First observation of J/\psi and \psi(2S) decaying to n K^0_S\bar\Lambda +c.c

The decays of $\jpsi$ and $\psip$ to ${n}{K^0_S}\bar{\Lambda}+c.c.$ are observed and measured for the first time, and the perturbative QCD ``12%'' rule is tested, based on $5.8 \times 10^7$ $\jpsi$ and $1.4 \times 10^7$ $\psip$ events collected with BESII detector at the Beijing Electron-Positron Collider. No obvious enhancement near $n\bar{\Lambda}$ threshold in $\jpsi \to {n}{K^0_S}\bar{\Lambda}+c.c.$ is observed, and the upper limit on the branching ratio of $\jpsi \to {K^0_S} X, X \to n \bar \Lambda$ is determined.


Introduction
Since the discovery of the J/ψ at Brookhaven [1] and SLAC [2] in 1974, more than one hundred exclusive decay modes of the J/ψ have been reported.According to Ref. [3], direct hadronic, electromagnetic and radiative decays make up roughly 65%, 14%, and 7% of the total J/ψ decay width, respectively.However, the measured hadronic decay channels sum up to less than 35 %.The BESII data sample of 5.8 ×10 7 J/ψ events provides a good opportunity to search for missing J/ψ hadronic decays.
The 5.8×10 7 J/ψ and 1.4×10 7 ψ(2S) events at BESII also offer a unique opportunity to search for new decay modes of J/ψ and ψ(2S) and test the "12% rule" in hadronic decays.In perturbative QCD, hadronic decays of the J/ψ and ψ(2S) are expected to proceed dominantly via three gluons or a single direct photon with widths proportional to the square of the cc wave function at the origin, which is well determined from dilepton decays.Thus for any hadronic final state h, the J/ψ and ψ(2S) decay branching fractions should satisfy the so called "12% rule" [5].
The leptonic branching fractions are taken from the particle data group (PDG) [6] tables.It is roughly obeyed for a number of exclusive hadronic decay channels except some V P , P P and V T channels [7][8] [9], where P, V and T denote members of the pseudoscalar, vector and tensor nonets, respectively.In this paper, the first observation and mea-surement of J/ψ and ψ(2S) to nK 0 S Λ + c.c., as well as a test of the perturbative QCD 12% rule are presented.The Λ * and N * resonance structures in J/ψ → nK 0 S Λ+c.c. are also shown, where no obvious enhancement near n Λ threshold is observed.The upper limit on the branching fraction of J/ψ → K 0 S X, X → n Λ is determined.

The BES Detector
The upgraded Beijing Spectrometer detector (BESII) is located at the Beijing Electron-Positron Collider (BEPC).BESII is a large solidangle magnetic spectrometer which is described in detail in Ref. [10].The momentum of charged particles is determined by a 40-layer cylindrical main drift chamber (MDC) which has a momentum resolution of σ p /p=1.78% 1 + p 2 (p in GeV/c).Particle identification is accomplished using specific ionization (dE/dx) measurements in the drift chamber and time-of-flight (TOF) information in a barrel-like array of 48 scintillation counters.The dE/dx resolution is σ dE/dx ≃ 8.0%; the TOF resolution for Bhabha events is σ T OF = 180 ps.Radially outside of the timeof-flight counters is a 12-radiation-length barrel shower counter (BSC) comprised of gas tubes interleaved with lead sheets.The BSC measures the energy and direction of photons with resolutions of σ E /E ≃ 21% √ E (E in GeV), σ φ = 7.9 mrad, and σ z = 2.3 cm.The iron flux return of the magnet is instrumented with three double layers of proportional counters that are used to identify muons.
A GEANT3 based Monte Carlo (MC) program (SIMBES) [11] with detailed consideration of the detector performance is used.The consistency between data and MC has been carefully checked in many high purity physics channels, and the agreement is reasonable.More details on this comparison can be found in Ref. [11].The detection efficiency and mass resolution for each decay mode in this analysis are obtained from MC simulation.

