Search for the Rare Decays $J/\psi \to D_{S}^{-} \pi^{+}$, $J/\psi \to D^{-} \pi^{+}$, and $J/\psi \to \bar D^{0} \bar K^{0}$

Rare decay modes $J/\psi \to D_{S}^{-} \pi^{+} + c.c.$, $J/\psi \to D^{-} \pi^{+} + c.c.$, and $J/\psi \to \bar D^{0} \bar K^{0} + c.c.$ are searched for using 5.77$\times 10^{7}$ $J/\psi$ events collected with the BESII detector at the BEPC. No signal above background is observed. We present upper limits on the branching fractions $B(J/\psi \to D_{S}^{-} \pi^{+})$ $<$ 1.4$\times10^{-4}$, $B(J/\psi \to D^{-} \pi^{+})$ $<7.5\times10^{-5}$, and $B(J/\psi \to \bar D^{0} \bar K^{0})$ $<$ 1.7$\times10^{-4}$ at the 90% confidence level.


INTRODUCTION
The hadronic decays and electromagnetic decays of J/ψ have been widely studied, however weak decays of J/ψ have not been studied in detail [1].For the J/ψ lying below the D D threshold, decays to D D are forbidden.Weak decays to one single charm meson accompanied by other non-charm mesons are allowed.The standard model predicts that the branching fractions of flavor changing processes via weak interactions, such as J/ψ → DX (where D stands for D S or D and X stands for π or K 0 S ) are at the level of 10 −8 or below [2] and thus smaller than those of strong and electromagnetic decays.This is unobservable in current experiments.Extensions to the standard model, such as Top Color models [3], the minimal super-symmetric standard model with or without R-parity [4] and the two Higgs doublet model [5], can enhance the branching fraction to ∼10 −5 .The study of J/ψ → D − S π + , J/ψ → D − π + and J/ψ → D0 K0 provide an experimental check and serve as a probe to new physics [6,7].Figure 1 shows the Feynman diagrams for these decay modes in the framework of the standard model, respectively.Charge conjugated states are implicitly included.In this paper, we'll present a search for J/ψ → D − S π + , J/ψ → D − π + and J/ψ → D0 K0 in a sample of 5.77×10 7 J/ψ events collected with the Beijing Spectrometer(BESII) [8] detector at the Beijing Electron-Positron Collider(BEPC) [9].

BESII Detector
BES is a conventional solenoidal magnetic detector that is described in detail in Ref. [10].BESII is the upgraded version of the BES detector [8].A 12-layer Vertex Chamber (VC) surrounding the beryllium beam pipe provides track and trigger information.A forty-layer main drift chamber (MDC) located just outside the VC provides measurements of charged particle trajectories covering 85% of 4π; it also provides ionization energy loss (dE/dx) measurements which are used for particle identification (PID).A momentum resolution of 0.017 √ 1 + p 2 (p in GeV/c) and a dE/dx resolution for hadronic tracks of ∼ 8% are obtained.Time of flight (TOF) of charged particles is measured with an array of 48 scintillation counters surrounding the MDC.The resolution is about 200 ps for hadrons.Outside the TOF counters, a 12 radiation length, lead-gas barrel shower counter (BSC), measures energies and positions of electrons and photons.Solid angle is covered over 80% and resolutions of σ E /E = 0.22/ √ E (E in GeV), σ φ = 7.9 mrad, and σ z = 2.3 cm are obtained.Outside the solenoidal coil, providing a 0.4 T magnetic field over the tracking volume, an instrumented flux return with three double-layer muon counters identify muons with momenta greater than 500 MeV/c.Monte Carlo simulations are performed using a GEANT3 based program (SIMBES) with detailed consideration of the detector geometry and response.The consistency between data and Monte Carlo has been checked in many reactions in J/ψ and ψ(2S) decays with reasonable agreement.Details are described in Ref. [11].

