- Email: [email protected]
Rapidity-rank structure of pp pairs in hadronic Z0 decays
28 September 2000
Physics Letters B 490 Ž2000. 61–70 www.elsevier.nlrlocaternpe
Rapidity-rank structure of pp pairs in hadronic Z 0 decays DELPHI Collaboration P. Abreu u , W. Adam ay, T. Adye ak , P. Adzic k , I. Ajinenko aq , Z. Albrecht q , T. Alderweireld b, G.D. Alekseev p, R. Alemany ax , T. Allmendinger q , P.P. Allport v, S. Almehed x , U. Amaldi i,ab, N. Amapane at , S. Amato av, E.G. Anassontzis c , P. Andersson as , A. Andreazza i , S. Andringa u , as ˚ P. Antilogus y, W-D. Apel q , Y. Arnoud i , B. Asman , J-E. Augustin y, A. Augustinus i , P. Baillon i , P. Bambade s , F. Barao u , G. Barbiellini au , R. Barbier y, D.Y. Bardin p, G. Barker q , A. Baroncelli am , M. Battaglia o , M. Baubillier w, K-H. Becks ba , M. Begalli f , A. Behrmann ba , P. Beilliere h , Yu. Belokopytov i , N.C. Benekos af , A.C. Benvenuti e, C. Berat n , M. Berggren w, D. Bertrand b, M. Besancon an , M. Bigi at , M.S. Bilenky p, M-A. Bizouard s , D. Bloch j, H.M. Blom ae, M. Bonesini ab, M. Boonekamp an , P.S.L. Booth v, A.W. Borgland d , G. Borisov s , C. Bosio ap, O. Botner aw, E. Boudinov ae, B. Bouquet s , C. Bourdarios s , T.J.V. Bowcock v, I. Boyko p, I. Bozovic k , M. Bozzo m , M. Bracko ar, P. Branchini am , R.A. Brenner aw, P. Bruckman i , J-M. Brunet h , L. Bugge ag , T. Buran ag , B. Buschbeck ay, P. Buschmann ba , S. Cabrera ax , M. Caccia aa , M. Calvi ab, T. Camporesi i , V. Canale al , F. Carena i , L. Carroll v, C. Caso m , M.V. Castillo Gimenez ax , A. Cattai i , F.R. Cavallo e, V. Chabaud i , Ph. Charpentier i , P. Checchia aj, G.A. Chelkov p, R. Chierici at , P. Chliapnikov i,aq , P. Chochula g , V. Chorowicz y, J. Chudoba ad , K. Cieslik r, P. Collins i , R. Contri m , E. Cortina ax , G. Cosme s , F. Cossutti i , H.B. Crawley a , D. Crennell ak , S. Crepe n , G. Crosetti m , J. Cuevas Maestro ah , S. Czellar o , M. Davenport i , W. Da Silva w, G. Della Ricca au , P. Delpierre z , N. Demaria i , A. De Angelis au , W. De Boer q , C. De Clercq b, B. De Lotto au , A. De Min aj, L. De Paula av, H. Dijkstra i , L. Di Ciaccio i,al , J. Dolbeau h , K. Doroba az , M. Dracos j, J. Drees ba , M. Dris af , A. Duperrin y, J-D. Durand i , G. Eigen d , T. Ekelof aw, G. Ekspong as , M. Ellert aw, M. Elsing i , J-P. Engel j, M. Espirito Santo u , G. Fanourakis k , D. Fassouliotis k , J. Fayot w, M. Feindt q , A. Ferrer ax , 0370-2693r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 0 0 . 0 0 8 6 8 - 6
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E. Ferrer-Ribas s , F. Ferro m , S. Fichet w, A. Firestone a , U. Flagmeyer ba , H. Foeth i , E. Fokitis af , F. Fontanelli m , B. Franek ak , A.G. Frodesen d , R. Fruhwirth ay, F. Fulda-Quenzer s , J. Fuster ax , A. Galloni v, D. Gamba at , S. Gamblin s , M. Gandelman av, C. Garcia ax , C. Gaspar i , M. Gaspar av, U. Gasparini aj, Ph. Gavillet i , E.N. Gazis af , D. Gele j, L. Gerdyukov aq , N. Ghodbane y, I. Gil ax , F. Glege ba , R. Gokieli i,az , B. Golob i,ar, G. Gomez-Ceballos ao , P. Goncalves u , I. Gonzalez Caballero ao , G. Gopal ak , L. Gorn a , V. Gracco m , J. Grahl a , E. Graziani am , P. Gris an , G. Grosdidier s , K. Grzelak az , J. Guy ak , C. Haag q , F. Hahn i , S. Hahn ba , S. Haider i , A. Hallgren aw, K. Hamacher ba , J. Hansen ag , F.J. Harris ai , V. Hedberg i,x , S. Heising q , J.J. Hernandez ax , P. Herquet b, H. Herr i , T.L. Hessing ai , J.