Upsilon spectroscopy at CESR

UPSILON SPECTROSCOPY AT CESR

Karl BERKELMAN Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853, US.A.

I

NORTH-HOLLAND PUBLISHING COMPANY - AMSTERDAM

PHYSICS REPORTS (Review Section of Physics Letters) 98. No. 3 (1983) 145—187. North-Holland Publishing Company

UPSILON---SPECTROSCOPY-AT-- CESR Karl BERKELMAN Laboratory of Nuclear Studies. Cornell University. Ithaca. New York 14853. U.S.A.

Received 28 April 1983

Contents:

I. Introduction 2. History of b-quark physics

147 5. Measurement of transitions 147 5.1. Branching ratios for hadronic- cascade decay: Y 147~Yr+hadrons --~-

2.2. Fermilab 2~4--Prehistory-2.3. DORIS 2.4. CESR 2.5. Future 3. Upsilon production measurements 3.1. Masses and potential models 3.2. Cross section measurements 3.3. Dilepton widths F~ 4. Upsilon decay observations 4.1. Evidence for the decay of the Y(1S) into three gluons 4.2. Inclusive Y(1S) decays 4.3. Branching ratios for dilepton pair decay: eTe, ~c~/z,

147 148 148 151 151 151 154 157 159 159 162 168

169

1—~ 5.2. Branching ratios for radiative decays: Y —~YXb and Xb~YY~

5.3. Implications for hadronic production 6. Derived results on upsilon decays and transitions 6.1. Indirectly measured branching ratios and widths 6.2. Rate for Y(IS) decay into three gluons 6.3. Dipion transition rates 6.4. Radiative transition rates 7. Searches 7.1. Axions 7.2. Other narrow resonances 8. Conclusions References

Ab~ac7~~

171 177 178 178 179 18(1 181 182 182 183 184 184

-------------------—--

Present information about the quarkonium system consisting of a b-quark and of its antiquark is reviewed with emphasis on the recent results obtained at the Cornell CESR machine.

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K. Berkelman, Upsilon spectroscopy at CESR

147

1. Introduction In this report I discuss the physics of the hadrons containing the b-quark and its antiquark, the upsilon system of bb bound states. The emphasis will be on experimental results obtained in the past few years at the Cornell Electron Storage Ring CESR by the CLEO and CUSB groups. The reader can find more details of earlier work covered in summaries presented at annual High-Energy or Lepton— Photon Conferences [1] and in a previous issue of Physics Reports [2]. I will not discuss here the B mesons consisting of a b-quark and a light quark, but will leave it for a future review.

2. History of b-quark physics 2.1. Prehistory Much of the theoretical and experimental development of the physics of the fifth quark was presaged by the earlier history of the fourth quark. In 1970 Glashow, Iliopoulos and Maiani [3] argued that in order to suppress strangeness changing neutral current decays there had to be a fourth quark, named the charmed quark c, in addition to the u, d and s. A threshold for pair production of a new quark also seemed to be the best explanation [41of the CEA Bypass [51and early SPEAR [6] data, showing that the ratio R of cross sections for e~e hadrons and e~e /L~j~increased with energy. So that when the ~t,(or J) was discovered at BNL [7] and SLAC [9] in 1974, it was immediately interpreted as the lowest cë bound state with J” = 1 The later experimental work carried out at SPEAR and DORIS [91on the spectroscopy of the charmonium (ce) bound states as well as the D mesons (cii and cd) beautifully confirmed the expectations following from the GIM model [31and the rapidly developing theory of quantum chromodynamics, QCD. The first concrete indication that there might be more came with the 1975 discovery at SPEAR of the tau lepton [10].The fact that there now seemed to be three lepton doublets (eve), (~v~), (Tv~)upset the balance between the leptons and the quarks (du), (sc). Already in 1973 Kobayashi and Maskawa [11] had shown that in a theory containing six quarks in three weak doublets one could still achieve the suppression of flavor changing neutral currents and in addition get CP violation in a natural way. The quarks of this hypothetical third generation of fundamental fermions were christened b (“bottom”) for the charge 1/3 member of the doublet and t (“top”) for the charge 2/3, with the corresponding new quantum numbers, or flavors, denoted by “beauty” and “truth”. Once one assumed a value for the mass of a new heavier quark, say the b quark, one could use the nonrelativistic potential -model developed for the spectroscopy of the cë states to predict the spectrum of bb states. Gottfried in fact worked out such a spectrum, assuming mb = 5 GeV, for the April 1977 proposal for the construction of CESR [121.It is fair to say, however, that the theoretical motivation for the existence of more than four quarks was not as compelling as the arguments which anticipated the discovery of charm. —~

—~

-.

—

2.2. Fermilab

In mid-1977 Herb et al. [13] saw a bump at 10 GeV in the mass spectrum of dimuons produced in p + Be collisions at Fermilab, reminiscent of the earlier discovery of the J (or ~‘)in the e~e spectrum at BNL. As the measurements improved in resolution and statistics [14]. it was possible to fit the bump to

148

K. Berkelman, Upsilon speciroscopy at CESR

three resonances at energies 9.4, 10.0 and 10.4 GeV, each with an apparent width consistent with the experimental mass resolution, 210 MeV r.m.s. The states were named Y (upsilon), Y’ and r, and were interpreted as JPC = 1-- bb bound states. The number of bound states, three, and the mass spacings were compatible with the expectations based on the charmonium potential models [15]. Since the first Fermilab experiments others at Fermilab and at the CERN ISR and SPS have also seen the Y in hadronic collisions [16], but none with mass resolution better than in the original experiment. 2.3. DORIS The discovery of the V provided the incentive to raise the energy of the DORIS e~e storage ring at DESY. This was accomplished in 1977 with higher magnet current and more RF cavities and klystrons. The two detectors, PLUTO and DASP, immediately began measuring the total cross section, scanning in center-of-mass energy around 9.4 GeV. PLUTO [17] was a superconducting solenoid magnetic detector with charged particle momentum measurement (~ip/p2= 0.03/GeV r.m.s. over f1/4ir = 87%), electromagnetic calorimetry (~EI\/E= 0.35 GeVh’2 r.m.s. over fu/41T = 96%), and muon identification (Q/4ir = 49%). The DASP apparatus [181,op~ratedby a new group DASP II, was actually two detectors, an electromagnetic calorimeter (~EI\/E= 0.30 GeV1~r.m.s. over (1/47,- = 70%) and two opposed magnetic spectrometer arms (fII4ir = 8%, total) with charged particle momentum measurement (~p/p2=O.O07IGeVr.m.s.), time of flight, electromagnetic calorimetry, and muon identification. The two groups soon located the V at a mass of 9.46 ±0.01 GeV with an apparent width consistent with the 10 MeV storage ring resolution [19, 201. The measñred cross seëtion integrated oi’er the~ resonance, when interpreted in terms of the coupling of a photon to a heavy quarkonium state, indicated a charge 1/3 for the quark. First measurements of the branching ratio for decay into two leptons [21—23](eke or ~s~p~)implied a total width F for the V of about 30 keV. The PLUTO group made an extensive analysis [24] of the topology of the V hadronic decays through three gluons. Taken together, these results established that there existed a new fifth quark b, of mass approximately 5 GeV, and that the V was indeed the lowest 3S 1 state of the bb bound system. After these first measurements the DESY—Heidelberg nonmagnetic detector [25] replaced the PLUTO This detector consisted a cylindrical chamber for calorimeter charged particle tracking 41T = experiment. 95%), surrounded by a sodium iodideof and lead glassdrift electromagnetic (6E/E = 0.04 (Q1E = 1 GeV, over Iu/4ir = 45%), and a muon identifier (11/4ir = 32%). The DESY—Heidelberg and at DASP II groups found the Y’ at a mass of 10.01 ±0.02 GeV [26, 27]. A new group LENA, formed to operate thé DESY—I-ieidèlberg detector, went on tóth äsüréThë~ipãi fãii~ätiö~oTthe V [2s], improve the measurement of Fee for the F [29],observe the transition V’—~Vir~rr [30],and extend the data on inclusive final-state hadrons [31]. 2.4. CESR In November, 1979, the Cornell Electron Storage Ring (CESR) [32] came into operation for e~e colliding beam experiments. The 260 iii diametea litig is huuscd iti thc s~uac tuisuCi a~the former luminosity of 1032 cm2 sect at an energy of 8 GeV per beam. With the usual F2 dependence of luminosity, this would imply 4 x 1031 cm2 sec~iii the upsilon region; but as is the case with ~1Iother -

-

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K. Berkelman, Upsilon speciroscopy at CESR

149

eke-rings, the design luminosity has not yet been achieved. For the first two years of CESR operation the peak luminosity at the upsilon was around 2 x i0~° cm2 sec1, which nevertheless was the highest luminosity of any ring at those energies. The circulating bunches, one of e~and one of e, intersect at two opposite points, occupied by the CLEO and CUSB experiments. CLEO (fig. 1) is a general-purpose magnetic detector [33] based on a 2 m diameter solenoid. Until mid-1981 the field was produced by a conventional aluminium coil, giving

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K. Berkelman, Upsilon speciroscopy at CESR

about 0.4 Tesla. Charged particle tracking and momentum measurement (until 1981 ~pIp2= 0.03/GeV r.m.s. over (l/4ir = 90%) were accomplished by a small cylindrical proportional chamber surrounding the beam pipe, a 2 m long cylindrical drift chamber occupying most of the space inside the solenoid, and an array of planar drift chambers just outside the coil. Charged hadrons are identified (over (l/4ir = 50%) using time of flight and either threshold gas Cerenkov counters (before 1981) or dE/dx measurements in wire proportional chambers. With this system charged kaons, for example, can be separated from pions and protons when the momentum is between 0.5 and LO GeV/c. Alternating layers of proportional tubes and lead provide electromagnetic calorimetry (~E/VE= 0.17 GeVU2 r.m.s. over f1/4ir = 70%), and iron followed by drift chambers allows muon identification (over (1/4ir = 78%). The CLEO detector is run by a Cornell, Harvard, Rochester, Rutgers, Syracuse, Vanderbilt collaboration. The CUSB nonmagnetic detector [2] (fig. 2) is optimized for high resolution measurements of electromagentic shower energies. Following a drift chamber for charged particle tracking without momentum measurement (over 47°< 0 < 133°) is an array of 332 sodium iodide scintillators with transverse and depth segmentation, backed by 256 lead glass Cerenkov counters to contain the tails of showers (~E/E= 0.04E114 r.m.s. with E in GeV, over (l/4ir = 60%). Physicists from Columbia, Stony Brook, Louisiana State and Munich (MPI) comprise the CUSB collaboration. In the first month of running, the two experiments located the three upsilon bound states [34, 35], drift chambers muon identifier

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Fig. 2. The CUSB detector.

K. Berkelman, Upsilon speciroscopy at CESR 11

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Fig. 3. The total cross section for e~e -~ hadrons in the upsilon region

1381.

now called Y(1S), V(2S), and V(3S), then went on to discover the V(4S) [36, 37] (see fig. 3). This fourth resonance proved to lie immediately above the threshold for decay into pairs of B mesons (B~= bu, B°= bd). The study of the weak decays of the B confirmed [39—49]many predictions of the standard electroweak theory with three generations of quarks and leptons. CLEO and CUSB also measured many decay branching ratios of the three bound upsilon states, including the dilepton rates [50—52],the three dipion transitions [50, 53—56], and the electric dipole radiative transitions from the V(2S) and V(3S) to the 3P states, xb(lP) and xb(2P) [57—59].By now more states have been seen in the upsilon system than in positronium! The detailed discussion of these measurements made at CESR forms the main body of this report. In mid-1981 the peak luminosity of CESR was increased by more than a factor of five, by moving the interaction region focusing quadrupoles closer to the collision point, thus lowering the vertical betatron function value f3~’from 11 cm to 3cm. At the same time the original CLEO solenoid coil was replaced by a superconducting coil, giving a higher field (1.0 Tesla) and thus an improved momentum resolution (~p/p2= 0.013/GeV r.m.s.). The CUSB experiment improved its solid angle coverage for electromagnetic calorimetry (now fl/4ir = 88%) and added a muon identifier (fu/4ir = 25%). 2.5. Future Tng3~e~e~It~in b-~uà~k ~h~si~s~ill~o~e frO~ ESRI I~DORIS~ for 11 GeV center-of-mass energy and higher luminosity, and from VEPP4, the 7 GeV on 7 GeV storage ring at Novosibirsk. The two DORIS interaction regions are occupied by the Crystal Ball nonmagnetic detector, moved from SPEAR, and by the new ARGUS solenoidal detector. At the time of this writing the VEPP4 transverse-field magnetic detector MD-i has already begun operation in the upsilon region and has made an accurate measurement of the V mass [60]. 3. Upsilon production measurements 3.1. Masses and potential models The upsilon 35~1-- bound states are observed in the total cross section for e~e hadrons as narrow resonances at center-of-mass beam energies equal to the upsilon masses (see fig. 3). The best value for —~

