Search for a strangeonium-like structure $Z_s$ decaying into $\phi \pi$ and a measurement of the cross section $e^+e^-\rightarrow\phi\pi\pi$

Using a data sample of $e^+e^-$ collision data corresponding to an integrated luminosity of 108 pb$^{-1}$ collected with the BESIII detector at a center-of-mass energy of 2.125 GeV, we study the process $e^+e^-\rightarrow \phi\pi\pi$ and search for a strangeoniumlike structure $Z_s$ decaying into $\phi\pi$. No signal is observed in the $\phi\pi$ mass spectrum. Upper limits on the cross sections for $Z_s$ production at the 90\% confidence level are determined. In addition, the cross sections of $e^+e^-\rightarrow\phi\pi^{+}\pi^{-}$ and $e^+e^-\rightarrow\phi\pi^{0}\pi^{0}$ at 2.125 GeV are measured to be $(436.2\pm6.4\pm30.1)$ pb and $(237.0\pm8.6\pm15.4)$ pb, respectively, where the first uncertainties are statistical and the second systematic.

PACS numbers: 13.25.Jx, 13.25.Gv,13.66.Bc A charged charmonium-like structure, Z c (3900), was observed in the π ± J/ψ final states by the BESIII and Belle experiments [1,2]. Subsequently, several analogous structures were reported and confirmed by different experiments [3][4][5][6][7]. These observations inspired extensive discussions of their nature, and one of the reasonable interpretations is the tetraquark state due to these structures carrying charge and prominently decaying into a pion and a conventional charmonium state [8]. More recently, the neutral partners of these charmonium-like structures were observed [9][10][11], which indicate the isotriplet property of these structures and hint of a new hadron spectroscopy.
By replacing the cc pair in the Z c structure with a ss, it is possible to consider an analogous Z s structure. Similar to Y(4260) → J/ψπ + π − in which the Z c (3900) was observed [1,2], the process φ(2170) → φπ + π − is considered as a unique place to search for the Z s structure, as the φ(2170) is regarded as the strangeonium-like states analogy to Y(4260) in charmonium sector [12]. Furthermore, the conventional isosinglet ss state decaying into φπ is suppressed by the conservation of isospin symmetry, while for a conventional meson composed of u, d quarks, the φπ decay mode is strongly suppressed by the Okubo-Zweig-Iizuka (OZI) rule [13]. Therefore, it is of interest to perform an experimental search for the strangeonium-like structure Z s since its observation may imply the existence of an exotic state.
In this Letter, we present a search for the Z s structure in the process e + e − → φππ using a data sample corresponding to an integrated luminosity of (108.49 ± 0.75) pb −1 [14], taken at a center-of-mass energy of 2.125 GeV with the BESIII detector. Since the observed Z c (3900) [1,2] and Z c (3885) [5] are close to the D * D mass threshold and have a narrow width, we will focus on the search for a narrow width Z s structure around the K * K mass threshold (1.4 GeV/c 2 ) in the φπ mass spectrum. This also allows us to test the novel scenario of the initial single pion emission mechanism (ISPE) [15]. The BESIII detector [16] is a magnetic spectrometer located at the Beijing Electron Position Collider (BEPCII), which is a double-ring e + e − collider with a peak luminosity of 10 33 cm −2 s −1 at a center-of-mass energy of 3.773 GeV. The cylindrical core of the BESIII detector consists of a heliumbased multi-layer drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all immersed 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 is 93% over 4π solid angle. The charged-particle momen-tum resolution at 1 GeV/c is 0.5%, and the specific energy loss (dE/d x) resolution is 6%. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end caps) region. The time resolution of TOF is 80 ps in the barrel and 110 ps in the end caps.
The GEANT4 [17] based Monte Carlo (MC) simulation software, which includes the geometric description of the BESIII detector and the detector response, is used to determine the detection efficiencies and estimate backgrounds.
To simulate the e + e − → φππ process, the lineshape reported by BaBar [18] is adopted. Intermediate states in the simulation of e + e − → φππ process are modeled according to the BESIII data as described later.