-M. Heuser ba , E. Higon ax , S-O. Holmgren as , P.J. Holt ai , S. Hoorelbeke b, M. Houlden v, J. Hrubec ay, M. Huber q , K. Huet b, G.J. Hughes v, K. Hultqvist i,as , J.N. Jackson v, R. Jacobsson i , P. Jalocha r, R. Janik g , Ch. Jarlskog x , G. Jarlskog x , P. Jarry an , B. Jean-Marie s , D. Jeans ai , E.K. Johansson as , P. Jonsson y, C. Joram i , P. Juillot j, L. Jungermann q , F. Kapusta w, K. Karafasoulis k , S. Katsanevas y, E.C. Katsoufis af , R. Keranen q , G. Kernel ar, B.P. Kersevan ar, Yu. Khokhlov aq , B.A. Khomenko p, N.N. Khovanski p, A. Kiiskinen o , B. King v, A. Kinvig v, N.J. Kjaer i , O. Klapp ba , H. Klein i , P. Kluit ae, P. Kokkinias k , V. Kostioukhine aq , C. Kourkoumelis c , O. Kouznetsov an , M. Krammer ay, E. Kriznic ar, Z. Krumstein p, P. Kubinec g , J. Kurowska az , K. Kurvinen o , J.W. Lamsa a , D.W. Lane a , V. Lapin aq , J-P. Laugier an , R. Lauhakangas o , G. Leder ay, F. Ledroit n , V. Lefebure b, L. Leinonen as , A. Leisos k , R. Leitner ad , J. Lemonne b, G. Lenzen ba , V. Lepeltier s , T. Lesiak r, M. Lethuillier an , J. Libby ai , W. Liebig ba , D. Liko i , A. Lipniacka i,as , I. Lippi aj, B. Loerstad x , J.G. Loken ai , J.H. Lopes av, J.M. Lopez ao , R. Lopez-Fernandez n , D. Loukas k , P. Lutz an , L. Lyons ai , J. MacNaughton ay, J.R. Mahon f , A. Maio u , A. Malek ba , T.G.M. Malmgren as , S. Maltezos af , V. Malychev p, F. Mandl ay, J. Marco ao , R. Marco ao , B. Marechal av, M. Margoni aj, J-C. Marin i , C. Mariotti i , A. Markou k , C. Martinez-Rivero s , F. Martinez-Vidal ax , S. Marti i Garcia i , J. Masik l , N. Mastroyiannopoulos k , F. Matorras ao , C. Matteuzzi ab, G. Matthiae al , F. Mazzucato aj, M. Mazzucato aj, M. Mc Cubbin v, R. Mc Kay a , R. Mc Nulty v, G. Mc Pherson v, C. Meroni aa , W.T. Meyer a , A. Miagkov aq , E. Migliore i , L. Mirabito y, W.A. Mitaroff ay, U. Mjoernmark x , T. Moa as , M. Moch q , R. Moeller ac , K. Moenig i,1, M.R. Monge m , D. Moraes av, X. Moreau w, P. Morettini m , G. Morton ai , U. Mueller ba , K. Muenich ba , M. Mulders ae, C. Mulet-Marquis n , R. Muresan x , W.J. Murray ak , B. Muryn r, G. Myatt ai , T. Myklebust ag , F. Naraghi n , M. Nassiakou k , F.L. Navarria e, S. Navas ax , K. Nawrocki az , P. Negri ab, N. Neufeld i , R. Nicolaidou an ,
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B.S. Nielsen ac , P. Niezurawski az , M. Nikolenko j,p, V. Nomokonov o , A. Nygren x , V. Obraztsov aq , A.G. Olshevski p, A. Onofre u , R. Orava o , G. Orazi j, K. Osterberg o , A. Ouraou an , M. Paganoni ab, S. Paiano e, R. Pain w, R. Paiva u , J. Palacios ai , H. Palka r, Th.D. Papadopoulou i,af , K. Papageorgiou k , L. Pape i , C. Parkes i , F. Parodi m , U. Parzefall v, A. Passeri am , O. Passon ba , T. Pavel x , M. Pegoraro aj, L. Peralta u , M. Pernicka ay, A. Perrotta e, C. Petridou au , A. Petrolini m , H.T. Phillips ak , F. Pierre an , M. Pimenta u , E. Piotto aa , T. Podobnik ar, M.E. Pol f , G. Polok r, P. Poropat au , V. Pozdniakov p, P. Privitera al , N. Pukhaeva p, A. Pullia ab, D. Radojicic ai , S. Ragazzi ab, H. Rahmani af , J. Rames l , P.N. Ratoff t , A.L. Read ag , P. Rebecchi i , N.G. Redaelli ab, M. Regler ay, J. Rehn q , D. Reid ae, R. Reinhardt ba , P.B. Renton ai , L.K. Resvanis c , F. Richard s , J. Ridky l , G. Rinaudo at , I. Ripp-Baudot j, O. Rohne ag , A. Romero at , P. Ronchese aj, E.I. Rosenberg a , P. Rosinsky g , P. Roudeau s , T. Rovelli e, Ch. Royon an , V. Ruhlmann-Kleider an , A. Ruiz ao , H. Saarikko o , Y. Sacquin an , A. Sadovsky p, G. Sajot n , J. Salt ax , D. Sampsonidis k , M. Sannino m , Ph. Schwemling w, B. Schwering ba , U. Schwickerath q , F. Scuri au , P. Seager t , Y. Sedykh p, A.M. Segar ai , N. Seibert q , R. Sekulin ak , R.C. Shellard f , M. Siebel ba , L. Simard an , F. Simonetto aj, A.N. Sisakian p, G. Smadja y, N. Smirnov aq , O. Smirnova x , G.R. Smith ak , A. Sokolov aq , A. Sopczak q , R. Sosnowski az , T. Spassov u , E. Spiriti am , S. Squarcia m , C. Stanescu am , S. Stanic ar, M. Stanitzki q , K. Stevenson ai , A. Stocchi s , J. Strauss ay, R. Strub j, B. Stugu d , M. Szczekowski az , M. Szeptycka az , T. Tabarelli ab, A. Taffard v, F. Tegenfeldt aw, F. Terranova ab, J. Thomas ai , J. Timmermans ae, N. Tinti e, L.G. Tkatchev p, M. Tobin v, S. Todorova j, A. Tomaradze b, B. Tome u , A. Tonazzo i , L. Tortora am , P. Tortosa ax , G. Transtromer x , D. Treille i , G. Tristram h , M. Trochimczuk az , C. Troncon aa , M-L. Turluer an , I.A. Tyapkin p, S. Tzamarias k , O. Ullaland i , V. Uvarov aq , G. Valenti i,e, E. Vallazza au , P. Van Dam ae, W. Van den Boeck b, J. Van Eldik i,ae, A. Van Lysebetten b, N. van Remortel b, I. Van Vulpen ae, G. Vegni aa , L. Ventura aj, W. Venus ak,i , F. Verbeure b, P. Verdier y, M. Verlato aj, L.S. Vertogradov p, V. Verzi aa , D. Vilanova an , L. Vitale au , E. Vlasov aq , A.S. Vodopyanov p, G. Voulgaris c , V. Vrba l , H. Wahlen ba , C. Walck as , A.J. Washbrook v, C. Weiser i , D. Wicke ba , J.H. Wickens b, G.R. Wilkinson ai , M. Winter j, M. Witek r, G. Wolf i , J. Yi a , O. Yushchenko aq , A. Zalewska r, P. Zalewski az , D. Zavrtanik ar, E. Zevgolatakos k , N.I. Zimin p,x , A. Zintchenko p, Ph. Zoller j, G.C. Zucchelli as , G. Zumerle aj b
a Department of Physics and Astronomy, Iowa State UniÕersity, Ames IA 50011-3160, USA Physics Department, UniÕ. Instelling Antwerpen, UniÕersiteitsplein 1, B-2610 Antwerpen, Belgium, and IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium, and Faculte´ des Sciences, UniÕ. de l’Etat Mons, AÕ. Maistriau 19, B-7000 Mons, Belgium c Physics Laboratory, UniÕersity of Athens, Solonos Str. 104, GR-10680 Athens, Greece
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d Department of Physics, UniÕersity of Bergen, Allegaten 55, NO-5007 Bergen, Norway ´ Dipartimento di Fisica, UniÕersita` di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy f Centro Brasileiro de Pesquisas Fısicas, rua XaÕier Sigaud 150, BR-22290 Rio de Janeiro, Brazil, ´ and Depto. de Fısica, Pont. UniÕ. Catolica, C.P. 38071 BR-22453 Rio de Janeiro, Brazil, ´ ´ and Inst. de Fısica, UniÕ. Estadual do Rio de Janeiro, rua Sao ´ ˜ Francisco XaÕier 524, Rio de Janeiro, Brazil g Comenius UniÕersity, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 BratislaÕa, SloÕakia h College ` de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France i CERN, CH-1211 GeneÕa 23, Switzerland j Institut de Recherches Subatomiques, IN2P3 - CNRSr ULP - BP20, FR-67037 Strasbourg Cedex, France k Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece l FZU, Inst. of Phys. of the C.A.S. High Energy Physics DiÕision, Na SloÕance 2, CZ-180 40 Praha 8, Czech Republic