152

K. Berkelman, Upsilon spectroscopy at CESR

the V(1S) mass, as determined at VEPP4 is 9459.7 ±0.6 MeV [60].The CESR [34—37]and DORIS [19, 20, 23, 26, 29] values for the masses of the upsilons were originally based on a calibration of the energies of the beams using measurements of the orbit geometry and of magnetic fields in the ring. The estimated accuracy in mass was 10 MeV at DORIS and 30 MeV at CESR, a larger ring with a more complicated sequence of magnets. In the VEPP4 measurement [601the ring energy was calibrated by measuring the frequency (1 of the external perturbing field required to depolarize the beams by resonant spin precession. (1 is related to the y of the beam and to the electron anomalous magnetic moment by (l=wo[1+y(g—2)/2], where w~is the orbit frequency, accurately known from the accelerating RF. In this report we will use this VEPP4 value of the V(1S) mass to define the energy scales at DORIS and CESR; that is, previously published DORIS masses will be multiplied by 9.4597/9.462, and CESR masses by 9.4597/9.433. The apparent width of the peaks is a consequence of the energy spread in the colliding beams, caused by synchrotron radiation. It is narrower at CESR and VEPP4 (6W = 4.1 MeV (WhO 0eV)2 r.m,s.) than at DORIS (6W = 11 MeV (WhO GeV)2), because of the larger radius of the CESR and VEPP4 rings. As in the case of the t,fr family, the very narrow intrinsic width of the resonances is taken as evidence that they are bound states of a new heavy quark b and its antiquark b. Strong decay into a pair of B mesons is energetically forbidden, and decays into final states not containing the b quark are suppressed by three factors of a 5 (see section 6.2). At about the time of the i/i discovery it became clear [61] that the heavy quark—antiquark spectroscopy might be understood in terms of the nonrelativistic Schrodinger equation with a more-orless empirical potential function. The first serious attempt at fitting the i/i mass spectrum used a potential of the form [62] V = Air + Br, the Coulomb form at short distances suggested by lowest order QCD, the linear form at large distances suggested by the string or flux-tube picture of quark confinement. In a later work [63] the short-distance Coulomb and the long-distance linear potentials were pieced together with a logarithmic form at intermediate distances. The strength of the Coulomb part was given a logarithmic dependence on the quark mass consistent with the running coupling constant at QCD [64] in order to fit the t/r and V systems simultaneously. Other approaches to the quantitative understanding of heavy quarkonium spectroscopy have been based on the bag model [65] and on the inverse scattering formalism [66]. The potential model which owes the most to QCD is that of Richardson [67], improved by Buchmiiller, Grunberg and Tye [68]. In this model, which we will call the RBGT potential, one starts with a Fourier transformed potential of the form 2) = —(1617/3) a 2)/Q2. V(Q 5(Q To obtain the running coupling constant a 2) one first considers the function 5(Q /3(p) = Q2 (dp/dQ2), which specifies the dimensionless logarithmic slope of the coupling p

=

a

5/4ir, expressed as a function of p. In the peittirbative -small-distance---(high---O~-small--p-)--limit-seeond-order--OC--D --implies 2— b 3+”, /3(p)~° —bop 1p

K. Berkelman, Upsilon spectroscopy at CESR

153

where b0 = 11— (2/3)N~, b1 = 102— (38/3)N5, and Nf is the number of active quark flavors. In the 2, large-p) limit we require that the potential be linear; that is, V = (1/2ira’)r, large-distance where a’ is the(low-Q Regge trajectory slope. This implies that

A function which smoothly interpolates between these two limits is given by =

[bop2(1— exp(—1/b~p))]~ + (b 1/b~p)exp(—24p).

The first term, due to Richardson, incorporates lowest-order QCD. The second, by Buchmüller et al., includes two-loop contributions. The exponential (with the factor of 24 empirically adjusted) is supposed to take care of higher orders. One can fix the magnitude of the coupling either at small p (small distances) by fixing the A in the second-order approximation for a5 (in the iii~scheme). 2/A2)’ (b 2/A2)/(b~In2 Q2/A2), (1) a~/4ir= (b0 in Q 1 ln Q or at large p (large distances) by fixing the Regge slope a’. We do not have the freedom to do both, since the scale of a 2 to match the experimental Regge canGeV. be fixed If we takedetermined, a’ = 1 GeV we Fourier transform V(Q2) to get slope, we need A 5 0.5 Withonly a once. 2) completely 5(Q V(r), insert it into the Schrödinger equation with an adjustable quark mass, and solve numerically for the energy levels. The agreement with the experimental i/i and Vmass spacings is remarkably good (table 1). Acceptable fits can still be made with A values down to about 100 MeV. Fig. 4 shows the r dependence of the RBGT potential compared with other models. Note also the average radii of the various fi and V wave functions. Where they concentrate, all potentials are very —

Table 1 Measured and predicted masses of upsilon states, in MeV’ State

Y(2S) Y(3S) Y(4S)

Xb(2PO)~ x~(2Pi) Xb(2P2) (xb(2P)~

Measured

Ring

Ref.

OCDb

Power lawc

9459.7 ±0.6 10013±10 10020 ±2 10351 ±2 10578 ±5 10234 ±7 10251 ±6 10266 ±5 10258 ±5

VEPP4 DORIS CESR CESR CESR CESR CESR CESR

60 19,20,26 34, 35 34, 35 36, 37 58, 59 58, 59 58, 59

(9460) (10020)

(9460) (10025)

10350 10520 10209 10241 10265 10251

(10360) 10600

10242

Masses in parentheses are not predictions, but theoretical input. Buchmüller et al. [68]. C Martin [70]. d The energy scale is that established by the VEPP4 [60]measurement of the Y(1S) mass. Measurements from other laboratories are scaled to agree with VEPP4 at the Y(1S). ‘The triplet .Yb(2P) states are tentatively labeled in the spectroscopic notation 2P 1 with the masses increasing with .1, as in the cë system. There is, however, no direct experimental evidence for the L and J assignments in the bb system. denotes center of gravity, that is, (M) = (M0 + 3M, + 5M2)/9.

154

K. Berkelman, Upsilon spectroscopy at CESR

0.Ol

0.05 O.l

0.5 l.O

r[fm}

Fig. 4. The radial dependence of various quarkonium potentials: (1) Martin [701, (2) Buchmüller et al. [681,(3) Bhanot and Rudaz [631,(4) Eichten et al. [621.States of the i/i and Y systems are indicated at their r.m.s. radii. -

nearly the same, and the behavior is neither Coulombic nor linear but nearly logarithmic. In fact, a completely empirical power law potential [69,70], V = A + Bra, with a small power n, fits the mass data as well as any of the more sophisticated potentials (table 1). It is clear then that the i/i and V mass measurements are not sensitive to the small-distance singular part of the potential derivable from perturbative QCD or even to the large-distance linear part. However, it cannot be an accident that a smooth interpolation between -the small-distance --behavior fixed--by OCD, with--the-- value--of A --derived from other phenomena, and the large-distance linear behavior fixed by Regge trajectories predicts the correct mass differences with no more adjustable input than the quark masses. Even if we cannot count it as a crucial test of QCD or make a definitive determination of A, this must still be considered a very successful consistency check. Indeed, independent of any particular potential model, we have learned that the q~binding is flavor independent, and that the use of a nonrelativistic potential is justified. Using the RBGT wave functions we have (v21c2) = 0.23 in the tJi and 0.077 in the V [68]. 3.2. Cross section measurements When we measure the beam energy dependence of the e~e cross section in the vicinity of a resonance, we can determine not only the mass of the state but also the strength of its coupling to the e~e channel. The measured hadronic e~e cross section at a given beam energy is

where N is the observed number of hadronic event candidates, B is the background, e is the event acceptance, and L is the time-integrated beam luminosity f ~ di. The integrated luminosity L is measured at CESR, as at all e~e rings, by observing small-angle Bhabha scattering and using the known QED cross section. The calibration of the small-angle monitors, which is very sensitive to alignment of the beam and counters, is checked by comparing with the Value of L from the large-angle Bhabha scattering in the main detector. The latter measurement is much less sensitive to alignment but suffers too much from low counting statistics to be useful for short term monitoring. In CLEO the small-angle Bhabha monitor covers the angular range 39 to 70 mrad. The large-angle comparison is made independently in two angular ranges, 13 to 29° and 55 to 90°.All

-

K. Berkelman, Upsilon spectroscopy at CESR

900

155

BHABHA ANGULAR DIST. IN OCTANT SHOWER COUNTERS

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200

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100

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luminosity measurements are consistent within ±3%r.m.s., from which we estimate a ±3.5%systematic error in L after radiative corrections. The CUSB measurement is similar. Fig. 5 shows an angular distribution of Bhabha events in the CLEO detector compared with the QED prediction. The acceptance e and the background contributions B both depend on the hardware trigger requirements and on the off-line event selection criteria. One adjusts them to keep the background contamination at or below 3%, but at the cost of some loss (20 to 40%) in efficiency for detecting and recognizing good events. The great majority of events which produce particles traversing a detector are cosmic rays, beam-gas collisions and beam-wall collisions. The hardware trigger prevents most such events from being recorded by requiring a minimum number of charged tracks or a minimum electromagnetic shower energy. The off-line analysis recognizes and rejects most of the surviving background, by refining the multiplicity and visible energy cuts, and by imposing conditions on the primary vertex position. At this stage one also eliminates most of the background from QED process (e~ee~e, js~, r~r, e~ey,~ etc.) and the two-photon collision processes (e~e-~e~eX). We estimate the remaining background B (a) by examining various distributions, such as visible energy and longitudinal vertex position, (b) by scanning events displayed pictorially, and (c) by simulating background data (QED and two-photon, for instance) to check the probability of passing the hadronic annihilation criteria. For measurements in the continuum away from the upsilon resonances BIN is 3±2%in the CLEO data and 1 to 5% in the CUSB data. Since none of the backgrounds have a rapid dependence on the beam energy, they do not contribute to the height of the peaks in the measurement of o-(W) versus W. To estimate the acceptance e for good events, including effects of geometric losses, trigger inefficiencies, and off-line selection losses, we use a Monte Carlo simulation of particle production and passage through the detector. The detailed specifications of the detector and the known interactions of particles in matter are used to generate raw data as realistically as possible. We pass these fake data through the same analysis chain with all of the selection criteria used for the real data, to determine directly the acceptance e. For any detector the result for e is rather insensitive to beam energy, but does

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K. Berkelman, Upsilon speciroscopy at CESR

depend on such characteristics of the primary interaction as multiplicity and sphericity, e varying typically between 60 and 80%. The uncertainties in the physics model used to generate the primary events contributes a systematic error of about ±4%in Perturbative QCD makes a definite prediction for the total cross section for hadronic final states at an energy away from resonances and far above the nearest lower flavor threshold [71]. Expressed in terms of the ratio R. = Uhad/O~ it is (in the th~scheme) ~.

(2) q~)[1 + a5/ir + 1.5(a~/17)2+ between the cë and bb thresholds. For each flavor and color of q~produced there is a term proportional to the quark charge squared (in units of e). The terms of higher order in the strong coupling a~ represent the effects of gluons. The coupling a~depends on energy W and the QCD scale constant A according to eq. (1), in next-to-leading order. A value of A near 120 MeV (see section 6.2) would imply a 5(10.5 GeV) = 0.14 and R(1O.5 GeV) = 3.49. In order to compare the measured cross section with the theoretical prediction, one has to correct the data for radiative effects. First, one subtracts the effect of initial state radiation followed by production of a nearby resonance of lower energy (see section 3.3). Then one corrects the nonresonant cross section for the presence of real and virtual radiation. If we assume the nonresonant cross section has an 2, the correction factorthat is approximately energy dependence proportional to W 1 + 6 = fTmeas/Ocorr = [z~W/(W/2 L~W)]2’ + 8~, R

=

..

3(q~+ q~+ q~+

—

where t=(a/rr)(ln W2/m~—1)0.044, 8o = (2a/17) [13(lnW2/m ~ 1)/12 + —

(3) 172/6

—

17/36],

(4)

and ~ W is the largest radiated energy loss which will still allow the event to be accepted as a hadronic final state. For W = 10 GeV and ~ W 2.5 GeV the correction factor 1+ 8 is 0.90. In the actual data reduction a more sophisticated correction procedure is used [72], but the results are about the same. The radiative correction introduces a systematic uncertainty of about 1% in the experimental results. Table 2 shows the corrected experimental values of R near 10 GeV obtained at DORIS and CESR. The uncertainties are predominantly systematic and probably account for the spread in results among -

Table 2 Measurements of R = ~ in the continuum between 9 GeV and the BB threshold W, GeV

R

Expt.

Ref.

