ψ(2S) Hadronic Decays to Vector-Tensor Final States

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One of the most dramatic problems confronting the understanding of hadronic charmonium decays is the strong suppression of c͑2S͒ !rp and K ‫ء‬ K 1 c.c. decays.In perturbative QCD, the most important lowestorder diagram for J͞c and c͑2S͒ decays to hadrons corresponds to the annihilation of the constituent c and c quarks into three gluons.In this case, the partial width for the decay is proportional to jC͑0͒j 2 , where C͑0͒ is the wave function at the origin in the nonrelativistic quark model for c c. Thus, it is reasonable to expect that, for any final hadronic state h, the J͞c and c͑2S͒ decay branching ratios will scale as [1] where the leptonic branching fractions are taken from the Particle Data Group (PDG) tables [2].It was first observed by the Mark II experiment [3] that, while this is true for a number of exclusive hadronic decay channels, it is badly violated for the vector plus pseudoscalarmeson (VP) final states, rp and K ‫ء‬ K.The preliminary BES results confirm the Mark II measurements at higher sensitivity.The present experimental limits on Q rp and 5080 0031-9007͞98͞81(23)͞5080(5)$15.00 © 1998 The American Physical Society Q K ‫ء‬ K indicate order-of-magnitude discrepancies with the expected ratio of branching fractions [2,4].This anomaly, called the rp puzzle, has generated considerable interest, and a number of theoretical explanations have been proposed [1].However, meager experimental progress has hindered the resolution of the puzzle.Until recently, no other examples of substantial differences between J͞c and c͑2S͒ hadronic decays have been documented.
In this Letter, we report the results of a study of c͑2S͒ decays into vector plus tensor meson (VT ) final states and present branching fraction limits for c͑2S͒ !vf 2 , ra 2 , K ‫0ء‬ K ‫0ء‬ 2 1 c.c., and ff 0 2 ͑1525͒.The data were taken with the BES detector at the BEPC e 1 e 2 storage ring and correspond to a total sample of ͑3.79 6 0.31͒ 3 10 6 produced c͑2S͒ events.The BES detector is described in detail elsewhere [5].A 40-layer main drift chamber in a 0.4 T magnetic field provides tracking and energyloss (dE͞dx) information.The momentum resolution is s p ͞p 1.7% p 1 1 p 2 ͑GeV͞c͒, and the dE͞dx resolution for hadron tracks for this data sample is about 9%.The tracking chamber is surrounded by an array of 48 time-of-flight (TOF) counters with a resolution of about 450 ps for hadrons.Radially outside of the TOF are an electromagnetic calorimeter with a resolution of s E ͞E 0.22͞ p E͑GeV͒, s f 4.5 mrad, and s u 12 mrad, and an array of m counters that are interspersed inside the steel plates that return the solenoid's magnetic flux.
For the c͑2S͒ !vf 2 and ra 2 decay channels, we use the reaction c͑2S͒ !p 1 p 2 p 1 p 2 p 0 ; for the c͑2S͒ !K ‫0ء‬ K ‫0ء‬ 2 1 c.c. and ff 0 2 decays, we use p 1 p 2 K 1 K 2 and K 1 K 2 K 1 K 2 final states, respectively.Each analysis requires events to have four charged tracks with total charge zero and, in the case of the p 1 p 2 p 1 p 2 p 0 final state, at least two photons.Tracks consistent with being electrons in the electromagnetic calorimeter or being muons in the muon detector are discarded.The dE͞dx and TOF measurements are used to select p or K tracks with a confidence level larger than 0.003 for each track and 0.01 for four tracks combined.Events are kinematically fit to four energy-momentum constraints, and those with a fit probability greater than 0.01 are accepted.Photon pairs that have a gg invariant mass within 2.5s (s 14 MeV) of the p 0 mass are assigned as candidate p 0 s.The detection efficiency is determined using 1 3 10 4 or 2 3 10 4 Monte Carlo (MC)-simulated events that are generated with a uniform phase space distribution.The p or K decays in the detector according to the PDG [2] lifetimes and branching fractions.The relative uncertainty of efficiency obtained in this way is estimated to be 20%.Efficiencies given in this paper refer to the specific VT final states.
