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[Article] Study of the f(0)(1500)/f(2)(1565) production in the exclusiveannihilation anti-n.anti-p -> pi+.pi+.pi- in flight

Original Citation:A. Bertin; M. Bruschi; M. Capponi; A. Collamati; S. De Castro; R. Donà; A. Ferretti; D. Galli; B.Giacobbe; U. Marconi; M. Piccinini; M. Poli; N. Semprini Cesari; R. Spighi; S. Vecchi; A. Vezzani;F. Vigotti; M. Villa; A. Vitale; A. Zoccoli; M. Corradini; A. Donzella; E. Lodi Rizzini; L. Venturelli;A. Zenoni; C. Cicalò; A. Masoni; G.Puddu; S. Serci; P. Temnikov.; G. Usai; O.E. Gortchakov; S.N.Prakhov; A.M. Rozhdestvensky; M.G. Sapozhnikov; V.I. Tretyak; P. Gianotti; C. Guaraldo; A. Lanaro;V. Lucherini; F. Nichitiu.; C. Petrascu; A. Rosca; V. Ableev; C. Cavion; U. Gastaldi; M. Lombardi; G.Maron; L. Vannucci; G. Vedovato; G. Bendiscioli; V. Filippini; A. Fontana; P. Montagna; A. Rotondi;A. Saino; P. Salvini; C. Scoglio; F. Balestra; D. Bergo; E. Botta; T. Bressani; M.P. Bussa; L. Busso;D. Calvo; P. Cerello; S. Costa; P. Damiani; O.Y. Denisov; F. D’Isep; C. Fanara; L. Fava; A. Feliciello;L. Ferrero; A. Filippi; R. Garfagnini; A. Grasso; A. Maggiora; S. Marcello; N. Mirfakhrai; D. Panzieri;E. Rossetto; F. Tosello; L. Valacca; M. Agnello; F. Iazzi; B. Minetti; G. Pauli; S. Tessaro; L. Santi(1998). Study of the f(0)(1500)/f(2)(1565) production in the exclusive annihilation anti-n.anti-p ->pi+.pi+.pi- in flight. In: PHYSICAL REVIEW D, vol. 57 n. 1, pp. 55-66. - ISSN 0556-2821

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Published version:DOI:10.1103/PhysRevD.57.55

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Study of the f 0„1500…/f 2„1565… production in the exclusive annihilation n̄p˜p1p1p2

in flightA. Bertin, M. Bruschi, M. Capponi, A. Collamati, S. De Castro, R. Dona`, A. Ferretti, D. Galli, B. Giacobbe, U. Marconi,

M. Piccinini, M. Poli,* N. Semprini Cesari, R. Spighi, S. Vecchi, A. Vezzani, F. Vigotti, M. Villa, A. Vitale, andA. Zoccoli

Dipartimento di Fisica, Universita` di Bologna and INFN, Sezione di Bologna, Bologna, Italy

M. Corradini, A. Donzella, E. Lodi Rizzini, L. Venturelli, and A. ZenoniDipartimento di Chimica e Fisica per l’Ingegneria e per i Materiali, Universita` di Brescia and INFN, Sezione di Pavia, Pavia, Italy

C. Cicalò, A. Masoni, G. Puddu, S. Serci, P. Temnikov,† and G. UsaiDipartimento di Fisica, Universita` di Cagliari and INFN, Sezione di Cagliari, Cagliari, Italy

O. E. Gortchakov, S. N. Prakhov, A. M. Rozhdestvensky, M. G. Sapozhnikov, and V. I. TretyakJoint Institute for Nuclear Research, Dubna, Moscow, Russia

P. Gianotti, C. Guaraldo, A. Lanaro, V. Lucherini, F. Nichitiu,‡ C. Petrascu,‡ and A. Rosca‡

Laboratori Nazionali di Frascati dell’INFN, Frascati, Italy

V. Ableev,§ C. Cavion, U. Gastaldi, M. Lombardi, G. Maron, L. Vannucci, and G. VedovatoLaboratori Nazionali di Legnaro dell’INFN, Legnaro, Italy

G. Bendiscioli, V. Filippini, A. Fontana, P. Montagna, A. Rotondi, A. Saino, P. Salvini, and C. ScoglioDipartimento di Fisica Nucleare e Teorica, Universita` di Pavia and INFN, Sezione di Pavia, Pavia, Italy

F. Balestra, D. Bergo, E. Botta, T. Bressani, M. P. Bussa, L. Busso, D. Calvo, P. Cerello, S. Costa, P. Damiani,O. Y. Denisov,§ F. D’Isep, C. Fanara, L. Fava, A. Feliciello, L. Ferrero, A. Filippi,i R. Garfagnini, A. Grasso, A. Maggiora,

S. Marcello, N. Mirfakhrai,¶ D. Panzieri, E. Rossetto, F. Tosello, and L. ValaccaIstituto di Fisica, Universita` di Torino and INFN, Sezione di Torino, Torino, Italy

M. Agnello, F. Iazzi, and B. MinettiPolitecnico di Torino, Dipartimento di Fisica and INFN, Sezione di Torino, Torino, Italy

G. Pauli and S. TessaroIstituto di Fisica, Universita` di Trieste and INFN, Sezione di Trieste, Trieste, Italy

L. SantiIstituto di Fisica, Universita` di Udine and INFN, Sezione di Trieste, Italy

~The OBELIX Collaboration!~Received 19 May 1997; revised manuscript received 20 August 1997; published 9 December 1997!