9.4 9.5 9.4 9.1—9.5 10.4 10.4

3.67±0.23±0.29 3.73±0.16±0.28 3.8±0.7 3.34±0.09±0.18 3.63±0.06±0.37 3.77±0.06±0.26

PLUTO DASP 11 DESY—Heid. LENA CUSB CLEO

73 74 26 75 76, 77 38

K. Berkelman, Upsilon speciroscopy at CESR

157

the various experiments. It will be difficult to reduce the errors significantly. Furthermore, the accuracy of the mean of the measurements is probably not much better than the quoted accuracy of any one result. The measurements are consistent with the QCD expectation. 3.3. Dilepton widths Fee In the absence of radiation the cross section for e~e annihilation into a final state f in the neighborhood of a resonance at c.m. energy W = M has the Breit—Wigner form o1(W) = (3irIM2) FeeFtI[( W M)2 + (1/2)21, —

with F, Fee and F~denoting the total decay width and the width into the e~e and I channels, respectively. In the case of the first three upsilon states the total width F is much less than the Gaussian r.m.s. spread 6W in c.m. collision energies in the storage ring, so that it is not directly observable. The peak area, however, is unaffected by the energy spreading and is given by the integral

J

o~(W)dW= (6 2/W) 17

Radiative effects add a long tail extending to higher W and depress the value of the integral, depending on the range of integration. The observed integral under the peak, up to a c.m. energy ~sW above the resonance, is related to the idealized integral without radiation by the approximate formula [78]

AObJAth

=

(2i~W/M)2’

(1 + ~W/2M)2’ + 8~,

where t and 8~are given by eqs. (3) and (4). Taking ~ W = 30 MeV and M = 10 GeV we have A 0b5/Ath 0.74 (a more accurate procedure is actually used to correct the data). For any given beam energy resolution 6W the combined effect of beam energy spreading and radiative tail is a known functional form [79]. We take the final state channels f to include all except thepractice, lepton pair 0had• In one channels makes a eke, ~s~t and T~1-; and we will call the corresponding cross section ~~1ëãst squares fit to ö~ad(W)vë ü~ 7iff~t Vi~h~iIO1 Off~fi~tf~Cti~ best firv~Iiiesfor M;~FeeFhad/F, ~nonres and 6 W. Since F = 3Fee + j’had, we substitute 1 3Bee (where Bee = Fee/F is the e~e branching ratio of the resonance) for Fhad/F in the above expression for f 0~hadd W. In order to extract ~ from the measured cross section integral, one then has to know Bee; but if Bee is small, one does not need to know it very accurately. The dominant errors in Fee are systematic and come from the errors in e (±4%)and L (±3.5%) in the formula for the measured cross section and from the radiative correction (±1%).Their combined effect is a systematic uncertainty of about ±6% for the narrow upsilon resonances. Most systematic effects cancel however in the ratios of Fee for different upsilon states. The DORIS and CESR data are compared in table 3. The vanRoyen—Weisskopf prediction [82] with the lowest-order QCD correction [83]is —

Fee =

(16a2q~/1~4’2) 1i4,(0)12 (1

—

16a~/317)

(5)

158

K. Berkelman, Upsilon spectroscopy at CESR Table 3 Measured and predicted dilepton widths in keV State

F,,

Expt.

Ref.

Y(IS)

1.33±0.14 1.35±0.11±0.22 1.23±0.10±0.14 1.14±0.05±0.10 1.30±0.05±0.08 1.22±0.06 0.61±0.11±0.11 0.53±0.07±0.06 0.50±0.03±0.03 0.52±0.03±0.04 0.52±0.03

PLUTO DASP 11 LENA CUSB CLEO average DASP 11 LENA CUSB CLEO average

21 23 28 53, 77 38

0.35 ±0.03 ±0.04 0.42±0.04±0.03 0.38 ±0.03 0.21 ±0.05 ±0.04 0.32±0.03±0.05 0.27±0.04

CUSB CLEO average CUSB CLEO average

35, 77 38

Y(2S)

Y(35) -

I1~4S)

OCD

Power law

1.15’ 80 29 53,77 38 052b

0.49’

037b

0.32’

0.30k

0.23’

76, 77 38

Voloshin and Zacharov [81]. Obtained from the Y(1S) prediction using ratios from Buchmüller et al. [68]. Obtained from the Y(1S) prediction using ratios from Martin [70].

in terms of the bb wave function at zero separation. This provides another test of the nonrelativistic quarkonium models, more sensitive to the short-distance behavior of the potential. The QCD-inspired RBGT potential [68]does quite well for the V(1S), and even for the ~‘, where the effect of the QCD correction is rather large. Nonsingular potentials, such as A + Br~[70] tend to give lower values for 19!40)12 and hence Fee. The ratios for higher states seem to be rather insentive to the QCD correction; that is, all models which successfully fit the masses give about the same predictions for the I ‘cc ratios. Probably the most reliable theoretical prediction for the dilepton width of the Y(1S) is based on QCD sum rules [84].One writes an energy moment of Rb(s), the bb contribution to O~had/~~,as both an asymptotic prediction from perturbative QCD and as an integral over bound states and continuum:

J

Rb(s) s’~ ds = A~3q~I(4m~)” 2 [F~~(1S)/M~÷t+ Fee(2S)/.M~r1+ F~~(3S)/~~ + =

917a

J

Rb(s)

s~ ds]

2M(B)

-

A~is a calculable constant depending on n and a 5. For large enough n the V(1S) contribution saturates the sum. Setting the right hand sides equal for both n = 3 and n 4, we can eliminate-the dependenc on the quark mass m~and solve for F~~(1S). The most recent result [811gives Fee(1S) 1.15±0.2OkeV, in good agreement with the data.

K. Berkelman, Upsilon spectroscopy at CESR

159

It should be noted that the agreement between theory and experiment confirms the b-quark charge assignment l~bI= If the b were an up-quark, Fee would be four times larger [66]. ~.

4. Upsilon decay observations 4.1. Evidence for the decay of the V(1S) into three gluons The only energetically allowed hadronic decay of the Y(1S) requires the b and the b to annihilate into lighter quarks. In QCD this must proceed through a three-gluon intermediate state. If the matrix element were to favor the case in which the three gluon directions are well separated the “Mercedes star” configuration—and if the transverse momenta of the hadrons produced in the fragmentation of each of the gluons were not too large, then one would be able to see three hadron jets in the V(1S) final states. Unfortunately, the two conditions are not well satisfied for the Y(1S) it is even worse for the ~!i. One must search for subtle effects in the distribution of events with respect to various measures of the event shape. For example, one defines a “thrust axis” [85] for each event by finding the direction in space along which the sum over all produced particles of the longitudinal momentum component magnitude is maximized. The “thrust” for the event is defined as —

—

Thrust = max ~ lPLI/~p1. Nonresonant q4 two-jet events have high thrust, with a distribution smeared by the fragmentation process and peaking (for W = 10 GeV) at Thrust = 0.90. This expected distribution is followed very closely by the nonresonant continuum events (fig. 6). An isotropic phase space production mechanism would have a thrust distribution peaked significantly lower, at 0.70. As the PLUTO group at DORIS

5.4

•o T(IS)—DIRECT CONTINUUM 0.4Gev -

PHASE SPACE

~\

~

~/~/ \\s \\\\ \•\~~ \~

I,11.1/s,” ~ ,,/‘~

—lz 3.0 .2 .550

.650

.750 THRUST

~.

.850

.950

Fig. 6. Thrust distributions for Y(1S) direct decays and nonresonant continuum events measured by CLEO [86], compared with Monte Carlo simulations.

-

160

K. Berkelman,-Upsilon spectroscopy atCESR

[24] first showed, the thrust distribution from direct V(1S) decays (with the appropriately weighted subtraction of the distribution for continuum background and photon-mediated q~decays of the V) is intermediate and distinct from both extremes, peaking at about 0.75, rather similar to the distribution expected for three gluon jets, provided one assumes that gluon fragmentation is similar to quark fragmentation. The more recent and extensive CLEO data [86] now permit a more precise statement. The thrust distribution from direct V(1S) decays (fig. 6) matches alinear combinat onof 75%~three-gluonand-25% phase-space theoretical distributions. The 25% phase space preferred by the data may be accounted for by an admixture of decays proceeding through four or more gluons, or by the possibility that a gluon jet may spread over a larger cone angle than a quark jet of the same energy, or by other shortcomings of the simulation of the three-gluon process. For each event one can also define three jet axes by finding the three directions in space for which the sum over all produced particles of the momentum projected on the nearest axis is maximized [87]. This gives the “triplicity”, defined as -

Triplicity = max ~ I~proil/~ p1. Because of overall momentum conservation, the three axes tend to lie in a plane, called the event plane. Again, as the PLUTO group [24] first showed, the triplicity distribution of direct V(1S) decays is intermediate between a phase-space distribution and a two-jet distribution, as expected for a decay through three gluons. The same is true for other measures of event shape: sphericity, planarity, jet fractional energies, jet separation angles, etc. Table 4 Measured and predicted coefficients a forplane polarnormal angle distributions of 2 0) and event (1 + aN cos2 13) the thrust axis (1 + aT cos in Y(1S) direct decay and in continuum events

Y(1S) direct QCD, vector gluons’ QCD, scalar gluon? Phase space PLUTOb LENA’ CLEO’1 Continuum, W = 10.5 GeV Theory’t CLEOd

aT

aN

0.39 —1.00 0 0.83 ±0.23 0.7 ±0.3 0.32±0.11

—0.33 1.00 0

0.83±0.03 0.78±0.11

—0.25±0.05 —0.30±0.04 —0.21±0.04

‘Koller and Walsh [88]. Berger et al. (PLUTO) [24]. ‘Niczyporuk et al. (LENA) [31]. Cabenda (CLEO) [86]. In order to make comparisons with PLUTO and LENA results, we show the coefficients obtained in the same way; that is, by making a model-dependent correction to the data so that the jet directions refer to the original gluon or quark directions. The coefficients for the observed directions, defined by the thrust and triplicity of the charged hadrons, compared with their QCD-plus-fragmentation predictions are given in this reference.

-

K. Berkelman, Upsilon spectroscopy as CESR

161

36C T(ISl~Direcl

2.40

T(ISl-Direct

o observed • acceptance corrected

(a)

(b)

I 80

I.20~

8 Do D

0

8

____________ III II

____________

I

360

It

III

Continuum

Continuum

(c)

(d)

I

—I z 240

.80

.20 0 0

o p 0

____________

0

.30

0

___________

50

70

90

.10

.30

Cos9

.50

.70

.90

Cos~

Fig. 7. Angular distributions for the thrust axis (a and c) and the event plane normal (b and d) in Y(IS) decays (a and b) and in nonresonant continuum events (c and d). Data are from CLEO [86].The curve shows the OCD prediction [88]including the effect of fragmentation.

~N

VS. q~

8 ~\—OGLUONS

AT(IS) DIRECT •CONTINUUM 10.4 GeV

.6 -4 2

—.6 —.8

~

~GLUONS 7-OGLUONS 0.0 aT

i

.~

.~

.~

2 0 and 1 + aN cos2 13 of the thrust axis and Fig. 8.plane event Predicted normal. [881and The solid measured curve results [86]coefficients from a uniform a~anddistribution aN in the of angular the plane distributions normal around I + aT the cos axis determining aT.

162

K. Berkelman, Upsilon speciroscopy at CESR

QCD makes two predictions for the orientation of the gluon directions with respect to the e~ebeam First, the direction of the most energetic gluon, essentially the thrust axis of the event, should have the polar angle distribution 1 + 0.39 cos2 0 with respect to the beam axis. And second, the normal to the event plane should have the polar angle distribution 1 0.33 cos2 /3. Table 4 shows the experimental values. The most accurate results, from CLEO (figs. 7, 8), are marginally consistent with the predictions of QCD with vector gluons, and rule out completely spin-zero gluons. While it is clear that the QCD three-gluon decay is the only theoretically motivated model which can explain the event topologies in direct Y(1S) decays, there is still no way to convince a skeptic that we have seen direct evidence for three gluons. For example, one could imagine a model in which the Y decayed about half the time into two jets and the rest of the time according to a phase-space distribution. All of the experimental event shape spectra—thrust, triplicity, and so on—could be reproduced by such a model. Even the measured coefficients in the angular distributions of the thrust axis and the event plane normal (fig. 8) are close to the values one would get from mixed two-jet and phase-space events, in which the event plane is determined merely by fluctuations in the fragmentation process. Such a model, of course, while consistent with the data, has no theoretical basis whatever. [88].

—

4.2. Inclusive V(1S) decays If the V(1S) decays predominantly into three gluons, and nonresonant annihilations occur primarily through quark—antiquark pairs, we can look for differences between gluon jets and quark jets by comparing V(1S) and nonresonant final states. Table 5 shows the results from CESR for the mean charged multiplicity flch in e~e hadrons as a function of center-of-mass energy W = Vs. In every case the observed distribution of number of charged particles per event has been corrected for inefficiencies and geometric aperture losses using Monte Carlo simulations of the production process and the performance of the detector. Uncertainties in the Monte Carlo assumptions are in fact the dominant source of experimental error. In the continuum the increase with energy of the multiplicity can be fit with any of a number of functional forms (with s in GeV): —~

flch =

1.73 s°35

[90],

,i~=2.0+0.2lns+0.18(lns)2 flch =

2.0 + 0.027 exp(1.9Vln s/0.32)

[91], -

[92,93].

