Measurement of cross section for $e^{+}e^{-}\rightarrow\Xi^{0}\bar{\Xi}^{0}$ near threshold

Using $e^+e^-$ collision data at ten center-of-mass energies between 2.644 and 3.080 GeV collected with the BESIII detector at BEPCII and corresponding to an integrated luminosity of about 500 pb$^{-1}$, we measure the cross sections and effective form factors for the process $e^{+}e^{-}\rightarrow\Xi^{0}\bar{\Xi}^{0}$ utilizing a single-tag method. A fit to the cross section of $e^{+}e^{-}\rightarrow\Xi^{0}\bar{\Xi}^{0}$ with a pQCD-driven power function is performed, from which no significant resonance or threshold enhancement is observed. In addition, the ratio of cross sections for the processes $e^{+}e^{-}\rightarrow\Xi^{-}\bar{\Xi}^{+}$ and $\Xi^{0}\bar{\Xi}^{0}$ is calculated using recent BESIII measurement and is found to be compatible with expectation from isospin symmetry.


Introduction
In the past few decades, many experiments have observed surprising behavior in the near-threshold region in the production cross section of nucleon pairs in e + e − collisions. The measured cross section for the process e + e − → pp is approximately constant in the energy range from threshold up to about 2 GeV [1,2,3,4,5,6,7,8], with an average value of about 0.85 nb. Similar behavior in the near threshold region has been observed in the processes e + e − → nn [9,10,11], e + e − → ΛΛ [12] and e + e − → Λ + cΛ − c [13,14] with average cross sections of 0.8 nb, 0.3 nb and 0.2 nb, respectively. The non-vanishing cross section near threshold and the wide-range plateau discussed above have attracted much interest and driven many theoretical studies, including scenarios that invoke BB bound states [15] or unobserved meson resonances [16], Coulomb final-state interactions or quark electromagnetic interaction that into account the asymmetry between attractive and repulsive Coulomb factors [17,18]. In the present context of QCD and of our understanding of the quark-gluon structure of hadrons, it is particularly interesting to understand these anomalous phenomena in the hyperon sector [19,20,21]. Recently, the BESIII collaboration performed high precision studies of possible threshold enhancement in the processes e + e − → Σ ±Σ∓ [22] and Ξ −Ξ+ [23] with an energy scan method, and also reported a non-vanishing cross section near threshold. To understand the nature of these threshold effects, measurements of the near-threshold pair production of other hyperons will be valuable.
Additionally, the electromagnetic structure of hadrons, parametrized in terms of electromagnetic form factors (EMFFs) [24], provides a key to understanding QCD effects in bound states. However, experimental information regarding the EMFFs of hyperons remains limited. The access to hyperon structure by EMFFs provides extra motivation for measurements of exclusive cross sections and EMFFs for baryon antibaryon pairs.
In this Letter, we report a measurement of the Born cross section and the effective form factor for the process e + e − → Ξ 0Ξ0 using a single-baryon-tag method at center-of-mass (CM) energies between 2.644 and 3.080 GeV. We fit the Born cross sections under various hypotheses for the Ξ 0Ξ0 production in e + e − annihilation. The data set used in this analysis corresponds to a total of about 500 pb −1 e + e − collision data [25,26] collected with the BESIII detector [27] at the BEPCII storage rings [28].

BESIII detector and Monte Carlo simulation
The BESIII detector [27] records symmetric e + e − collisions provided by the BEPCII storage rings [28]. BESIII has collected large data samples in the τ -charm threshold region [29]. The cylindrical core of the BE-SIII detector covers 93% of the full solid angle and consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon-identification modules interleaved with steel. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end-cap) region. The time resolution in the TOF barrel region is 68 ps. The end-cap TOF system was upgraded in 2015 using multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [30].
To determine the detection efficiency 100,000 simulated e + e − → Ξ 0Ξ0 events are generated for each energy point with phase space modeling in the CONEXC generator [31], which takes into account the beamenergy spread and corrections from initial-states radiation (ISR). The Ξ 0 is simulated via EVTGEN [32] in its decay to the π 0 Λ mode with the subsequent decay Λ → pπ − with phase space model. The anti-baryons are allowed to decay inclusively according to the branching fractions from the Particle Data Group (PDG) [33] (unless otherwise noted, the charge-conjugate state of the Ξ 0 mode is included by default below). The response of the BESIII detector is modeled with Monte Carlo (MC) simulations using a framework based on GEANT4 [34]. Large simulated samples of generic e + e − → hadrons events (inclusive MC) implemented by the CONEXC generator [31] are used to estimate background.