In the p 1 p 2 p 1 p 2 p 0 sample, the major background contributions are from c͑2S͒ !p 1 p 2 J͞c followed by J͞c !p 1 p 2 p 0 and from c͑2S͒ !hJ͞c, where h !p 1 p 2 p 0 and the J͞c decays to leptons.The former is rejected by removing events where any p 1 p 2 p 0 com-bination has an invariant mass within 50 MeV of the J͞c mass.The latter is removed by eliminating events where any p 1 p 2 pair has an invariant mass greater than 2.9 GeV͞c 2 .There are 939 events selected as c͑2S͒ !p 1 p 2 p 1 p 2 p 0 candidate events.The p 1 p 2 p 0 mass spectrum of the selected events, shown in Fig. 1, has a clear v signal with a mass resolution s 13.4 MeV.Candidate v mesons are required to have a p 1 p 2 p combination with an invariant mass in the range 740 , m p 1 p 2 p 0 , 820 MeV. Figure 2 shows the invariant mass spectrum for p 1 p 2 pairs recoiling against candidate v mesons.There is no obvious signal in the region of the f 2 ͑1270͒.A fit to the spectrum using a Breit-Wigner function with mass and width fixed at the PDG values (m 1275 MeV, G 185 MeV) and convoluted with a Gaussian resolution function with s 12.3 MeV, together with a quadratic background shape, yields 8.8 6 9.2 vf 2 events, which imply a 90% confidence level upper limit of 23.8 events.Using the isospin ratio 2:1 for f 2 decays into p 1 p 2 to p 0 p 0 and the experimental efficiency of 0.074, we determine an upper limit on the branching fraction of We use the c͑2S͒ !p 1 p 2 p 1 p 2 p 0 sample with the events that are consistent with vp 1 p 2 removed to search for c͑2S͒ !ra 2 !rrp.Here we select the p 1 p 2 and p 0 p 6 combination that has the minimum value of the quantity [6] p ͑m p 1 p 2 2 m r 0 ͒ 2 1 ͑m p 0 p 6 2 m r 6 ͒ 2 and require this minimum value to be less than 200 MeV.The combined r 0 p 6 and r 6 p 7 invariant mass plot, shown in Fig. 3 FIG. 1.The p 1 p 2 p 0 invariant mass distribution for c͑2S͒ !p 1 p 2 p 1 p 2 p 0 events (four entries͞event).invariance to correct for the unseen a 2 !rp decay channels and the MC-determined experimental efficiency of 0.074, we determine In the selection of p 1 p2 K 1 K 2 final states, each event has four possible p 1 , p 2 , K 1 , and K 2 track assignments.For each assignment that satisfies the four-constraint kinematic fit with a probability greater than 0.01, the TOF and dE͞dx measurements and the kinematic fit quality are combined to determine a global x 2 .The track assignment with the smallest global x 2 is selected as a candidate p 1 p 2 K 1 K 2 event.The main background which remains from c͑2S͒ !p 1 p 2 J͞c is eliminated by requiring the mass recoiling against the p 1 p 2 to differ from m J͞c by more than 50 MeV.There are 614 events after the above selections.Those K 6 p 7 pairs with an invariant mass in the range 800 , m K 6 p 7 , 1000 MeV are considered to be K ‫0ء‬ candidates.The contamination from c͑2S͒ !fp 1 p 2 with f !K 1 K 2 is found to be negligible.The K 6 p 7 mass spectrum, shown in Fig. 4, has a pronounced peak at the mass of the K ‫0ء‬ .The invariant mass distribution of K 6 p 7 tracks recoiling against the K ‫0ء‬ candidates, shown in Fig. 5, is fit with two  The MC-determined experimental mass resolutions are 4.9 MeV for the K ‫0ء‬ and 6.7 MeV for the K ‫0ء‬ 2 .The fit yields 1.4 6 8.6 K ‫0ء‬ K ‫0ء‬ 2 events, which imply a 90% confidence level upper limit of 17.2 events.Using the isospin ratio K 6 p 7 :K 0 p 0 2:1 for both the K ‫0ء‬ and K ‫0ء‬ 2 decays and the MC-determined efficiency of 0.171, we determine the limit In the selection of K 1 K 2 K 1 K 2 final states, the TOF and dE͞dx measurements are used to select kaon tracks.Events are kinematically fit to four energy-momentum constraints, and those with a fit probability greater than 0.01 are accepted.Backgrounds from other c͑2S͒ decays are negligible.Figure 6 shows the K 1 K 2 mass spectrum for the 41 selected K 1 K 2 K 1 K 2 candidate events; there is a strong f͑1020͒ signal.Here the experimental mass resolution is s 4.1 MeV.We identify all K 1 K 2 Entries/20MeV/c 2 FIG. 5.The invariant mass distribution for p 6 K 7 tracks recoiling against a K ‫0ء‬ for c͑2S͒ !p 1 p 2 K 1 K 2 events.The curve shows a fit to quadratic background plus K ‫0ء‬ and K ‫0ء‬ Entries/10MeV/c 2 FIG. 6.The K 1 K 2 invariant mass distribution for c͑2S͒ !K 1 K 2 K 1 K 2 events (four entries͞event).
