Charmonium decays to axial-vector plus pseudoscalar mesons

A sample of 3.79 3 10 6 c (cid:1) 2 S (cid:2) events is used to study the decays of charmonium to axial-vector plus pseudoscalar mesons. The branching fraction for the decay c (cid:1) 2 S (cid:2) ! b 6 1 (cid:1) 1235 (cid:2) p 7 agrees with expectations based on scaling the corresponding J (cid:3) c branching fraction. Flavor-SU(3)-violating K 1 (cid:1) 1270 (cid:2) - K 1 (cid:1) 1400 (cid:2) asymmetries with opposite character for c (cid:1) 2 S (cid:2) and J (cid:3) c decays are observed. This contrasting behavior cannot be accommodated by adjustments of the singlet-triplet mixing angle.

(Received 13 January 1999; revised manuscript received 7 July 1999) A sample of 3.79 3 10 6 c͑2S͒ events is used to study the decays of charmonium to axial-vector plus pseudoscalar mesons. The branching fraction for the decay c͑2S͒ ! b 6 1 ͑1235͒p 7 agrees with expectations based on scaling the corresponding J͞c branching fraction. Flavor-SU(3)-violating K 1 ͑1270͒-K 1 ͑1400͒ asymmetries with opposite character for c͑2S͒ and J͞c decays are observed. This contrasting behavior cannot be accommodated by adjustments of the singlet-triplet mixing angle. PACS numbers: 13.25.Gv In perturbative QCD, the dominant process for hadronic decays of both the J͞c and the c͑2S͒ is annihilation into three gluons followed by the hadronization of these gluons into physically observable hadrons. The similarity between the parton-level final states has led to the conjecture that the ratio of the J͞c and c͑2S͒ decay branching fractions into any exclusive final state X h is given by the ratio of the square of the wave function at the origin of the constituent cc quark state, which is well determined from the dilepton decay rates [1], B͓J͞c ! e 1 e 2 ͔ 0.141 6 0.012 . This conjecture is sometimes referred to as the 14% rule [2]. Although this conjecture seems to work reasonably well for a number of decay channels, it fails badly in the case of c͑2S͒ two-body decays to vector plus pseudoscalar meson final states-the decay c͑2S͒ ! rp is suppressed relative to the 14% rule expectation by more than a factor 1918 0031-9007͞99͞83(10)͞1918(4)$15.00 © 1999 The American Physical Society of 50 [3,4]. This conundrum is commonly called the rp puzzle [5]. In addition, the BES group has reported suppressions by factors of at least 3 in the vector plus tensor meson final states: K ‫ء‬ K ‫ء‬ 2 , ra 2 , vf 2 , and ff 0 2 [6]. To date, no convincing evidence has been uncovered for hadronic c͑2S͒ decays that are enhanced relative to the 14% rule expectation. Since at least one explanation for the rp puzzle involves a mechanism that suppresses all c͑2S͒ decays to lowest-lying two-body mesons final states [7], it is useful to examine all possibilities. Here we report first measurements of c͑2S͒ decays to axial-vector plus pseudoscalar mesons.
There are two lowest-lying axial-vector-meson octets. These correspond to the singlet ( 1 P 1 ) and triplet ( 3 P 1 ) spin configurations of two quarks in a P-wave orbital angular momentum state. The nonstrange, isospin I 1 members of the two octets have opposite G parity: the b 1 ͑1235͒ is in the 1 P 1 octet and has G 11, while the a 1 ͑1260͒ is in the 3 P 1 octet and has G 21. Since strong decays of the J͞c and c͑2S͒ conserve G parity, decays to the axial-vector-pseudoscalar (AP) pair b 1 p are allowed and seen in J͞c decays; decays to a 1 p final states are forbidden and not seen in J͞c decays.
The strange members of the 3 P 1 and 1 P 1 octets, the K A and K B , respectively, are mixtures of the observed physical states, the K 1 ͑1270͒ and the K 1 ͑1400͒, where and the mixing angle is near u Ӎ 45 ± [8]. The dominant K 1 ͑1270͒ decay mode is to Kr (B 42% 6 6%); the K 1 ͑1400͒ decays almost always to K ‫ء‬ p (B 94% 6 6%).
