Search for ψ ( 3770 ) → charmless final states involving η or π 0 mesons

We search for ψ(3770) → π+π−η, K+K−η, pp̄η, ρ0π+π−η, K+K−π+π−η, pp̄π+π−η, pp̄K+K−η and pp̄K+K−π0 using data samples of 17.3 and 6.5 pb−1 integrated luminosities recorded at the center-of-mass energies of 3.773 and 3.65 GeV, respectively, by the BES-II detector operating at the BEPC collider. We obtain cross section measurements at both energies and upper limits on ψ(3770) decay branching fractions to the final states studied. 12 Eur. Phys. J. C (2010) 66: 11–16


Introduction
The ψ(3770) has been thoroughly studied. It is popularly interpreted as a mixture of D-wave and S-wave of a cc bound state [1]. Since it lies just above the open charm pair DD threshold but belowDD * threshold, it was thought to almost entirely decay into DD meson pairs [2]. Under the assumption that there is only one single ψ(3770) resonance in the energy range from 3.70 to 3.89 GeV, the BES Collaboration measured the branching fraction for ψ(3770) → non-DD decays to be (14.7 ± 3.2)% [3][4][5][6][7]. So far, however, the sum of the exclusive non-DD decay branching fractions measured by both the BES and CLEO Collaborations remains to be less than 2% [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The anomalously large branching fraction for ψ(3770) → non-DD decays indicates that, either the conventional knowledge about the ψ(3770) production and decays may need to be improved, or there are new structures or new dynamics effects at the considered energies [22,23], or there may exist other exclusive non-DD decays of the ψ(3770) not yet detected. In experiments, it is important to investigate more exclusive light hadron processes produced in e + e − annihilation at and off the ψ(3770) resonance peak. By comparing the measured cross sections at and off the ψ(3770) resonance peak, one may derive some helpful information about the non-DD decays of ψ(3770).

The BES-II detector
BES-II is a conventional cylindrical magnetic detector [24,25] operated at the Beijing Electron-Positron Collider (BEPC). A 12-layer vertex chamber (VC) surrounding the beryllium beam pipe provides input to the event trigger, as well as coordinate information. A forty-layer main drift chamber (MDC) located just outside the VC yields precise measurements of charged particle trajectories with a solid angle coverage of 85% of 4π ; it also provides ionization energy loss (dE/dx) measurements which are used for particle identification. Momentum resolution of 1.7% 1 + p 2 (p in GeV/c) and dE/dx resolution of 8.5% for Bhabha scattering electrons are obtained for the data taken at √ s = 3.773 GeV. An array of 48 scintillation counters surrounding the MDC measures the time of flight (TOF) of charged particles with a resolution of about 180 ps for electrons. Outside the TOF, a 12 radiation length, lead-gas barrel shower counter (BSC), operating in limited streamer mode, measures the energies of electrons and photons over 80% of the total solid angle with an energy resolution of σ E /E = 0.22/ √ E (E in GeV) and spatial resolutions of σ φ = 7.9 mrad and σ z = 2.3 cm for electrons. A solenoidal magnet outside the BSC provides a 0.4 T magnetic field in the central tracking region of the detector. Three doublelayer muon counters instrument the magnet flux return and serve to identify muons with momentum greater than 0.5 GeV/c. They cover 68% of the total solid angle.

Data and Monte Carlo
The analyzed data samples correspond to 17.3 pb −1 and 6.5 pb −1 integrated luminosities, which were collected at √ s = 3.773 and 3.65 GeV, respectively, with the BES-II detector at the BEPC collider. These data samples were taken during 2001 and 2003. Throughout this paper we denote the two data sets the ψ(3770) and the continuum data, respectively.
For the determination of the detection efficiency and the estimation of the background, we generate Monte Carlo events of e + e − → exclusive light hadrons by using a phase space generator based on the Monte Carlo simulation for the BES-II detector [26]. The generator, which was used in previous analyses [10][11][12][13][14][15], includes initial state radiation (ISR) and photon vacuum polarization corrections [27] with 1/s cross section energy dependence. The generator also includes final state radiation [28], decreasing the detection efficiency by less than 0.5%.

