study of the reaction p¯pŸfffrom 1.1 to 2.0 gev/ca study has been performed of the reaction...

PHYSICAL REVIEW D 1 MAY 1998VOLUME 57, NUMBER 9

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Study of the reaction p̄p˜ff from 1.1 to 2.0 GeV/c

C. Evangelista and A. PalanoUniversity of Bari and INFN, I-70126 Bari, Italy

D. Drijard, N. H. Hamann,* R. T. Jones,† B. Mouëllic, S. Ohlsson, and J.-M. PerreauCERN, CH-1211 Geneva, Switzerland

W. Eyrich, M. Moosburger, S. Pomp, and F. StinzingUniversity of Erlangen-Nu¨rnberg, W-8520 Erlangen, Germany

H. Fischer, J. Franz, E. Ro¨ssle, H. Schmitt, and H. Wirth‡

University of Freiburg, W-7800 Freiburg, Germany

A. Buzzo, K. Kirsebom, M. Lo Vetere, M. Macrı`, M. Marinelli, S. Passaggio, M. G. Pia, A. Pozzo, E. Robutti, andA. Santroni

University of Genova and INFN, I-16132 Genova, Italy

P. T. Debevec, R. A. Eisenstein,§ P. G. Harris,i D. W. Hertzog, S. A. Hughes, P. E. Reimer,¶ and J. RitterUniversity of Illinois, Urbana, Illinois 61801

R. Geyer, K. Kilian, W. Oelert, K. Ro¨hrich,‡ M. Rook, and O. SteinkampInstitut für Kernphysik, Forschungszentrum Ju¨lich, D-5170 Jülich, Germany

H. Korsmo and B. Stugu**University of Oslo, N-0316 Oslo, Norway

T. JohanssonUppsala University, S-75121 Uppsala, Sweden

~Received 13 January 1998; published 7 April 1998!

A study has been performed of the reactionp̄p→4K6 using in-flight antiprotons from 1.1 to 2.0 GeV/cincident momentum interacting with a hydrogen jet target. The reaction is dominated by the production of a

pair of f mesons. Thep̄p→ff cross section rises sharply above threshold and then falls continuously as afunction of increasing antiproton momentum. The overall magnitude of the cross section exceeds expectationsfrom a simple application of the Okubo-Zweig-Iizuka rule by two orders of magnitude. In a fine scan around

the j/ f J(2230) resonance, no structure is observed. A limit is set for the double branching ratio B(j→ p̄p)3B(j→ff),631025 for a spin 2 resonance of M52.235 GeV andG515 MeV. @S0556-2821~98!02511-9#

PACS number~s!: 14.40.2n, 13.75.2n, 25.43.1t

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I. INTRODUCTION

Beyond the common families of baryonic (qqq) and me-sonic (qq̄) states, glueballs~gg or ggg!, hybrids (qq̄g) andmulti-quark systems~e.g.,qq̄qq̄! are predicted to exist baseon the current understanding of QCD and QCD-inspired pnomenological models of hadrons. The question of the e

*Deceased.†Present address: University of Connecticut, Storrs, CT.‡Present address: Creative Services, St. Genis, France.§Now at National Science Foundation, Washington, D.C.iPresent address: University of Sussex, Falmer, Brighton, UK¶Present address: Los Alamos National Laboratory, Los Alam

NM 87545.** Present address: University of Bergen, Norway.

570556-2821/98/57~9!/5370~12!/$15.00

-s-

tence of these unusual hadronic bound systems is fundamtal and should lead to a broader understanding ofbehavior of QCD in the non-perturbative region. The expement described below investigates the existence of gluohadrons in the mass range between 2.1 and 2.4 GeV/c2. Thetechnique requires a state, if found, to couple appreciablboth antiproton-proton~the entrance channel! and ff ~theexit channel!. The parameter space explored is of particuinterest in a search for the tensor glueball.

