# Measurements of decays into , , , , and

###### Abstract

Decays of the into Vector plus Pseudoscalar meson final states have been studied with 14 million events collected with the BESII detector. Branching fractions of , , and , and upper limits of and are obtained: , , and ; and , and at the 90 % C.L.. These results are used to test the pQCD “12% rule”.

###### pacs:

13.25.Gv, 12.38.Qk,14.40.Gx## I Introduction

It is expected in perturbative QCD that both and decays to light hadrons proceed dominantly via three gluons or a single virtual photon, with widths proportional to the squares of the wave functions at the origin qcd15 , which are well determined from dilepton decays PDG2004 . This led to the “12% rule”, i.e.

A strong violation of this conjecture was first observed by the MarkII experiment in the Vector-Pseudoscalar meson (VP) final states, and rhopi . Significant suppressions observed in four Vector-Tensor decay modes (, , , and ) BESII_VT make the puzzle even more mysterious. Numerous theoretical explanations have been suggested qcd15_th , but the puzzle still remains one of the most intriguing questions in charmonium physics. Recently both CLEO and BES reported new measurements of VP channels CLEOC_VP ; BES_kstark ; BES_rhopi with higher statistics and confirmed the severe suppression for and .

In this letter, we report measurements of decays into 5 VP channels: , , , , and using 14 million events collected with the BESII detector, where the branching fractions of and are the first observations. The results are compared with the corresponding branching fractions to test the “12% rule”. Also, the branching fractions provide useful informations on DOZI suppressed decay and on the quark components of and jdecay .

## Ii The Besii Detector

The Beijing Spectrometer (BESII) is a conventional cylindrical magnetic detector that is described in detail in Ref. BES-II . 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 of ; it also provides ionization energy loss () measurements which are used for particle identification. Momentum resolution of ( in GeV/) and resolution for hadron tracks of are obtained. An array of 48 scintillation counters surrounding the MDC measures the time of flight (TOF) of charged particles with a resolution of about 200 ps for hadrons. Outside the TOF counters, a 12 radiation length, lead-gas barrel shower counter (BSC), operating in limited streamer mode, measures the energies of electrons and photons over of the total solid angle with an energy resolution of ( in GeV). A solenoidal magnet outside the BSC provides a 0.4 T magnetic field in the central tracking region of the detector. Three double-layer muon counters instrument the magnet flux return and serve to identify muons with momentum greater than 500 MeV/. They cover of the total solid angle.

In this analysis, a GEANT3 based Monte Carlo package with detailed consideration of the 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 reasonable J3pi .

## Iii Event Selection

The data sample used for this analysis consists of events N_psip , collected with BESII at the center-of-mass energy . The decay channels investigated are into , , , , and , where decays to , to , to or , and and to 2. The events have either two or four charged tracks plus () photons.

A neutral cluster is considered to be a photon candidate if the following requirements are satisfied: it is located within the BSC fiducial region, the energy deposited in the BSC is greater than 50 MeV, the first hit appears in the first 6 radiation lengths, the angle in the plane (perpendicular to the beam direction) between the cluster and the nearest charged track is greater than (this requirement is not applied for channels involving more than two photons), and the angle between the cluster development direction in the BSC and the photon emission direction from the beam interaction point (IP) is less than .

Each charged track is required to be well fitted by a three-dimensional helix, to have a momentum transverse to the beam direction greater than 70 MeV/, to originate from the IP region, cm and cm, and to have a polar angle . Here , , and are the , , and coordinates of the point of closest approach of the track to the beam axis.

The TOF and measurements for each charged track are used to calculate values and the corresponding confidence levels for the hypotheses that a track is a pion, kaon, or proton, where () is the particle type. For events with decays, charged kaon candidates are required to have larger than 0.01 or larger than and ; while for events with decays, at least half of the charged pion candidates in each event are required to have .