Criteria of event selection
For the event selection, we require that there are at least two or four charged tracks in each event. All charged tracks used in this analysis are required to be well reconstructed in the MDC with good helix fits. They are required to be within | cos θ | < 0.85, where θ is the polar angle with respect to the beam axis, and to originate from the interaction region V 2 x + V 2 y < 2.0 cm and |V z | < 20.0 cm, where, V x , V y and V z are the x, y and z coordinates of the point of the closest approach of the charged track relative to the beam axis. For each charged track, the combined dE/dx and TOF measurements are used to calculate the χ 2 (= χ 2 dE/dx + χ 2 TOF ) values and the corresponding confidence levels for the hypotheses that the particle is a pion, kaon, or proton (CL π , CL K and CL p ). If the combined confidence level CL π for a pion hypothesis is greater than 0.001, it is identified as a pion. If the combined confidence level CL K for a kaon hypothesis is greater than the combined confidence level CL π for a pion hypothesis, it is identified as a kaon. If the combined confidence level CL p for a proton hypothesis satisfies CL p /(CL π + CL K + CL p ) > 0.6, it is identified as a proton.
For each process, there are two photons in the final state. To select the photons, we use the BSC measurement information. A neutral cluster is considered a good photon if it satisfies the following selection criteria. The energy of the cluster deposited in the BSC is greater than 50 MeV, the electromagnetic shower starts in the first five readout layers, the opening angle between the cluster and the nearest charged track is greater than 22 • [29][30][31][32] and the opening angle between the cluster development direction and the photon emission direction is less than 37 • [29][30][31][32].
In order to improve track momentum resolution and suppress background, we perform an energy-momentum conservation kinematic fit on each accepted charged and neutral track combination. Those combinations are retained if the χ 2 probability of the fit is greater than 0.01. For each process, it is likely that there are more than one combination satisfying the above selection criteria in each event. In this case we choose the combination with the largest χ 2 probability.
For the final states π + π − η and K + K − η, to veto the background events from the process ψ(3686) → J /ψη with J /ψ → μ + μ − or J /ψ → e + e − , which are produced via initial state radiative return, we require that the invariant masses of the π + π − and K + K − combinations be less than 3.0 GeV/c 2 , respectively. To suppress background events from the process e + e − → (γ )e + e − , we require that the sum of the energies deposited in the BSC of the two charged tracks should be less than 1.1 GeV. To remove background events from the process e + e − → (γ )μ + μ − , we require that at least one of the two charged tracks be within | cos θ | < 0.68 and have momentum greater than 0.5 GeV/c, but it must not be identified as muon [9]. To study the process e + e − → ρ 0 π + π − η, we calculate the π + π − invariant masses M π + π − of the selected π + π − π + π − γ γ events, with the fitted momentum vectors from the kinematic fit. The mass window of |M π + π − − 0.7755| < 0.15 GeV/c 2 is taken as the ρ 0 signal region.
In Fig. 1(e ) [(f )], no obvious η signal is observed. There are 10 (6) events in the η signal region, and 17 (5) events outside the η signal region. By supposing that the distribution of the combinatorial γ γ background is flat, 5.7 ± 1.4 (1.7 ± 0.7) background events are estimated in the η signal region. After background subtraction, we obtain 4.3 ± 3.4 (4.3 ± 2.6) events for e + e − → K + K − π + π − η (ppπ + π − η) observed from the continuum data. In the other figures, only a few events are observed. We obtain the numbers N obs of Fig. 2 Distributions of the γ γ invariant masses for the selected combinations of e + e − → ppK + K − γ γ from the ψ(3770) data (left) and the continuum data (right), where the pair of arrows denotes the π 0 signal region events by counting the events with M γ γ in the η or π 0 signal region. The mass window of |M γ γ − M η/π 0 | < 3σ M η/π 0 is taken as the η/π 0 signal region, where M η/π 0 is the η/π 0 nominal mass [7], σ M η/π 0 is the η/π 0 mass resolution determined by the Monte Carlo simulation.
The numbers of observed events together with the expected backgrounds for all final states studied are quoted in the second and third columns of Tables 1 and 2.

