10 −5 ; the mass of the observed structure is almost 6σ away from that of the Y (2175) in PDG [11], suggesting the structure might not be the Y (2175). Assuming the J P value of the structure as 1 + , the significance of the structure is evaluated to be 4.9σ; the mass and width are determined to be (2062.8 ± 13.1 ± 4.2) MeV/c 2 and (177 ± 36 ± 20) MeV, respectively; the product branching fraction B(J/ψ → ηX) × B(X → φη ) is measured to be (9.6 ± 1.4 ± 1.6) × 10 −5 . The angular distribution is studied and the 1 − and 1 + assumptions could hardly be distinguished due to the limited statistics. No candidates in PDG have compatible mass, width and J P values with the new structure. More studies with the larger J/ψ data sample in the future might help to better understand the observed structure, among which the J P determination and precise measurements of the mass, width, and product branching fraction are especially important.