Bottomonium and Charmonium at
Bottomonium and Charmonium at
Department of Physics, Indiana University,
Bloomington, Indiana 47405, USA
The bottomonium and charmonium systems have long proved to be a rich source of QCD physics. Recent CLEO contributions in three disparate areas are presented: (1) the study of quark and gluon hadronization using decays; (2) the interpretation of heavy charmonium states, including non- candidates; and (3) the exploration of light quark physics using the decays of narrow charmonium states as a well-controlled source of light quark hadrons.
The experiment at the Cornell Electron Storage Ring (CESR) is uniquely situated to make simultaneous contributions to both the bottomonium and charmonium systems in a clean environment. Between 2000 and 2003 ran with center of mass energies in the region. A subset of this period was spent below threshold, where 20M, 10M, and 5M decays of the , , and , respectively, were collected. In 2003, CESR lowered its energy to the charmonium region and the detector was slightly modified to become CLEO-c . Since that time, there has been an energy scan from 3.97 to 4.26 (), samples collected at 4170 (, largely for physics) and the (, largely for physics), and a total of nearly 28M decays have been recorded, only 3M of which have been analyzed.
Three (of many) topics recently addressed by the collaboration will be discussed below. The reach is wide: from fragmentation in bottomonium decays, to the interpretation of heavy charmonium states, to the use of narrow charmonium states as a source of light quark hadrons.
2 Bottomonium and Fragmentation
The bottomonium system provides many opportunities to study the hadronization of quarks and gluons. The number of gluons involved in the decay of a bottomonium state can be controlled by the charge-conjugation eigenvalue of the initial state: the states decay through three gluons; the states decay through two. In addition, the continuum – where proceeds without going through a resonance – can be used as a source of quarks. Thus, particle production can be studied and compared in a number of different environments.
2.1 Quark and Gluon Fragmentation
In 1984, first noticed an enhancement in baryon production in (from decays) over (from the continuum), i.e., the number of baryons produced per decay was greater than the number produced per continuum event . The interpretation of this phenomenon, however, was complicated by the fact that the system consists of three partons (or three strings), while the system only has two partons (or one string). A recent analysis has confirmed these findings with greater precision and has extended the comparison beyond decays to the decays of the and states as well. Figure 1a shows new measurements of the enhancements of particle production in over , where the “enhancement” of a particle species is defined as the ratio of the number of particles produced per event in decays to the number produced per event from the continuum. The ratio is binned in particle momentum and integrated. The MC predictions incorporate the JETSET 7.3 fragmentation model. In addition, the new analysis compares particle production in (radiative decays) and (radiative continuum events). The comparison in this case is between systems both having two partons and one string. The energy of the radiated photon is used to monitor parton energies. Figure 1b shows the enhancements of over , where in this case the ratio is binned in the energy of the radiated photon and integrated. A few conclusions can be drawn from these studies: (1) baryon enhancements in vs. are somewhat smaller than in vs. ; (2) the number of partons is important, not just ; and (3) the JETSET 7.3 fragmentation model does not reproduce the data.
2.2 Anti-Deuteron Production
The production of (anti)deuterons in decays provides another opportunity to study the hadronization of quarks and gluons. In this case, models predict that the gluons from the decay first hadronize into independent (anti)protons and (anti)neutrons, which in turn “coalesce” into (anti)deuterons due to their proximity in phase space. has measured the production of anti-deuterons in and decays and has set limits on their production in decays . The production of anti-deuterons is easier to measure experimentally than the production of deuterons since anti-deuterons are not produced in hadronic interactions with the detector and the small background makes them easy to spot using in the drift chambers. The relative branching fraction of inclusive to was found to be . For comparison, a 90% C.L. upper limit of anti-deuteron production in the continuum was set at at , which, given an hadronic cross-section of the continuum of around 3000 , results in less than 1 in events producing an anti-deuteron. This is a factor of three less than what is seen in decays.