Gluonic hadrons are expected to populate the low m

region of the hadron spectrum together with normalqq̄states. Recent lattice QCD calculations locate the sc(JPC5011) glueball mass in the range of 1.5 to 1.7 Ge@1#. The tensor (JPC5211) is the next low-lying glueballand is found to be approximately 1.5 times more massthan the scalar, thus it is postulated that it might be inregion explored by this experiment.

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5370 © 1998 The American Physical Society

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57 5371STUDY OF THE REACTIONp̄p→ff FROM 1.1 TO 2.0 GeV/c

Several experimental approaches have been usesearch for glueballs. The common theme is to choose acess, where a kinematical or dynamical filter strongly

duces the large production of standardqq̄ mesons. Reactionintensively explored are peripheral hadron interactions@2#,J/c radiative decays@3#, central production@4#, gg colli-

sions@5# and p̄p annihilations@6#.

The study of thep̄p→ff reaction is motivated by theexpectation that, with essentially no common valence quabetween the initial and final states, the reaction is forbiddin first order. Indeed, a strict application of the empiricOkubo-Zweig-Iizuka~OZI! rule @7# suggests a cross sectio

for p̄p→ff of approximately 10 nb. In a previous publication @8#, we reported the cross section at 1.4 GeV/c incidentantiproton momentum to be 3.760.8 mb and thus two ordersof magnitude greater than estimated. The largep̄p→ffcross section has been interpreted as coming from two-processes@9,10#, from intermediate glue@11#, and/or fromthe intrinsic strangeness in the nucleons@12#.

Here we review the appropriateness of the energy raof our study with respect to the possibility of excitinggluonic resonance. As evidence, consider the current picof candidate glueball states. Thef 0(1500), discovered by theCrystal Barrel experiment at the CERN Low-Energy Anproton Ring~LEAR!, has a width ofG'120 MeV and hasbeen observed to decay top0p0,hh @13#, hh8 @14# andKK̄@15# following p̄p annihilation at rest. The existence of thstate has been confirmed in in-flightp̄p annihilations by ex-periment E760 at Fermilab@16#. It has been interpreted athe leading scalar glueball candidate. Alternate explanatfeature strong gluonic content; the state could be a mixof a glueball and nearby ordinaryqq̄ systems@17#. If iden-tified with the scalar glueball, the implication from the latticcalculations is that the tensor mass should be in the 2.1 toGeV range, where candidate glueball states have alrebeen identified. These states include thej/ f J(2230) which isobserved in radiativeJ/c decays toKK̄ @18# and also indecays topp and pp̄ @19#. The width of this state (G'30620 MeV) is unexpectedly small, and has stimulated csiderable interest. The spin-parity is undetermined, bulimited to (even)1. This channel is of interest to the preseexperiment since it couples top̄p. In another study@20# fromthis experiment, stringent limits were established ondouble branching ratio B(j→ p̄p)3B(j→KS0KS0) for thecase of a narrow~i.e., G,30 MeV! state.

Resonances in theff system have been observedJ/c→gff by Mark III and DM2. Each group saw a widbump aboveff threshold peaking near 2.2 GeV and havia width of approximately 100 MeV. The preferredJP assign-ment is 02, however, 21 contributions cannot be exclude@21#.

The ff system has been studied in exclusivep2p@22,23# and inclusivep2Be induced interactions@24#. Thisreaction is expected to be highly suppressed based onabove OZI argument related to disconnected quark-linegrams. However the suppression is not observed near throld, a fact which could be explained by the productionintermediate gluonic resonances@11#. A partial wave analy-

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sis ~PWA! of the exclusive data revealed the presencethree interfering JPC5211 resonances, thef 2(2010),f 2(2300) andf 2(2340), originally calledgT states. The in-clusive data show evidence for two structures with paraeters compatible with those measured for thegT states, but aPWA was not possible.