Table 5 Measured mean ch4rged multiplicities. corrected for efficienctes~ State

fl~h

Y(IS) Y(2S) Y(3S)

9.79±0.04±0.50 1f).36 ±0.06 ±(1.50 9.92 ±0.08 ±0.50 11.75 ±0.21±0.30 10.17±0.05±0.50 8.26±0.03±0.40

Y(4S)

Y(lS), direct” Continuum, W

10.4GeV

Plunkett [38]and Perchonok [89](CLEO). Electromagnetic decays into dileptons and q~are subtracted. a

K. Berkelman, Upsilon speciroscopy at CESR

163

Mutriplicities observed on the upsilon resonances are always higher than in the nearby continuum. In order to remove the dependence on the storage ring energy resolution, we have to correct for the continuum background present in the event sample observed on resonance. It is also customary to remove at the same time the contribution of the q~upsilon decays through the virtual photon, since these final states should have the same character as the continuum background. The remainder of the upsilon decays are called “upsilon direct”. That is, we assume that flpk Upk =

11cont fT~ 0nt+

+ t~Y,dir

~ RB,~,J(1 ~ u~0~~) [1 (3 + R) B~]/(1 3B~)

iicont (O~pk—

(°~pk—

—

—

—

and solve for ñ Y,dir, given the measured values for cTPk, 0~cont, flpk, ~ R and B~.In order to compare the multiplicities in gluon and quark jets, we plot in fig. 9 the dependence of the mean multiplicity per jet flch/Njet on the mean jet energy WiNjet. We take ‘~~et= 2 for the q~continuum and Njet = 3 for the Y(1S) direct decays. The Y(25) and Y(3S) direct decays cannot be so3Peasily3Pcharacterized, since the cascade decays to3Plower bb states can result in either two jets (via ~50 0 or 2, for instance) or three jets ~ tp5 or 1). The Y(4S), which decays into BB, will not be discussed here. Comparing the continuum and Y(1S) data at the same mean energy per jet (3.2 GeV), we see that the gluon jets from the Y(1S) may have somewhat higher mean charged multiplicity than quark jets produced in the continuum. There are at least two reasons why one might expect a fragmenting gluon to produce more hadrons than a fragmenting quark. First, a gluon has to begin hadronization by turning into a q~pair (or a gluon pair), thus behaving perhaps as two jets. Secondly, the three-gluon non-Abelian coupling strength is 9/4 times as strong as the qqg coupling, so that gluon emission should be more frequent for gluons than for quarks. It might be interesting to compare the detailed shapes of the quark and gluon multiplicity distributions, or at least the dispersions, DCh = (fl~h~ 11th). There is no clean way to do this at fixed energy per jet, however. The three gluons in upsilon decay can share the energy in various ways, each taking anywhere between zero and 50% of the upsilon mass, and the jets do not separate well enough in most events to allow a measurement of the energy of each jet. Requiring cleanly separated jets would bias the multiplicity distributions. ‘‘‘I

I

‘‘I’’’

I

ADONE

T(IS)dIrect-~ ~

j

2~

—

z -c 4’

7’

~T(4S)— B8 norileptonic

—

I

a

NjetS

-

...

I

0.5

2 W/N jet

5 10 Energy per jet, in 0eV

20

Fig. 9. Mean charged multiplicity per jet as afunction of total energy W per jet [38.93].All data are from the q~continuum, plotted with Njat = 2, except as noted otherwise.

K. Berkelman, Upsilon spectroscopy at CESR

164.

IOC

.

0

OTASSO W’ 14GeV W’22GeV W’34GeV • CLEO W’ 0.5GeV

I.

-

T(IS)direct

(a

I

a

•

£

ST.

••4~ -

b

1aa

0.1

4 4 4

0.01

0

0.1

0.2

0.3

a

0.4 a

0.5

0.6

0.7

0.8

2p/W

Fig. 10. CLEOdata [48]for s doidx,,, from Y(1S) decays and from nonresonant continuum events, compared with continuum data from TASSO[94].The Y(1S) data are arbitrarily normalized, since the magnitude of the observed peak cross section contains a factor which depends on the storage ring energy resolution.

For the same reason, there is not much to be learned from comparing the inclusive charged particle momentum spectra for the continuum q~events and the Y(1S)-direct ggg events that is not already implied by the charged multiplicities and the number of jets per event. For the record, however, we show in fig. 10 the CLEO data [48] for (i/o-) doidx~,with x~,= 2p/ W, for all charged particles from Y(1S)-direct decays, compared with nearby continuum events. Since the mean multiplicity per event is higher for the upsilon, the momentum spectrum is somewhat softer, fitting a form exp(—11.6x~)instead of the exp(—8.9x~)characteristic of the continuum. In the CLEO detector charged kaons and protons (or antiprotons) are identified by time of flight in scintillation counters (fig. 11) or by ionization dE/dx in multiwire proportional chambers (fig. 12), provided the momenta are high enough to penetrate the solenoid coil and low enough to have distinguishable velocities. A neutral kaon or lambda (or antilambda) appears in the tracking chamber as a pair of charged particles forming a separate vertex (see fig. 13, for example). The identification is made by reconstructing the invariant mass (fig. 14). Other unstable particles, such as p°,K*, ~, D and D* appear as peaks in the spectrum of reconstructed invariant masses (see fig. 15, for example). 20C

I

I

‘a

lOG

I

I

I

I

I

60

_________

(b

~

~/10.iP10GeV

O

.250 .500 .750 1.00 MASS(GeV)

~ig ll.--.gaw-C O--mis~-epeeta-derived-fron~ ttn~e“t fhg!~k~ for energy losses along with particle trajectories. -

1.25

0

0.30 0.60 0.90 1.20 1.50 MASS(GeV)

-[331-~t’~ mt~e~t~ rv~’ges.“~-p~~” ~ -

-

‘~“~

K. Berkelman, Upsilon spectroscopy at CESR

ir 1600

K

165

p

-

U,

~l200 -

-

-

I I-)

--

,..

~600

a

-

---

-

.

a

~

a-

--,-

-

e4~~

111111111

0.1

0.2

I

I

I

0.5 .0 2.0 DRIFT CHAMBER MOMENTUM

I

1111

5.0

Fig. 12. Observed ionization versus momentum for particles traversing the CLEO dE/dx proportional wire chambers [33].

/~~‘\ /1

\

/

~_c

yc~

Fig. 13. End view display of the CLEO main drift chamber and inner proportional chamber showing hit wires and reconstructed tracks for a typical Y(1S) decay [33].Tracks 2 and 11 are KI secondaries, and tracks 4 and 5 come from a A. Track 12 apparently scattered in the beam pipe.

Table 6 shows CLEO data [48, 95] on the average numbers of various particle species per event in the upsilon decays and in the continuum. In addition to correcting the observed rates for detector efficiency and geometric acceptance, we have also applied model-dependent factors to compensate for the yields outside the momentum ranges in which the particles can be identified. The most striking difference between gluon and quark fragmentation seems to be the higher rate of baryons in the gluon fragmentation. The spectra in (s//3) do-/dx are shown in figs. 16—19.

166

K. Berkelman, Upsilon spectroscopy at CESR

46

b)T(is)

M~

Fig. 14. Invariant mass plots for reconstructed V°candidates

M,

7.p,GeV

from

Y(1S) decays in CLEO [42,48]: (a) Kl—a ir~ir,(b)

A —a

pir and

A—a

pirt

mmiii

1.60 1.80 2.00 2)2.20 2.40 Fig. - 15.Inv.ariantmass plotfor D9-v K,r~and D°-vK~,r candidaLesftomthed~caysoLcandidatD~(D~ MK,, (GeV/c ~D~~.andD~ CLEO data in the nonresonant continuum [95].In this plot the ratio z = ED/Ebam,, is restricted to z >0.7.

a

~ .ff

I

4

• CLEC o CLEO C lASSO a TASSO 0 MARK I 0 DASP

KtIIO.5 GeV) K°(IO.5G8V) Kt(12,3OGeV)

