Observation of $\chi_{cJ}\to \Lambda\bar \Lambda \eta$

By analyzing $(448.1\pm2.9)\times10^6$ $\psi(3686)$ events collected with the BESIII detector operating at the BEPCII collider, the decays of $\chi_{cJ} \to \Lambda\bar \Lambda \eta$ ($J=0$, 1 and 2) are observed for the first time with statistical significances of $13.9\sigma$, $6.7\sigma$, and $8.2\sigma$, respectively. The product branching fractions of $\psi(3686)\to\gamma\chi_{cJ}$ and $\chi_{cJ}\to \Lambda\bar \Lambda \eta$ are measured. Dividing by the world averages of the branching fractions of $\psi(3686)\to\gamma\chi_{cJ}$, the branching fractions of $\chi_{cJ}\to \Lambda\bar \Lambda \eta$ decays are determined to be $(2.31\pm0.30\pm0.21)\times10^{-4}$, $(5.86\pm1.38\pm0.68)\times10^{-5}$, and $(1.05\pm0.21\pm0.15)\times10^{-4}$ for $J=0$, 1 and 2, respectively, where the first uncertainties are statistical and the second systematic.


I. INTRODUCTION
Studies of the processes involving BBP , where B and P denote baryons and pseudoscalar mesons, respectively, are important to search for possible BB threshold enhancements and excited baryon states decaying into BP . An enhancement around the ΛΛ production threshold was observed in the e + e − → ϕΛΛ process [1], and the interpretation of ΛΛ enhancement originating from decay of the η(2225) → ΛΛ [2] was rejected with a significance of 7σ. Similar structure was also reported in the B meson decays B 0 → ΛΛK 0 and B + → ΛΛK + [3]. On the other hand, an excited Λ state, Λ(1670), was observed in the Λη mass spectra in the near-threshold reaction K − p → ηΛ [4] and the charmonium decay ψ(3686) → ΛΛη [5]. However, experimental results on the ΛΛ production threshold enhancement and on excited Λ states decaying into Λη are still limited. Comprehensive investigations of the BBP system in the various charmonium state decays are desirable. To date, only a few studies of χ cJ → BBP (J = 0, 1, 2) have been performed [6], and no investigation of χ cJ → ΛΛη has been reported. Observation of χ cJ → ΛΛη would provide an opportunity to better understand the enhancement around the ΛΛ production threshold and a possible excited Λ state, e.g., Λ(1670).
In the quark model, the χ cJ mesons are identified as 3 P J charmonium states. Because of parity conservation, they can not be produced by e + e − annihilation directly. As a result, the decays of χ cJ have not been studied as extensively as the vector charmonium states J/ψ and ψ(3686) in both experiment and theory. However, the radiative decays of ψ(3686) into χ cJ mesons have branching fractions of about 9% [6] for each χ cJ state, thereby offering an ideal testbed to investigate χ cJ meson decays.