The spin-parity analysis of then̄ p→p1p1p2 exclusive reaction in flight is presented. The main aim is tostudy the (p1p2) invariant mass spectrum in the region around 1500 MeV. The analysis was performed witha Breit-Wigner parametrization for all the resonant states and, for the scalar sector in the mass region below 1.2GeV, by means of a K-matrix-like treatment. It clearly shows the need for two states, a scalar one (011) withmass and width (1522625) MeV and (108633) MeV, and a tensorial one (211) with mass (1575618) MeV and width (119624) MeV, respectively. In addition, the analysis requires the presence of ascalar state at (1280655) MeV, (323613) MeV broad, and of a second vectorial one, in addition to ther0(770) signal, with mass and width (1348633) MeV and (275610) MeV, respectively.@S0556-2821~98!01401-5#

PACS number~s!: 13.75.Cs, 12.39.Mk, 14.40.Cs

*Dipartimento di Energetica ‘‘Sergio Stecco,’’ Universita` diFirenze, Firenze, Italy.

†On leave of absence from Institute for Nuclear Research andNuclear Energy, Sofia, Bulgaria.

‡On leave of absence from National Institute of Research andDevelopment for Physics and Nuclear Engineering ‘‘Horia Hu-lubei,’’ Bucharest-Magurele, Romania.

§On leave of absence from Joint Institute for Nuclear Research,Dubna, Moscow, Russia.

i Corresponding author. E-mail address: filippi@to.infn.it; FAX:11.39.11.6707325

¶On leave of absence from Shahid Beheshty University, Teheran,Iran.

PHYSICAL REVIEW D 1 JANUARY 1998VOLUME 57, NUMBER 1

570556-2821/97/57~1!/55~12!/$10.00 55 © 1997 The American Physical Society

I. INTRODUCTION

The annihilation of a (NN̄) system provides a useful toolto study the production of new mesons, in addition to the

ordinary q q̄-like ones which find a natural location in theSU~3! nonets. In fact, it helps us to understand whether newobjects, which are unlikely to be classified as ordinary me-sons due both to their quantum numbers and to the lack ofavailable slots in the nonets, are due to effects related to

(NN̄) dynamics or are items of a new kind of matter, com-posed by gluons only~the glueballs! or by mixings between

quarks and gluons. The existence of such non-q q̄ mesons ispredicted by QCD, which up to now is the most reliabletheory for the description of strong interaction phenomena,but still has to be fully proved on experimental grounds.

A possible candidate for a glueball state is a relatively‘‘new’’ resonant structure emerging at about 1500 MeV inthe (p1p2) invariant mass spectra, observed in the final

states ofNN̄ annihilation reactions.After the initial observation of a state at about 1500 MeV

in annihilation processes in liquid hydrogen and deuteriumbubble chambers@1#, its first sound spin-parity assignmentwas given by the Asterix Collaboration by means of a com-parative study of thep̄p→p1p2p0 annihilation reaction atrest, in two separate samples, experimentally selected andcharacterized by a different content ofP-wave initial states@2#. Its observation, mainly in theP-wave enriched sample,and a complete spin-parity analysis by means of Breit-Wigner parametrization for resonances, led them to assert itstensorial (211) nature. The mass and width were found tobe 1565620 MeV and 170640 MeV, respectively; this stateis reported in the last Particle Data Group~PDG! issue@3# asf 2(1565).

The study of thep̄p→p1p2p0 channel is rather diffi-cult; complications arise from the double isospin choice forthep p̄ state (I 50 or I 51) and from the presence of severalintermediate states, such as ther ’s triplet, which interfere inthe pp mass region around 1500 MeV. The Asterix and theOBELIX experiments could overcome these complicationsby exploiting different techniques allowing a reliable selec-tion of the initial state~i.e., the simultaneous detection ofL-X rays @2# and the use of targets in different pressureconditions @4#!. On the other hand, when studying thep p̄→3p0 annihilation channel, one has to deal with combi-natorial effects, but in this case the isospin is fixed~to 1!, sothat the total number of initial states is reduced byI andJPC

conservation laws. The Crystal Barrel Collaboration exten-sively studied this channel and published several papersabout the properties of the state at about 1500 MeV, eachtime with increased statistics and with improved analysismethods@5–9#: The first paper asserted the presence of atensorial resonance, atm51515 MeV, which could reallybe identified with the 211 state found by Asterix@5#. Lateron the need for a scalar signal was put forward@6,10#. Ascalar component was then added to a tensorial one, of re-duced strength, to obtain good fits@7#; this scalar state is nowclassified asf 0(1500) @3#. These results were confirmed byan updated study with high statistics~712 000 events! @8#.The new study was performed by applying theK-matrix

analysis technique@11#, which assures unitarity even in thepresence of several overlapping states with the same quan-tum numbers. It led to the conclusion that, in addition to thenarrow f 0(975) and a broadf 0(1300) backgroundlike signalreported now by PDG@3# as f 0(1370), a third scalar reso-nance of mass (1500615) MeV and widthG5(120625)MeV is actually needed, as well as a secondD-wave contri-bution @in addition to f 2(1270)#, at about 1520 MeV. Thefractional contribution of these two states to the 3p0 annihi-lation channel was found to be 12% for thef 0(1500) and17% for thef 2(1520). These results were recently confirmedby a coupled-channel analysis@9# on p̄p→3p0,p̄p→2hp0, and p̄p→2p0h data samples, and the mass forthe tensorial signal was suggested to be about 1552 MeV.