bI p,~ • CLEO (10.5 GeVI OTASSOU2,300.V) a DA$P(3.63.67GeV) ~ MARK 11(29GeV)

~~~T~fronL

(a2~~)

K0 130,33GeV)

-

K0 (6.8-7.6GeV) Kt(3.6-3.67GeVI

-

1% -

~i

0.01

--

O

0.2

0.4 • 0.6 X~2E/W

0.8

•

0

0.2

0.4 0.6 X~2E/W

0.8

Fig. 16. Inclusive (a) kaon and (b) antiproton energy spectra from CLEO [48]produced in the nonresonant Continuum near W = 10 GeV, compared with continuum data at other energies [93].

167

Table 6 Measured mean particle multiplicities per event, corrected for acceptancea Particle

Y(1S)

Y(3S)

Y(45)

Continuum

0.95±0.04 1.02±0.07 0.66±0.26 0.35±0.16 0.12±0.05

0.93±0.05

1.58±0.13

0.90±0.04

K°,K° K*± K*o, K*O

0.84±0.09

1.24±0.21

0.89±0.04

0.55±0.11

0.56±0.11

0.55±0.15

0.27±0.07 0.08±0.02

0.38±0.13 0.09±0.04

0.55 ±0.05

0.59 ±0.05 0.15±0.03

0.45 ±0.02 0.01±0.06

0.43±0.13 0.11±0.04 0.4±0.2 0.21 ±0.15 0.08±0.01

p,p(=2 x ~) jl,A a

0.25±0.03

Andrews et al. [48]and Bebek et al. [95](CLEO). a)

T(IS)

b)

CONTINUUM

•A

•

It

K° 2~ K±

0

x2~

0

II 0

(‘4—

C

0.01

0

I

I

~

I

0.2

0.4

0.6

0.8

-

-

-

-

-

___________

0

__________________________

0.2

0.4

X~2E/W

0.6

0.8

Xa2E/W

Fig. 17. Inclusive energy spectra from CLEO [48]for A, K°,~ and K~from (a) the Y(1S) and (b) the nearby nonresonant continuum. I

I

•D**THIS EXPT., 10 6eV 05

b~ I DID 01

~

AD° MARK I,

7GeV

oD~MARK I,

~

0.1

0

2

3

p(GeV/c) Fig. 18. Comparison of K° and K** inclusive momentum spectra, measured by CLEO [48]in the 10 GeV nonresonant continuum.

0.2

0.4

0.6

~2E

0.8

1.0

w Fig. 19. Inclusive energy spectrum of D*±measured by CLEO in the nonresonant continuum near W = 10 GeV [95],compared with Mark I D data [96].

K. Berkelman, Upsilon spectroscopy at CESR

168

4.3. Branching ratios for dilepton pair decay: e~e,~

r~4~r

Once one knows Fee from the integral over the peak in the hadronic cross section, a measurement of Bee, the decay branching ratio of the upsilon state into eke, can be used to calculate the total decay

width ot the state, F~T~/B~. Fortunately, the-~e~and

-lIiiat states are the~easiest~Dnes~toidentify experimentally. There is a background, however, from nonresonant QED lepton pairs, which cannot be distinguished event by event, but must be determined by comparing rates on and off the resonance peak. In principle, as long as one has confidence in the QED lepton pair cross section, one needs not to measure the nonresonant rate; but in practice such a measurement is an important check on the detection efficiency and rejection of cosmic ray background. The cross section for muon pair decays of an upsilon state, measured at the peak of the resonance, is -

=

o-h°~dB,~/(i — 3B~),

which in practice is a few percent of the hadronic peak cross section. The QED background is QED_

o-,~

COfltJD

—o-~, 0dI1~,

which is about 1/4 of the hadronic continuum cross section. So compared to the measurement of hadron yields, not only are the muon pair rates much lower, but the signal-to-background ratio is much worse (0.8 for the Y(1S) to about 0.1 for the Y(3S)). For electron pairs the signal from upsilon decays should be the same as for muon pairs, but the QED electron pair background is nine times the QED muon pair rate at 0 = 90°and very much higher at smaller 0. So most of the upsilon decay measurements are based on the observation of muon pairs, and their accuracy is limited by counting statistics. Although tau pairs are more difficult to identify unambiguously, measurements of B,.,. have also been made [52]. Table 7 summarizes the direct measurements of Bee, Bk,. and B,.,. for the various Y states. There is no evidence for violation of e-~i-runiversality, so we will henceforth assume that Bee = Bp..~= B,.,. and will represent any one of the three lepton pair branching ratios by B~. Table 7 Measured dilepton branching ratios, in % State

Decay

Y(IS)

e*e_

Y(2S)

av. ~

Y(3S)

~i~s

DORIS av. 5.1 ±3.0c 3.0±0.9’~

<3.6

CLEO

CUSBb

av.

2.7±0.3±0.3 3.4±0.8 3.4±0.5±0.5

3.1±0.7

5.1 ±0.7 2.8±0.3

2.5±1.5

3.4±0.7 3.0 ±0.3 1.9±1.4 2.9±1.0

1.9±1.3±0.5 3.3±1.3±0.7

• Andrews et al. [51],Giles et al. [52],Mueller et al. [54](CLEO). Lee-Franzini (CUSB) [50]. Berger et al. (PLUTO) [22]. Niczyporuk et al. (LENA) [28]. Derived from B[Y(2S)—a ,r~1r Y(1S), Y(1S)—a t~1t]/B[Y(2S)—air~r Y(1S)].

K. Berkelman, Upsilon spectroscopy at CESR

169

5. Measurement of transitions 5.1. Branching ratios for hadronic cascade decay: Y,

Yf + hadrons

—*

If we assume isospin conservation, the transition Y,

Y1 + hadrons (fig. 20) with the lowest threshold in the mass difference M1 Mf is the dipion transition Y, irii~Y1,having a threshold of about 2m,. = 270 MeV (ignoring recoil). For mass differences above about 549 MeV the transition Y~—~ 77Y~ should also be possible. The decay sequence Y, ir~ir~Y~,followed by Y1 e~ e or ~ is an easily identified four-track event in any detector (fig. 21). All three transitions i f have been observed [30, 53—56]: Y(2S)—* Y(1S), Y(3S)—a Y(1S) and Y(3S)—~Y(2S), usually with both and Y1~e~e(see table 8). The measured product of the two branching ratios ~ however, is always rather small, so the accuracy is limited by statistics. Furthermore, the determination of B1,~alone involves dividing by B1~,which is also not very accurately known. CLEO [54, 56] has measured the Y(2S)—* Y(iS) and Y(3S)—* Y(1S) dipion branching ratios without any requirement on the Y(iS) decay, observing the M~peak in the spectrum of masses recoiling against all combinations of opposite-sign pions in Y(2S or 3S)-4 ir~irX (fig. 22). In spite of the large background of pions from the Y(iS) decays, the high rates make it a good measurement of the branching ratio B~,1,independent of B1,,~.In fact, one can then derive from the measurements of B1,1 —*

—

—*

—*

—*

-

—~

~

MeV 3S 900

3

\

800

2iP~~.~~T2

“~\

5.o±u.o

2~5P_~~/

700

-7::---

600 23S

B~~I.e±I.o

2’S

\‘/ ,../\/ ~

500

~“{~

~

400

\

\

/

-..~--—.

\

\

\\

/i,/~~/

~, / / ~

t30.2t3.9)

/

300

/ / // //

//‘/

200

/ // 1/

/

II, II

/

/

/

// / /

/

/

/ /

/

J/~’ 1/

too / I, /,//// / ///.~2/ 0

t3S e~qa3.3±0.5

I’S

—2,r ———

-100

Fig. 20. Spectroscopy of upsilon states, showing hadronic (2ir) and radiative (y) transitions.

170

K. Berkelman, Upsilon spectroscopy at CESR

Fig. 21. Examples from CLEO [54]of Y(2S)—a iT~ir Y(1S), followed by (a) Y(1S)—a~i~.C or (b) Y(1S)—ae~e~.

Table 8 Measured 1r~iT transition branching ratios in %, with and without observation of the dimuon decay of the final-upsilon-state - iTir transition Y(25) -a ~

~T

Y(1S)

Quantity

Measurement

B,,,,B,~

0.61 ±0.26 LENA 0.63±0.13 CUSB 0.68±0.17 CLEO 0.64±0.10 average 26±13 LENA 19.1±3.1 CLEO 21.3 ±4.0 from B,,,,B~.with 20.1 ±2,4 average 0.14±0.03±0.02 CLEO 0.12±0.04 CUSB

B,,,.

Y(3S)—air~irY(1S)

Y(3S) -a

ir

Y(2S)

B,,,.B,~

Expt.

Ref. 30 53 54 30 54 B~=

3.0%

56 50

0.13±0.03 5.4±1.3±0.5

average

B,,,,

B,,,,B,. B,,,.

4.3 ±1.1 4.7 ±0.9 0.06 ±0.02 3.1±2.0

from B,,,,B,~with B~= 3.0% average CUSB 77 from B,,,,B~with B~= 1.9%

CLEO

56

and the product B1,1B1.~a value for B5,,~which can be compared with the values obtained directly from measurements taken on the Y(iS) resonance (see table 8). The agreement is excellent. If isospin is conserved, there should be half as many transitions as ir~n~. Thus the total branching ratio for Y1—~‘iri,-Y1 is 3/2 times the observed B1,1 for 1T~’~1~. The available Q for the Y(2S)—* ~Y(1S) decay is 559.5—548.8 = 10.7 MeV, much smaller than the 40.3 MeV available in the corresponding3=~(i’1/8, -+ ~i to transition. therefore phase space make the One ~Y/irirY ratio expects much smaller than suppression, by[97]. a relative factor no (py/p.,~) = 0.07 It is therefore surprise that the Y(2S)—s’ ~Y(iS) mode has not been seen. The M 3~ M2~mass difference is below threshold for the ~ transition. The Y(3S) ~Y(iS) decay, with a Q of 341.9 MeV, could be significant, but has so far not been seen. ~°~°

—

—~

K. Berkelman, Upsilon spectroscopy at CESR I

14

I

Ib)

I

I

I

I

I

I

I

~ 1 14~4~ ~t4~~1 1

‘0°c

:::

I

171

9000

6000

.

3000

200-

4 I

9.3

~11

Ill 9.4

I

I

[11

9.5

I

9.6

I

I

I

9.4

I

9.6

I

I

9.8

I

I

10.0

Missing Moss, in GeV

Fig. 22. (a) CLEO [54]spectrum of missing masses recoiling against ~ ir (points) or like-sign dipions (histogram) from Y(2S) decays. The curve is a fit to the Y(1S) missing mass peak plus background of random pairings. The dashed histogram shows the same plot for events in which the Y(1S) is seen to decay into e~e or ~ ~ -. (b) The same spectrum [56]for Y(3S) decays.

CLEO has searched at the Y(3S) in the dipion missing mass spectrum for the transition to the spin-singlet 11P 1 state: tP

Y(3S)—~ir~ir(1 1). No indication was seen near the mass expected from potential models; the 90% confidence upper limit on the branching fraction is 3% [48]. 5.2. Branching ratios for radiative decays: Y, YXb and Xb —~-yYf 3P,, states of the bb system form triplets of closely spaced levels. We label the states with the Thequantum number; that is, the triplet intermediate in mass between the Y(1S) and Y(2S) (see fig. radial 20) is xb(lPJ) and the one between the Y(2S) and Y(3S) is xb(2P 1) with J = 0, 1, 2. Because their charge conjugation quantum number, C= +1, is opposite to that of the photon, the Xb states cannot be produced directly in e~e~ collisions, but must be observed in the radiative of the higher Y 3P, statesdecays has been obtained bystates. three Evidence for the radiative transitions from the ~ states to the methods. —~

5.2.1. Two-jet excess The earliest indication [57] of radiative decays was rather indirect. We will discuss it in connection with the Y(2S)—* YXb(1P) example, but it applies as well to the Y(3S) decays. In lowest order in QCD a bb state will annihilate into two or three gluons, depending on whether J is even or odd. That is, we expect xb(lPo) —~gg, xb(lPl) -+ ggg and xb(1P 2) —~gg. We can divide all possible Y(2S) decay modes into two classes, three-jet decays and two-jet decays. The three-jet decays include the direct ggg and (depending on the detector) ggy decays, the dipion transitions to Y(1S) with the Y(1S) decaying

172

K. Berkelman, Upsilon spectroscopy at CESR

through ggg or ggy, and the radiative decay to xb(1P1). The two-jet decays include the electromagnetic decays into q~via a virtual photon, the dipion transition to Y(1S) followed by Y(1S)—~q~, and the radiative decay to xb(lPo) or xb(1P 2).

As we saw in section 4.1, the shape of the thrust distributio of fl2S~decays s Sensitive to he proportion of two- and three-jet final states. The shape of the two-jet distribution is well known from q~ final states off the resonance. The three-jet spectrum is obtained from Y(1S) data after subtracting the known two-jet contribution. One corrects these sample thrust distributions for extra dipions or photons to represent the appropriate Y(2S)—~Y(1S) transitions, then fits the measured thrust distribution for all Y(2S) decays to a linear combination of two- and three-jet contributions, using the known q4 and dipion branching ratios and adjusting the branching ratio to yxb(lPo) and yxb(lP2) for best fit. CLEO [38] CUSB perfonned 2P)and cases, with[571 the have resultsboth as given in tablethis 9. thrust analysis for the Y(2S)—* yxb(lP) and Y(3S) yxb( -

—~

Table 9 Radiative transition measurements. Upper limits are 90% confidence limits CUSB

-

TWO-JET EXCESS BR

CLEOb

Y(2S)—ay~ 5(1Po.2)

BR Y(3S)—ayxb(1P02, 2P02) INCLUSIVE SINGLE PHOTONS E~ Y(3S)-a yx~(2Po) 2PI) E~ Y(35)_a YXb(2P2) Y(3S)—a YXb( BR Y(3S) -a YXb(2P0) BR Y(3S)-ay~s(2Pi) BR Y(3S)—ay~ 5(2P2) 2P0.I.2) BR Y(3S)—a yxb(lPo.1.2) )‘Xb( TWO-PHOTON CASCADE E~ Y(3S)—ayxs(2P 5) 2P2) Y(3S)-ayxb(2P1) E~ Y(35)_a yxb( ~ 1BR X BR Y(3S) — yxb(2PJ) —a yyY(2S) ~~BR X BR Y(3S)—a yXb(2Pj)—a yyY(1S) ~~BR X BR Y(35)—a VXb(IPJ)-a 77Y(1S) 2Po) BEST AVERAGES E~ Y(3S)-a Y(3S)—a vxb(2PI) yxb(

7±3 20±4

6±5%

22±5%

117±5±4 100 ±3 ±4 MeV MeV 85 ±2 ±4 MeV 7 ±4% 13±4% 33 13±4% ±3/a <5%

119±5±5 MeV 84±3±5 MeV 99±2±5MeV 5.9 ±2.1 3.6±1.2 <3 116±4MeV