Event Selection
Due to a large J/ψ hadronic decay background, non-leptonic decay modes do not offer ultimate sensitivity.In this analysis, D S and D mesons are reconstructed via semileptonic decay modes: D − S → φe − ν e , D − → K * 0 e − ν e and D − → K 0 e − ν e , D0 → K + e − ν e .The neutrino is undetectable in the detector, but carries energy and momentum.D S and D mesons can not be identified by their invariant mass.However, two body constraints can be applied in the mode J/ψ → DX.Thus they are identified using the momentum information of X meson.
Four charged tracks are required in all selected modes, and the total charge must be equal to zero.In order to ensure well-measured momenta and reliable particle identification, all the tracks are required to be reconstructed in the main drift chamber with a good helix fit.Each track is required to satisfy the geometry selection criterion | cos θ| < 0.8 , where θ is the polar angle, and must originate from the beam interaction region (except the decay daughters of K 0 S ), which is defined by R xy < 2.0cm and |z| < 20.0cm, where R xy and |z| are the closest approach of the charged track in the xy plane and z direction.
A kaon or pion candidate is required to satisfy W K,π > 0.1%, where W K,π is the weighted likelihood of the hypothesis of kaon or pion, which combines the TOF and dE/dx information.To reduce the misidentification rate, the likelihood ratio R K,π = W K,π /(W K + W π ) for kaon or pion is required to be greater than 0.7.The ratio of the energy deposit in the BSC to the momentum is used to construct the likelihood for electron identification, W e > 1% and R e = W e /(W π + W K + W π ) > 0.85 are required for electron candidate.The angle between the identified electron and the nearest charged track is required to be greater than 12 • to remove backgrounds from photon conversion.Low momentum electrons and pions can not be unambiguously identified, leading to a momentum cut P e > 0.25 GeV/c for electrons.
Neutral Kaons are identified via the decay to π + π − .All pairs of oppositely charged tracks are assumed to be π + π − .The distance between the K 0 S decay vertex and the beam axis is required to exceed 5 mm the in xy plane.Background from J/ψ's decaying to states with extra neutral particles is removed by constraining the number of isolated photons to be zero.An isolated photon is a photon with an angle between the nearest charged track and the cluster of at least 22 • and a difference between the angle of the cluster development direction in the BSC and the reconstructed photon emission direction of less than 60 • .In addition the energy deposit in the BSC is required to be larger than 0.1 GeV.
The neutrino of the semi-leptonic decay of the reaction J/ψ → DX remains undetected.A kinematic quantity U miss = E miss − P miss is used to identify missing neutrinos, where E miss and P miss are the energy and momentum of the neutrino.Ideally U miss should be consistent with zero.A requirement of |U miss | < 0.1 GeV may remove backgrounds from J/ψ decaying to K 0 L , η and partial π 0 final states which can not be rejected through the initial selection.Events with missing energy due to misidentified pions are rejected by P miss > 0.2 GeV/c.Missing particles are required to be in the sensitive region of the detector to further supress hadronic background.
In the decay mode J/ψ → D − S π + , D − S mesons are reconstructed through their decay to D − S → φe − ν e , φ candidates are reconstructed from two oppositely charged kaons, namely: φ → K + K − .The invariant mass of φ candidates is required to be within 0.015 GeV/c 2 of the φ nominal mass.In the decay mode J/ψ → D − π + , D − mesons are reconstructed through their decays to D − → K * 0 e − ν e and D − → K 0 e − ν e .The K * 0 candidates are formed out of K − and π + candidates.Their invariant mass is required to fulfil |M Kπ − M K * 0 | < 0.060 GeV/c 2 .The K 0 S candidates are formed out of π + and π − candidates.The mass window is |M π + π − − M K 0 S | < 0.020 GeV/c 2 .As far as the decay mode J/ψ → D0 K0 is concerned, D0 mesons are reconstructed through their decay to K + e − ν e .Figure 2 shows the invariant mass distribution of KK, Kπ and ππ from the various decay modes.