A number of results by OBELIX concerning the proper-ties of the structures at about 1500 MeV have been published@12–14#. They show that a single tensorial signal is by nomeans enough to give a good description of the structure atabout 1500 MeV. An attempt to introduce a scalar contribu-tion was quite successful, and it was shown that it could bedominant especially below 1550 MeV. On the contrary, forhigher masses a contribution from a tensorial state seemed tobe required by the fit.

In this paper we report the results of the study of thef 0(1500)/f 2(1565) resonances in the in-flight annihilationreaction n̄ p→2p1p2, taking into account a possible de-pendence on then̄ momentum as well.

II. n̄p˜p1p1p2 REACTION

A. Experimental environment

Concerning the selection ofI 5 1 initial states, the sameproperties of thep p̄→3p0 annihilation channel are sharedby other reactions, such asp̄d→2p2p1ps andn̄ p→2p1p2. While the first was initially studied in bubblechamber@1,15#, the second one could never be investigateddue to the lack ofn̄ beams. Only the OBELIX experimentcould study such annihilations thanks to a unique facilitywhich allowed the production of antineutrons by means of ap̄p→n n̄ charge exchange reaction@16#.

1. Experimental apparatus and the production of the n¯ beam

Only a few hints will be given here about the experimen-tal setup and its main performances; a more detailed descrip-tion may be found, for example, in Ref.@17#.

OBELIX is a magnetic spectrometer which operated atthe CERN LEAR machine until its closure. It was designedin order to study low energy antiprotons and antineutronsannihilations on nucleons and nuclei, with the main purposeof investigating nuclear dynamics effects and meson spec-troscopy with high statistics. The apparatus exhibits a cylin-drical symmetry and its central detectors operate in a 0.5 Tmagnetic field provided by the Open Axial Field magnet.Moving radially from the axis, coincident with thep̄ /n̄ beamline, it is composed of the following: a cylindrical target,filled with different gases or liquids according to the mea-surement to be performed; a spiral projection chamber asvertex detector; two cylindrical layers of plastic scintillators,

56 57A. BERTIN et al.

which constitute the time-of-flight~TOF! system and whichsandwich the tracking device, a Jet Drift Chamber. The time-of-flight system provides in real time (;200 ns! informationabout the multiplicity of the annihilation event and its topol-ogy and delivers a fast signal on which the first level triggerof the apparatus is based@18#. It allows charged particle (K,p, p! identification, at least up to 600 MeV/c momenta, andmoreover it is essential for the evaluation of then̄ momen-tum; its overall resolution is about 1 ns full width at halfmaximum ~FWHM!. The tracking device is also used forparticle identification bydE/dx measurements. Its spatialresolution is aboutsrf5160 mm in the (rf) plane andsz51.2 cm along the wires;dE/dx resolution is aboutsE /E;12% and allows one to discriminate pions from ka-ons up to 600 MeV/c, and to identify protons up to1 GeV/c. Its momentum resolution is ;3.2% at930 MeV/c. Finally, four supermodules of a High AngularResolution Gamma Detector enclose the central detector.

The apparatus is endowed with a facility, unique in theworld, for the production of an antineutron beam. The an-tineutron production occurs in a LH2 cylindrical targetplaced along thep̄-beam axis in the upstream hollow pole ofthe magnet, at about 2 m from the center of the apparatus; itslength depends on the momentum of the incoming antipro-tons @19#.

The produced antineutrons are collimated by a suitablelead collimator system and then annihilate in the reactiontarget placed at the center of the apparatus~instead of thevertex detector!; depending on thep̄ beam momentum andon the collimator shape, the number of producedn̄ ’s lies inthe range 30–50/106 p̄ , and out of these about 20% interactin flight in the reaction target. The features of then̄ beam arecontinuously kept under control by a suitable monitor placeddownstream the spectrometer.

The measurement of eachn̄ momentum is performed bymeans of the time-of-flight technique, measuring the timebetween the arrival of an antiproton and the impact time ofthe fastest of the annihilation products on the inner scintilla-tor barrel system. This measurement is affected by a totalerror less than 5%@19#. The n̄ ’s are produced with a con-tinuous momentum distribution ranging from;50 MeV/c( n̄ from p̄ with 98.6 MeV/c, the CEX threshold momen-tum! up to a maximum depending on thep̄ momentum, andcorresponding in general ton̄ production near the entrancewindow of the target.

The full description of this facility and its performancesmay be found in Ref.@19#.