### iii.1 and

The final state is utilized to measure these two channels. Two good charged tracks with net charge zero and at least two photon candidates are required. Next a four constraint (4C) kinematic fit () to the hypothesis is performed, and the confidence level of the fit is required to be larger than 0.01. If there are more than two photons, the fit is repeated using all permutations of photons, and the two photon combination with the minimum is selected. This procedure is used for all channels. To suppress backgrounds from misidentification, the combined chisquare Chisquare , , for the assignment is required to be smaller than those of and . Figure 1 shows the scatter plot of the invariant mass of () versus that of the two gammas (). A clear cluster can be observed in the signal region, while only one event appears in the region.

To select decay candidates, we require GeV/. Here the experiment mass resolution for is 2.5 MeV/. The invariant mass distribution for events with candidates is shown in Fig. 2. Fitting this distribution with and functions determined from Monte Carlo simulation, plus an background determined by the sideband and a first order polynomial to describe phase space background, events are obtained with the statistical significance of significance . While for the channel, the observed events and the estimated background in the signal region are 4 and 6.2, respectively, which corresponds to the upper limit of 4.4 events at the 90% confidence level upperlimit .

### iii.2

Two decay modes of are used, and . Their final states are , where for and for , . Events with four charged tracks with net charge zero and at least photon candidates are selected. A 4C kinematic fit is performed for the hypothesis , and the confidence level of the fit is required to be larger than 0.01. The corresponding for the assignment is required to be smaller than those of and .

The additional requirement GeV/, is used to select candidates, and the spectrum of selected events is shown in Fig. 3. By fitting this spectrum with an function, plus an background determined by the sideband and a second order polynomial for phase space background, candidate events are obtained. The statistical significance is about . Here, the shape of is determined from Monte Carlo simulation of , , and .

For the final state , the candidate events are required to satisfy GeV/. Backgrounds from , and , are eliminated with two additional requirements GeV/ and GeV/, respectively.

With the requirement GeV/, the invariant mass distribution for candidate events is shown in Figure 4. Fitting the spectrum with an function plus a second order polynomial for background, candidate events are obtained. The statistical significance is about . The shape is determined from Monte Carlo simulation of , and , .

### iii.3

Here, the final state studied is . Events with two charged tracks with net charge zero and four or five photon candidates are selected. A 4C kinematic fit is performed for the hypothesis , and the fit confidence level is required to be larger than 0.01. To remove background from misidentification, is required to be smaller than that of . Candidate events must satisfy GeV/ and GeV/ for the four photon candidates (), where the subscripts permute over all six combinations. Events with one and only one combination satisfying the above criteria are kept for further analysis.

Figure 5 shows the invariant mass distribution after the above selection; no clear signal is seen. The distribution is fitted with an signal determined by Monte Carlo simulation and a polynomial background, the observed events and the estimated background in the signal region are 23 and 25.0, respectively, which corresponds to the upper limit of 9.7 events at the 90% confidence level.

### iii.4

Two decay modes are used in this measurement, similar to the measurement of . Final states studied are , where for and for . Events with four charged tracks with net charge zero and or photons candidates are selected. A 4C kinematic fit to the hypothesis is performed, and its confidence level is required to be larger than 0.01 and larger than that of to suppress possible backgrounds due to particle misidentification. Backgrounds from are rejected with the requirement that the mass recoiling from every pair satisfy GeV/.

For , one and only one pair among the three good photon candidates is required to satisfy GeV/; this pair is taken as a . To avoid contamination from , the invariant mass should be less than 3.5 GeV. Since the dominant decay of into is , an additional requirement GeV is applied to select candidates, where is any combination from the four charged pion candidates.

An additional requirement GeV/ is used to select candidates. The invariant mass spectrum for selected events is shown in Fig. 6. It is fitted with an function determined by Monte Carlo simulation for , , plus a second order polynomial for background, as shown in Fig. 6; events are obtained with a statistical significance of .

For the final state , the selection of and is the same as for the channel. Only events with only one candidate ( GeV/) and one candidate ( GeV/) from amongst the four photons are kept for further analysis.