Analysis
The analyzed J/ψ and ψ(2S) → nK 0 S Λ with K 0 S → π + π − and Λ → pπ + (and c.c.) final states contain four charged tracks and an undetected neutron or anti-neutron.We require the candidate events to satisfy the following common selection criteria: 1. Events must have four good charged tracks with zero net charge.A good charged track is a track that is well fitted to a threedimensional helix, originates from the interaction region and has a polar angle θ in the range | cos θ| < 0.8.Because of the long decay lengths before K 0 S and Λ decay to π + π − and pπ + , the interaction region is defined as R xy < 0.12 m and |z| < 0.3 m.Here, R xy is the distance from the beamline to the point of closest approach of the track to the beamline, and |z| is the distance along the beamline to this point from the interaction point.
2. For each charged track in an event, χ 2 P ID (i) is determined using both dE/dx and TOF information: where i corresponds to the particle hypothesis.A charged track is identified as a p if χ 2 P ID for the p hypothesis is less than those for the π or K hypotheses.For the channels studied, one charged track must be identified as a p or p.
and Λ → pπ + decays are reconstructed using secondary vertex fitting, and the π + from the Λ decay is identified.
required.To reject the backgrounds from channels containing a K 0 S but no Λ, like e.g.J/ψ → pK 0 S Σ − + c.c., we require L xy (Λ), the distance from the reconstructed Λ vertex to the event origin, to be larger than 5 mm. Figure 3 shows the scatter plot of m pπ + versus m π + π − , and clear Λ and K 0 S signals are seen.Figure 4 shows the Λ decay length distributions for data and MC simulation for events satisfying Λ( Λ) and K 0 S mass selection requirements and χ 2 1C < 5.The missing mass distribution   Events/5MeV/c 2 The sum of these backgrounds, normalized by their branching fractions, is shown as the crosshatched area in Fig. 6, and it is consistent with the background under the peak for data.
Using a Gaussian to describe the K 0 S and a second order polynomial function to model the background shape, a fit to the m π + π − distribution is performed, shown as the curve in Fig. 6.A total of 1058±33 K 0 S events are obtained.No K 0

S
signal is observed in the m π + π − invariant mass distribution for events which recoil against the Λ sideband region (1.140 < m pπ < 1.164 GeV/c 2 ).The detection efficiency for the signal is 6.09%, which is determined from a uniform phase space MC simulation.The branching fraction is: where N obs is the number of events observed (1058±33); N bg is the number of background events from J/ψ → nK 0 S Σ0 (42 ± 8) and pK 0 S Σ− (12 ± 3); ǫ is the detection efficiency; N J/ψ is the number of J/ψ events; and B( Λ → pπ + ) and B(K 0 S → π + π − ) are the branching fractions of Λ → pπ + and K 0 S → π + π − [6].The error is statistical only.
If we fit the charge conjugate channels separately, we obtain 502±22 events with an efficiency of 6.02% for J/ψ → nK 0 S Λ, 560 ± 24 events, an efficiency of 6.16% for J/ψ → nK 0 S Λ, and the following branching fractions: , where the errors are statistical only.These results are consistent with each other in 1.5σ.
In order to obtain a clean sample of J/ψ → nK 0 S Λ and nK 0 S Λ, we require events to satisfy the Λ( Λ) and K 0 S mass selection requirements, χ 2 1C < 5, and L xy (Λ) > 5 mm, and also require the K 0 S decay length L xy (K 0 S ) > 5 mm to eliminate backgrounds without a K 0 S in the final state, such as J/ψ → ΛΣ − π + .After this final selection, the background contribution is estimated to be less than 5%.Figure 7 shows the scatter plot of m π − p versus m π + π − for J/ψ → nK 0 S Λ candidate events for all but the Λ( Λ) and K 0 S mass selection requirements, where the boxes in the plot show the signal and sideband regions.The invariant mass spectra of ΛK 0 S , nK 0 S , and Λn(Λn), as well as the Dalitz plot for all selection requirements are shown in Fig. 8.In the ΛK 0 S invariant mass spectrum, an enhancement near ΛK 0 S threshold is evident, as is found in the ΛK mass spectrum in J/ψ → pK − Λ [12].If the enhancement is fitted with an acceptance weighted S-wave Breit-Wigner function and a function f bg (δ) describing the phase space "background" contribution, the fit leads to M=1.648±0.006GeV/c 2 and Γ = 61 ± 21MeV/c 2 , respectively.Here the errors are only statistical.The systematic uncertainties are not included since more accurate measurements of the mass and width should come from a full PWA involving interferences among N * and Λ * states.The fitted mass and width are consistent with those obtained from a partial wave analysis of J/ψ → pK − Λ [12].The X(2075) signal which was seen in the p Λ invariant mass spectrum in J/ψ → pK − Λ is not significant here.Using a Bayesian approach [13] and fixing the mass and width of X(2075) to 2075 MeV/c 2 and 90 MeV/c 2 respectively, the upper limit on the number of events observed N UL obs is 54 events at the 90% C.L.
The N * state at around 1.9 GeV/c 2 in the ΛK 0 S invariant mass spectrum and the Λ * states at around 1.5 and 1.7 GeV/c 2 in the nK 0 S invariant mass spectrum are present.A larger data sample and a partial wave analysis are needed to analyze these N * and Λ * states.events.The statistical significance of the K 0 S is about 7.2σ.The 2 ± 1 background events from the Λ( Λ) sidebands and 2±1 background events from ψ(2S) → nK 0 S Σ0 are subtracted.A uniform phase space MC simulation determines the detection efficiency to be 9.16%.The corresponding branching fraction is: Here the error is statistical only.

Systematic Errors
In this analysis, the systematic errors on the branching fractions mainly come from following sources.

Kinematic fit
The systematic error from the 1C kinematic fit should be smaller than that from the 4C kinematic fit, since there are fewer constraints.Various studies show that the uncertainty of the 4C kinematic fit is around 4% [14].Here we conservatively take 4% as the error from the 1C kinematic fit.