II. BESIII DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector is a magnetic spectrometer [8] located at the Beijing Electron Positron Collider (BEPCII) [9]. The cylindrical core of the BESIII detector consists of a main drift chamber filled with heliumbased gas (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 flux-return yoke is instrumented with resistive plate chambers arranged in 9 layers in the barrel and 8 layers in the endcaps for muon identification. The acceptance of charged particles and photons is 93% of 4π solid angle. The charged-particle momentum resolution at 1.0 GeV/c is 0.5%, and the specific energy loss 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 [10] Monte-Carlo (MC) software, which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiencies and to estimate the background levels. The simulation takes into account the beam energy spread and initial state radiation (ISR) in the e + e − annihilation modeled with the generator kkmc [11]. The inclu-sive MC samples consist of 5.06×10 8 ψ(3686) events, the ISR production of the J/ψ state, and the continuum processes incorporated in kkmc. The known decay modes are modeled with evtgen [12] using the branching fractions taken from the Particle Data Group [6], and the remaining unknown decays from the charmonium states with lundcharm [13]. Final state radiation is incorporated with photos [14].
All charged tracks are required to satisfy |Z v | < 20 cm and | cos θ| < 0.93, where Z v denotes the distance from the interaction point to the point of closest approach of the reconstructed track to the z axis, which is the symmetry axis of the MDC, and θ is the polar angle relative to the z axis. Candidate events must have four charged tracks with zero net charge and at least three good photons. The Λ(Λ) candidates are reconstructed using vertex fits of all oppositely charged track pairs, which are assumed to be pπ − (pπ + ) without particle identification. To suppress the pπ − (pπ + ) combinatorial background, the reconstructed decay lengths of the Λ(Λ) candidates are required to be more than twice their standard deviations. Figure 1 shows the distributions of M pπ − and M pπ − versus Mp π + of survived candidates in data. The invariant mass of pπ − (pπ + ) is required to be within the Λ(Λ) signal region, defined as The twodimensional (2D) ΛΛ signal region is defined as the square region with both pπ − andpπ + combinations lying in the Λ(Λ) signal regions. The ΛΛ sideband I regions are defined as the square regions with either one of the pπ − orpπ + combinations locating in the 1D Λ(Λ) sideband regions and the other in the 1D signal region. The sideband II regions are defined as the square regions with both pπ − andpπ + combinations locating in the 1D Λ(Λ) sideband regions.
Good photon candidates are chosen from isolated clusters in the EMC. Their energies are required to be greater than 25 MeV in the barrel (| cos θ| < 0.8) and 50 MeV in the end cap (0.86 < | cos θ| < 0.92) regions. Reconstructed clusters due to electronic noise or beam backgrounds are suppressed by requiring the timing information to be within [0, 700] ns after the event start time. To suppress fake photons produced by hadronic interactions in the EMC and secondary photons from bremsstrahlung, clusters within a cone angle of 20 • around the extrapolated position in the EMC of any charged track are rejected. The energy deposited in the neighbor TOF counters is taken into account to improve the reconstruction efficiency and energy resolution.
To further suppress the combinatorial background, a four-momentum conservation constraint (4C) kinematic fit under the hypothesis of e + e − → ΛΛγγγ is applied to the events. The combination with the minimum χ 2 4C is kept for further analysis. The χ 2 4C of the kinematic fit is required to be less than 50 based on optimization with the Punzi significance method [15] with the formula where ϵ is the detection efficiency and B is the number of background events from the inclusive ψ(3686) MC sample. This requirement will reject 84% of background and lose 14% of signal efficiency.
The three selected photons are ordered according to their energies with E γ1 > E γ2 > E γ3 , defined as γ 1 , γ 2 , and γ 3 . The η candidates are reconstructed from either γ 1 γ 2 or γ 1 γ 3 pair. Based on MC study, excluding η candidates from γ 2 γ 3 could suppress the background by 6% with the signal efficiency loss less than 0.1%, and improves the Punzi significance by 3%. Figure 2 shows the M γγ distribution of η candidates of the accepted events in data. The η signal and sideband regions are defined as |M γγ − 0.54| < 0.04 GeV/c 2 and 0.08 < |M γγ − 0.54| < 0.12 GeV/c 2 , respectively. Events with both M γ1γ2 and M γ1γ3 being in the η signal region are excluded from analysis. Events with neither M γ1γ2 or M γ1γ3 within the signal region, but either M γ1γ2 or M γ1γ3 in the sideband region, are taken as sideband events.
A total of 144 candidate events survive from all requirements. Figure 3(a) shows the distribution of M ΛΛη of the accepted candidate events in data. Clear signals of χ c0 , χ c1 , and χ c2 are observed. The distributions of M ΛΛ , M Λη , and MΛ η from all χ cJ signal regions of the data sample are shown in Fig. 4. Here, the signal regions of χ c0 , χ c1 , and χ c2 are defined as [3.385, 3.445] GeV/c 2 , [3.490, 3.530] GeV/c 2 , and [3.536, 3.576] GeV/c 2 , respectively. With present statistics, it is impossible to conclude that there is an enhancement near the ΛΛ production threshold in Fig. 4(a). In addition, no obvious excited Λ state is found in Fig. 4(b) or Fig. 4(c). Meanwhile, we can not conclude whether there is any structure difference between the M ΛΛ , M Λη , and MΛ η spectra from different χ cJ signal regions.