2. Meson spectroscopy with n¯

Even if the globally available statistics is lower than whatcould be obtained in thep̄d reaction, and the experimentalrealization of then̄ beam a rather difficult challenge, then̄ pannihilation has the advantage that the final states are com-pletely unaffected by the rescattering problems which, on thecontrary, spoil the observations ofp̄n ones. As will beshown later,n̄ p→2p1p2 events can be selected by meansof a 4C kinematic fit which rejects most of the backgroundcontribution. Moreover, they do not suffer combinatorial ef-fects as strong as those emerging, for example, in the 3p0

channel.Since the antineutrons annihilate in flight, the available

energy for the annihilation reaction changes event by event.This lets studying various annihilation effects, such as theproduction rates of initial partial waves and the branchingfractions of intermediate states, as a function ofn̄ momen-tum. However, care must be taken when dealing with ampli-tudes as well as with normalizations, since both of them varyevent by event as a function of the available energy. More-over, the amplitude should take into account that in in-flightannihilation it is necessary to sum incoherently over polar-izations@20,21#.

B. Data reduction criteria

With the n̄ facility a total of about 213106 annihilationsin a liquid hydrogen target have been collected, in differentLEAR beam conditions (pp̄.305 MeV/c in 1991–1992,pp̄.412 MeV/c in 1993–1994–1995, entailing differentmaxima for n̄ momentum!. In Table I the total availablestatistics for three-prong events is reported, selected accord-ing to four pn̄ intervals.

The analysis has been performed independently on all ofthe reportedpn̄ different ranges. Each sample had to bematched with a dedicated Monte Carlo calculation, whoseevent content is reported in Table I as well. The MonteCarlo–generated events have been reduced applying thesame selection criteria as for the experimental data; it waschosen not to mix more than two samples belonging to dif-ferent data taking periods, for consistency reasons.

Useful data are selected applying powerful quality cutswhich drastically reduce the total background. All eventshave been collected by applying a loose multiplicity trigger~by means of OBELIX time-of-flight system: the tighter re-quirement was of at least three and two hits, respectively, onthe inner and outer detectors!; the off-line analysis discardedevents either not fully reconstructed in the OBELIX tracking

TABLE I. Total three-prong statistics under study: real data and Monte Carlo–generated events. In thetext we refer, for simplicity of notation, to each of the data samples by the numbers 1, 2, 3, and 4 for theglobal one.

pn̄ range Experimental events Monte Carlo events

1 ;50

device and not showing a common vertex or with a wrongtotal charge and multiplicity, as well as annihilations occur-ring outside the reaction target or on its mylar walls. Energy-momentum conservation cuts were employed so as to elimi-nate possible undetected neutral particles; the total energywas required to be larger than 1.8 GeV and the total c.m.momentum less than 100 MeV/c. All surviving events werethen submitted to a 4C kinematic fit to check then̄ p→2p1p2hypothesis, and out of it only those with a con-

fidence level larger than 5% have been selected; a furtherrejection was applied to events whose confidence level, forthe 1C fit to the kinematic hypothesisn̄ p→2p1p2p0,turned out to be larger than 5% too. At the end of dataselection the background contribution was reduced to 0.4%of the globally available statistics. In Fig. 1 the missing massspectrum for the events under examination is reported; theblack area corresponds to the events selected applying theabove criteria.

In Fig. 2 symmetrized Dalitz plots@m2(p1p2) vsm2(p1p2)] for each of the four examined samples areshown. A common feature is evident, i.e., the presence ofthree bands corresponding to the production of the neutralr@m2(p1p2)50.5 GeV2], of the f 2~1270! @m

2~p1p2!51.6GeV2], and a third band at aboutm2~p1p2!52.4 GeV2,which can be attributed to the production off 0~1500!/f 2(1565). These states can be singled out as well by lookingat the p1p2 invariant mass projections, reported in Figs.3~a!–3~d!.

Concerning thep1p1 invariant mass spectrum, no par-ticular dynamical effect should be observed, but kinematicreflections only. As reported in Figs. 3~e!–3~h!, a significantchange in thep1p1 invariant mass spectra shape is evidentas n̄ momentum increases, with an enhancement at about 1GeV; this is probably to be understood as a strong kinematicreflection of f 2(1270).

III. SPIN-PARITY ANALYSIS TECHNIQUES

A. Introduction

The investigation of the nature off 0(1500)/f 2(1565) hadbeen performed by means of a spin-parity analysis; the prop-erties of this structure and the production of other resonancesas well, such asr0(770) andf 2(1270), were studied.

FIG. 1. Missing mass spectrum forn̄ p→2p1p2 events withtopological selection only~white area! and for events selected byapplying energy-momentum conservation cuts and 4C kinematic fit~black area!.

FIG. 2. Symmetrized Dalitzplots: invariant mass squared(p1,2

1 p2) vs (p2,11 p2). ~a!

sample 1, 50

The contribution of a scalarpp S-wave interaction wasinserted in the fit as well. Phase shift analyses showed that alarge part of this contribution comes from the narrowf 0(980) resonance, coupled to bothpp andKK̄, and emerg-ing over a large background which extends from 400 MeVup to about 1.2 GeV. The representation of this contributionis rather problematic and several ways to parametrize it havebeen proposed in the literature. Some of them are derivedfrom pp scattering processes in peripheral interactions@22#,others from central collisions as well as from other pro-cesses. The widely used Au-Morgan-Pennington~AMP! pa-rametrization@23# is, for instance, based on a low energydiffusion data compendium.