Event selection
The selection of e + e − → Ξ 0Ξ0 events with a full reconstruction method suffers from a low reconstruction efficiency. Hence, a single baryon Ξ 0 tag technique is employed, i.e., only one Ξ 0 baryon is reconstructed via the π 0 Λ decay mode with Λ → pπ − and π 0 → γγ, and the presence of the anti-baryonΞ 0 is inferred from the recoil mass of the detected Ξ 0 .
Charged tracks are required to be reconstructed in the MDC within the angular coverage of the MDC: |cos θ| < 0.93, where θ is the polar angle with respect to the e + beam direction. Information from dE/dx measured in the MDC combined with the TOF is used to construct a particle-identification probability for the hypotheses of a pion, kaon, and proton. Each track is assigned to the particle type with the highest probability. Events with at least one negatively charged pion and one proton are kept for further analysis.
Photons are reconstructed from isolated showers in the EMC. The energy deposited in the nearby TOF counter is included to improve the reconstruction efficiency and energy resolution. Photon energies are required to be greater than 25 MeV in the EMC barrel region |cos θ| < 0.8), or greater than 50 MeV in the EMC end cap (0.86 < |cos θ| < 0.92). The showers in the angular range between the barrel and the end cap are poorly reconstructed and are excluded from the analysis. Furthermore, the EMC timing of the photon candidate must be in coincidence with collision events, 0 ≤ t ≤ 700 ns, in order to suppress electronic noise and energy deposits unrelated to the collision events. At least two photon candidates are required.
To reconstruct the π 0 candidates, a one-constraint (1C) kinematic fit is employed for all γγ combinations by constraining the invariant mass of two photons to the π 0 nominal mass [33], and a requirement is placed on the goodness-of-fit, χ 2 1C < 20, to suppress non-π 0 backgrounds. Here the fitted momentum of π 0 is used to further analysis. To reconstruct Λ candidates, a secondary vertex fit [35] is applied to all pπ − combinations and those with a goodness-of-fit χ 2 < 500 are selected. In the case when there is more than one combination satisfying this requirement then that one with the minimum value of |M pπ − m Λ | among all pπ combinations is chosen, where M pπ is the invariant mass of the pπ pair, and m Λ is the nominal mass of the Λ baryon [33]. The pπ − invariant mass of the selected candidate is required to be within 5 MeV/c 2 of the nominal Λ mass, a criterion determined by optimizing the figure of merit (FOM) S √ S+B based on the MC simulation. Here S is the number of signal MC events and B is the number of the background events expected from simulation. To further suppress background from non-Λ events, the Λ decay length, i.e.,, the distance between its production and decay positions, is required to be greater than zero. The Ξ 0 candidates are reconstructed from the combination of the selected π 0 and Λ candidates by minimizing the variable |M π 0 Λ − m Ξ 0 |, where M π 0 Λ is the invariant mass of the π 0 Λ pair, and m Ξ 0 is the nominal mass of the Ξ 0 baryon taken from the PDG [33]. In order to suppress background further, the π 0 Λ invariant mass is required to be within 10 MeV/c 2 of the nominal Ξ 0 mass, where the cut value is again set from FOM studies.
To selectΞ 0 anti-baryon candidates, we use the distribution of mass recoiling against the selected π 0 Λ system, where E π 0 Λ and p π 0 Λ are the energy and momentum of the selected π 0 Λ candidate in the CM system, and √ s is the CM energy. Figure 1 shows the distribution of M π 0 Λ versus M recoil π 0 Λ for all energy points. A clear accumulation is observed around the Ξ 0 nominal mass.

Extraction of signal yields
The signal yield for the process e + e − → Ξ 0Ξ0 at each energy point is determined by performing an extended unbinned maximum-likelihood fit to the M recoil π 0 Λ spectrum in the range from 1.20 GeV/c 2 to 1.45 GeV/c 2 . In the fit, the signal shape for the process e + e − → Ξ 0Ξ0 at each energy point is represented by the simulated MC shape. After applying the same event selection on the inclusive MC samples at each CM energy, it is found that some background is present at each energy point, mainly coming from e + e − → πΣΣ events. These events distribute smoothly in the region of interest and can be described by a second-order polynomial function, while for two energy points near the Ξ 0Ξ0 mass threshold at 2.644 and 2.646 GeV, the background is modeled by an Argus function [36]. The signal significances for the energy points 2.644, 2.646, 2.700 and 2.950 GeV are found to be below three standard deviations. For these energy points, the upper limits for e + e − → Ξ 0Ξ0 production are calculated at the 90% confidence level (C.L.) based on the profile likelihood method incorporating systematic uncertainties [37]. Figure 2 shows the fit to the distribution of M recoil π 0 Λ for the e + e − → Ξ 0Ξ0 process at each energy point after applying the event selection described above. Note that single-baryon-tag method means that in a small fraction of events both the Ξ 0 andΞ 0 hyperons are reconstructed, which means that the recoil-mass fit introduces double counting into the analysis. A correction factor of 1.08 is applied to the statistical uncertainty to account for this effect [23,38] based on MC simulation, while for two energy points near the Ξ 0Ξ0 mass threshold at 2.644 and 2.646 GeV, the correction factor is estimated to be 1.03. The number of observed events is summarized in Table 1.