In the limit of strict flavor-SU(3) symmetry, the amplitudes for two-body decays to conjugate mesons in the same pair of octets should be equal. Thus, since decays to a 1 p are forbidden by G parity, decays to K A K are disallowed by SU(3), and one expects relatively pure K B K final states in J͞c and c͑2S͒ decays. And, since u Ӎ 45 ± , there should be roughly equal amounts of K 1 ͑1270͒ and This analysis is based on a sample of ͑3.79 6 0.31͒ 3 10 6 e 1 e 2 ! c͑2S͒ events [9], collected in the BES detector at the BEPC storage ring. The BES detector is described in some detail in Ref. [10]. The features that are most important for the analysis reported here are the 40-layer main cylindrical drift chamber (MDC), the 48scintillation counter time-of-flight (TOF) system, and the 12-layer lead-gas barrel electromagnetic shower counter (BSC). These are all situated in a 0.4 T solenoidal magnetic field. Charged particle track trajectories are measured in the MDC with a momentum resolution of s p ͞p 1.7% p 1 1 p 2 (p in GeV). The directions and energies of high energy g rays are measured in the BSC with angular and energy resolutions of s f 4.5 mrad, s u 12 mrad, and s E ͞E 0.22͞ p E (E in GeV), respectively. We re-strict our analysis to photons and charged tracks that are in the polar angle region j cosuj , 0.80. For hadron tracks the time resolution of the barrel TOF is about 450 ps and the dE͞dx resolution is about 11%, allowing for a p͞K separation up to 600 MeV. For the combination of tracks that passes the kinematic fit with the best x 2 , the dE͞dx and TOF information is used to determine the probability that the candidate kaon tracks are consistent with being kaons. If the candidate kaon tracks have a probability less than 10%, the event is discarded.
Since the dominant decay mode of the b 1 is b 1 ! vp, we apply a five-constraint kinematic fit to events of the type c͑2S͒ ! p 1 p 2 p 1 p 2 gg, where the gg invariant mass is further constrained to be equal to M p 0 . The p 1 p 2 p 0 mass distribution for events that pass the five-constraint fit is shown in Fig. 1a, where there is a prominent peak. The peak is well fit with a Breit-Wigner shape with mass and width of the v͑782͒ convoluted with a Gaussian resolution function with s 9.6 MeV. We identify the best p 1 p 2 p 0 combination with invariant mass in the range M v 6 30 MeV as an v candidate. Figure 1b shows the vp mass distribution for events where the p 1 p 2 pair recoiling against the v has an invariant mass greater than 1.55 GeV. The latter requirement reduces the contamination from vf 2 final states. The peak in Fig. 1b is well fit with an S-wave Breit-Wigner function with mass and width fixed at the Particle Data Group (PDG) values for the b 1 (M b 1 1.232 and G b 1 0.142 GeV) and a background shape that has a phase-space behavior at threshold that evolves to a constant level at higher masses. There are 79.8 6 12.1 events in the fitted b 1 meson signal peak [11].
Using the detection efficiency of 0.046 6 0.003, which was determined from a Monte Carlo simulation, we B͓c͑2S͒ ! b 6 1 p 7 ͔ ͑5.2 6 0.8 6 1.0͒ 3 10 24 , where the first error is statistical and the second is systematic [13]. The result is higher than, but consistent with, the 14% rule expectation applied to the PDG result for the J͞c [14].
For the K 1 K decays, we select events of the type c͑2S͒ ! K 1 K 2 p 1 p 2 on the basis of the quality of a four-constraint kinematic fit. This final state includes the dominant K 6 1 ͑1270͒ and K 6 1 ͑1400͒ decay channels. We identify p 1 p 2 pairs with invariant mass in the range M r 6 150 MeV as r͑770͒ candidates and K 6 p 7 pairs with invariant mass in the range M K ‫ء‬ 6 50 MeV as K ‫ء‬ ͑892͒ candidates.