3 Interpretation of Heavy Charmonium States
The past few years have seen something of a renaissance in charmonium spectroscopy with the discovery of the unexpected and states, among others. The and , in particular, have been the source of much speculation due to their multiple sightings and the difficulties encountered in attempting to incorporate them into the conventional spectrum. The contributions of to their interpretation will be discussed below. In addition, has recently made measurements pertaining to the charmonium character of the , which is more often used as a source of . While the is well-known and has been assumed to be the expected state of charmonium, pinning down its properties contributes to our global understanding of the charmonium spectrum.
The was first observed by decaying to using collisions with initial state radiation (ISR). This production mechanism requires the have . However, there is no place for a vector with this mass in the conventional spectrum. On one interpretation the is a hybrid meson, a pair exhibiting an explicit gluonic degree of freedom. has made two recent contributions regarding the nature of the . First, an energy scan was performed between 3.97 and 4.26 . A rise in the production cross section was observed for both and at 4.26 in the ratio of roughly 2:1. This ratio suggests the is an isoscalar. Second, (using data in the region) has confirmed the initial observation by in from ISR (Figure 2a). This both confirms its existence and its nature. The measured mass and width, and , respectively, are also consistent with .
The was first observed by in the reaction . It has subsequently been studied in several different channels by a variety of different experiments. From its decay and production patterns it likely has . One of the most tantalizing properties of this state is that its mass is very close to threshold, suggesting that it could be a molecule or a four-quark state. Prior to the new measurement by , the binding energy of the (), assuming it to be a bound state, was , where the error, perhaps surprisingly, was dominated by the mass of the . improved this situation with a new precision mass measurement using the well-constrained decay (Figure 2b) and found the mass to be . This results in a small positive binding energy from zero: . This lends further credence to the molecular interpretation of the .
The existence of the has been established for a long time. However, because it predominantly decays to its behavior as a state of charmonium has been relatively unexplored in comparison to its lighter partners. The electromagnetic transitions, , because they are straightforward to calculate, provide a natural place to study the charmonium nature of the . has recently measured these transitions in two independent analyses. In the first , the processes were measured by reconstructing the in their transitions to and then requiring the to decay to or (Figure 3a). In the second , the were reconstructed in several exclusive hadronic modes and then normalized to the process using the same exclusive modes (Figure 3b). The first method favors the measurement of the transitions to and while the second method is more suited to the transition to . Combining the results of the two analyses, the partial widths of were found to be for , for , and an upper limit of at 90% C.L. was set for . These measurements are consistent with relativistic calculations assuming the is the state of charmonium.
4 Using Charmonium to Study Light Quarks
In addition to providing valuable information in its own right, the charmonium system can also serve as a well-controlled source of light quark states. While much effort has gone into the study of and decays (e.g. radiative decays to glueballs), the decays of the states are less familiar and hold complementary information. The states are produced proficiently through the reaction , with rates around 9% for , 1, and 2, and can be reconstructed cleanly in many different decay modes in the detector.
As an exploratory study into the analysis of the resonance substructure of decays, has recently analyzed a series of three-body decays using approximately 3M events collected with the and CLEO-c detectors. This anticipates the new sample of approximately 25M events. The decay modes analyzed include , , , , , , , and . Branching fractions were measured to each of these final states, many for the first time. Figure 4 shows decays to three particularly well-populated final states. The decays to , , and included sufficient statistics for a rudimentary Dalitz analysis. Figure 5 shows the results of a fit to the Dalitz plot using a crude non-interfering resonance model. Dominant contributions were found from , , and with fit fractions of , and , respectively. No evidence for new structures was found in either or the two modes.
Studies analyzing substructure using the full sample of 28M decays are underway. One reaction that looks particularly promising is the decay , which was shown to exhibit a rich substructure of and states in a recent analysis .
We gratefully acknowledge the effort of the CESR staff in providing us with excellent luminosity and running conditions. This work was supported by the National Science Foundation and the U.S. Department of Energy.
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