We report below on the evaluation of 58 independemeasurements of the reactionp̄p→4K6 from which we de-termine the cross sections forp̄p→ff, p̄p→fK1K2 andp̄p→4K6. A threshold enhancement is evident in theffcross section data. In the narrow region aroundj/ f J(2230) resonance, 17 measurements of theff cross sec-tion are reported in narrow energy steps covering a rang45 MeV. Limits are set on the non-observation of this sta

II. THE EXPERIMENT

The JETSET~PS202! @25# experiment is designed to measure the reaction

p̄p→ff→K1K2K1K2 ~1!

as a function of incident antiproton momentum fro1.1 GeV/c to the highest momenta available at LEA(2.0 GeV/c). The experiment makes use of the LEAR anproton beam incident on an internal target provided byhydrogen-cluster jet system. To obtain a measure of thesolute ~and relative! luminosity at different antiproton momenta,p̄p elastic scattering events were recorded in parausing a special dedicated trigger.

One key feature of reaction~1! in the energy range covered by this experiment is the fact that the outgoing kaare constrained to a forward cone below 60°. Dominantp̄p annihilation are the production of charged and neupions. These unwanted background reactions producetively fast charged particles and photons spread over a mlarger angular range. The design of the detector and etronic trigger takes advantage of these facts by providgood charged-particle tracking and particle identificati~PID! for forward angles, fast charged-particle multiplicifor triggering, and a large-acceptance photon rejection stem. The philosophy followed to record and identify 4K6

events is to trigger only on the proper multiplicity pattern.the offline analysis, events are required to have four wdetermined tracks in the right kinematical range. Finathese tracks are associated with hits in the PID detectordetermine compatibility with identification as kaons from t4K final state.

A schematic view of the apparatus is shown in Fig. 1.basic structure is a hydrogen-cluster jet target~not shown!@26# with a densityr5431012 atoms/cm2, surrounded by acompact detector. The jet is oriented horizontally and intsects the circulating antiproton beam at right angles. Arouthe interaction volume the LEAR ring is equipped with aoval vacuum chamber~0.03 radiation lengths thick! havinghorizontal and vertical half-axes of 78 and 38 mm, resptively. This limits the geometrical acceptance of the detecto polar anglesu lab.7°, with complete coverage of azimuthal angles only foru lab.15°.

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5372 57C. EVANGELISTA et al.

The overall structure of the detector includes a ‘‘forwardand a ‘‘barrel’’ sector with polar angular coverage from 745° and 45°–135°, respectively. Immediately outside ofbeam pipe is an ‘‘inner’’ scintillation hodoscope array semented in azimuth into 40~forward! and 20~barrel! compo-nents. These are used in conjunction with a triple-la‘‘outer’’ hodoscope~144 total elements! @27# to form multi-plicity patterns for use in the trigger. In the reactionp̄p→4K6 at least three charged tracks are required withiforward 45° cone around the beam axis. The fourth kaona maximum polar angle of 60°. The inner scintillator arrextends to this angle, while the barrel outer array incluangles up to 135° to veto events with large angle tracks.

Between these scintillator arrays are cylindrical drchambers~‘‘straws’’ ! which are used for tracking@28#. Theyare arranged in 12 planes with alternating horizontal andtical orientation in the forward region. In the barrel, 14straws are formed into a tightly packed bundle aligned wand surrounding the beam pipe.

Three separate devices are incorporated with the purpof providing PID information. These include 3500 silicopad counters which measure energy loss. They are parlarly effective at the low end of the expectedb range. Ahodoscope consisting of 24 forward and 24 barrel threshČerenkov counters is positioned just inside of the outer stillator array. These counters are used to limit the numbe‘‘fast’’ particles that are accepted at the trigger level~typi-cally

select


FIG. 2. DE ~see text! distributions for~a! Monte Carlo simulation of the reactionp̄p→4K6 at 1.5 GeV/c; ~b! Raw four-prong data fordifferent momenta ranges: Light line: 1.2 GeV/c, gray line: 1.65 GeV/c, black line: 2.0 GeV/c; ~c! Application of thedE/dx criterion onlyto data in the 1.4– 1.45 GeV/c region;~d! Adding the threshold Cˇ erenkov compatibility condition to this data;~e! Adding the criterion fromthe RICH and from theg veto;~f! Final DE distribution for all the data taken in the experiment. The shaded area shows the cut used tothe reaction.