A globally unitary treatment of the scalar sector of theamplitude is provided by theK-matrix formalism, used, forexample, in Refs.@8,9#. In Ref. @8# the scalarK matrix in-cludes three poles, corresponding tof 0(980), a broad statenamed asf 0(1300), andf 0(1500). In Ref.@9# a fourth polewas included, corresponding to a wide background reso-nance@named by the authors asf 0(1000) and classified inlast PDG issue asf 0(400–1200!#. Lately, a new method forthe representation of the scalar amplitude was proposed byBugg et al. @24,25#. In these papers the regions below andabove 1.2 GeV are treated separately: the first one by meansof a ‘‘partial’’ K matrix expressing the interference betweenf 0(980) and the slowly varying background@thef 0(400–1200!#, the second one by means of two relativisticBreit-Wigner functions for the description of the resonantstatesf 0(1370) andf 0(1500).

In the present analysis several tests have been made tosingle out the best parametrization for the OBELIX data; wewill recall later the results of this investigation.

Concerning the vectorial sector, the contribution of a pos-sible radial excitation of ther(770) ~as ar8 with unknownmass and width! was inserted in the fits as well. In a recentpaper@26# the Crystal Barrel Collaboration suggests that atleast two more vector mesons are needed to get a good fit ofthe channelp̄d→p22p0ps . The first of them has a mass of1411614 MeV and a width of 343 MeV, while the secondone peaks at about 1700 MeV. Moreover, a parallel analysisof the channelp̄p→p1p2p0 of OBELIX data ~annihila-tions at rest on hydrogen targets in various density condi-tions! @4# requires mandatorily at least the first radial excita-tion at about 1400 MeV. In the present analysis a satisfactoryfit is obtained with the lowest massr8 only.

B. Global amplitude

The present analysis differs in some aspects from thosealready described in the literature. First of alln̄ p annihila-tion occurs in flight, and so the square modulus of the totaltransition amplitude~the ‘‘intensity’’! is a sum over the he-licity components of the initial states, namely,

Ttot5 (l1 ,l2

U(J

Hl1 ,l2J f l

JU2, ~3.1!wherel1 andl2 are the helicities ofn̄ andp, l5l12l2, J

FIG. 3. Dalitz plot projections:Thick black points with errors:(p1p2) invariant mass spectrafor ~a! sample 1, 50

is the total angular momentum,Hl1 ,l2J are the helicity cou-

plings, andf lJ is the partial wave amplitude projected on the

helicity basis.Eachf l

J is written as a superposition of partial amplitudes,each related to two-body isobar statei :

f J5(i

giJAi

J ~3.2!

~we will drop in the following thel index referring to adefinite helicity projection!. Thegi ’s are complex parametersto be determined from a fit of the probability density, nor-malized to unity, and representing the production strengthsof the i two-body state—they can almost be interpreted asbranching fractions, in spite of interference effects whichwill be shown later to be rather weak. TheAi

J partial waveamplitudes for thei th state contains the true dynamics of theproblem; they are written as

AiJ5(

rZir

JPC~p,q!Fir ~q!, ~3.3!

whereZJPC

are known as ‘‘Zemach functions’’@27# and ex-press the spin-angular dependence, whileF represents theenergy-dependent part, given by proper Breit-Wigner func-tions in the case of resonances or by different parametriza-tions for nonresonant interactions, such as thepp S wave.The indexr runs over all the available combinations of twopions forming thei th isobar state. The Zemach covarianttensors@28# are written following the Rarita-Schwinger for-mulation, by means of the four-momentum vectors of thedipion (q) and of the recoiling pion (p) and depend on thespin J of the resonance and on the relative angular momen-tum between the resonance products. It was shown that thecovariant tensor formalism of Ref.@28# is equivalent to thehelicity formalism @20,21# written in the covariant form ofChung@29#.

Since the c.m. energy is not too large (,1.92 GeV forpn̄

cent, and so it was not inserted in the fit. A similar annihila-tion frequency fromD waves was found in the analysis ofthe reactionn̄ p→p1p0 @32#.

The in-flight annihilation mechanism, provided onechooses correctly the working frame~the reaction rest frame

with z direction along then̄ momentum vector!, involvesonly some of the initial partial waves available components;using the shorthandS, V, and T notation to indicate1S0~scalar!, 3P1 ~vector!, and

3P2 ~tensor! waves,Ttot may bewritten as

Ttot5a2uSu21b2uT~0!u21c2$uV~11!u21uV~21!u2%1d2$uT~11!u21uT~21!u2%

12cdRe$@V~21!T* ~21!2V~11!T* ~11!#exp~ if!%, ~3.12!

with a5A2ReH11S , b5A2ReH11

T , c5ReH21V , d

5ReH21T , andf5(argH21

V 2argH21T ). Only orbital angu-

lar momenta up to 2 have been considered.Additional details of the analysis procedure may be found

in @33#.

C. Treatment of pp S waves

As already stated in Sec. III A, for the parametrization ofthe pp S wave in the mass region under 1.2 GeV, it is notpossible to use a simple propagator and decay factor, but it isnecessary to adopt a complex amplitude which could de-scribe the two-body elastic scatteringpp→pp, as well as,at least, the inelastic scatteringpp→KK̄, due to the openingof KK̄ threshold.