pairs with m K 1 K 2 , 1040 MeV as candidate f mesons.
Figure 7 shows the invariant mass distribution for the K 1 K 2 pairs that are recoiling against candidate f mesons.No evidence for an enhancement at the mass of the f 0 2 resonance is apparent.There are three events in the Fig. 7 distribution within 680 MeV of the f 0 2 mass (m 1525 MeV, G 76 MeV).The 90% confidence level upper limit on this number of events is 6.68.Using the MC-determined efficiency of 0.181, we determine an upper limit for the branching fraction of B͑ ͑ ͑c͑2S͒ !ff 0 2 ͑1525͒͒ ͒ ͒ , 4.5 3 10 25 ͑C.L. 90%͒ .
Table I summarizes the results of branching fraction measurements for the c͑2S͒ !VT decay modes reported here.For comparison, the table includes the data for the corresponding J͞c decays [7] as well as the ratios of the c͑2S͒ to J͞c branching fractions.All four c͑2S͒ !VT decay modes are suppressed by a factor of at least 3 compared to the expectations of Eq. ( 1).An even higher statistics study would be required to determine whether or not the suppression of the VT decays is as severe as that of the rp and K ‫ء‬ K decay channels.It is noted that, in a perturbative QCD quark scheme, VP decays are forbidden Entries/10MeV/c 2 FIG. 7. The invariant mass distribution of K 1 K 2 pairs recoiling against candidate f mesons for c͑2S͒ !K 1 K 2 K 1 K 2 events.Three events fall into 80 MeV͞c 2 region around the f 0 2 mass.by hadron helicity conservation (HHC) [8], whereas VT decays are HHC allowed [9].
In conclusion, we have presented first measurements of c͑2S͒ decays to vf 2 , ra 2 , K ‫0ء‬ K ‫0ء‬ 2 , and ff 0 2 ͑1525͒.The upper limits established for the branching fractions for each of these decay modes are well below the level obtained by scaling the corresponding J͞c branching fraction according to expectations based on perturbative QCD.The puzzle of the hadronic decays of the J͞c and c͑2S͒ extends from the VP decay to the VT decays.

2 FIG. 2 .
FIG.2.The invariant mass distribution of p 1 p 2 pairs recoiling against candidate v mesons for events of the type c͑2S͒ !vp 1 p 2 .The curve shows a fit to quadratic background plus a f 2 resonance (see text).

MEntries/20MeV/c 2 FIG. 3 .
FIG.3.The rp invariant mass distribution for events of the type c͑2S͒ !r 0 r 7 p 6 .The curve shows a fit to quadratic background plus an a 2 resonance (see text).

M
(πK) (GeV/c 2 ) , has no indication of an a 2 ͑1320͒ meson signal.A fit to this spectrum with the a 2 represented by a resolution-broadened Breit-Wigner line shape with mass and width fixed at PDG values (m 1318.1 MeV, G 107 MeV) and a quadratic background function gives 3.9 6 15.7 a 2 events, which correspond to less than 29.6 events at the 90% confidence level.Using isospin