The K 6 r mass distribution exhibits a strong enhancement near M Kr 1.27 GeV, as shown in Fig. 2a. We fit the K 6 r 0 mass distribution with a specially devised function, f Kr , that takes into account the distortions to the line shape caused by the restricted phase space available for the K 1 ͑1270͒ ! Kr decay [15]. This plus a smooth background function that has a phase-space behavior near threshold provides an adequate fit to the data for masses below 2.0 GeV and yields a K 1 ͑1270͒ signal of 53.5 6 9.5 events [11]. Using the detection efficiency of 0.085 6 0.012, we determine the branching fraction result of [16] B͓c͑2S͒ ! K 6 1 ͑1270͒K 7 ͔ ͑10.0 6 1.8 6 2.1͒ 3 10 24 . In the K ‫ء‬ p 6 invariant mass distribution, shown in Fig. 2b, there is little evidence for a K 1 ͑1400͒ signal. Since the Kr and K ‫ء‬ p selection cuts are not mutually Events/20 MeV   FIG. 2. The (a) K 6 r 0 and (b) K ‫0ء‬ p 6 mass distributions from c͑2S͒ ! K 1 K 2 p 1 p 2 events. Note the difference in the vertical scales. The curves are the results of the fits discussed in the text. exclusive, some feedthrough from K 1 ͑1270͒ ! Kr into the K ‫ء‬ p channel is expected, and seen. The smooth curve in Fig. 2b is the result of a fit using f Kr for the K 1 ͑1270͒, an S-wave Breit-Wigner with mass and width fixed at the PDG values for the K 1 ͑1400͒ and a smooth background shape as was used for the Kr distribution. The resulting 29.8 6 9.2 K 1 ͑1400͒ ! K ‫ء‬ p events and the efficiency of 0.090 6 0.012 are used to derive a 90% C.L. upper limit of [17] B͓c͑2S͒ ! K 6 1 ͑1400͒K 7 ͔ , 3.1 3 10 24 90% C.L. Contrary to flavor-SU(3) expectations, the c͑2S͒ ! K 1 ͑1400͒K branching fraction is smaller than that for the K 1 ͑1270͒K channel by at least a factor of 3. To accommodate this with the mixing angle, a value of u , 29 ± would be required.
In the absence of any published results for J͞c decays to these channels, we used the c͑2S͒ ! p 1 p 2 J͞c cascade events in our c͑2S͒ data sample to make a first measurement of the branching fractions for J͞c ! K 1 ͑1270͒K and K 1 ͑1400͒K. We select events that fit a five-constraint fit to the c͑2S͒ ! p 1 p 2 J͞c; J͞c ! K 1 K 2 p 1 p 2 hypothesis. We use the particle species assignment that gives the best x 2 value, and we use the same Kr and K ‫ء‬ p event selection criteria that are used for the analysis of direct c͑2S͒ decays.
In contrast to the case for the c͑2S͒, the Kr mass spectrum in J͞c ! K 1 K 2 p 1 p 2 decays, shown in Fig. 3a, has little evidence for the K 1 ͑1270͒. The small K 1 ͑1270͒ signal of 7.7 6 5.8 K 1 ͑1270͒ events [18] and the efficiency of 0.025 6 0.004 are used to infer a 90% C.L. upper limit of [16,17] B͓J͞c ! K 6 1 ͑1270͒K 7 ͔ , 3.0 3 10 23 90% C.L.; this is more than a factor of 2 below the result expected from applying the 14% rule to our result for c͑2S͒ decays to this channel.
In further contrast to the c͑2S͒, the K ‫0ء‬ p 6 mass distribution for the J͞c decays, shown in Fig. 3b, exhibits a clear K 1 ͑1400͒ signal; the fit to the K ‫ء‬ p mass spectrum yields 59.0 6 13.1 events in the K 1 ͑1400͒ signal [11]. The related efficiency is 0.030 6 0.004. We find B͓J͞c ! K 6 1 ͑1400͒K 7 ͔ ͑3.8 6 0.8 6 1.2͒ 3 10 23 , which is above our upper limit for the K 1 ͑1270͒K mode, indicating a flavor-SU(3) violation in J͞c decays that is opposite to that seen in c͑2S͒ decays. Accommodating this effect in J͞c decays by adjusting the mixing angle would require a value of u . 48 ± , in contradiction to the u , 29 ± result from c͑2S͒ decays.
In conclusion, we report first measurements for the c͑2S͒ ! b 6 1 p 7 and K 6 1 ͑1270͒K 7 decay branching fractions and a 90% C.L. upper limit for B͓c͑2S͒ ! K 6 1 ͑1400͒K 7 ͔. We find that two of the AP decays are relatively strong exclusive hadron channels for the c͑2S͒. In addition, we report the first observation of the J͞c ! K 6 1 ͑1400͒K 7 decay mode and a 90% C.L. upper limit for J͞c ! K 6 1 ͑1270͒K 7 . 1920