Candidate events of e + e − → φπ + π − (φ → K + K − ) are required to have three or four charged tracks. Charged tracks are reconstructed from hits in the MDC within the polar angle range | cos θ| < 0.93. The tracks are required to pass the interaction point within 10 cm along the beam direction and within 1 cm in the plane perpendicular to the beam. For each charged track, the TOF and the dE/d x information are combined to form particle identification (PID) confidence levels for the π, K, and p hypotheses, and the particle type with the highest confidence level is assigned to each track. Two pions with opposite charges and at least one kaon are required to be identified. A one-constraint (1C) kinematic fit is performed under the hypothesis that the Kπ + π − missing mass corresponds to the kaon mass, and the corresponding χ 2 , denoted as χ 2 1C (π + π − KK miss ), is required to be less than 10. For events with two reconstructed and identified kaons, the combination with the smaller χ 2 1C (π + π − KK miss ) is retained.
Candidate events of e + e − → φπ 0 π 0 (φ → K + K − , π 0 → γγ) are required to have one or two charged tracks and at least four photon candidates. Photon candidates are reconstructed from isolated showers in the EMC, and the corresponding energies are required to be at least 25 MeV in the barrel (| cos θ| < 0.80) or 50 MeV in the end caps (0.86 < | cos θ| < 0.92). To eliminate showers associated with charged particles, the angle between the cluster and the nearest charged track must be larger than 10 degrees. An EMC cluster timing requirement of 0 ≤ t ≤ 700 ns is also applied to suppress electronic noise and energy deposits unrelated to the event. At least one kaon is required to be identified. A 1C kinematic fit is then performed under the hypothesis that the K4γ missing mass is the kaon mass. For events with two identified kaons or more than four photons, the combination with the smallest χ 2 1C (4γKK miss ) is retained and required to be less than 20. The four selected photons are grouped into pairs to form π 0 mesons. Two π 0 candidates are then selected by minimizing the quantity (M(γγ) 1 − m π 0 ) 2 + (M(γγ) 2 − m π 0 ) 2 , where m π 0 is the nomi-nal π 0 mass from Particle Data Group (PDG) [19]. In order to select a clean sample, both M(γγ) 1 and M(γγ) 2 are required to be within ±20 MeV/c 2 of m π 0 .
After applying the above selection criteria, the K + K − invariant mass, M(K + K − ), is computed using the fourmomenta of the reconstructed K and K miss from the kinematic fit. The M(K + K − ) spectra for the selected candidate events are shown in Figs. 1 (a) and (b), where φ signals are clearly seen. The Dalitz plots of the φπ + π − and φπ 0 π 0 events are shown in Figs. 2 (a) and (b), respectively, where the M(K + K − ) is required to be in the φ mass range, |M(K + K − ) − m φ | < 0.01 GeV/c 2 , and m φ is the nominal φ mass from PDG [19]. The apparent structures are from the decay processes e + e − → φf 0 (980) with f 0 (980) decaying to π + π − or π 0 π 0 final states, which are also clearly indicated in the ππ invariant mass spectra, M(ππ), displayed in Figs. 2 (c) and (d). Contributions from ρK + K − and ωK + K − are clearly seen in the K + K − π + π − channel, while no obvious contribution is observed in the neutral process. In addition, K * (892)K ∓ π ± events also contaminate the charged process. The candidate events of e + e − → φππ dominantly come from the processes with intermediate states f 0 (980) and σ, as shown in Figs. 2 (c) and (d).
To obtain the production yields of Z s , a good description of data without the Z s signal is essential. Therefore, a partial wave analysis (PWA) of the e + e − → φππ candidate events   is performed, since no obvious Z s structure is observed. A detailed description of the PWA procedure can be found in Ref. [20]. In the fit, the e + e − → φππ process is described by four subprocesses: e + e − → φf 0 (980), φσ, φf 0 (1370), and φf 2 (1270). The resonance parameters are fixed on the values determined in previous BES results [21,22]. Non-φ backgrounds estimated from the φ sidebands are represented by a non-interfering term. The projections of nominal PWA results on the M(ππ) distributions are shown as the solid lines in Figs. 2 (c) and (d). Based on the nominal PWA results, a dedicated MC sample is generated, which is used to explore the Z s signal yields and estimate the detection efficiency.