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The distribution is asymmetric, and its width increases wincreasing incidentp̄ momentum.

The four-prong data, prior to application of any PID iformation, show a broadDE distribution with no obviousstructure. This is consistent with expectations since thevents are dominated by background. The shape variatiosuch rawDE distributions over the span of incident momenta explored by our experiment is shown in Fig. 2~b!.

B. Particle identification

In order to isolate thep̄p→4K6 events from the verylarge background, use of different selection criteria basedthe particle identification devices is made. First we requan energy loss (dE/dx) compatibility as measured in thsilicon detectors. This is evaluated by forming a confidenlevel for each measurement, using a parametrization ofLandau distribution and integrating the tail beyond the msured value. The confidence levels for each measurementhen combined into adE/dx confidence level. The detectorwere calibrated using a sample of well-defined tracks wknown momenta. They come from fully identifiedp̄p elasticscattering events and fromp̄p→ p̄pp1p2 events. This latterreaction was isolated almost background free by makingof the Čerenkov identification and by the requirement oflarge energy deposit from the outgoingp̄ in the forward elec-tromagnetic calorimeter@32#. A plot of the pulse height inthe silicon pads vsb is shown in Fig. 3~a! for the barrelregion and in Fig. 3~b! for the forward region. The first plomakes use of elastic events, while the second distribution

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been obtained fromp̄p→ p̄pp1p2 data. Application of thedE/dx compatibility requirement on a sample of the 1.41.45 GeV/c data results in aDE distribution as shown in

Fig. 2~c!. At this stage thep̄p→4K6 events are already inevidence.

The Čerenkov effect produces a responseR(b) in photo-electrons that is monotonically increasing forb>b th . Twodifferent radiators were used: liquid freon~FC72! @33#, in thevery first data taking only, having a threshold atb50.79,and subsequently water having a threshold at 0.75. The reof theb measurement from the Cˇ erenkov response events othe water radiator is compared in Fig. 4~a! to the expectedbfrom elastic events.

For the freon data, we show in Fig. 4~b! the ‘‘efficiency’’versusb, where we have defined efficiency as the ratio btween theb distribution of the tracks crossing the Cˇ erenkovcounters which give light to theb distribution of all thetracks. This study is based on events of the typep̄p→ p̄pp1p2. A smooth increase as a function ofb is seenwhich indicates the expected threshold behavior. The nzero efficiency below threshold is caused by light producin the plexiglass containment wall of the counters.

The response function of the liquid Cˇ erenkov counters isused to calculate the expected signal from a passing traca given hypothesized momentum. The expected and msured responses are compared on the basis of Poisson stics. The resulting confidence levels for the four tracksthen combined with the one obtained from thedE/dx infor-mation to form an overall particle identification confidenlevel which is required to be at least 5%. The effect of ad


FIG. 3. ~a! Pulse height in analog to digital converter~ADC! units for the barrel silicon pads vsb for a sample of elasticp̄p events.~b!

Pulse height in ADC units for the forward silicon pads vsb from a sample ofp or p̄ from the reactionp̄p→ p̄pp1p2.

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ing the Čerenkov information can be seen in Fig. 2~d!.The response function of the RICH is determined by m

surements of elastic events in which the forward-scatteantiproton of known momentum penetrates the detector.tails of this detector performance are found elsewhere@29#,however, a representative example of theb resolution isshown in Fig. 5. The difference between the expectedmeasuredb distribution exhibits a Gaussian behavior withresolution ofDb/b'2%. In analyzing the response of thdetector, we find that a large fraction of background eveproduces a RICHb measurement which is unphysicalgreater than 1. The most effective cut eliminates this baground, yet retains the good events, by simply requiring tthe b measured by the RICH be less than 0.9.

