Measurement of (5S) decays
to and mesons
Decays of the (5S) resonance to channels with and mesons are studied using a 23.6 fb data sample collected with the Belle detector at the KEKB asymmetric-energy collider. Fully reconstructed , , and decays are used to obtain the charged and neutral production rates per event, and . Assuming equal rates to and mesons in all channels produced at the (5S) energy, we measure the fractions for transitions to two-body and three-body channels with meson pairs, , , , , , and . The latter three fractions are obtained assuming isospin conservation.
pacs:13.25.Gv, 13.25.Hw, 14.40.Pq, 14.40.Nd
The Belle Collaboration
New aspects of beauty dynamics can be explored using the large data sample recently collected by Belle at the center-of-mass (CM) energy of the (5S) resonance (also referred to as (10860)). Decays of bottomonium states with masses higher than the mass of the (4S) are almost unexplored with only a very limited number of experimental and theoretical studies to date. At the (5S) energy a quark pair can be produced and hadronize into various final states, which can be classified as two-body (, , , ) cleoi ; beli , two-body (, , , ), three-body (, , , ), and four-body () channels. Here denotes a or meson and denotes a or meson. The excited states decay to their ground states via and . Moreover, a quark pair can also hadronize to a bottomonium state accompanied by , or mesons, for example through a (5S)(1S) decay chen . In addition, initial-state radiation (ISR) can affect the final states listed above and must be taken into account isr . Fractions for all of these channels provide important information about -quark dynamics.
The first study of production at the (5S) was performed by CLEO cleoc ; cleob using a fb data sample. They found the fraction of events with pairs to be . CLEO interpreted the remaining as the fraction of events with mesons. Within the large uncertainties this fraction is 1.6 larger than the event fraction , directly measured by Belle beli . Both values for this fraction were obtained assuming that contributions from channels with bottomonium states are negligibly small. Among the pair events CLEO found the two-body fractions for the and channels to be and cleoc , respectively. The channel and multibody channels were not observed and corresponding upper limits were set.
Several theoretical papers have been devoted to (5S) decays to final states with two-body and pairs teoa ; teob ; teoc ; teod . The channel is predicted to be dominant with the fraction over all events within the range teoc ; teod . In these model calculations the other two possible channels have smaller fractions with predictions covering a broad range. Multibody channels have also been theoretically studied sim ; lel ; the three-body fractions are found to be about two or three orders of magnitude smaller than the two-body fractions. Interesting information about a possible gluonic component of the (5S) can also be obtained from measurements of the three-body decays est , if 200 or more events can be reconstructed in a three-body channel.
Here we fully reconstruct the decay modes , , (using two modes), and . Charge-conjugate modes are implicitly included throughout this work. The reconstructed modes have large and precisely measured branching fractions pdg and contain only charged particles.
The data were collected with the Belle detector belle at KEKB kekb , an asymmetric-energy double storage ring collider. This analysis is based on a sample of taken at the (5S) CM energy of 10867 MeV and containing produced events beli . The Belle detector is a general-purpose magnetic spectrometer described in detail elsewhere belle .
Charged tracks are assigned as pions or kaons based on a likelihood ratio , which includes information obtained from the three Belle particle identification detector subsystems belle . The identification efficiency for particles used in this analysis varies from 85 to 92 (91 to 98) for kaons (pions). The electron and muon identification requirements are described in Refs. ele ; muo .
The , , and candidates are reconstructed in the , , , , and modes. We require the invariant masses to be in the following intervals around the nominal masses: MeV/ for , MeV/ for and , MeV/ for , and MeV/ for . A vertex- and mass-constrained fit is applied to , and candidates to improve the signal resolution.
decays are fully reconstructed and identified using two variables: the energy difference and the beam-energy-constrained mass , where and are the energy and momentum of the candidate in the CM system, and is the CM beam energy. The intermediate two-body and multibody channels with pairs cluster in distinct regions of the and plane. However, all channels are distributed along a straight line described approximately by the function , where is the nominal mass (fixed to GeV/).
After all selections the dominant background is from continuum events ( or ). Events with mesons tend to be spherical, whereas continuum events are expected to be jet-like. To suppress continuum background, we apply topological cuts. The ratio of the second to the zeroth Fox-Wolfram moments fox is required to be less than 0.5 for the low background final states with a , and less than 0.4 for all others. The angle in the CM between the thrust axis of the particles forming the candidate and the thrust axis of all other particles in the event, , must satisfy for the final states with a , and for all others. More than one candidate per event is allowed, however the probability of multiple candidates is less than 1 for the modes used here, where the final states contain charged particles only.