IV. BACKGROUND STUDIES
Possible non-Λ(Λ) background and non-η peaking background from ψ(3686) decays are studied with sideband events. Figures 3(b) and 3(c) show the M ΛΛη distributions of candidate events in the ΛΛ sideband I region and η sideband region, respectively. No significant non-Λ(Λ) peaking background and non-η peaking background is observed. For the ΛΛ sideband II region, only three events are remained, which are negligible.
Potential backgrounds with ΛΛη + X final states are estimated by analyzing the inclusive ψ(3686) MC sample with TopoAna [16]. No peaking background is found except for χ c2 → Σ 0Λ η. However, the χ c2 → Σ 0Λ η decay is an isospin-violating process and no branching fraction is available. The yield of this background is estimated by assuming that the ratio B(χc2→Σ 0Λ η) B(χc2→ΛΛη) is comparable with B(J/ψ→Σ 0Λ ) B(J/ψ→ΛΛ) = 1.5% or B(ψ(3686)→Σ 0Λ ) B(ψ(3686)→ΛΛ) = 3.2% [6] based on isospin symmetry. MC studies show that the ratio of the yield of this background relative to our signal is less than 0.1%. Therefore this background is also negligible in this analysis.
Finally, the possible quantum electrodynamics (QED) contribution is examined by using the continuum data corresponding to an integrated luminosity of 44.45 pb −1 taken at the center-of-mass energy of 3.65 GeV [17]. No event survives the selection criteria. Therefore, the QED contribution is also neglected in this analysis.

V. BRANCHING FRACTIONS
To determine signal yields, an unbinned maximum likelihood fit is performed on the M ΛΛη distribution of the accepted candidates in data. In the fit, the χ cJ signals are described with individual Breit-Wigner functions 1 (M ΛΛη −mχ cJ ) 2 +Γ 2 χ cJ /4 convolved with a Gaussian function. The masses and widths of Breit-Wigner functions are fixed to their world average values [6]. The mean and width of the Gaussian function are free parameters. Because the potential peaking background is negligible, a linear function is chosen to describe the combinatorial background shape. For each signal decay mode, the statistical significance is calculated with ∆(ln L) = ln L max − ln L 0 and ∆ndf = 3. Here, the L max and L 0 are the maximum likelihoods with and without the signal component in the fits; the ∆ndf is the variation of number of degrees of freedom. The statistical signficances are 13.7σ, 6.2σ, and 7.7σ for χ c0 → ΛΛη, χ c1 → ΛΛη, and χ c2 → ΛΛη, respectively. As shown in Fig. 3(a), we obtain the signal yields of χ c0 , χ c1 and χ c2 to be 66.9 ± 8.8, 21.3 ± 5.0, and 31.6 ± 6.2, respectively, where the uncertainties are statistical only.