Strictly speaking, none of thepp S waves available inthe literature really fits the production environment of then̄ p→2p1p2 annihilation. Therefore several tests havebeen performed to check the consistency of various kinds ofparametrizations. The AMP parametrization@23#, the oneused by Gaspero in Ref.@34#, and that proposed by Bugget al. @24# and used in@25#, have been chosen to this end.The parametrization by Gaspero@34# reproduces phenom-enologically, by means of a polynomial interpolation, somesets of phase shift data collected by various experiments. Theproduction fractions of initial partial waves and of resonantintermediate states obtained both with Gaspero’s and withAMP parametrization are, within errors, equivalent; full de-tails of these results are reported in@33#.

The best results are anyway obtained in our analysis byusing the parametrization by Bugget al. @24#, described inSec. III A. In this case, the elements of the two-poleK ma-trix used for the description of the ‘‘low mass’’ scalar sector,which will be globally referred to ass in the following, areweighted by means of complex production coefficients, di-rectly taken from Ref.@24#. The energy-dependent part of thescalar amplitude, to be directly inserted in Eq.~3.3!, is writ-ten as

Fs5~L11L2s!K̂111L3K̂12

12r1r2D̂2 i ~r1K̂111r2K̂22!, ~3.13!

whereL i are the cited complex production parameters,r i areusual elements of the two-body phase-space matrix;D̂ is theK-matrix determinant, whileAs is, as usual, the c.m. avail-

able energy. Since in our analysis theL i production param-eters are fixed, we are not able to separate the different con-tributions of f 0(980) and off 0(400–1200! to the globalsstate.

The two ‘‘low mass’’ scalar poles resemble in a way thetwo low mass ones embedded in the AMP parametrization.Above 1.2 GeV the AMP parametrization includes an addi-tional S-matrix pole also, at about 1400 MeV. In the ap-proach of Bugget al. @24# this contribution is inserted as aninterfering relativistic Breit-Wigner function, with mass andwidth to be adjusted by the fit, and represents what is gener-ally understood to be thef 0(1370) state, which severalanalyses claim to be about 350 MeV broad@3#.

In the following we will describe the results obtained ap-plying this parametrization to our data.

D. Fits quality estimators

Because of the event-by-event dependence on energy, thecorrect function to be minimized is the negative logarithm ofthe global likelihood probability density:

L5)i 51

Nm i

E mdV , ~3.14!

where m i is the event-by-event intensity, properly normal-ized by means of a large number of pure phase-space MonteCarlo events, andm is the total probability density evaluatedby using the Monte Carlo-generated events. In this way allelementary amplitudes take quite naturally into account theapparatus efficiency and acceptance.

With three charged pions the acceptance of the OBELIXapparatus is nearly flat~within 3%!. In this case it is possibleto perform fits with reasonably small Monte Carlo sampleswithout losing statistical significance for the larger contribu-tion by systematic errors. It was chosen to use Monte Carlosamples about 3 times as wealthy as the corresponding ex-perimental ones.

The quality of fits can be gathered by studying, in addi-tion to the trend of the likelihood value, thex2 evaluated onthe theoretical symmetrized Dalitz plot, defined as@2#

xD2 5(

i , j

cells~ni j 2t i j !

2

sexpt2 1s th

2, ~3.15!

57 61STUDY OF THE f 0(1500)/f 2(1565) PRODUCTION . . .

whereni j and t i j (sexpt ands th) are the global contents~er-rors! of the i j th cell of experimental and theoretical Dalitzplots. In the evaluation of symmetrized Dalitz plotx2 theerrors on the cell contents are given bysexpt

2 5ni j /2 ~due tothe fact that each event has two entries:n is the effectivenumber of physical events belonging toi j th cell!. For thetheoretical plot, on the contrary, for each of the cells we have

s th2 5 (

events

wi j2 /25t i j

2 /2pi j , ~3.16!

wherewi j is the weight~squared amplitude! of each of thephase space Monte Carlo events belonging to thei j th cell,whose number per cell ispi j . t i j is now obtained by thesimple sum ofwi j weights for all of the Monte Carlo eventbelonging to thei j th cell.

The theoretical Dalitz plot and the experimental one arenormalized to the same number of entries, and for thex2

evaluation only the cells with more than five events weretaken into account. Since the Monte Carlo data samples arelarger by a factor of at least 2 than the experimental ones,each Monte Carlo–modeled spectrum is affected by a statis-tical error which amounts to about the 60–70 % of that ac-tually affecting the experimental data distributions.

E. Production fractions

The production rates of each initial partial wave are cal-culated as

f JPC5

(l

wJPCl uHJPC

l u2

(J

(l

wJPCl uHJPC

l u2, ~3.17!

where the helicity amplitudesH are inferred from the fit@thea, b, c, andd coefficients of Eq.~3.12!# and thewJPC

l ’s arestatistical spin weights of each amplitude, obtained by inte-gration over the full available spectrum.

Each uHJPCl u2 gives the probability of the occurrence of

the l component of a givenJPC initial state only, and thishas to be taken into account when constructing the total

probability density. The spin weights have the same meaningof the partial wave amplitude in Eq.~3.12!, after integrationover the spectrum.

The contribution of the interference term, coming fromthe combination of3P1 and

3P2 l561 components, isalways less than 3%; this can be inferred from Fig. 4, whichshows the contribution of each partial wave—and of the in-terference term as well—to the total amplitude, for data inthe ;50–400 MeV/c full momentum range. In Fig. 4, thelower line ~solid gray! corresponds to the interference con-tribution.