The two-dimensional and scatter plots for the , , ( and ) and modes are obtained and are shown in Fig. 1. Events are clearly concentrated along the line corresponding to pair production. The signal regions shown in Fig. 1 are restricted to a MeV interval in (corresponding to (2.5–4.0) for the studied modes) and to the kinematically allowed GeV/GeV/ range. The location of specific channels within the signal bands will be discussed below and is shown in Fig. 2a.
We use inclined projections of the two-dimensional scatter plots for all events within the range GeV/GeV/ to obtain integrated decay event yields. We fit these distributions with a function including two terms: a Gaussian to describe the signal and a first-order polynomial to describe background. The regions where cross-channel backgrounds can contribute are not used in the fits.
Using the fit results, the charged and neutral production rates per event are obtained from the formula:
where is the event yield obtained from the fit for a specific mode , is the reconstruction efficiency including intermediate branching fractions, and is the corresponding decay branching fraction pdg . The event yields, efficiencies, and production rates are listed in Table I.
The systematic uncertainties include those due to the determination of the number of events (4.7), charged track reconstruction efficiency (1 per track), particle identification (0.5–1.0 per and , 2 per electron, 3 per muon), , and mass cut efficiencies (2), signal and background modeling in the fit procedure (2), MC statistics in efficiency determination (1–2), shape of the meson angular distribution relative to the beam axis direction in the CM system (1), and PDG branching fractions (3–5). All systematic uncertainties are combined in quadrature to obtain the total systematic uncertainty. The same set of uncertainties is used below to obtain the total systematic uncertainties for values averaged over several modes, however the correlated and uncorrelated uncertainties are treated separately in this case. All uncorrelated uncertainties from all modes are varied individually to obtain their contribution to the total systematic uncertainty of the averaged value, while correlated uncertainties are varied simultaneously for all channels.
Using the rates shown in Table 1, the average production rates and are obtained. As expected, these rates are equal within uncertainties. The average of charged and neutral modes is . Within uncertainties this rate is consistent with the CLEO value of cleob .
Since the and values are consistent with isospin symmetry, it is reasonable to assume that equal numbers of and mesons are produced in all possible channels. Therefore the five decay modes are treated simultaneously everywhere below. First, events in the signal bands shown in Fig. 1 are projected onto . To describe combinatorial backgrounds under the signal, we define sidebands, which have the same shape as the signal region, but are shifted by 70 MeV in , and project similarly onto . Assuming that background is distributed linearly in , we model the combinatorial background by taking the average of the two sideband distributions.
Figure 2(a) shows the distributions for the possible two-, three- and four-body channels obtained from MC simulation for the decay. The three-body and four-body channels are simulated assuming a pure phase-space decay model. Figure 2(a) shows that the two-body channels are well separated. The three-body , and channels have broader distributions in the higher mass region 5.35 GeV/. The four-body channel is the cross-hatched peak on the right side of Fig. 2(a).
The matrix elements responsible for the three- and four-body decays are not known, and the rates of the three- and four-body contributions cannot be obtained in a model-independent way from a fit to these distributions. We therefore restrict the fit to the region GeV/ 5.348 GeV/ to extract the two-body channel fractions. To obtain the sum of the other contributions in the large region, only the events from the interval GeV/ 5.440 GeV/ are selected. For these distributions we apply a fit procedure similar to that used above to obtain the full production rate for the entire interval GeV/ 5.440 GeV/. The total signal yield, summed over all modes and channels in this region, is .
The fitting procedure used to extract the production rates of the two-body decay channels treats the five signal and five sideband distributions simultaneously. The following four components with fixed shapes and floating normalizations are included in the fit for each distribution: , , , and combinatorial background. The shapes of the signal components are taken from MC simulation, and those of combinatorial background are modeled by the sideband data. The normalization parameters (channel fractions) for the two-body components are constrained to be equal for all five studied decays. The sum of background-subtracted distributions for the five studied decays is shown in Fig. 2(b), where the result of the likelihood fit in the region GeV/5.348 GeV/ used to obtain two-body channel fractions is superimposed. The fractions obtained from the fit are listed in Table II. The systematic uncertainties include all those described above as well as uncertainties due to the signal shape modeling (3).
To reconstruct the three-body channels, we look for an additional charged pion produced directly in the channels. For each charged pion not included in the reconstructed candidate, we form right-sign , , or combinations. We then compute the variables and for the missing meson, using the energy and momentum of the reconstructed combination in the CM: and . In the and channels, the value will be shifted due to unreconstructed photons from decays.