4.8 ±4.0% 2.4±I.9a/,, 3.1 ±2.2%

100±3MeV

E 7 BR BR BR BR BR BR ~ 1BR X BR/~1BR ~1BR X BR/IIBR

2P0) Y(3S) —a yxe(2P2)

Y(3S)-a YXb( Y(35)—’yxa(2P,) Y(35)—a yXb(2P2) Y(3S)-a YXb(lPO.I.2) Y(3S)-a YXb(lPO,2)

857 ±23% MeV 13±3% 13 ±3% <5% 1 ±5%

Y(25)-. yxb(lPo.2)

7 ±3%

xs(2Po,i,s)-a yY(1S) x~(2Po,i~)-° yY(2S)

11±3%

16±6%

a Peterson et al. [57],Han et al. [58]and Eigen et al. [59](CUSB). Preliminary CUSB results [77] from recent Y(2S) running are not included. ~Plunkett [38],Andrews et al. [48](CLEO).

K. Berkelman, Upsilon spectroscopy at CESR

173

5.2.2. Single photon inclusive speclrum As was done in the case of 9!!’ 7.k’~one can look for peaks in the single photon inclusive spectrum Y1—s’ 7X, corresponding to X = Xb with J = 0, 1, 2. This method is more difficult for the upsilon decays —‘

than in the charmonium case, because the photon background from ir°decays is much higher and the overall rates are much lower. The CUSB detector, optimized for high-resolution photon detection, is suited for the search for the radiated photons in the inclusive y spectrum. The strongest evidence so far [58]comes from the single photon spectrum at the Y(3S) (flg.23a)/lTkeshape of the background spectrum, mainly from ~°dec~y.s, is known very well from the Y(1S) decays (fig. 23c), with an additional, calculable contribution from Y(3S).-* ir°ir°Y(1S).There2P),is but a clear excess over to theresolve background in the range it is not possible clearly the three 2P 75 to 125 MeV, as expected for Y(3S)—~yxb( 0, 2P1, 2P2 states. The photon energy resolution of the CUSB detector is measured at low energy by radioactive sources and at 5 GeV by Bhabha scattering events, and is checked at intermediate energies by noting the spread in observed mass of the reconstructed ~°‘s The observed enhancement in the Y(3S) photon spectrum around 100 MeV (fig. 24a) is definitely broader than the experimental resolution (7% r.m.s., 2500

11111111

11111111

300 I

111111111

2000

(0)

200

I

TIIIIII\

‘°°°

~

(bi

600

~

-

-

“400

~

0:

:: ~/~\ :

300 ~t20O a,

Ic)

Ic)

0:

~

100 PHOTON ENERGY (MeV)

Ib1

ioo

—

10

-

::

1000

Fig. 23. CUSB [58]inclusive photon spectra from (a) the Y(3S), (b) the continuum, and (c) the Y(1S).

10

100

1000

PHOTON ENERGY 1MeV)

Fig. 24. (a) CUSB (58] inclusive photon spectrum from the Y(3S) with smoothed background from ir°subtracted (see text). (b) The CUSB energy resolution function for 100 MeV photons. (c) The same spectrum as in (a), showing the fit to three peaks.

K. Berkelman, Upsilon spectroscopy at CESR

174

see fig. 24b), so that a single narrow line is ruled out. The fit to thr~e±~~ ilñAithrit4 degrees of freedom, while the fit to only two lines has x2 = 24 for 16 degrees of freedom. The three-line fit yields the energies and branching ratios given in table 9. The photons from the transition Y(3S)—* yxb(lP) expected around 400 MeV are not evident in the inclusive photon spectrum (fig. 23a). This implies an upper limit on the overall branching ratio of about At the time of this writing an extensive run has just been completed at the energy of the Y(2S). CUSB has reported [77] a preliminary analysis of their inclusive single photon spectrum, which shows evidence (figs. 25a,b) for the three peaks associated with the transitions to the 1P 0, 1P1, 1P2 states. The preliminary results are consistent with a xb(lP) center-of-gravity mass of 9906 MeV, fine structure ,rrT1vrI~

I

I

I

I

a

~ 1O24~

-

-

~

~iagno.

-

-

4~~II.

~76uo

1

I

10.

-

I

~O.

-

~56O.

b

I

I

I

I

I II

I

I

I~

100.

I

I I I

-

500.

plioroN

11)00.

ENEI~~

(14EV)

T1~~1IIII1

~48O. =

--

~4OO.

-

~320 -

240.

-

-

—160.

-

-

-

-

Ii 10.

~O.

100.

500.

11)00.

1-1-lOroN ENEPG’l

(14EV)

Fig. 25. (a) CUSB (771 inclusive photon spectrum from the Y(2S). (b) The same with a smoothed background (from s’°)subtracted.

K. Berkelman, Upsilon spectroscopy at CESR

175

splittings of M2 — M1 = 20 MeV and M1 ~ = 21 MeV, and a net branching ratio of 15 ±5% for the sum of the three transitions. Because of the preliminary nature of these results, they are not included in tables 1 and 9. —

5.2.3. Cascade radiative decays Again as in the case of charmonium, one can look for the two photons and two leptons from the chain of decays Y~-~YXb,

Y~-~t.

Xb~YYf,

The yield of events is proportional to the product of three branching ratios, generally each being smaller in the upsilon system than in charmonium. Even so, several such events have been seen by CUSB [591, corresponding to cascade decays of the Y(3S) to the Y(1S) and to the Y(2S) via the xb(2P). Fig. 26 shows two-dimensional plots of the energies of the two photons. The clustering of energies near 100 MeV for the lowest energy photon of the pair is evidence for the Y(3S) yxb(2P) decay, and the clustering of the higher energy photons near 460 and 780 MeV should correspond to the decays from the xb(2P) to the Y(2S) and Y(1S). The CUSB group has fit their data for the energies near 100 MeV to three peaks with their known resolution function, and obtain2PJ) the states. resultsSimilar shown data in table forbeen the have 9also energies and product branching ratios corresponding to three xb( obtained by CLEO [48]. The recent run at the Y(2S) resonance has also yielded preliminary results from CUSB [77] on the cascade decays Y(2S)—~yxb(1PJ)-4 yyY(1S)—t. y~g’~1’(see fig. 27). —~

900~~I

I

‘N

I

I

I

I

e~e~

~

700

I

I

I

e~e~e~e

-.

4~S~~6 I

100

I

.

I

300

I

I

500 EYLOW

I

00 (MeV)

I

I 300

I

I

500

Fig. 26. Scatter plot of lowest and highest energies for the two photons from the cascade decay Y(3S)—a yxb—a yy(e~eor ~ CUSB [59].

The data are from

176

K. Berkelman, Upsilon spectroscopy at CESR

12 -

e°e— yy(~)COMBINED -

ON T(2S)

60

80

100

20

40

160

E~(MeV)

Fig. 27. Preliminary CUSB data [77] on the energy spectrum of the lowest energy photon of the two from the cascade decay Y(2S)-a yXb-e

77Y(1S)

yy(e~e or

5.2.4. Summary of results from the three methods 2P) states, TheinCLEO data onand photon energies at and involving the xb(masses for given table 9,and are CUSB all consistent, are averaged thebranching bottom ofratios the table. The implied the xb(2P) triplet are given in table 1 along with the masses for the 3S 1 states. The center of gravity of the three states, weighted by 2J + 1, agrees with the predictions of the potential models about as well as 3S the masses of the 1 states do. 3P., triplet requires a theory of the spin dependence of understanding of the potential. fine structure in so thefar not been possible to derive one from first principles. theAn heavy quark—antiquark It has One popular approach is to assume the Coulomb-plus-linear potential model [62], V(r) = —4aJ3r + kr, with a one-gluon-exchange spin dependence for the Loulomb part, analogous to the- Breit—Fermi Hamiltonian in QED, plus a term for the linear part derived from the assumption that the interaction is scalar or that the confinement flux is purely electric. This gives -

~

2(L S) ajm2r3 — (L S) k/m2r + 4a~[3(s 2r3 1~ ~)(S2• t) s1 s2]13m 32ira. s 3(r)/9m2. 1 s2 6 There is some controversy over the sign of the confinement term (containing k). Eichten and Feinberg [98]use + instead of the — of BuchmUller [99].It makes very little numerical difference in the predicted fine st~ W~V~f~~rbb ably ~mportantnwuncertainties1w the choice of quark mass and effective a~value (for a more serious calculation, see ref. [100]).The observed 2P., splittings (table 1) tend to be smaller than most predictions. .

+

--

.

—

K. Berkelman, Upsilon spectroscopy at CESR

177

We will postpone the comparison of the measured radiative branching ratios with theory until we have derived the corresponding widths. 5.3. Implications for hadronic production

Although the three lowest upsilon 3S states were first reported in a Fermilab p + Be experiment [13], it has until recently not been possible to determine their relative production rates in hadronic collisions. They were detected as overlapping peaks above the Drell—Yan continuum in dimuon production, with fitted yield ratios for the Y(1S), Y(2S) and Y(3S) equal to 1, 0.31±0.03and 0.15±0.017[14]. To convert these ratios to ratios of production rates, one needs to use the ee data for the three dimuon decay branching ratios as well as the branching ratios for the higher upsilon states to decay into the lower states, either directly or via a Xb state. The situation is diagrammed in fig. 28. After some straightforward algebra the ratios of production yields in p + Be collisions are 0.6±0.4

for Y(2S)/Y(1S)

0.2±0.1

for Y(3S)/Y(1S).

and

Note that the yield for each state includes that via production of a higher non-1 state, such as Xb, followed by decay to the 1-- upsilon. So far we cannot distinguish such a process from direct upsilon production. The errors are large, dominated by the uncertainties in the dimuon branching ratios. The results suggest, however, that the higher upsilons may be produced with comparable cross sections relative to the lowest. -

p1. Be

3S)

~6:O.2

T(IS) .9%

/~/~ I

2.9%

,LL~L 0.31

O.I5

Fig. 28. Flow chart relating production of upsilon states in p + Be collisions to observed lepton pair rates in the Y(1S), Y(2S) and Y(3S) mass peaks. Data are from Fermilab [14]and CESR (table 9).

178

K. Berkelman, Upsilon speciroscopy at CESR

6. Derived results on upsilon decays and transitions 6.1. Indirectly measured branching ratios and widths We believe now that the important underlying dynamics of the decays of the upsilon states concerns the quarks, leptons, gluons and photons, and not so much the pions, kaons and other hadrons that one sees in the actual final states. If we are ever able to list all the partial widths for upsilon decays into exclusive meson states, it will most likely tell us mainly about soft fragmentation processes and rather little about fundamental interactions. Fortunately we can now give the rates for the important decay modes in terms of quarks, leptons, gluons, and photons. As we have seen in section 4.3, the branching ratios for decays into muon pairs and for transitions to lower upsilon states via dipion or photon emission can be measured directly, at least in principle. Branching ratios for electron and tau pairs follow from the assumption of lepton universality. The branching ratio for electromagnetic decay in a q~jpair via a virtual photon should be just RB,~,where R is the usual nonresonant q~to ,a~scross section ratio, provided only that we assume that the yq~vertex factorizes. We assume the CESR measured value for R below the bb threshold, that is, R = 3.7. For each upsilon bound state, Fee is the only decay width that can be measured directly (see section 3.3). Other widths, in particular the total width F, can be scaled from the corresponding branching ratios using the factor FeeIBp.,~. We have to get the branching ratio for the three-gluon decay (including the ggy possibility) by closure; that is, after all other significant modes are accounted for, the remainder is assumed to be ggg -and ggy.For example, for the Y(IS) we assume -

3+R)B,~

=

Bggg+Bggy+(

-

--

- -

1.

We have no data on the gluon—gluon—photon decays. QCD however predicts

BggylBggg

=

36aq~!5a. 0.04,

so that uncertainty in Bggy is unlikely to have much effect on our determination of Bggg: Bggg =

0.96[1

—

(3 + R)B~I.

Thus it is possible to derive all the important branching ratios and widths for the Y(1S), Y(2S) and Y(3S) from the measurements (see table 10). However, for the Y(2S) and Y(3S) the widths other than Fee are rather poorly determined, because of the large errors in the B,~.,.measurements. Using a little theoretical input, however, one can avoid B,,,. with an alternate way of determining widths. As we have seen in eq. (5), the vanRoyen—Weisskopf formula gives F 2times a factor 0~for any upsilon as tb~0)j which is independent of which upsilon state we are lookingat. Similarly, in OCThthe widthsfor decay into ggg and ggy are each given by the product of the wave function factor (see section 6.2) times a factor independent of upsilon state. We therefore expect (Fggg + Fggy)!Fee to be the same for Y(2S) and Y(35) as it is for Y(1S), where it is rather well measured. Values for Y(2S) and Y(3S) decay widths obtained using this assumption (table 10) agree within errors with those that depend on B,,,. measurements, but are more accurate. -