Determination of Born cross section
The Born cross section for e + e − → Ξ 0Ξ0 is calculated by where N obs is the number of the observed signal events, L is the integrated luminosity related to the CM energy, the factor 2 is required for the inclusion of the c.c. mode, (1 + δ) is the ISR correction factor [39], 1 |1−Π| 2 is the vacuum polarization (VP) correction factor [40], ǫ is the detection efficiency and B denotes the product of the known branching fractions for the decays Ξ 0 → π 0 Λ, Λ → pπ − and π 0 → γγ, respectively [33]. The ISR correction factor is obtained using the QED calculation as described in Ref. [41] and taking Eq. (6) used to fit the cross section measured in this analysis parameterized as input. The measured cross sections are summarized in Table 1.

Determination of effective form factor
Assuming that spin-1/2 baryon pair production is dominated by one-photon exchange, the Born crosssection for the process e + e − → Ξ 0Ξ0 can be parameterized in terms of the two EMFFs G E (s) and G M (s) [42] as follows: Also listed at each point is the integrated luminosity L, the VP correction factor 1 |1− | 2 , the ISR correction factor 1 + δ , the detection efficiency ǫ, the number of the observed signal events N obs (N U P ), and the signal significance S(σ), taking account of both statistical and systematic uncertainties. The values between the parentheses for σ B and |G eff (s)| are the corresponding upper limits at 90% C.L. where α is the fine structure constant, the variable β = 1 − 1/τ is the BB velocity, τ = s/4m 2 Ξ 0 , m Ξ 0 the Ξ 0 mass, and s is the square of the measured CM energy. The effective form factor is defined as a combination of the EMFFs and, through substitution of Eq. (3) into Eq. (4), is proportional to the square root of the Born cross-section: The measured values of the effective form factors are summarized in Table 1.

Fit to Born cross section
A least-χ 2 method [43] is used to fit the Born crosssection for the process e + e − → Ξ 0Ξ0 with the assumption of two alternative functions. The first of these is a perturbative-QCD (pQCD) driven energy power function [44], where c 0 is the normalization, c 1 is the mean effect of a set of possible intermediate states. This model has been applied successfully in studies of e + e − → ΛΛ [12], Σ ±Σ∓ [22], and Ξ −Ξ+ [23] production. The fit returns c 0 = (20.3 ± 9.6) pb · GeV −10 and c 1 = (1.52 ± 0.13) GeV, where the uncertainty includes both statistical and systematic contributions. Figure 3 shows the fit result with quality χ 2 /ndof = 19.9/8.0, where the number of freedom degree (ndof ) is calculated by subtracting the number of free parameters in the fit from the total number of energy points. The second function is a coherent sum of a pQCD-driven energy power function plus a Breit-Wigner (BW) function to test the resonance reported in the charged mode [23] Here the mass and width are fixed to the values of the charged mode [23], φ is a relative phase between the BW function and the power function and P ( √ s) is the two-body phase space factor. In Eq. (8), Γ ee is the electronic partial width, M and Γ are the mass and width of BW, respectively, and B is the branching fraction. The significance for the resonance described by the BW is estimated to be 2.0σ including the systematic uncertainty, which receives contributions from the Born cross section for this measurement and the uncertainty in the knowledge of the mass and width of the resonance from previous studies [23]. The fit has a quality of χ 2 /ndof = 10.7/4.0 and is shown in Figure 3. The comparison of fit quality for both models is fair. Note that neither fit model describes the point near 2.8 GeV well, which may be due to statistical fluctuation or the contribution of one or more additional unknown resonances. A Bayesian approach [45] gives the upper limit on the product of the electronic partial width and the branching fractions for this possible resonance decaying to the Ξ 0Ξ0 to be Γ ee B < 0.3 eV at the 90% C.L. , after taking into account the systematic uncertainties described in the following.