One background reaction which frequently satisfiestrigger conditions of the experiment is

p̄p→ p̄pp1p2 ~3!

which is particularly important forp̄ momenta above

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1.6 GeV/c. Reaction~3! is identified by the same selectiocriteria as those applied to findp̄p→4K6 events. Events soidentified are removed from the final 4K6 sample.

At the final stage of event selection, those events wisolatedg’s in the barrel region are removed. This eliminatmost of the events with multipleg’s or p0’s. The finalDEdistribution after applying all the above selection criteriashown in Fig. 2~e! for the 1.4 to 1.45 GeV/c sample and inFig. 2~f! for all of the data taken in the experiment combineA clear signal, peaked at aDE of zero, is seen which isevidence for events of the typep̄p→4K6. The final selec-tion of events is made by requiringDE

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four years. However, in the following analysis, measuments at the same or nearly the same momentum havegrouped together in order to reduce statistical and systemerrors. The distribution of luminosities as a function of tmomentum are summarized in Table I.

The luminosity was monitored via the known cross stion of elasticp̄p scattering. Two independent methods weemployed to measure it. In the first method, the rate ofincidence between opposite pixels formed in the outer trigscintillator hodoscope was used to count elastic events90° in the c.m. system. The second method made ussmall microstrip detectors placed near 90° in the barre

FIG. 5. Expected minus measuredb from the RICH detector forelastic events.

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detect the recoil particle from low-angle elastic scatter@34#. The data have been normalized as a function of timeusing minimum bias scalers which were found to be vereliable and stable over the lifetime of the experiment. Trelative luminosity error is 2%.

The acceptance for the elastic and 4K events was com-puted by aGEANT @35# based Monte Carlo simulation of thphysical detector and trigger conditions. The Monte Caevents were subjected to the same reconstruction criteriaanalysis cuts as the real data. We generated Monte Cevents for each of the 58 momentum settings, takinto account the changes in the layout of the apparaand trigger conditions. For the physics analysis, three re

tions were generated:p̄p→ff, p̄p→fK1K2 and p̄p→K1K2K1K2. The simulation assumed phase space dtributions for all three reactions. The distributions of the toacceptance as a function of the incidentp̄ momentum areshown as fitted polynomials in Fig. 6~a!.

The differential acceptance function forp̄p→ff isgreatly affected by the kinematics of the reaction andlayout of the detector. The distribution of cosQcm is shownin Fig. 6~b! for all the data. Here,Qcm is defined as thecenter-of-mass scattering angle of the outgoingf. A strongdepletion of events occurs in the forward region, due to lof tracks in the beam pipe. On the other hand, the acceptain the x angle is almost flat as it can be seen in Fig. 6~c!.Herex is defined as the angle formed by the twof’s decayplanes, in theff center of mass system. Figure 6~c! showsthe distribution of the x angle for the data in the1.26– 1.65 GeV/c region ~points with error bars!, together

TABLE I. Cross sections forp̄p→ff, fK1K2 and 4K.