- -

-

K. Berkelman, Upsilon spectroscopy at CESR

179

Table 10 Branching ratios and widths derived-from measurements Decay

B, %0

Y(IS)-4all

ggg+ggy’ ggg’ all q~ irirY(1S)~ YXb(1P)”

ggg+ggy’ ggg’ Y(3S)—aall 5 irirY(1S) irirY(2S)5 YXb(1P)~l

YXb(2P)

ggg+ggy’ gggl a

2.9±1.0 11±4 7.0±1.4 4.6±3.0

42±5 1.26±0.06 4.7±0.2 34±4 32±4 27±19 0.52±0.03 1.9±0.1 8±6 3±2 13±9 12±9 13±4 0.38±0.03 1.3±0.1 0.9±0.4 0.6±0.4

1±5

0.1 ±0.5

34±3 34±10 33±10

4.5±1.6 4.5±2.0 4.3±2.0

100

q~d

key”

1,

3.0±0.3 11.1±1.1 80±2 77±2 100

1.9±1.4 7±5 30±4 10±5

47±11 45±11 100

F, keVc

29±5 0.52±0.03 1.9±0.1 8.7±2.0 2.9±1.4 14±3 13±3 24±3 0.38±0.03 1.3±0.1 1.7±0.5 1.1 ±0.7 0.2±1.0 8.1±1.3 10.1 ±1.4 9.7±1.4

Branching ratios from tables 7. 8, 9, except as noted. Derived from branching ratios, scaling with F,,/B,,,, from

measured 1~,(table 3) and B,,,. (table 7).

‘Derived

by assuming that ~

+ Fgg

5)IF00 is the same as for the Y(1S) and using the measured branching ratios for the cascade tranTqq measured RFee with sition modes. The B,,,R is= 3.7. not used. 0 Assumes Assumes i~’ggg+ Egg,, = I’ (3 + R)T,,,. — F,,,,~— E,~. Assumes Eggy = 0.04 Fggg. Assumes E(~r°ir°fl = (1/2)E(ir~ir1’). Assumes FIyxs(1P 1)1 = (1/2) E(y~~(1P,2)].

6.2. Rate for Y(1S) decay into three gluons QCD predicts the partial width Fggg for the Y(1S) decay into three gluons. The lowest order result [1011contains three powers of ~ corresponding to the three gluons: 2 9)181.1W’2] ~ I~~(0)I~. Fggg [160(1T We can remove the dependence on the wave function by dividing by the vanRoyen—Weisskopf prediction for F~(eq. (5)). Although the leading order QCD correction for Fee has been known for some time [83],it is only recently that Mackenzie and Lepage [102] have succeeded in calculating the next higher order for 1’gas~ which now includes the effects of four gluons and of gq~.The results for the ratio is -

FggglFee =

-

[10 (ir2 —9) a~(M)/811Tq~a2][l (25/2) ln(0.48My/M) a,/IT]. —

(6)

180

K. Berkelman, Upsilon spectroscopy at CESR

The higher-order term is written to show explicitly the dependence on the energy M at which a0 is to be evaluated. If we had a formula correct to all orders in a0, the choice of M would not matter. We can hope that the value M = 0.48M~which makes the second term vanish will also minimize the effect of the unknown higher orders. Then equating the expression for FgggIFee in eq. (6) to the experimental value and solving for a,, we have a,(0.48My) = 0.164±0.006. Note that the effect of the 10% experimental error in B,,,. is greatly reduced in the a0 result because of the cubic dependence. Using the second-order formula for a0 (eq. (1)), we get for the scale parameter in the th~scheme A = 120+ 25, —20MeV.

We can check the Y(1S) result by repeating the analysis for the ~i, although one does not expect the perturbation expansion to converge as fast at lower energy. The result is A = 53 + 16, —12 MeV. If we attribute to some unknown assume that is linear 2/c2) the anddiscrepancy use the ç(, and Y(1S) data to relativistic determine effect, A andwe thecan coefficient k in the thecorrection ad hoc correction in (v factor (1 + k(v21c2)) multiplying our previous expression for Fggglfee. The result is A = 170 MeV. This is probably not a defensible way to determine A, but it may give us an idea of the possible uncertainty in the theory. The conclusion is that A is measured from the FggglFee ratio of the Y(1S) to be 120 MeV with an experimental uncertainty of about 25 MeV and a probably larger theoretical uncertainty. This result compares well with recent determinations from other experiments [1031.The fact that similar values of a 0 are derived from deep inelastic nucleon structure functions, gluon bremsstrahlung, quarkonium potential models, and ~(i and Y decay rates is a striking success of QCD. 6.3. Dipion transition rates

In QCD the transition Y, irirY~takes place through the emission of two gluons, which then form the two pions. Since the total energy of the two pions is only 560 MeV, we cannot expect perturbative methods to apply. However, since the energy is very small relative to the Y masses, we can treat the transition as the radiation of a long wave length field by a pointlike source, that is, we can use the first term of a multipole expansion in the gluon field [104]. The result is a prediction for the width for Y(2S)—~ini-Y(1S) in terms of the corresponding width for i//—~ inn/i and the relative wave function spreads for the Y(2S) and ~i’: 2y~/~r~,))2= (108 keV)(1/10) = 11 keV, ~ = F ~((r which is consistent with the data (table 9). This is actually a significant test of QCD; for example, if the -gluon--had-sp n--0-instea&--of---l the-predtrionfor1±,~ would have beewai ~i~d titiagnitude larger. Using soft pion techniques, one also successfully predicts [104] the shape of the dipion mass spectrum (fig. 29a). The rates for dipion transitions from the Y(3S) are expected to be much lower, and indeed they are (table 9). One unexpected result is that the dipion mass spectrum in Y(3S)—* ir~i~Y(1S) is rather flat (fig. 29b), instead of being peaked near the high-mass limit as in the case of the transition from the —*

-

K. Berkelman, Upsilon spectroscopy at CESR I I

01 T t2SI

I

I

7T”7TT

I

(ISI

I

I

bI T 13S)

I

I

—. Ir’7T—T

181 I

PSI

4 1T Y(1S) events in which the Y(1S) is identified by its decay Fig. 29. Dipion invariant mass spectrum for (a) Y(2S)-3 1T’~ Y(1S) and (b) Y(3S)—~IT into lepton pairs. The shaded area corresponds to CUSB events 153,551; the rest is CLEO events [54,561. The curves show the shapes expected from eq. (7) with B = 0 (solid) and A = 0 (dashed).

Y(2S). Assuming PCAC and the multiple expansion, the most general form for the dipion transition amplitude is .41

=

Aq,, 1q,.2+ Bq01q02,

(7)

where q1 and q2 are the pion four momenta. In the Y(2S) to Y(1S) transition the first term dominates (the solid curves in fig. 29); but the Y(3S) to Y(1S) decay comes mainly from the second term (the dashed curves), that is, A/B = —0.15 ±0.12. Theoretically, this is not understood. 6.4. Radiative transition rates 3S 3P The 1 —~ 0,1,2 radiative transitions proceed in lowest multipole order by the emission an electric 2, about of0.03 for the dipole photon. The Higher multipoles upsilon-system. prediction is are suppressed by successive factors of (kr/2) -

FEl(3Sl—~3PJ)=(4/27)aq~(2J+1)k3

J

R~(r)rR,(r)dr~,

where R is a bb radial wave function normalized so that

JRt(r)R 1(r)dr=

-

~,

and k is the photon energy. One expects various corrections to this formula: higher multipoles, interference of er” with the bound-state wave function, radiative effects, and relativistic corrections. Such effects may explain the factor-of-two discrepancy between theory and experiment in the charmonium El rates. In general, the corrections should be less for the heavier bb system than the c~.

K. Berkelman, Upsilon spectroscopy at CESR

182

In the upsilon system the uncorrected predictions for the sum of the three FEs(3S—~2P), based on various potential models [62, 64, 66, 681, generally lie in the range 5 to 8 keV, when scaled with k3 to the measured photon energies. This is to be compared with the observed 8.1 ±1.4 keV (table 10). For FEl(2S—~1P) the predictions are 3 to 5 keV, in rough agreement with either the 2.9 ± 1.4 keV of table 10, or with the preliminary CUSB result of about 5 keV from the most recent Y(2S) data run [77].

7. Searches 7.1. Axions In an attempt to construct a gauge theory of the strong interaction which is naturally parity and time reversal symmetric, Wilczek and Weinberg [105]have postulated the axion, a light neutral pseudoscalar Higgs particle. The axion would couple weakly to fermions with a strength proportional to mass. It is therefore reasonable to look for it in the decays of particles containing the heaviest known fundamental fermions. The reaction we have considered at CESR is Y(lS) ya. The axion should be neutral, and provided it has a mass less than 10 MeV, it should live long enough to leave the detector. The signature of the reaction then is a photon of energy half the upsilon mass, and nothing else happening in the apparatus. CLEO, CUSB and LENA have carried out such a search, and find no events consistent with the Y—* ‘ya hypothesis. The 90% confidence upper limits on the branching ratio are —*

3.0 x l0~

CLEO [106],

x 10~

CUSB [107],

9.1 x i0~

LENA [108].

3.5

The CUSB group has also looked in Y(3S) decays and find a branching ratio limit 1.2 x I0~. The predicted radiative decay rate for a vector meson into an axion contains a free parameter X, the -ratio of the--vacuum expectation values of ~ heavy quarks in the meson are up (charge 2/3) or down (charge —1/3) [105]: F(VUP

ya) = F(V~~

-~

-~ ~t

~

GFm ~X2/V~ira, -

F(Vdfl—~ya)= F(Vd 0t)

GFm~fl/V21TaX2.

Note however that the product of branching ratios measured for the Y (the down case) and the ~(i (the up~case)-is-independent of the unknown X -parameter--and-isthefore-anambiguous-prediction-of-the----theory [109]: 2a2 B(Y-s. ya)~B(~ti-sya) = B(Y-~~ B(t/i-t. j.~G~m~m~/21T =(L6±0.3)x1O-~. .

-

-

An upper limit on the product of branching ratios on the left side of the equation can be obtained by multiplying the 3 x 10~from CESR with the previously measured Crystal Ball [1101 upper limit

K. Berkelman, Upsilon spectroscopy at CESR

183

B(t/i —~ ‘ya) = 1.4 x 10~,yielding a product 4.2 x 10~which is clearly inconsistent with the prediction. A standard axion of mass less than 10 MeV is then completely ruled out by experiment. Since the measured limit on B(Y—t. ya) applies to any low mass, long lived, weakly interacting particle, it is evidence also against a low mass version of the U particle of supersymmetric theories [1111. 7.2. Other narrow resonances 3S

In the upsilon spectrum below BB threshold the nonrelativistic potential models predict only three

1 states appearing as prominent resonances in the cross section for e~e—~ 3Dhadrons; namely, the Y(lS), 1 states, which would allow them to show up 3D as resonances in the e~e cross section. In charmonium it is the fortuitous near coincidence of the 1 ~!i”(3770) with the DD threshold that enhances the mixing enough to make the i/i” 3D easily detectible. In the bb system the first two 1 levels are expected at 10.14 and 10.43 GeV mass [68], and there is unlikely to be enough S—D mixing to make them visible as resonance peaks. The quark—antiquark energy level system could perhaps have more states not present in the otherwise analogous positronium spectrum. In QCD the fact that the gluons can couple to each other implies more degrees of freedom, and in the string picture these show up as vibrational modes of the string [112]. Such states also occur in the bag model description [113]. To fix the parameters in the vibrating string model one tries to identify one of the many levels in the charmonium spectrum above DD threshold as such a vibrational state. Buchmüller and Tye [114] consider two possibilities, the i/i(3.96) and the i/i(4.03). They then predict the mass M~and strength F~eof the corresponding level in the bb system for each of the two assumptions. CLEO [38] and CUSB [76] have each fit their cross section data between the Y(2S) and Y(4S) to define at each energy the upper limit on the Fee for a narrow resonance. Fig. 30 shows the results compared with the expectations [114]for a vibrational state. It is clear that except for the Y(3S) there is no state in that mass range with a Fee greater than about 20 eV. For D states this is expected, but for the vibrational states the measured upper limits clearly contradict the first theoretical estimates. Y(25) and Y(3S). There is however the possibility of some S admixture in