Since no obvious Z s signal is observed, the upper limit on its production is determined. A series of unbinned maximum likelihood fits to the M(φπ l ) distribution is performed by varying the number of Z s signal events. In each fit, the corresponding probability density function (PDF) is a lin-  Table I. The correlated systematic uncertainties on the upper limit of Z s signal yields associated with the fit range, signal shape, φ and π 0 mass window requirements, φ sideband range, and the φππ PWA model are considered by performing alternative fits and taking the maximum value of N UL as the upper limit, while the uncorrelated systematic uncertainties described in detail later are taken into account by smearing the likelihood curves.
where L is the integrated luminosity of the data taken at 2.125 GeV, and determined to be (108.49 ± 0.75) pb −1 [14] from large-angle Bhabha scattering events; (1 + δ) is a radiative correction factor calculated to the second-order in QED [23] by assuming that the line shape follows the measured cross section of the BaBar experiment [18], determined as 0.982 and 0.955 for the e + e − → φπ + π − and φπ 0 π 0 channels, respectively; ε is the efficiency; and B is either for φπ 0 π 0 [19]. The corresponding upper limits on the cross sections of Z s production are summarized in Table I. The e + e − → φππ signal yields are obtained from extended unbinned maximum likelihood fits to the M(K + K − ) distributions. In the fit, the φ peak is modeled as the signal MC simulated shape convoluted with a Gaussian function to account for the mass resolution difference between data and MC simulation, while the background is described by a second-order polynomial function. The fits to M(K + K − ) spectra, shown in Figs. 1 (a) and (b), yield (9421 ± 138) φπ + π − and (1649 ± 60) φπ 0 π 0 events. The detection efficiencies are (52.7± 0.1)% and (16.0± 0.1)%, respectively, obtained from the signal MC samples generated according to the nominal PWA results. The cross sections for e + e − → φπ + π − and e + e − → φπ 0 π 0 are determined to be (343.0±5.1) pb and (208.3 ± 7.6) pb, respectively.
Sources of systematic uncertainties and their corresponding contributions to the measurements of the cross sections are summarized in Table II. The uncertainties of the MDC tracking efficiency for each charged kaon and pion and the photon selection efficiency are studied with a control sample e + e − → φπ + π − taken at the energy of 2.125 GeV and a control sample of J/ψ → π + π − π 0 , respectively, and the differences between data and MC simulation are less than 1.5% per charged track and 1.0% per photon. Similarly, the uncertainties related to the pion and kaon PID efficiencies are also studied with the sample e + e − → φπ + π − taken at the energy of 2.125 GeV, and the average differences of the PID efficiencies between data and MC simulation are determined to be 3% and 1% for each charged kaon and pion, respectively, which are taken as the systematic uncertainties.
Uncertainties associated with kinematic fits come from the inconsistency of the track helix parameters between data and MC simulation. The helix parameters for the charged tracks of MC samples are corrected to eliminate the inconsistency, as described in Ref. [24], and the agreement of χ 2 distributions between data and MC simulation is much improved. We take half of the differences on the selection efficiencies with and without the correction as the systematic uncertainties, which are 2.1% for φπ + π − and 0.1% for φπ 0 π 0 channels, respectively. The difference of the selection efficiencies associated with the π 0 mass window requirement between data and MC simulation is estimated to be about 0.1%, which is taken as the systematic uncertainty for the mode e + e − → φπ 0 π 0 .
In the measurement of the cross section for e + e − → φππ, are taken from the PDG [19], where the overall uncertainty, 1.1%, is taken as the systematic uncertainty. The luminosity is determined to be (108.49 ± 0.75) pb −1 in Ref. [14] with an uncertainty of 0.7%. Uncertainties in the Y(2125) resonance parameters and possible distortions of the Y(2125) line shape introduce small systematic uncertainties in the radiative correction factor and the efficiency. This is estimated using the different line shapes measured by BaBar and Belle, and the difference in (1 + δ) · ε are taken as a systematic error, 3.1% for e + e − → φπ + π − and 1.2% for e + e − → φπ 0 π 0 , respectively.
In summary, a search for a strangeonium-like structure, Z s , in the process e + e − → φππ is performed using 108 pb  production at the 90% C.L. are determined around the K * K mass threshold (around 1.4 GeV/c 2 ) with different width hypotheses, as summarized in Table I. The results indicate the ISPE mechanism at K * K threshold is not as significant as predicted in Ref. [15]. Further study with larger statistics is essential to examine the existence of Z s structure and test the ISPE mechanism.
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key