Figure 3(a) shows the corrected projections for MC simulated , , , and events where the mode is generated. The reconstructed candidates are selected from the signal region within the intervals GeV/GeV/ and GeV. The value is corrected by adding to it the value . This does not introduce any bias for the original mesons, but improves the resolution, because these two values have partially anticorrelated uncertainties. Figure 3a shows that the , and channel contributions are well separated. The reconstruction efficiency for the four-body channel (the small peak in the rightmost part of Fig. 3(a)) is small and model dependent. Therefore, we do not include the four-body channel in the fit procedure described below. The background due to random charged tracks from the unobserved meson is also shown.
Finally, the distribution is obtained in data for the sum of the five reconstructed modes (Fig. 3(b)). We fit this distribution with a function including four terms: three Gaussians with fixed shapes and free normalizations to describe the , , and contributions, and a second-order polynomial to describe the background. The central positions and widths of the Gaussians are obtained from fits to the MC simulated distributions shown in Fig. 3(a) and are fixed in the fit to data.
The event yields and rates are listed in Table III. The three-body rates are calculated assuming the ratio of charged and neutral directly produced pions to be 2:1 as expected from isospin conservation. The pion reconstruction efficiencies are obtained from the three-body phase-space matrix element MC simulation to be , and for the , , and channels, respectively. In neutral modes, an efficiency correction is applied to take into account the effect of 19 mixing. The systematic uncertainties due to the fit procedure (1.5 signal events for each channel) and MC efficiency calculations (4–10) are also included in the total systematic uncertainties. The statistical significance of the signal is 4.4.
It is interesting to note that by directly reconstructing pions, we observe only about one half of the rate obtained above for the large region (Table II) resulting in a deficit of . If the difference were due to events, we would expect events in the three rightmost bins of the distribution of Fig. 3(b), where only one is observed. In addition, the four-body channel is theoretically expected to have a rate at least an order of magnitude smaller than the three-body channel rates, because there is limited phase-space for the creation of an additional pion. Instead, we find that the deficit can be explained by ISR contributions such as (4S). We calculate a probability of 10 for hard photon emission isr by the electron or positron beam with subsequent production, and estimate that 40 of such events are due to radiative return to the (4S) resonance. This estimate agrees with the observed residual and explains the peaking structure on the right side of Fig. 2(b), which is dominated by radiative return to the (4S) or slightly higher energies.
|Channel||Yield (),||Fraction over||Fraction per|
We analyze other potential sources and backgrounds for the events in the multibody region. The rate for a event to produce the (4S) and two pions is expected to be less than 1 chen . The wide meson can be produced at the (5S) CM energy with a subsequent decay resulting in three- or four-body channels, however this process is expected to be negligible due to the very small phase-space. The decay could contribute as a background to the multibody channels, however, the corresponding branching fraction is estimated to be less than 10.
In conclusion, the production of and mesons is measured at the energy of the (5S). Using fully reconstructed and mesons the production rates per event are measured to be and . The average value agrees within uncertainties with the CLEO value of cleob . Taking into account the event rate at the (5S) of pdg (this value was obtained neglecting bottomonium, resulting in an additional absolute uncertainty of about ), and assuming the fraction of final states with a bottomonium meson to be , some room for unobserved transitions still remains.
Assuming equal production of and mesons we also measure the fractions for event transitions to the two-body channels with meson pairs, , , . The channel is measured for the first time. These fractions are in rough agreement with theoretical predictions teoc ; teod , however further adjustment of the theoretical models is required.
Using the additional charged pion directly produced in channels, we measure the three-body channel fractions in a model-dependent way. The decay channel is observed for the first time with the fraction . This measured three-body fraction is significantly larger than those predicted in sim ; lel .
We thank the KEKB group for the excellent operation of the accelerator, the KEK cryogenics group for the efficient operation of the solenoid, and the KEK computer group and the National Institute of Informatics for valuable computing and SINET3 network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council and the Australian Department of Industry, Innovation, Science and Research; the National Natural Science Foundation of China under contract No. 10575109, 10775142, 10875115 and 10825524; the Ministry of Education, Youth and Sports of the Czech Republic under contract No. LA10033 and MSM0021620859; the Department of Science and Technology of India; the BK21 and WCU program of the Ministry Education Science and Technology, National Research Foundation of Korea, and NSDC of the Korea Institute of Science and Technology Information; the Polish Ministry of Science and Higher Education; the Ministry of Education and Science of the Russian Federation and the Russian Federal Agency for Atomic Energy; the Slovenian Research Agency; the Swiss National Science Foundation; the National Science Council and the Ministry of Education of Taiwan; and the U.S. Department of Energy. This work is supported by a Grant-in-Aid from MEXT for Science Research in a Priority Area (“New Development of Flavor Physics”), and from JSPS for Creative Scientific Research (“Evolution of Tau-lepton Physics”).
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