Momentum regionGeV/c

c.m.energyGeV/c2

Luminositynb21

s~ff!mb

s(fK1K2)mb

c.m.energyGeV/c2

s(4K6)mb

1.188–1.200 2.147 26.8 2.8660.46 0.2560.49 2.158 0.1560.15

1.237–1.278 2.168 32.8 3.4560.31 0.9660.32

1.300–1.330 2.190 69.1 3.5460.18 0.2360.21 2.195 0.5660.13

1.360 2.205 33.4 3.8460.24 0.2760.26

1.390–1.400 2.218 60.7 3.5560.17 0.6360.22 2.219 0.5060.17

1.404–1.405 2.220 53.9 3.8860.17 0.5460.21

1.410–1.415 2.223 38.0 4.0060.20 0.3960.25 2.225 0.5260.15

1.420 2.226 25.7 3.8460.24 0.7160.29

1.425–1.430 2.228 26.4 3.0960.22 0.9760.32

1.435 2.231 47.7 3.3360.17 1.1660.235 2.233 0.5860.15

1.440–1.450 2.235 35.1 3.4160.19 1.1960.26

1.465–1.480 2.242 48.7 3.0260.15 1.0760.22 2.247 0.4460.26

1.500–1.506 2.255 42.7 3.0160.16 1.7760.25

1.550 2.272 24.3 2.2560.17 1.9060.31 2.282 0.3460.33

1.600 2.289 20.1 2.1560.21 2.4060.40

1.650 2.307 13.6 1.9760.24 3.2660.45

1.700–1.750 2.333 32.6 2.0460.14 3.5660.30 2.348 0.9560.52

1.800 2.360 39.3 2.0460.12 4.3060.25

1.900–1.950 2.404 15.4 1.6160.18 3.6360.41 2.424 2.5560.93

2.000 2.430 52.1 1.9360.11 3.9160.24


FIG. 6. ~a! Acceptance for the three reactionsp̄p→ff, p̄p→fK1K2 and p̄p→4K6. Distribution of ~b! cosQcm and ~c! x for thereactionp̄p→ff in the momentum range between 1.26 and 1.65 GeV/c. The data are represented with error bars. In~c! the solid linerepresents the distribution expected for phase space.

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with the distribution ofx for Monte Carlo phase space geerated data folded with the acceptance of the apparatus.missing forward angle acceptance inQcm affects our abilityto extract totalff cross sections as described later.

Systematic errors on the cross section measurementsbeen estimated using the known cross section forp̄p→p̄pp1p2 @32# whose determination was found to begood agreement with previous measurements. We alsothe fact that the cross sections at several energy pointsmeasured several times under different experimental cotions. We estimate the overall uncertainty on the absoscale of theff cross section to be 20%.

V. THE DATA

For the selectedp̄p→K1K2K1K2 event candidates weshow in Fig. 7, in Fig. 8~a! and in Fig. 8~b! the scatter plot ofthe invariant massesm(K3K4) vs m(K1K2). Figure 7 showsall the available data as a surface plot, where a strong amulation of events can be observed at the nominalff posi-tion. Figure 8~a! and 8~b! illustrate the same data under thform of a scatter diagram for two different regions of incdent p̄ momentum, i.e. below and above 1.5 GeV/c, respec-tively. Notice that, due to the absence of charge informatithree combinations per event enter in these plots. Weserve in these distributions a strong enhancement at thesition of the ff. In the higher momentum region we alsobserve horizontal and vertical bands which indicatepresence of thep̄p→fK1K2 final state. Monte Carlo simulations confirm that the diagonal bands represent the retion of the ff peak due to the multiple combinations. Slecting onef, i.e. requiring onem(K3K4) combination to liein the region 1.00– 1.04 GeV/c2 and plotting the oppositecombinationm(K1K2), we obtain the distributions shown iFig. 8~c! and 8~d!, where a cleanf peak is visible. Thestructure is well centered at the nominalf mass.

VI. CHANNEL LIKELIHOOD FIT

In order to separate theff cross section from thefK1K2 final state and from the 4K and other backgroundmixture, the channel likelihood technique@36# was used. Themethod performs a maximum likelihood fit to the data usthree amplitudes:ff, fK1K2 and phase space~which is a

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mixture of 4K and background and cannot be separatedthis stage!. The different channels have been describedthe following amplitudes:

ff:Aff5 (i , j 51

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Bi~mKK!.

The likelihood function employed is the following:

L5xffAffI ff

1xfKKAfKKI fKK

1~12xff2xfKK!.

In the above expressionsxff and xfKK represent the frac-tions of the ff and fK1K2 channels, respectivelyBi(mKK) represents thef line shape functions,I ff andI fKK

FIG. 7. m(K3 ,K4) vs m(K1 ,K2) ~three combinations per even!for all the events.


FIG. 8. m(K3 ,K4) vs m(K1 ,K2) ~three combinations per event! for ~a! p̄ incident momentum below 1.5 GeV/c and ~b! above1.5 GeV/c. ~c!, ~d! mass projections of~a! and ~b! in the f band, i.e. plots ofm(K1K2) for 1.00

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FIG. 10. Combinatorial m(KK) distribution ~six entries per event! for incident p̄ momentum~a! below and~b! above 1.5 GeV/c. Thewhite region represents theff contribution, the gray region shows thefK1K2 contribution and the black region shows the phase sp(background14K) contribution.

