Study of J/Psi decays into eta Kstar Kstar-bar

We report the first observation of $\mPJpsi \to \mPeta\mPKst\mAPKst$ decay in a $\mPJpsi$ sample of 58 million events collected with the BESII detector. The branching fraction is determined to be $(1.15 \pm 0.13 \pm 0.22)\times 10^{-3}$. The selected signal event sample is further used to search for the $\mPY$ resonance through $\mPJpsi \to \mPeta \mPY, \mPY\to\mPKst\mAPKst$. No evidence of a signal is seen. An upper limit of \mathrm{Br}(\mPJpsi \to \mPeta \mPY)\cdot\mathrm{Br}(\mPY\to\mPKst\mAPKst)<2.52\times 10^{-4} is set at the 90% confidence level.


Introduction
Following the observation of Y (2175) by the BaBar Collaboration in e + e − → γ ISR φf 0 (980) via initial-state radiation [1], the resonance was observed by the BES Collaboration in J/ψ → ηφf 0 (980) [2] and more recently by the Belle Collaboration in e + e − → γ ISR φπ + π − [3].Since both the Y (2175) and Y (4260) [4] are observed in e + e − annihilation via initial-state radiation and these two resonances have similar decay modes, it was speculated that Y (2175) may be an s-quark version of Y (4260) [1].There have been a number of different interpretations proposed for the Y (4260), that include a gcc hybrid [5] [6] [7], a 4 3 S 1 cc state [8], a [cs] S [cs] S tetraquark state [9], or a baryonium [10].Likewise Y (2175) has been correspondingly interpreted as: a gss hybrid [11], a 2 3 D 1 ss state [12], or a ssss tetraquark state [13].None of these interpretations has either been established or ruled out by experimental observations.According to Ref. [12], a hybrid state may have very different decay patterns compared to a quarkonium state.Measuring the branching fractions of some decay modes may shed light on understanding the nature of Y (2175).Among those promising decay modes, Y (2175) → K * 0 K * 0 is of special importance.This decay mode is forbidden if Y (2175) is a hybrid state but allowed if it is a quarkonium state.
On the other hand, there are still lots of unknown decay modes of J/ψ and investigating more of them is useful to understand the mechanism of J/ψ decays.Based on a sample of 58M J/ψ events collected by the BESII detector at the Beijing Electron-Positron Collider (BEPC), a search for the process J/ψ → ηY (2175), Y (2175) → K * 0 K * 0 is performed.In addition, the first measurement of the branching fraction Br(J/ψ → ηK * 0 K * 0 ) is obtained.

Detector and data samples
The upgraded Beijing Spectrometer detector (BESII) was located at the Beijing Electron-Positron Collider (BEPC).BESII was a large solid-angle magnetic spectrometer which is de-scribed in detail in Ref. [14].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 time-of-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) package (SIMBES) [15] with detailed consideration of real detector performance (such as dead electronic channels) is used.The consistency between data and Monte Carlo has been carefully checked in many high purity physics channels, and the agreement is quite reasonable [15].

Analysis
The decay channel under investigation, J/ψ → ηK * 0 K * 0 , η → γγ, K * 0 → K + π − , K * 0 → K − π + , has two charged kaons, two charged pions, and two photons in its final state.A candidate event is therefore required to have four good charged tracks reconstructed in the MDC with net charge zero and at least two isolated photons in the BSC.A good charged track is required to (1) be well fitted to a three dimensional helix in order to ensure a correct error matrix in the kinematic fit; (2) originate from the interaction region, i.e. the point of closest approach of the track to the beam axis is within 2 cm of the beam axis and within 20 cm from the center of the interaction region along the beam line; (3) have a polar angle θ, within the range | cos θ| < 0.8; and (4) have a transverse momentum greater than 70 MeV/c.The TOF and dE/dx information is combined to form a particle identification confidence level for the π, K, and p hypotheses, and the particle type with the highest confidence level is assigned to each track.The four charged tracks selected are further required to be consistent with an unambiguously identified K + π + K − π − combination.An isolated neutral cluster is considered as a good photon when (1) the energy deposited in the BSC is greater than 60 MeV, (2) the angle between the nearest charged track and the cluster is greater than 15 • , (3) the angle between the cluster development direction in the BSC and the photon emission direction is less than 30 • , and (4) at least two layers have deposits in the BSC and the first hit is in the beginning six layers.A four-constraint (4-C) kinematic fit is performed to the hypothesis J/ψ → γγK + K − π + π − , and if there are more than two good photons, the combination with the smallest χ 2 γγK + K − π + π − value is selected.We further require that χ 2 γγK + K − π + π − < 20.Because we are not interest in the events of which the two photons come from π 0 , we require the invariant mass of two photons to be greater than 0.3 GeV/c 2 .