4’vib) 0.12 ~ 0.08

4.03 GeV ~

~ M (‘ M(~(~vjb)=

V

3.96 GeV

0.04

,,~,,,,

10.3

~II~,/II,

(0.4 W, in GeV

10.5

Fig. 30. Measured upper limits for dilepton width J’~ of a narrow resonance at masses between the Y(2S) and Y(3S) and between the Y(3S) and Y(4S). Data are from CLEO [38](solid) and CUSB [76](dashed).

184

K. Berkelman, Upsilon spectroscopy at CESR

8. Conclusions Quantum chromodynamics, our best candidate for the long-sought theory of strong interactions, is so far able to make clear predictions only in rather favorable situations. One such area of applicability is the spectroscopy of heavy quark—antiquark bound systems, the upsilon being the most favorable. The masses of the various levels and the rates for electromagnetic and hadronic decays and transitions among the levels provide critical tests of the theory and insights into its detailed application to hadron dynamics. The experiments have shown that the quark—antiquark potential is flavor independent and consistent with the expected radial dependence, interpolating between the Coulombic one-gluon exchange form at short distances and the linear confining form at large separation. The relative stability of the upsilon against hadronic decay is quantitatively accounted for by a value of a, in accord with that derived in deep inelastic lepton scattering and other experiments. The electric dipole transition rates in the bb system seem to match the predictions better than in the cë case. In short, the spectroscopy of the upsilons has so far confirmed many of the theoretical expectations and has greatly strengthened the acceptance of QCD. There are however many problems in heavy quarkonium spectroscopy still unsolved. There is as yet no convincing direct evidence for asymptotic freedom, the hypothesis that a3 decreases with increasing energy. No one knows the spin dependence of the quark—antiquark potential at intermediate distances. 3P Xb This when we arebetween able to 35measure the fine-structure splitting of the statescan andbethelearned hyperfine splitting Y statesaccurately and the yet-to-be-discovered 1S flb states. I am indebted to my colleagues in CLEO, as well as to S. Herb and H. Tye, for valuable help in preparing this review.

References [1] ED. Bloom, XXI Intern. Conf. on High-Energy Physics, eds. P. Petiau and M. Porneuf (Paris, 1982); A. Silverman, Proc. 1981 Intern. Symp. on Lepton and Photon Interactions at High Energies, ed. W. Pfeil (University of Bonn, Bonn, 1981) p. 138; RD. Schamberger, ibid., p. 217. [2] P. Franzini and J. Lee-Franzini, Phys. Reports 81(1982) 240. [3] S.L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D2 (1970) 1285. [4]J.D. Bjorken, Proc. 6th Intern. Symp. on Electron, and Photon Interactions at High Energies.- ed. H. Roilnik (North-Holland, Amsterdam, 1974) p. 25. [5] A. Litke et al., Phys. Rev. Lett. 30 (1973) 1189; G. Tarnopolsky et al., Phys. Rev. Lett. 32 (1974) 432. [6] J.-E. Augustin et al. (Mark I), Phys. Rev. Let(. 34 (1975) 764. [7] J.J. Aubert et al., Phys. Rev. Lett. 33 (1974) 1404. [8] J.-E. Augustin et al. (Mark I), Phys. Rev. Lett. 33 (1974) 1406. [9]B.H. Wiik and G. Wolf, Electron-Positron Interactions (Springer, New York, 1979). [10] ML. Perl et al. (Mark I), Phys. Rev. Lett. 35 (1975) 1489. [11] M. Kobayashi, T. Maskawa, Prog. Theor. Phys. 49 (1973) 652. [12] B.D. McDaniel, Proposal to the National Science Foundation for Modification of the Cornell Electron Synchrotron to provide an Electron—Positron Colliding Beam Facility (Cornell University, April 1977, unpublished). [13] SW. Herb et al., Phys. Rev. LetI. 39 (1977) 252. [14]W.R. Innes et al., Phys. Rev. Lett. 39 (1977) 1240; K. Ueno et al., Phys. Rev. Lett. 42 (1979) 486. [15] E. Eichten and K. Gottfried, Phys. Lett. 66B (1977) 286.

K. Berkelman, Upsilon speciroscopy at CESR

[16] S. Wojcicki, High Energy Physics—1980, eds. L. Durand and L.G. Pondrom (American

Institute of Physics, New York, 1980) p. 1430. [17] L. Criegee and G. Knies (PLUTO), Phys. Reports 83 (1982) 152. [181R. Brandelik et a!. (DASP), Z. Phys. Cl (1979) 233. [19]C. Berger et al. (PLUTO), Phys. Lett. 76B (1978) 243. [201C.W. Darde8 ct al. (DASP II), Phys. Lett. 76B (1978) 246. [21] C. Berger et al. (PLUTO), Z. Phys. Cl (1979) 343. [22] C. Berger et al. (PLUTO), Phys. Lett. 93B (1980)497. [23] C.W. Darden et al. (DASP H), Phys. Lett. 80B (1979) 419; H. Albrecht et al. (DASP II), Phys. Lett. 93B (1980) 500. [24] C. Berger et al. (PLUTO), Phys. Lett. 78B (1978) 176; 82B (1979) 449; Z. Phys. C8 (1981) 101. [25]W. Bartel et al. (DESY-Heid.), Phys. Lett. MB (1976) 483; 77B (1978) 331. [26]J.K. Bienlein et a!. (DESY-Heid.) Phys. Lett. 78B (1978) 360; P. Bock et al. (DESY—Heid.), Z. Phys. C6 (1980)125. [27] C.W. Darden et al. (DASP II), Phys. Lett. 78B (1978) 364. [28] B. Niczyporuk et al. (LENA), Phys. Rev. Lett. 46 (1981) 92. [29] B. Niczyporuk et a!. (LENA), Phys. Lett. 99B (1981) 169. [30] B. Niczyporuk et al. (LENA), Phys. Lett. 100B (1981) 95. [31] B. Niczyporuk et al. (LENA), Z. Phys. C9 (1981) 1. [32] B.D. McDaniel et a!., CESR Design Report, CLNS 360. [331D. Andrews et al. (CLE0), Nucl. Instr. Methods (to be published). [34] D. Andrews et al. (CLEO), Phys. Rev. Lett. 44 (1980)1108. [351T. Bohnnger et a!. (CUSB), Phys. Rev. Lett. 44 (1980) 1111. [36] D. Andrews et a!. (CLEO), Phys. Rev. Lett. 45 (1980) 219. [37] G. Finocchiaro et al. (CUSB), Phys. Rev. Lett. 45 (1980) 222. [38] R. Plunkett (CLEO), Cornell Univ. thesis, 1982. [39] C. Bebek et al. (CLEO), Phys. Rev. Lett. 46 (1981) 84. [40] K. Chadwick et a!. (CLEO), Phys. Rev. Lett. 46 (1981) 88. [41] L.J. Spencer et al. (CUSB), Phys. Rev. Lett. 47 (1981) 771. [42] A. Brody et al. (CLEO), Phys. Rev. Lett. 48 (1982) 1070. [43] MS. Alam et a!. (CLEO), Phys. Rev. Lett. 49 (1982) 357. [44] K. Chadwick et a!. (CLEO), Phys. Rev. D27 (1983) 475. [45] C. Klopfenstein et al. (CUSB), Preprint submitted to XXI Intern. Conf. on High Energy Physics, Paris, July 1982. [46] A. Chen et a!. (CLEO), Phys. Lett. (to be published). [47] P.M. Tuts et a!. (CUSB), Preprint submitted to XXI Intern. Conf. on High Energy Physics, Paris, July 1982. [481D. Andrews et al. (CLE0), Contributions to the XXI Intern. Conf. on High Energy Physics, Paris, July 1982; CLNS 82/547. [491S. Berends et a!. (CLEO), Phys. Rev. Lett. 50 (1983) 881. [50] J. Lee-Franzini, XXI Intern. Conf. on High-Energy Physics, eds. P. Petiau and M. Porneuf (Paris, 1982). [51] D. Andrcws et al. (CLE0), Phys. Rev. Lett. 50 (1983) 807. [52] R. Giles et al. (CLEO), Phys. Rev. Lett. 50 (1983) 877. 1531 G. Mageras et al. (CUSB), Phys. Rev. Lett. 46 (1981) 1115. [54] ii. Mueller et al. (CLE0), Phys. Rev. Lett. 46 (1981) 1181. [551G. Mageras et a!. (CUSB). preprint submitted to XXI Intern. Conf. on High Energy Physics, Paris, July 1982. [56] J. Green et a!. (CLEO), Phys. Rev. Lett. 49 (1982) 617. [57] D. Peterson et a!. (CUSB), Phys. Lett. 114B (1982) 277. [58] K. Han et a!. (CUSB), Phys. Rev. Lett. 49 (1982) 1612. [59] G. Eigen et a!. (CUSB), Phys. Rev. Lett. 49 (1982) 1616. [60] AS. Artamonov et al., Novosibirsk preprint 82—94. [61] T. Appelquist and H.D. Politzer, Phys. Rev. Lett. 34 (1975) 43. [62] E. Eichten et al., Phys. Rev. D17 (1978) 3090; D21 (1980) 203. [63] G. Bhanot and S. Rudaz, Phys. Lett. 78B (1978) 119. [64] H. Krasemann and S. Ono, Nucl. Phys. B154 (1979) 283. [651W.C. Haxton and L. l-le!ler, Phys. Rev. D22 (1980) 1198. [66] C. Quigg and iL. Rosner, Phys. Rev. D23 (1981) 2625, and earlier references cited therein. [67] J.L. Richardson, Phys. Lett. 8211 (1979) 272. [68] W. Buchmüller, G. Grunberg and S.-H.H. Tye, Phys. Rev. Lett. 45 (1980) 103; 587(E); W. BuchmOl!er and S.-H.H. Tye, Phys. Rev. 024 (1981) 132: 0. Abe, M. Haruyama and A. Kanasawa, Phys. Rev. D27 (1983) 675. [69] M. Machacek and Y. Tomozawa, Ann. Phys. 110 (1978)407. [70] A. Martin, Phys. Lett. 93B (1980) 338; 100B (1981) 515.

185

186

K. Berkelman, Upsilon spectroscopy at CESR

fTlJ T.--Appequist-and-H orgi~-Phy&-Rev~ E.C. Poggio et a!., Phys. Rev. D13 (1976)1958; M. Dine and J. Sapirstein, Phys. Rev. Lett. 43(1979) 668; KG. Chetyrkin et a!., Phys. Lett. 85B (1979) 277; W. Ce!master and R.J. Gonsalves, Phys. Rev. Lett. 44 (1979) 560. [72] G. Bonneau and F. Martin, NucI. Phys. B27 (1971) 381. [73] C. Gerke (PLUTO), Univ. of Hamburg thesis, DESY PLUTO 80/03. [74] S. Weseler (DASP II), Univ. of Heidelberg thesis, IHEP.HD/ARGUS/81-3. [75] B. Niczyporuk et a!. (LENA), DESY 82-052. [76] E. Rice et a!. (CUSB), Phys. Rev. Lett. 48 (1982) 906; E. Rice (CUSB), Columbia Univ. thesis, 1982. [77] CUSB collaboration, Upsilon Physics at CESR with CUSB, April 1983 (unpublished). [78] DR. Yennie, Phys. Rev. Lett. 34 (1975) 239. [79] J.D. Jackson and DL. Scharre, NucI. Instr. Methods 128 (1975) 13. [80] W. Schmidt-Parzefall, High-Energy Physics—1980, eds. L. Durand and L.G. Pondrom (American Institute of Physics, New York. 1980) p. 692. [811M. Voloshin and V.!. Zacharov, Phys. Rev. Lett. 45 (1980) 688. [82] R. vanRoyen and V.F. Weisskopf, Nuovo Cimento 50A (1967) 617. [83] R. Barbieri et a!., Phys. Lett. 57B (1975) 455: W. Celmaster, Phys. Rev. 019 (1979) 1517. [84] V.A. Novikov et a!., Phys. Reports 41C (1978) 1; MA. Shifman, Proc. 1981 Intern. Symp. on Lepton and Photon Interactions at High Energies, ed. W. Pfeil (University of Bonn, Bonn, 1981) p. 242. [85] S. Brandt, C. Peyrou, R. Sosnowski and A. Wroblewski, Phys. Lett. 12 (1964) 57; E. Farhi, Phys. Rev. Lett. 39 (1977) 1587; A. deRujula, J. Ellis, E.G. Floratos and M.K. Gaillard, NucI. Phys. B138 (1978) 387. [86] R. Cabenda (CLE0), Cornell Univ. thesis, 1982; see also CLNS 81/513. [87] S. Brandt and H.D. Dahmen, Z. Phys. Cl (1979) 61. [881K. Koller and IF. Walsh, Phys. Lett. 72B (1977); NucI. Phys. B140 (1978) 449. [891R. Perchonok (CLEO), Cornell Univ. thesis, 1982. [90] E. Fermi, Prog. in Theor. Phys. 5 (1950) 570; C. Berger et a!. (PLUTO), Phys. Lett. 95B (1980) 313. [91] G. Wolf, DESY 79/4!. [92] W. Furmanski, R. Petronzio and S. Pokorski, NucI. Phys. B155 (1979) 253. [93] R. Felst, Proc. 1981 Symp. on Lepton and Photon Interactions at High Energies, ed. W. Pfei! (University of Bonn, Bonn, 1981) p. 52. [941R. Brandelik et a!. (lASSO), Phys. Lett. 114B (1982) 65. [95] C. Bebek ci a!. (CLEO), Phys. Rev. Lett. 49 (1982) 610. [96] PA. Rapidis et a!. (Mark I), Phys. Lett. MB (1979) 507. [97] W. Tanenbaum et a!. (Mark 1), Phys. Rev. D17 (1978) 1731; W. Bartel et a!. (DESY—Heid.), Phys. Lett. 79B (1978)492; R. Brandelik et a!. (DASP), Nuci. Phys. B160 (1979) 426. [981E. Eichten and FL. Feinberg, Phys. Rev. Lett. 93B (1980) 103. [99] W. Buchmüller, Phys. Lett. 112B (1982) 479. [100] SN. Gupta, S.F. Radford and W.W. Repko, Phys. Rev. 026 (1982) 3305. [101] T. Appe!quist and H.D. Politzer, Phys. Rev. D12 (1975) 1404; R. Barbieri, R. Gatto and R. Koger!er, Phys. Lett. 6011 (1976) 183; R. Barbieri, R. Gatto and E. Remiddi, Phys. Lett. 61B (1976)465. [102] P. Mackenzie and G.P. Lepage, Phys. Rev. Lett. 47 (1981) 1244. [103] A.J. Buras, Proc. 1981 Intern. Symp. on Lepton and Photon Interactions at High Energies, ed. W. Neil (University of Bonn, Bonn, 1981) p. 636. [1041K. Gottfried, Phys. Rev. Lett. 40 (1978) 598; T.-M. Yan, Phys. Rev. D22 (1980) 21. Y. Kuang and T.-M. Yan, Phys. Rev. 024 (1981) 2874. [105] F. Wilczek, Phys. Rev. Lett. 40 (1978) 279; S. Weinberg, Phys. Rev. Lett. 40 (1978) 223. [1061MS. Alam et al. (CLEO), Phys. Rev. D27 (1983) 1665. [107] M. Sivertz et a!. (CUSB), Phys. Rev. D26 (1982) 717. [108] B. Niczyporuk et al. (LENA), DESY 82-068. [109]F.C. Porter and K.C. Konigsmann, Phys. Rev. D25 (1982) 1993; G. Girardi, LAPP-TH-58, April 1982.

K. Berkelman, Upsilon spectroscopy at CESR [110] C. Edwards ci a!. (Crystal Ball), Phys. Rev. Lett. 48 (1982)903. [1111P. Fayet, in: Supersymmetry versus Experiment Workshop, TH.331 1/EP.83/63-CERN. [1121R.C. Giles and S.-H.H. lye, Phys. Rev. Lett. 37 (1976) 1175; Phys. Rev. D16 (1977) 1079. [113]P. Hasenfratz, R.R. Horgan, I. Kuti and J.M. Richard, Phys. Lett. 95B (1980) 299. [114]W. Buchmü!!cr and S-HI-I. Tye, Phys. Rev. Lett. 44 (1980) 850.

18