Background estimation
At √ s = 3.773 and 3.65 GeV, the exclusive light hadron processes are produced from e + e − annihilation continuum. However, J /ψ and ψ(3686) decays are also produced due to initial state radiative return. These decays may contaminate the exclusive light hadron processes. Due to the misidentification between charged kaon and pion, the other exclusive light hadron processes may also contaminate the processes in question. The ψ(3770) decays, including the final states of DD, J /ψπ + π − , J /ψη, J /ψπ 0 and γ χ cJ (J = 0, 1, 2), may also contaminate the processes under study. We estimate the number of such background events as in Refs. [10][11][12][13][14][15] from the Monte Carlo simulation Table 1 Observed cross sections measured at √ s = 3.773 GeV, where, N obs is the observed number of events, N b is the number of all the background events, N net is the number of signal events, N up is the upper limit on the number of events at 90% C.L., is the detection efficiency, δ sys is the relative systematic error, σ is the observed cross section and σ up is the observed cross section upper limit set at 90% C.L.

Observed cross sections
In this analysis we ignore possible interference between resonance and continuum production, and neglect the difference of the vacuum polarization corrections at √ s = 3.773 and 3.65 GeV. The observed cross section for the process e + e − → f (f denotes a exclusive light hadron final state) can be determined by where, N net is the number of signal events for e + e − → f , L is the integrated luminosity of the data collected, is the efficiency for detection of the exclusive process, B(η/π 0 → γ γ ) is the branching fraction for η/π 0 → γ γ . The measured cross sections are quoted in the last columns of Tables 1 and 2, where the first error given is statistical and the second systematic. The latter error includes uncertainties in the integrated luminosity (∼2.1% [4]), the photon selection (∼2.0% per photon), the tracking efficiency (∼2.0% per track), the particle identification (∼0.5% per pion or kaon, ∼2.0% per proton), the kinematic fit (∼1.5% [32] For other processes, however, only a few events are observed in the data. We set upper limits σ up on their observed cross sections at 90% C.L., which are also quoted in the last columns of Tables 1 and 2. In this procedure, upper limits on the observed numbers of events for these processes are set by using the Feldman-Cousins method [33] and neglecting background.

Upper limits on the observed cross section and the branching fraction for ψ(3770) → f
Assuming that there are no other unknown structures and dynamics effects in addition to a single ψ(3770) between 3.70 and 3.89 GeV, we can determine the observed cross section for ψ(3770) → f at √ s = 3.773 GeV by where, σ 3.773 GeV e + e − →f and σ 3.65 GeV e + e − →f are the observed cross sections for e + e − → f measured at √ s = 3.773 and 3.65 GeV, respectively; f s is the normalization factor for 1/s dependence of the cross section. The results on the numbers of σ ψ(3770)→f for the final states π + π − η, ppη, ρ 0 π + π − η, K + K − π + π − η and ppπ + π − η are summarized in the second column of Table 3, where the first error is statistical, the second (third) energy-dependent (common) systematic error. The energy-dependent systematic uncertainty is from the uncertainties in the Monte Carlo statistics, the fit to the mass spectrum and the background estimation, while the common systematic uncertainty is from the other uncertainties.
For some final states, such as K + K − η, ppK + K − η and ppK + K − π 0 , no event is observed in the continuum data. Upper limit σ up ψ(3770)→f on the observed cross section for ψ(3770) → f is set by σ up , which is upper limit on the observed cross section for e + e − → f at √ s = 3.773 GeV set at 90% C.L. For other final states, however, σ up ψ(3770)→f is set under the Gaussian distribution hypothesis for σ ψ(3770)→f . These are quoted in the third column of Table 3. The observed cross section for ψ(3770) production at √ s = 3.773 GeV was measured to be σ obs ψ(3770) = (7.15 ± 0.27 ± 0.27) nb [3,10,34] by the BES Collaboration. Upper limit on the branching fraction for ψ(3770) → f can be determined by which are quoted in the last column of Table 3. Here, the δ is to consider the uncertainty of the measured σ obs ψ(3770) .