Systematic uncertainty
Several sources of systematic uncertainties are considered on the Born cross section measurement. They include the Ξ reconstruction efficiency, the fit range, the background shape, the mass resolution and the fit models for the cross section. Knowledge of the decay branching fractions of intermediate states and the luminosity measurement give additional contributions. All of the systematic uncertainties are discussed in detail below.
1. The understanding of the Ξ 0 reconstruction efficiency, which in turn depends on the photonselection efficiency, the π 0 reconstruction efficiency, the Λ reconstruction efficiency, the requirements on the mass of the Λ and Ξ 0 , and the decay length of the Λ candidates, is studied with a control sample of J/ψ → Ξ 0Ξ0 events via single-and double-tag methods. The selection criteria for the charged tracks, and the reconstruction of Λ and Ξ 0 candidates are exactly the same as those described in Sec. 3. The Ξ 0 reconstruction efficiency is defined as the ratio of the number of double-tag Ξ 0Ξ0 events to that from the single tags. For studying the reconstruction efficiency for two energy points near threshold, care is taken to ensure that the momenta of the two pions in the final state of the control sample is within the same range as those of the signal decays. A detailed description of the method can be found in Ref. [46]. The difference in the Ξ 0 reconstruction efficiency between the data and MC samples is assigned as the uncertainty. 2. The uncertainty due to the fitting range is estimated by shifting the fitting range of M recoil π 0 Λ by 20 MeV/c 2 . The difference in yields is taken as the systematic uncertainty of the fit range. 3. The uncertainties due to the background shape arise mainly from the level of the wrongcombination background and the form of the polynomial function used. For the wrongcombination background, there are transition π 0 's with similar momenta in both the baryon and antibaryon decay chains within the signal events. Incorrect use of these in the Ξ 0 reconstruction leads to the wrong-combination background. The impact of this component on the background shape is studied by studying how the shape changes as the association criteria for the neutral pions are varied in the MC. The uncertainty associated with the polynomial function is estimated by changing from a second order to a third order function. The observed difference in the yields is taken as the systematic uncertainty due to the background shape. 4. The uncertainty associated with knowledge of the mass resolution is estimated by changing the nominal PDF to the MC-simulated shape convolved with Gaussian function whose mean and width are free parameters. The difference in yields is taken as the systematic uncertainty due to the mass resolution. 5. In this analysis, the detection efficiency for each energy point is determined from MC simulated with the phase space model, which may not describe the angular distribution well. Thus, a joint angular distribution formalism [47] combined with the measured parameters in J/ψ → Ξ 0Ξ0 decay is employed to validate the detection efficiency, where the angular distribution parameter is set to unity which is its maximally allowed value. The difference in the efficiency for both models is taken as the systematic uncertainty associated with the angular distribution. 6. The uncertainty of the fit model used to evaluate the line shape of Born cross section incorporating the effect of ISR factor is estimated by floating and fixing the index of the pQCD energy power function. The resulting change in selection efficiency is taken as the systematic uncertainty due to the fitting model of line shape. 7. The uncertainties associated with the branching fractions of the intermediate states Ξ 0 and Λ are taken from the PDG [33]. 8. The luminosity at all energy points is measured using the Bhabha events, with an uncertainty of about 1.0% [48].
The various systematic uncertainties on the crosssection measurements are summarized in Table 2, where the values in parentheses represent the corresponding values for the two energy points near threshold. Assuming all sources to be independent, the total systematic uncertainty is obtained by summing over the individual contributions in quadrature.

Discussion and conclusion
Born cross sections and effective form factors for the exclusive process e + e − → Ξ 0Ξ0 are measured by means of a single baryon tag method for the first time. The e + e − collision data are collected at ten center-ofmass energies between 2.644 and 3.080 GeV by the BESIII detector at BEPCII, and correspond to a total integrated luminosity of about 500 pb −1 . The measured Born cross sections are described adequately with a pQCD-driven energy power function, which tend to zero around 2.64 GeV and so do not exhibit any obvious threshold enhancement. Allowing for a resonance at around 3.0 GeV, as reported in Ref. [23], gives a signal with a significance of 2.0σ, including both statistical and systematic uncertainties. The upper limit on the product of the electronic partial width and the branching fractions for this resonance decaying to the Ξ 0Ξ0 final state is estimated to be Γ ee B < 0.3 eV at 90% C.L.. The fit models considered do not describe the data well at 2.8 GeV, which is behavior that warrants closer study when larger data sets become available. The effective form factor is determined at each energy point, but the samples are not large enough to allow separate measurements of G E (s) and G M (s). A comparison of the measured Born cross sections between the charged mode e + e − → Ξ −Ξ+ [23] and the neutral mode e + e − → Ξ 0Ξ0 , as shown in Fig. 4, shows consistent behavior with the current level of experimental precision. The ratio of Born cross sections for both modes is within 1σ of the expectation of isospin symmetry. These results provide more information for understanding the insight into the nature of hyperon pair production in e + e − annihilation near threshold.