Bottomonium and Charmonium Results from CLEO\address
Department of Physics, Luther College, 700 College Drive
Decorah, IA, 52101, USA
Heavy Quarkonium Physics continues to be a focus of the work done by the CLEO Collaboration. We present several results in the spectroscopy of both bottomonium and charmonium systems using CLEO’s data sets taken at the , and resonances.
In 2000, CLEO stopped running at the for B-meson studies, and began an eight-year study of the states of bottomonium, charmonium and open charm mesons, the latter two of which were performed primarily as the experiment evolved into CLEO-c. We present here several results from our full charmonium and bottomonium data sets.
2 Hadronic Transitions
The study of hadronic transitions among heavy quarkonium states provides important tests for non-perturbative Quantum Chromodynamics (QCD) . In the multipole expansion,  hadronic transitions among heavy quarkonium states proceed by emission and hadronization of soft gluons. The non-relativistic nature of the bottomonium system and the richness of the spectrum of bound states make it an excellent laboratory for the study of the low- hadronization process.
First, we report  improved measurements of the branching fractions for transitions among the vector states of the bottomonium system. Dipion transitions from to the lower vector states () and from to have been of interest ever since their first observation in 1982. There has recently been a resurgence of interest in dipion transitions following the observation of new transitions by several experiments. Additional motivation to update measurements of the branching fractions for bottomonium dipion transitions comes from the prospects of using as a clean source of tagged to study exclusive decays, including searches for invisible decay modes.
|Mode||BF (%)||PDG BF (%)|
In this analysis, we study the transitions both inclusively (in which case we detect only the pair of charged pions) and exclusively (in which case we detect, in addition to the charged or neutral pair of pions, the decay of the daughter state to either or ). In each case, the primary quantity used to identify our observation of the dipion transitions of interest is mass recoiling against the dipion system. From the recoil mass histograms, yields for each process may be obtained and converted to the branching fractions presented in Table 1. In every case the branching fractions obtained are more precise than the current PDG  world average.
We next present the first observation  of a transition in bottomonium involving mesons. In order to produce a pseudoscalar meson or in transitions (involving the flip of a heavy quark’s spin), one quark of the hadronic system must emit an M1 (magnetic dipole) gluon while the other emits an M1 or E2 (electric quadrupole) gluon. The observation of the spin-flip of a b-quark can shed light on its chromomagnetic moment.
In this analysis, the daughter state is tagged via its decay to . Branching fractions are then obtained from the invariant mass distributions of the or daughters. (See Figure 1) The backgrounds from various sources are very small, and expected to be linear in the region of interest. We thus obtain:
For the other or transitions studied, only upper limits were obtained.
3 Hadronic Annihilation Decays
By contrast to the processes discussed above, hadronic annihilation of heavy quarkonia is a comparatively high process, and thus they probe quite different features of QCD.
3.1 Decays to Light Hadrons
CLEO has also, for the first time, observed  decays of bottomonia into light hadrons. Using data taken at the higher vector states and , we tag the production of by observation of the appropriate E1 photons. We then reconstruct over 650 different exclusive final states, and obtain the yield from the invariant mass distributions for each. We observe fourteen modes in which there are signals for each of and , having branching fractions in the range . These results can be of use in validating models of fragmentation of heavy states, and for exclusive reconstruction of and .
3.2 Inclusive Decays to Open Charm
We have also studied  inclusive decays of to open charm. For even-J states, we expect that hadronic decays occur via , whereas for the J=1 states, is forbidden, and the most probable intermediate state is . We may test these expectations by seeking decays involving open charm, which would tend to be suppressed for and enhanced, with an expectation of of the hadronic rate for the intermediate state.
In this analysis, for events containing at least one the spectrum of detected photons is fitted to obtain rates of production from each state. The ratio of the rate to the total hadronic rate (roughly the total width minus the radiative width in each case) is calculated. For the states, we confirm theoretical expectations, obtaining: only were significant results obtained - and each confirms the expectation of for the states:
These results represent the first measurements for the branching fractions and offer the opportunity for the refinement of models of hadronic annihilation decays.
4 Radiative Transitions and Decays
The study of radiative transitions and decays offers a third probe of QCD.
4.1 Annihilation of J/ to
An important test of QED has been the study of the decay of Ortho-positronium, and similarly the decay of ortho-charmonium, J/, can serve as a laboratory for the investigation of the QCD by comparing the rate for this decay to the rates for , or . Prior to our observation  of this decay only Ortho-positronium was known to decay to .
Production of J/ was tagged via the process , and events containing three additional showers in the electromagnetic calorimeter were selected. Events for which the invariant mass of any pair of these showers corresponded to or were removed. An excess of 24.2 events is observed on top of expected backrounds. We thus obtain
with which zeroth order predictions  generally agree, but first-order perturbative QCD corrections are huge; this measurement presents a significant challenge, therefore, for theory.
4.2 Decays of Vector Charmonium to + Pseudoscalar Mesons
Naively, one expects that the ratio of decay rates of heavy quarkonia via to that via to scale as . However, this is not borne out in the charmonium system; a recent CLEO-c measurement revealed the ratio for is only half of that for J/. We have probed this result by searching for decays of and J/ to + which proceed via . Of particular interest is the ratio , which is expected to satisfy . Previous measurements revealed and at 90% CL .
We searched for all the above pseudoscalar decays of J/, and and found  that at 90% CL. We’ve tightened the result for , with , and obtain a much lower limit of at 90% CL. Such a small value of poses a significant challenge to our understanding of these decays.
4.3 Radiative Production of from
The M1 radiative transitions represent fundamental processes whose rates serve as important benchmarks for theory, but both are very poorly measured. In addition, the partial with measurements of are dependent upon these poor measurements. CLEO-c has made new and much improved measurements  of each of these branching fractions.
In this analysis, we measure the yield from the inclusive photon spectrum from and the yields from the exclusive photon spectra (using identical exclusive final states of ) from and from . We obtain from the inclusive photon spectrum, and from the exclusive photon spectra. Multiplying these two numbers yields the branching fraction . We thus find:
These are each significantly larger than, but much more precise than the previous PDG  average, and will result in a renormalization of nearly all exclusive branching fractions. Interestingly the masses reported by experiments which observe in M1 transitions average 5 MeV below those reported by experiments which produce through fusion or annihilation. In our study, we observed that depending on the lineshape assumed, we can obtain a mass consistent with either M1 transition or direct-production results. We thus note that a very careful study of the M1 lineshape is clearly in order if the mass is to be extracted from M1 transitions.
The author thanks the Organizing Committee for a fabulous conference in a gorgeous setting, and in particular J. Tran Thanh Van for his idea so many years ago which has brought forth over forty years of fruitful discussion and the wonderful spirit of Moriond. The author also gratefully acknowledges the support of National Science Foundation Grant No. PHY-0603831.
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