VI. SYSTEMATIC UNCERTAINTIES
The systematic uncertainties in the branching fraction measurements, described below, come from several sources, as summarized in Table 2.
The efficiencies of Λ(Λ) reconstruction, including the tracking efficiencies of the pπ − (pπ + ) pair, decay length requirement, mass window requirement, vertex fit and second vertex fit, are studied using the control samples of J/ψ → pK −Λ + c.c. and J/ψ → ΛΛ. The efficiency difference between data and MC simulation ∆ϵ i = ϵ data i /ϵ MC i − 1 in each momentum and cos θ bin of data is weighted by w i = Ni Ntot , where N i is the number of generated MC events in the i-th bin and N tot is the total number of generated MC events. The differences of the detection efficiencies between data and MC simulation w i × ∆ϵ i are assigned as the corresponding systematic uncertainties, which are 1.6%, 2.9%, and 3.0% for Λ and 0.2%, 2.3%, and 2.7% forΛ in χ c0 → ΛΛη, χ c1 → ΛΛη, Table 1. Signal yields in data, detection efficiencies, and the branching fractions B(ψ(3686) → γχcJ ), B(ψ(3686) → γχcJ ) · B(χcJ → ΛΛη), and B(χcJ → ΛΛη). The first errors are statistical and the second systematic. and χ c2 → ΛΛη, respectively.
The systematic uncertainty due to the photon detection is determined to be 1.0% per photon by using the control sample J/ψ → π + π − π 0 [18].
The systematic uncertainty related to the η mass window is studied with the control sample of ψ(3686) → ηJ/ψ, J/ψ → l + l − (l = e, µ). The difference of the acceptance efficiencies between data and MC simulation, 1.0%, is taken to be the corresponding systematic uncertainty.
The systematic uncertainties arising from rejections of J/ψ → ΛΛγ, χ cJ → ΛΛπ 0 , and Σ(Σ) → Λ(Λ)γ are estimated by varying individual rejection windows by one time of resolutions in M ΛΛγ , M γγ , and M Λ(Λ)γ , respectively. Totally 1000 pseudo-data-sets are sampled with replacement data for each case according to the bootstrap method [19]. For each pseudo-data set, similar fit is performed on M ΛΛη as the fit to real data. We examine the pull distribution relative to the fit yield of real data, which is where N real sig is the fit yield of real data, and N pseudo sig and σ N pseudo sig are the fit yield and its statistical uncertainty of pseudo-data, respectively. We fit to this pull distribution with a Gaussian function. If the mean value is larger than two times of its standard deviation, the maximum deviation will be assigned as the corresponding systematic uncertainty. The systematic uncertainties due to J/ψ → ΛΛγ, χ cJ → ΛΛπ 0 , and Σ(Σ) → Λ(Λ)γ rejections are assigned to be 0.9%, 1.8%, and 6.3% for χ c1 → ΛΛη; and 8.1%, 2.9%, and 4.5% for χ c2 → ΛΛη, respectively; while those for χ c0 → ΛΛη are negligible with deviation less than 2σ.
The systematic uncertainties in the M ΛΛη fit are considered in two aspects. The systematic uncertainties associated with the signal shape are estimated by using alternative signal shapes based on MC simulation. The changes of the fitted signal yields, 2.2%, 2.3%, and 1.9% for χ c0 → ΛΛη, χ c1 → ΛΛη, and χ c2 → ΛΛη, respectively, are taken as the corresponding systematic uncertainties. The systematic uncertainties from the background shape are estimated by using a second order polynomial. The changes of the fitted signal yields, 6.4%, 3.3%, and 1.0% for χ c0 → ΛΛη, χ c1 → ΛΛη, and χ c2 → ΛΛη, respectively, are taken as the corresponding systematic uncertainties. Adding them in quadrature, we obtain the systematic uncertainties due to the M ΛΛη fit to be 6.8%, 4.0%, and 2.1% for χ c0 → ΛΛη, χ c1 → ΛΛη, and χ c2 → ΛΛη, respectively.
The systematic uncertainty due to the BODY3 generator is estimated by varying the weight in each bin by ±1σ. The weights in various bins are obtained with data after subtracting the normalized background from inclusive ψ(3686) MC sample. The change of the weighted signal efficiency caused by each bin is obtained to be ∆ϵ i . Summing ∆ϵ i over all bins with n bin i=1 ∆ϵ 2 i , the associated systematic uncertainties are obtained to be 3.4%, 4.7%, and 7.5% for χ c0 → ΛΛη, χ c1 → ΛΛη, and χ c2 → ΛΛη, respectively.
The systematic uncertainties of the 4C kinematic fit are assigned as the differences between the detection effi-ciencies before and after the helix parameter corrections [20], which are 2.0% for χ c0 → ΛΛη, 2.3% for χ c1 → ΛΛη, and 2.8% for χ c2 → ΛΛη.
The uncertainties due to the limited MC statistics are calculated from 1−ϵ N ·ϵ , where ϵ is the detection efficiency and N is the number of signal MC events. They are 0.7%, 0.6%, and 0.6% for χ c0 → ΛΛη, χ c1 → ΛΛη, and χ c2 → ΛΛη, respectively.
For each signal decay, the total systematic uncertainty is calculated by adding systematic uncertainties quadratically under the assumption that all sources are independent.

VII. SUMMARY
By analyzing (448.1 ± 2.9) × 10 6 ψ(3686) events collected with the BESIII detector, we observe the decays of χ c0,1,2 → ΛΛη for the first time. The product branching fractions of ψ(3686) → γχ cJ and χ cJ → ΛΛη are determined. Dividing by the world averages of the branching fractions of ψ(3686) → γχ cJ , we determine the branching fractions of χ cJ → ΛΛη as summarized in Table 1. The current available statistics is not sufficient to draw any conclusion that there is an enhancement near the ΛΛ production. We looked at the M Λη or MΛ η spectra and did not find any excited Λ state.

VIII. ACKNOWLEDGMENTS
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support.