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The normalization of the amplitudes was computedmerically using the Monte Carlo simulations of the reactip̄p→4K. The resulting integrals were then fit to polynomals as functions of the incidentp̄ momentum. Changes in thlayout of the apparatus and trigger conditions have little

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fect on the values of these integrals as seen in Fig. 9, whthese integrals and the fitted polynomials are shown.

The channel likelihood fit gives the fractions of eventswell as a probability for each event to belong to one of tthree hypotheses. The results of the fits are visually d

ted

FIG. 11. DE distributions for the nine regions in increasing values of incidentp̄ momentum. The gray area represents the estimabackground.

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played in Fig. 10. Here we show the combinatorialm(KK)distribution~six entries per event! for incident p̄ momentumbelow and above 1.5 GeV/c. The white region represent thff contribution, the gray region shows thefK1K2 contri-bution, while the black region shows the phase sp(background14K) contribution. We notice that nof peakhas been left in the phase space distribution, indicativesuccessful fit. We also notice the strong increase offK1K2 contribution in the higher momentum region. Thanalysis gives a total of approximately 11 400ff events.

The channel likelihood method is able to separatethreeff, fK1K2 and (background14K) contributions. Inorder to separate the 4K contribution from the backgroundwe made use of theDE distributions as discussed in SeIII A. For this purpose, in order to reduce the errors, a furthcompression of the data was performed, grouping themnine slices of incidentp̄ momentum. TheDE distributionsfor all intervals are shown in Fig. 11. A clean peak atDE50 over some background is observed which representstotal amount of the reactionp̄p→4K including ff andfK1K2 contributions. These distributions have been fittusing a Monte Carlo generated shape for theDE distributionwhich includes simulations at all energies offf and 4Kfinal states, and a background parametrization using theof two Gaussians. The number of non-resonant 4K eventswas therefore obtained by

N4K5NT2Nff2NfKK2Nb .

In the above expression, the number of 4K events is thedifference between the total number of events in each(NT), the ff (Nff) and fK

1K2 (NfKK) yields whichwere obtained from the channel likelihood fits, and the baground (Nb) is drawn from the fits to theDE distributions.Due to the uncertainty in the background subtraction, a 5systematic error has been added quadratically to the stacal errors. The background below the 4K signal is relativelysmall, being in average of the order of 10% increasing20% only in the higher momentum regions.

VII. CROSS SECTIONS

Having determined the number of events for each chnel, we have computed the corresponding cross sections

s5events

acceptance3luminosity.

Due to decreasing performance of the threshold Cˇ erenkovcounters in the last period of the data taking, part of dsuffer an additional 20% systematic normalization errThese data represent about 30% of the total and havebeen used in the calculation of the cross sections. Howeproperly scaled, these data can be used in the study oangular distributions. These cross sections have beenrected for unseenf decay modes and are displayed in TabI and shown in Fig. 12.

The ff cross section has been corrected assuming pspace in the calculation of the acceptance. This is not rea strong assumption as it can be seen from Fig. 6~c!. Inaddition, a spin parity analysis of theff final state has been

e

ae

e

rin

he

d

m

in

-

%ti-

o

-s

a.otr,

heor-

selly

performed@37#. This analysis shows that theff system isdominated byJPC5211. Correcting the mass spectrum witthe results from the spin-parity analysis has little influenon the shape of the integrated acceptance as a function off mass.

Notice that:The ff, fK1K2 and 4K6 cross sections have differen

shapes. Theff cross section, in particular, has a strothreshold enhancement, while thefK1K2 and 4K6 crosssections have a smooth increase as a function of the centmass energy.

The ff cross section is rather large, about 3.5mb in thethreshold region.