In a similar way, the branching fractions for all isobarshave been evaluated as in@2#:

BFi5(J

xi2

(l

xl2

f JPC, ~3.18!

where thexi values, which express the production weightsfor the i -type isobar and depend on theJPC quantum num-bers of the state, are obtained from the minimization proce-dure. Using Eq.~3.18! the interference effects between reso-nances are, again, necessarily neglected; provided they arenot too heavy, the ‘‘branching fraction’’ values represent areliable suggestion of the strength of the production of asingle state.

IV. RESULTS FROM THE FITS

A. Strategy

The main difference from the previous analyses is thatf 0/f 2 masses and widths are left free in the fits, and so for eachof them minimization errors can be quoted. On the contrary,the r0 and f 2~1270! masses have been fixed to the valuesquoted by PDG@3#; a fit on the shape onp1p2 invariantmass spectrum with noninterfering Breit-Wigner functionsshows a quite good agreement of the OBELIX data to them.The mass and width of the other unknown states, namely, thef 0(1370) and ther8(1450), were searched for afterwards,after having settled those of the structures in the 1500 MeVregion.

FIG. 4. Contribution of each partial wave to the global spectra~Monte Carlo events modeled by the fit,;50

Four independent analyses were carried over for data be-longing to the cited samples. As a general result, the fits withthe double contribution by eitherf 0~1500! and f 2(1565) givebetter results both forL values, and forx2 evaluated onDalitz plots; the fits with the scalar contribution only alwaysshow a better likelihood value in comparison to a singletensorial signal. This result is clearly shown in Fig. 5, wherefor the values of lnL andxD2 are separately reported for eachdata sample under examination, with reference to fits per-formed in the four different hypotheses~a! ~black triangles!no resonance in the region at about 1500 MeV,~b! ~blacksquares! tensorial signal only,~c! ~black circles! scalar signalonly, and~d! ~open circles! both scalar and tensorial signals.

All the results relative to the behavior in the 1500 MeVregion are independent of the method chosen to parametrizepp S-wave contribution.

B. Final results

All the results which will be quoted here have been ob-tained by convergent and stable fits. They all refer to a‘‘minimum environment’’ which had been found in a thor-ough independent way for each data sample.

Quoting as systematic error the maximum spread of themasses and widths values obtained in the best fit solutionsand as statistical ones the maximum of the minimization er-rors delivered byMINUIT @35# in all of the performed fits, theaverage values~over the wholen̄ momentum spectrum! for

f 0 and f 2 masses and widths are

m„f 0~1500!…5152265stat625syst MeV,

G„f 0~1500!…510868stat632syst MeV ,

m„f 2~1565!…51575615stat610syst MeV,

G„f 2~1565!…5119618stat616syst MeV.

After having set these values it was checked whether theinsertion of new states not directly emerging from the Dalitz

TABLE II. Comparison between quality of fit estimators in dif-ferent best fits performed on the sample with the greatest availablestatistics ~35 118 events!, by means of scalar amplitude param-etrized as in Ref.@24,25# @~1c! and following#, and in the case ofAMP @~1a!# @23# and Gaspero’s version@~1b!# @34#.

lnL xD2

~1a! s AMP –7412 2098/1257~1b! s Gaspero@34# – 7425 1906/1257~1c! s @24,25# –7467 1939/1251~2! s 1 f 0(1370) –7494 1826/1232~3! s 1 f 0(1370)1r8(1450) –7741 1567/1239

FIG. 5. Trend of quality of fitestimators (2 lnL and x2 calcu-lated on the Dalitz plot!, for thebest fit obtained in all of the fourdata samples under examination.The markers correspond to thedifferent hypotheses:~1! black tri-angle, no resonance in the 1500MeV region; ~2! black squares,tensorial signal only;~3! blackcircle, scalar signal only;~4! opencircle, both scalar and tensorialresonances. ThexD

2 for the lesswealthy data sample (;50

plots, namely,f 0(1370) andr8(1450), could produce anysignificant change in the quality of the fits. The effect of theintroduction of these two states may be better evaluated bystudying the trend of the quality estimators in the fits per-formed on the most wealthy data sample. In Table II thevalues of2 lnL and xD2 obtained in the three different hy-potheses:~1! s contribution only,~2! s and f 0(1370) con-tributions, and~3! s, f 0(1370), andr8(1450) contribu-tions are reported. Concerning the first hypothesis, lines~1a!,~1b!, and~1c! report, respectively, the values of the estima-tors obtained in a fit to the same data sample by using for thes state the AMP parametrization, Gaspero’s one, and the onesuggested by Bugget al., for comparison purposes.

The greater flexibility of the amplitude suggested by Bugget al. immediately delivers better values for all of the esti-mators even in the simpler hypothesis~1! @presence of scalarinteraction below 1.2 GeV only, withoutf 0(1370) contribu-tion#; a greater improvement is gained with the introductionof ther8 signal. The best fits occurs for the following valuesfor f 0(1370) andr8(1450) masses and widths:

m„f 0~1370!…51280655stat MeV,

G„f 0~1370!…5323613stat MeV,

m„r8~1450!…51348633stat MeV,

G„r8~1450!…5275610stat MeV,

where the errors are statistical only and express the maxi-mum minimization error obtained in several fits.