Branching fraction of
After applying the above event selection criteria, Fig. 1(a) shows the scatter plot of which is shown as the middle box in Fig. 1(a).Other boxes shown are side-band regions, and events in these regions are used to estimate the background in the signal region.The K ± π ∓ invariant mass spectra are shown in Fig. 1(b), where the solid histogram is shows the γγ invariant mass spectrum for events in the signal region, where an η is seen.In Fig. 2(a), the shaded histogram is the spectrum obtained requiring two good photons, while the dashed histogram is the spectrum for more than two photons.When there are more than two photons, the ratio of signal over background is much lower.In order to remove potential backgrounds as much as possible, we also require the number of good photons to be two.
Figure 2(b) shows the γγ invariant mass spectrum of events surviving the above selection, while the shaded histogram is the normalized background estimated using the side-band regions shown in Fig. 1(a).The number of J/ψ → ηK * 0 K * 0 events is determined by fitting the spectra in Fig. 2(b).The J/ψ → ηK * 0 K * 0 branching fraction is determined using where N sig = 347 is the number of events in the signal region, obtained by fitting the spectrum in Fig. 2(b) (the blank histogram); N sb = 138 is the number of background events estimated from side-band regions, obtained by fitting the spectrum in Fig. 2(b) (the shaded histogram); N J/ψ is the total number of J/ψ events [17]; ǫ = 1.79% is the detection efficiency obtained from MC simulation of J/ψ → ηK * 0 K * 0 ; and Br(K * 0 → K + π − ), Br(K * 0 → K − π + ) and Br(η → γγ) are the corresponding branching fractions.Figures 3(a) and 3(b) show respectively the fitting results of the signal and side-band events, where the shape of the γγ invariant mass spectrum obtained from the MC sample J/ψ → ηK * 0 K * 0 is used as the signal shape and a third order Chebyshev polynomial is used as the background shape.The J/ψ → ηK * 0 K * 0 branching fraction is determined to be where the error is statistical only.It is the first measurement for this decay mode of J/ψ and it is shown that this mode is a typical three bodies decay.The branching fraction is compatible with the result of Br(J/ψ → ηK + K − π + π − ) = (1.84±0.28)×10−3 given by BaBar Collaboration [16].It is worth mention of that this branching fraction is several times smaller than the radiative decay mode J/ψ → γK * 0 K * 0 which is very different from the situation of pp that the branching fraction of J/ψ → ηpp is much bigger than J/ψ → γpp.3.2.J/ψ → ηY (2175) → ηK * 0 K * 0 Next, we search for a possible resonance recoiling against η.So in addition to the above requirements, we require that the γγ invariant mass satisfies |M γγ − m η | < 0.04 GeV/c 2 and define the side-band region to be 0.1 GeV/c 2 < |M γγ − m η | < 0.14 GeV/c 2 .The K * 0 K * 0 invariant mass spectrum recoiling against η for J/ψ → ηK * 0 K * 0 is shown in Fig. 4, where the dashed histogram is the contribution from phase space for J/ψ → ηK * 0 K * 0 and the shaded histogram is the contribution from the normalized side-band events in the η, K * 0 and K * 0 side-band regions.There is no obvious enhancement in the region around 2.175 GeV/c 2 .
The backgrounds in the selected event sample are studied with MC simulations.For the decay J/ψ → ηK * 0 K * 0 , the possible main background channels are: There is no peak around 2.175 GeV/c 2 in the K * 0 K * 0 invariant mass distribution in any background channel.
We fit the mass distribution to determine a possible signal, where three parts are included in the total probability distribution function (p.d.f): (1) for the signal p.d.f, we use the shape of the K * 0 K * 0 invariant mass spectrum obtained from MC simulation of J/ψ → ηY (2175) → ηK * 0 K * 0 produced with the mass and width of Y (2175) fixed to BaBar's results; (2) for the normalized phase space contribution p.d.f., we use the shape of the K * 0 K * 0 invariant mass distribution obtained in the J/ψ → ηK * 0 K * 0 MC simulation, normalized with the branching ratio obtained in the previous section; (3) for the other possible backgrounds, we use a third order Chebyshev polynomial.
The product branching ratio is determined using where N obs = 11 ± 12 is the number of signal events, N J/ψ is the total number of J/ψ events [17], ǫ = 1.57% is the detection efficiency obtained from MC simulation of J/ψ → ηY (2175) → ηK * 0 K * 0 , where the first step decay used an angular distribution 1 + cos 2 θ, θ is the polar angle of the η momentum in the center of mass frame, Br(K * 0 → K + π − ) and Br(K * 0 → K − π + ) and Br(η → γγ) are the corresponding branching fractions.The error is only the statistical error.The signal significance is only 0.88σ.The upper limit of Br(J/ψ → ηY (2175)) • Br(Y (2175) → K * 0 K * 0 ) at the 90% confidence level is obtained using a Bayesian approach [18].We obtain the upper limit: where N obs up = 31 is upper limit at the 90% confidence level, σ sys is the systematic error discussed below, and the other symbols are defined as above.

Systematic Errors
In this analysis, the systematic errors on the branching fraction and upper limit mainly come from the following sources:

MDC Tracking efficiency and kinematic fitting
The systematic errors from MDC tracking and kinematic fitting are estimated by using simulations with different MDC wire resolutions [15].In this analysis, the systematic errors from this source are 12.8% for J/ψ → ηK * 0 K * 0 and 12.0% for J/ψ → ηY (2175) → ηK * 0 K * 0 .