No evidence for narrow structures is found.The largeff production close to threshold can be inte

preted as a violation of the~OZI! rule. If the OZI rule isinterpreted to forbid strangeness production inp̄p annihila-tions then the processp̄p→ff can proceed only via thesmall ūu,d̄d component present in thef wave function.With a deviation from ideal mixingu2u0 of only 1

0 to 40,the f is nearly 100%s̄s. We can therefore derive an uppelimit tan4(u2u0)'2.5310

25 for the ratio of cross sectionsff /svv for production in p̄p annihilation. Although thecross section ofp̄p→vv has not been measured directly, aestimate can be obtained from the total 2p12p22p0 crosssection@38#, which was measured to be about 5 mb in tenergy range of our experiment. There are many reacchannels that contribute to this final state. If we estimate t

FIG. 12. Cross sections inmb for the reactions~a! p̄p→ff, ~b!p̄p→fK1K2 and~c! p̄p→2K12K2 corrected for unseenf decaymodes.

,

heatn

ntta

al

er:

l

tum

ng

ion

i-thom

lainac-

ific

-

e of

r of

ors-ro-

veryns

ctedthe

t an

w

un9this


it is 10% vv, then the expectedff cross section is 10 nbtwo orders of magnitude lower than our measurements.

VIII. SEARCH FOR j/f J„2230…

To search for thej/ f J(2230) resonance, a fine scan of tff cross section was performed during two different dtaking periods. The results from these scans are showFig. 13 and displayed in Table II.

Here the empty and full dots distinguish the two differesets of the data, showing good agreement in the size offf cross section. No narrow structure is visible in the daWe have fitted theff mass spectrum using a polynomi

FIG. 13. Cross section inmb for the reactionp̄p→ff in a finescan over two different periods of data collection corrected forseenf decay modes. Open circles: 1991 data; full circles: 19data. The line is the result from the fit described in the text,curve represents a Breit-Wigner resonance whose amplitudethe 95% c.l. upper limit for the production of aj/ f J(2230) with amass of 2235 MeV and a width of 15 MeV.

TABLE II. ff cross section for the fine scan.

c.m. energyGeV/c2

s~ff!mb

2.219 4.1560.342.221 4.1660.362.221 3.8760.542.222 3.9460.352.224 4.4060.362.226 3.9060.342.226 3.6860.342.228 3.0060.302.229 3.2060.322.231 3.7360.352.231 2.9760.332.233 4.2060.352.235 3.5260.342.236 2.4860.302.242 3.3860.452.247 2.6860.392.254 2.6360.35

ain

the.

and a Breit-Wigner form representing thej/ f J(2230) withm52235 MeV andG515 MeV, parameters measured in threactionJ/c→gj wherej→ p̄p by the Beijing Spectromete~BES! experiment@19#. The Breit-Wigner form is written as

sBW5~wiwf !~2J11!

~2S111!~2S211!

4p~\c!2

s24mp2

3G2

~As2mres!21G2/4. ~4!

Here (wiwf) is the double branching ratio,wiwf5B(X→ p̄p)3B(X→ff). TheSi terms are the spins of the initiaproton and antiproton (1/2), andJ is the total angular mo-mentum of the resonance, reducing the angular momenterm, (2J11)/@(2S111)(2S211)# to 5/4 in the case of aJ52 resonance. A limit on the product of the branchiratios of B(j→ p̄p)3B(j→ff)

ini

sti-ci-

ncil,


ACKNOWLEDGMENTS

We thank the teams of the CERN Antiproton Complex,particular the LEAR staff. This work has been supportedpart by CERN, the German Bundesministerium fu¨r Bildung,

’97

on,

n-

c-

ul

s,

n

Wissenschaft, Forschung und Technologie, the Italian Ituto Nazionale di Fisica Nucleare, the Swedish Natural Sence Research Council, the Norwegian Research Couand the United States National Science Foundation.

le:

.

5

m.

m-

.

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study of the reaction p¯pŸfffrom 1.1 to 2.0 gev/ca study has been performed of the reaction...

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