The introduction of these states has no effect on the pro-duction fractions of the states located in the 1500 MeV re-gion; the superposition of thes state and of thef 0(1370)contribution is about equivalent~within errors! to the globalpp S-wave contribution obtained by means of AMP param-etrization. In spite of the differences in the parametrizations,the mass and width values keep on being in good agreementto the mean values reported above; this shows the stability of

FIG. 6. Results from fit: thesolid black line represents the fit,and the points with errors are theexperimental data. On verticalrows the plots refer to the differ-ent data samples: type~A! ;50

the achieved solution and its independence of the way thebackgroundpp interaction is represented.

Concerning the other resonant state production fractionsobtained by means of AMP and/or Gaspero’s parametriza-tions, they are somewhat different from those obtained withthe one of Bugget al.; this is seemingly due to the absenceof f 0(1370) contribution, which in both AMP and Gaspero’streatments was not inserted in order to avoid possible doublecounting. This difference is evident especially in the produc-tion of f 2(1270) mesons; moreover, the production rates arealtered by the presence of ar8 state. The effect of thisr8signal is to lower thef 2(1270) production rate, since the twostates are overlapping. Full details of the results obtained byusing AMP and Gaspero’s parametrizations are reported inRef. @36#.

Some typical distributions, with the results of the fits ob-tained using the parametrization of the Bugget al. superim-posed, are shown in Fig. 6 for the four data samples underexamination.

In Table III the production fractions of each partial wave,normalized to 100%, are reported, as a function of then̄momentum. The first quoted errors are statistical and areobtained by simple Gaussian propagation on the values de-livered by MINUIT ; the second ones are systematic and takeinto account the spread of the parameter values delivered inseveral acceptable fits. Table IV reports the partial branchingfractions of each resonant state, evaluated by means of Eq.~3.18!. All results are reported for the three data samples 1,2, and 3.

From Tables III and IV the following general trends maybe inferred, as the incomingn̄ momentum increases: a de-crease inS-wave production and a slight increase ofP waveproduction, resulting from a steep increase of the3P2 com-ponent as well as a softer decrease of3P1 one; concerningthe branching fractions a decreasing contribution of theppS wave below 1.2 GeV (s); an almost constant contributionfrom f 0(1500); a strongly increasing production off 2(1270); an increasing production fraction off 2(1565); thetrends for the production of both vectorial mesons, namely,r0(770) andr8, are somewhat similar, not showing a mono-tonical trend but rather a maximum in the range 200–300MeV/c; a somewhat decreasing production off 0(1370), al-though affected by rather large errors; the production of the

scalar componentf 0(1500) is always dominant overf 2(1565); the errors are still too large to assert any specifictrend, but the already mentioned increase off 2(1565) pro-duction with the increase ofn̄ momentum.

V. CONCLUSIONS

The present analysis, performed on the total sample ofn̄ p→p1p1p2 annihilation data, collected by the OBELIXexperiment, led to obtain the masses and widths values forboth f 0(1500) andf 2(1565). These values agree well, withinerrors, to what previously found by other experiments andreported by PDG@3#. The f 0(1500) features are, in addition,in full agreement to what is obtained by the OBELIX experi-ment in a parallel analysis on thep̄p→p1p2p0 channel@4#. In this channel, the interference mechanism betweenchargedr ’s may be at the origin of the slight differenceconcerning thef 2(1565) mass.

In conclusion, by exploiting a good deal of high qualitydata, we confirm the presence of a scalar resonance in the1500 MeV mass region, as well as a weaker tensorial struc-ture, of similar mass and width. Their overall contributionamounts to about 15% of the whole spectrum, a value ingood agreement with a preliminary evaluation, based on notinterfering Breit-Wigner integration and performed on a lim-ited statistics set of data@16#.

The production fractions of both the states, as well astheir masses and widths, remain stable within statistical andsystematic errors even when the fits are performed with dif-ferent starting conditions, and with different kinds of param-etrizations of thepp nonresonatingS wave, in the regionbelow under 1.2 GeV.

ACKNOWLEDGMENTS

We gratefully acknowledge the LEAR operating staff forthe excellentp̄ beam quality and the intensity that could besuccessfully provided during the dedicated runs. We are par-ticularly indebted to G. Bochaton, V. Mazzone, G. Novellini,and V. Sergo for their invaluable contribution in designing,constructing, and operating the cryogenic targets used in theexperiment. F. Impavido and A. Pia provided clever assis-tance in the construction and setting up of the mechanicalelements of the antineutron beam.

TABLE IV. Isobar branching fractions in percent for different ranges ofn̄ momentum.s parametrizedfollowing Refs.@24,25#.

;50–200 MeV/c 200–300 MeV/c 300–405 MeV/c

s 28.960.1612.2 17.6060.0666.53 11.5460.04610.60r0(770) 6.2460.0463.05 18.2160.0463.20 14.0560.0464.47f 2(1270) 10.1260.0664.22 25.0660.05610.00 36.660.168.8f 0(1370) 32.0860.1067.48 6.5560.02612.59 9.6060.03614.06r8(1450) 9.0260.0661.8 15.7260.0463.72 10.5160.0365.62f 0(1500) 10.1760.0661.59 10.2160.0361.31 9.6960.0361.88f 2(1565) 3.4860.0361.29 6.6360.0262.94 7.9560.0361.01

57 65STUDY OF THE f 0(1500)/f 2(1565) PRODUCTION . . .

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