An additional requirement GeV is made to select candidates. The invariant mass spectrum is shown in Fig. 7. It is fitted with an function determined by Monte Carlo simulation for , , plus a second order polynomial for background, as shown in Figure 7. With 1 event observed in the signal region and 3.2 background events estimated from sidebands, the candidate signal is event (at 68.3% C.L.) assuming the Poisson variate upperlimit .

## Iv Systematic errors

Many sources of systematic error are considered. Systematic errors associated with the efficiency are determined by comparing and data and Monte Carlo simulation for very clean decay channels, such as , which allows the determination of systematic errors associated with the MDC tracking, kinematic fitting, particle identification, and photon selection efficiencies BESII_VT ; J3pi .

Since the decay to includes and non-resonant , the invariant mass spectrum in the Monte Carlo simulation is obtained from , data. The uncertainty of their detection efficiency from invariant mass spectrum is 3%, which is included in systematic errors.

The uncertainties of the branching fractions of intermediate states, the background shapes in fitting, and the total number of events are also sources of systematic errors. Table 1 summarizes the systematic errors for all channels.

Contributions from the continuum hadrons wangp are estimated using a data sample of pb taken at GeV 3650 , corresponding to about one-third of the integrated luminosity at the . Since no signal is observed for any channel analyzed, the continuum contribution and possible interference are not taken into consideration.

Tracking | 4.0 | 4.0 | 8.0 | 4.0 | 8.0 |
---|---|---|---|---|---|

selection | 4.0 | 4.0 | 4.0 | 8.0 | 8.0 |

Kinematic fit | 6.0 | 6.0 | 6.0 | 4.0 | 4.0 |

PID Efficiency | 2.0 | 2.0 | 2.0 | ||

– | – | 1.9 | – | 1.9 | |

Background shape | 0.0 | 11.0 | 16. | 0.0 | 18.9 |

MC statistics | 1.4 | 2.1 | 1.8 | 1.3 | 2.0 |

Branching ratios | 1.4 | 1.6 | 3.8 | 1.0 | 3.5 |

4.0 | |||||

Total | 9.6 | 15. | 21. | 11. | 23. |

## V Results and Discussion

The branching fraction for is calculated from

where X is the intermediate state, Y the final state, and the detection efficiency.

Table 2 summarizes the observed numbers of events, detection efficiencies, and branching fractions or upper limits for the channels studied. The branching fractions of and are calculated from the sum of events observed in the and channels , and an efficiency determined from the individual efficiencies weighted by the branching fractions of these two channels. The upper limit for branching fraction at 90% confidence level is . For comparison, the table includes the corresponding branching fractions of decays PDG2004 , as well as the ratios of the to branching fractions. Decays of to and are suppressed by a factor of 2 and 12, respectively, compared with the 12% rule, while and are consistent with the rule within large errors. It is worth pointing out that the ratio of is and for and decays, respectively, which are consistent within 2, while the ratio of is for decay, which is much larger than that of decay.

This analysis without considering the continuum contribution (although not seen at present measurement) and possible interference might bring some uncertainty, which could only be clarified later by more accurate experiments such as CLEO-c or BESIII BESIII . If the continuum contribution is treated incoherently, the continuum events, assuming the Poisson distribution, for , and channels are at 68.3% confidence level with the normalized integrated luminosity, this yields the branching fractions of , and to be , and , respectively.

(%) | (%) | ||||
---|---|---|---|---|---|

16.1 | – | ||||

18.9 | |||||

11.1 | |||||

3.8 | |||||

8.4 | |||||

6.3 | |||||

2.6 | |||||

1.8 | |||||

2.3 |

In conclusion, the branching fractions for , , and and upper limits for and are presented. Our results for and are first measurements, while our results for , , and are consistent with those of CLEO CLEOC_VP .

###### Acknowledgements.

The BES collaboration thanks the staff of BEPC for their hard efforts. This work is supported in part by the National Natural Science Foundation of China under contracts Nos. 19991480, 10225524, 10225525, 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); by the National Natural Science Foundation of China under Contract No. 10175060 (USTC); and by the Department of Energy under Contract No. DE-FG03-94ER40833 (U Hawaii).## References

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