Photon detection efficiency
The photon detection efficiency is studied in reference [15].The results indicate that the systematic error is less than 1% for each photon.Two good photons are required in this analysis, so 2% is taken as the systematic error for the photon detection efficiency.

Particle identification (PID)
In references [15] and [19], the efficiencies of pion and kaon identification are analyzed.The systematic error from PID is about 1% for each charged track.In this analysis, four charged tracks are required, so 4% is taken as the systematic error from PID.

Number of J/ψ events
The number of J/ψ events is (57.70±2.62)×10 6, determined from the number of inclusive 4-prong hadrons [17].The uncertainty 4.72% is taken as a systematic error.4.6.Fitting 4.6.1.J/ψ → ηK * 0 K * 0 branching fraction When fitting the γγ invariant mass spectrum, as described in section III.A, the η signal shape obtained from MC is fixed, and different order polynomials are used for the background shape.The difference is taken as the systematic error for the background uncertainty.We also use different regions in fitting the invariant mass spectrum.The total systematic error from fitting is 6.7%.
) upper limit When fitting the invariant mass spectrum of K * 0 K * 0 , as described in section III.B, there are three sources of systematic error: for the first p.d.f, we used the different resonance parameters measured by BaBar and BES, and take the difference as the systematic error from the uncertainty of signal parameters; for the second, the systematic error comes from the error of the branching fraction of J/ψ → ηK * 0 K * 0 measured in section III.A; for the third, we used the difference between fitting with a third order Chebyshev polynomial and fitting with the invariant mass shape from K * 0 K * 0 side-band events as the systematic error for the background uncertainty.Combin-  .The K * 0 K * 0 invariant mass spectrum, where points with error bars are candidate events, the dashed histogram is from MC phase space for J/ψ → ηK * 0 K * 0 , the shaded histogram is from side-band events, and the solid curve is the fitting result, where the Y(2175) shape used is from MC simulation.ing these contributions, 16.3% is obtained as the systematic error from fitting.

Different selection of side-band regions
We used different side-band regions to estimate the backgrounds both in section III.A and III.B, and take the difference as a source of systematic error.The result is 10.0% for the measurement of branching fraction and 4.2% for the upper limit.

Number of photons
To estimate the systematic error from the requirement of two good photons, we compare the efficiency difference for this requirement between data and MC sample, and obtain 4.4%, which is taken as the systematic error from the two photon requirement.

K * simulation
The K * is simulated with a P-wave relativistic Breit-Wigner function BW = , where r is the interaction radius and the value (3.4 ± 0.6 ± 0.3)(GeV /c) −1 measured by a K − π + scattering experiment [20] is used.Varying the value of r by 1σ, the difference of the detection efficiencies for J/ψ → ηK * 0 K * 0 , J/ψ → ηY (2175) → ηK * 0 K * 0 is taken as the systematic error from the uncertainty of the r value.
The systematic errors from the different sources and the total systematic errors are shown in Table I.

Summary
With 58M BESII J/ψ events, the branching fraction of J/ψ → ηK * 0 K * 0 is measured for the first time: No obvious enhancement near 2.175 GeV/c 2 in the invariant mass spectrum of K * 0 K * 0 is observed.

Figure 1 .
Figure 1.(a) Scatter plot of M K + π − versus M K − π + invariant mass, where the middle box is the signal region and the other boxes are the side-band regions.(b) The invariant mass spectra of K ± π ∓ ; the solid histogram is K + π − and the dashed is K − π + .

Figure 2 .
Figure 2. (a)The γγ invariant mass spectrum for data; the dashed histogram is from the N γ > 2 events, the shaded histogram is from the N γ = 2 events, and the blank histogram is from all events.(b) The γγ invariant mass spectrum for N γ = 2, where the blank histogram is from signal region events, and the shaded one is from the side-band regions events.

Figure 3 . 2 )Figure 4
Figure 3. Unbinned fitting results of γγ invariant mass spectra: (a) for the signal region events; (b) for the side-band region events, where the signal shape is obtained from the MC γγ invariant mass distribution and the background shape is a third order Chebyshev polynomial.

− 4 .
Due to the limited statistics, we can not distinguish whether the Y (2175) is a hybrid or quarkonium state.The BES collaboration thanks the staff of BEPC and computing center for their hard efforts.This work is supported in part by the National Natural Science Foundation of China under contracts Nos.10491300, 10225524, 10225525, 10425523, 10625524, 10521003, 10821063, 10825524, the Chinese Academy of Sciences under contract No. KJ 95T-03, the 100 Talents Program of CAS under Contract Nos.U-11, U-24, U-25, and the Knowledge Innovation Project of CAS under Contract Nos.U-602, U-34 (IHEP), the National Natural Science Foundation of China under Contract No. 10225522 (Tsinghua University), and the Department of Energy under Contract No. DE-FG02-04ER41291 (U.Hawaii).