Monte Carlo Simulation
Detection efficiencies are determined by detailed Monte Carlo simulations.J/ψ → D − S π + , J/ψ → D − π + and J/ψ → D0 K0 production and decay, including the detector response are simulated.50,000 Monte Carlo events are generated for each decay mode.Branching fractions of D − S , D − , and D0 decays are taken from the world average values [12].The detection efficiencies and branching fractions are listed in Table 1  Table 1 Detection efficiencies and branching fractions [12].

Decay mode
Intermediate decay

Systematic Errors
The systematic error of the branching fraction is dominated by uncertainties of MDC simulation (including systematic uncertainties of the tracking efficiency and other requirements).The efficiency varies between 14.2% and 19.9%.We estimate a systematic error of 2% for requiring the number of isolated photons to be equal to zero, using J/ψ → ρπ decays [13].The systematic uncertainty of false electron identification is estimated to be 5% for each electron.Differences in the pion and kaon identification between Data and Monte Carlo simulation indicate a systematic error of 1.5% for each track.The errors on the intermediate decay branching fractions of D − S , D − , D0 , φ, and K * 0 are taken from the PDG [12].The statistical error of the Monte Carlo sample is also taken into account.The total number of J/ψ events is (57.7±2.7)×10 6[14], determined from inclusive 4-prong hadronic final states, and 4.7% is taken as a systematic uncertainty.All systematic errors are summarized in Table 2.

Results
Since no excess is observed for the reactions J/ψ → D − S π + , J/ψ → D − π + and J/ψ → D0 K0 is observed above background, upper limits for the three decays are calculated.Using a Bayesian method, the upper limits for the observed number of events at the 90% confidence level are 1.70 for J/ψ → D − S π + , 6.21 for J/ψ → D − π + and 4.61 for J/ψ → D0 K0 as shown in Fig. 4. The upper limits on branching fractions are calculated by where n obs U L is the upper limit of the observed number of events at the 90% confidence level.N J/ψ is the total number of J/ψ events, ε and B are the detection efficiency and branching fraction, respectively.For the decay mode J/ψ → D − π + , εB is the sum of the products obtained from decay modes D − → K 0 * e − ν e and D − → K 0 e − ν e .σ sys is the systematic error of the three decay modes, in the range of 18.3% to 24.7%.In the decay mode J/ψ → D − π + , D − mesons are reconstructed from two decay modes, the systematic uncertainty is 21.2% weighted by their branching fractions.
Table 3 Numbers used in the calculation of upper limits on the branching fractions of J/ψ → D In summary, we have searched for the decays of J/ψ → D − S π + , J/ψ → D − π + and J/ψ → D0 K0 using 5.77 × 10 7 J/ψ events taken by the BESII detector at the BEPC e + e − collider.No evidence for any of these decays is found.The final results for the 90% confidence level upper limit of the branching fractions are listed in Table 3.

Figure 3
Figure 3 shows the recoil momentum distribution of D S or D meson for the three decay modes after all selection criteria.The two decay modes of D − → K 0 * e − ν e and D − → K 0 e − ν e are combined in Fig.3(b).

Fig. 2 .
Fig. 2. The invariant mass distribution of resonance candidates (a) φ from J/ψ → D − S π + , (b) K 0 S from J/ψ → D0 K0 , (c) K * 0 from J/ψ → D − π + , D − → K 0 * e − ν e , and (d)K 0 S from J/ψ → D − π + , D − → K 0 e − ν e .Data is shown as dots with error bar, the expected signal shape from Monte Carlo simulated signal events is shown as a histogram.The mass cuts are illustrated by arrows and are discussed in the text.

Fig. 4 .
Fig. 4. Likelihood distributions for the observed number of events for (a) J/ψ → D − S π + , (b) J/ψ → D − π + , and (c) J/ψ → D0 K0 .The observed number of events at a Bayesian 90% confidence level for the three channels are indicated by arrows in the plots. .