Particle identification
In Ref. [11], the particle identification efficiency of π, K, and p are analyzed in detail.Here, only one charged track is required to be identified as a p or p, and the systematic error from particle identification is less than 2%.

Λ and K 0
S vertex finding In Ref. [15], J/ψ → Λ Λ → π + π − pp is chosen as the reference channel to study the systematic error of the Λ vertex finding algorithm, and 1.2% is determined as the systematic error for one Λ vertex.For K 0 S , the efficiency of the secondary vertex finding is studied using J/ψ → K * (892) K + c.c. events, and the systematic error is about 4.1% [16].

MC model
Different hadronization models for simulating the hadronic interactions give different detection efficiencies.Their differences are taken as systematic errors.The systematic errors are 7.0% and 14.7% for J/ψ → nK 0 S Λ and its conjugate channel, respectively, and 11.1% for ψ(2S) → nK 0 S Λ + c.c..The efficiency differences with or without considering the intermediate N * and Λ * states are also taken as the systematic errors.They are 5.3% and 4.5% for J/ψ → nK 0 S Λ and J/ψ → nK 0 S Λ, respectively.

Background uncertainty
The background uncertainties come from the uncertainties associated with the estimation of the sideband backgrounds, continuum events, and the events from other background as well as the uncertainties of the background shape, different fit ranges, etc.Therefore, the statistical errors in the estimated background events, the largest difference in changing the background shape, and the difference of changing the fit ranges are taken as the systematic errors for the background uncertainty.

Intermediate decay branching fractions
The branching fractions of Λ → pπ − and the K 0 S → π + π − decays are taken from the PDG [6].The errors on these branching fractions are taken as systematic errors in our measurements.
The above systematic errors are all listed in Table 1.The total systematic error is determined by adding all terms in quadrature.

Results
The decays of J/ψ and ψ(2S) to nK 0 S Λ+c.c. are observed for the first time, and their branching fractions are: The ratio of the branching fractions of ψ(2S) and J/ψ decaying to nK 0 S Λ + c.c. is Q h = (12.6 ± 3.5)% and obeys the 12% rule well.
There is no obvious enhancement near n Λ threshold.The upper limit on the branching fraction on the near-threshold enhancement X(2075) at n Λ threshold at the 90 % C.L. is: where N UL obs is 54 events; ǫ=5.32% is the detection efficiency considering the angular distributions; N J/ψ is the number of J/ψ events; B(Λ → pπ − ) and B(K 0 S → π + π − ) are the Λ → pπ − and K 0 S → π + π − branching fractions, and δ sys is the systematic error (17.3%).Taking into account the isospin factor, the branching fraction upper limit for B(J/ψ → K 0 S X) • B(X → n Λ + c.c.) is not inconsistent with that for B(J/ψ → KX) • B(X → p Λ + c.c.) [4].

Figure 1 2 Figure 1 .
Figure1is the missing mass spectrum determined from the charged tracks in J/ψ → nK 0 S Λ + c.c. candidate events satisfying Λ( Λ) and K 0 S mass selections and L xy (Λ) > 5 mm.A clear peak at the nominal neutron mass is observed.The second peak in the high missing mass region comes from J/ψ → nK 0 S Σ0 (1385) + c.c. and J/ψ → Σ − Σ+ (1385) + c.c. backgrounds.To suppress background and improve the resolution, a one constraint (1C) kinematic fit with a missing neutron is applied under the J/ψ → pnπ + π − π + hypothesis.The distribution of 1C fit χ 2 pnπ + π − π + for the above selection is shown in Fig.2.The agreement between data and MC simulation is reasonable, and in the following, χ 2 1C < 5 is required.

Figure 4 .
Figure 4.The Λ( Λ) decay length distributions with the Λ( Λ) and K 0 S mass selection requirements and χ 2 1C < 5 for data and MC.The histogram is the sum of signal MC and background from K 0 S sidebands, and the crosses are data.

Figure 5 .
Figure 5.The missing mass spectrum of charged tracks in J/ψ → nK 0 S Λ + c.c. for events satisfying the requirements in Fig. 4 and L xy (Λ) > 5 mm.

Figure 6 .
Figure 6.The π + π − invariant mass distribution for J/ψ → nK 0 S Λ + c.c. candidates satisfying the Λ( Λ) mass selection requirements, χ 2 1C < 5, and L xy (Λ) > 5 mm.The fit is also shown.The crosshatched area is the sum of the backgrounds after normalization, as described in the text.

3. 2 .SFigure 7 .
Figure 7.The scatter plot of m π − p versus m π + π − for J/ψ → nK 0 S Λ candidates after all selection requirements except for the Λ and K 0 S mass requirements.The boxes in the plot show the signal and sideband regions.

2 Figure 8 .
Figure 8.The invariant mass spectra of (a) ΛK 0 S , (b) nK 0 S , and (c) nΛ, as well as (d) the Dalitz plot for candidate events after all selection criteria.The crosses show the sideband backgrounds.

Table 1
Summary of the systematic errors.