m Dipartimento di Fisica, UniÕersita` di GenoÕa and INFN, Via Dodecaneso 33, IT-16146 GenoÕa, Italy n Institut des Sciences Nucleaires, IN2P3-CNRS, UniÕersite´ de Grenoble 1, FR-38026 Grenoble Cedex, France ´ o Helsinki Institute of Physics, HIP, P.O. Box 9, FI-00014 Helsinki, Finland p Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federation q Institut fur ¨ Experimentelle Kernphysik, UniÕersitat ¨ Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany r Institute of Nuclear Physics and UniÕersity of Mining and Metalurgy, Ul. Kawiory 26a, PL-30055 Krakow, Poland s UniÕersite´ de Paris-Sud, Lab. de l’Accelerateur Lineaire, IN2P3-CNRS, Bat. ´´ ´ ˆ 200, FR-91405 Orsay Cedex, France t School of Physics and Chemistry, UniÕersity of Lancaster, Lancaster LA1 4YB, UK u LIP, IST, FCUL - AÕ. Elias Garcia, 14-1o , PT-1000 Lisboa Codex, Portugal v Department of Physics, UniÕersity of LiÕerpool, P.O. Box 147, LiÕerpool L69 3BX, UK w LPNHE, IN2P3-CNRS, UniÕ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris Cedex 05, France x Department of Physics, UniÕersity of Lund, SolÕegatan 14, SE-223 63 Lund, Sweden ¨ y UniÕersite´ Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France z UniÕ. d’Aix - Marseille II - CPP, IN2P3-CNRS, FR-13288 Marseille Cedex 09, France aa Dipartimento di Fisica, UniÕersita` di Milano and INFN-MILANO, Via Celoria 16, IT-20133 Milan, Italy ab Dipartimento di Fisica, UniÕ. di Milano-Bicocca and INFN-MILANO, Piazza delle Scienze 2, IT-20126 Milan, Italy ac Niels Bohr Institute, BlegdamsÕej 17, DK-2100 Copenhagen Ø, Denmark ad IPNP of MFF, Charles UniÕ., Areal MFF, V HolesoÕickach 2, CZ-180 00 Praha 8, Czech Republic ae NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands af National Technical UniÕersity, Physics Department, Zografou Campus, GR-15773 Athens, Greece ag Physics Department, UniÕersity of Oslo, Blindern, NO-1000 Oslo 3, Norway ah Dpto. Fisica, UniÕ. OÕiedo, AÕda. CalÕo Sotelo s r n, ES-33007 OÕiedo, Spain ai Department of Physics, UniÕersity of Oxford, Keble Road, Oxford OX1 3RH, UK aj Dipartimento di Fisica, UniÕersita` di PadoÕa and INFN, Via Marzolo 8, IT-35131 Padua, Italy ak Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK al Dipartimento di Fisica, UniÕersita` di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy am Dipartimento di Fisica, UniÕersita` di Roma III and INFN, Via della Vasca NaÕale 84, IT-00146 Rome, Italy an DAPNIAr SerÕice de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-YÕette Cedex, France ao Instituto de Fisica de Cantabria (CSIC-UC), AÕda. los Castros s r n, ES-39006 Santander, Spain ap Dipartimento di Fisica, UniÕersita` degli Studi di Roma La Sapienza, Piazzale Aldo Moro 2, IT-00185 Rome, Italy aq Inst. for High Energy Physics, SerpukoÕ P.O. Box 35, ProtÕino (Moscow Region), Russian Federation ar J. Stefan Institute, JamoÕa 39, SI-1000 Ljubljana, SloÕenia and Laboratory for Astroparticle Physics, NoÕa Gorica Polytechnic, KostanjeÕiska 16a, SI-5000 NoÕa Gorica, SloÕenia, and Department of Physics, UniÕersity of Ljubljana, SI-1000 Ljubljana, SloÕenia as Fysikum, Stockholm UniÕersity, Box 6730, SE-113 85 Stockholm, Sweden at Dipartimento di Fisica Sperimentale, UniÕersita` di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy au Dipartimento di Fisica, UniÕersita` di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy, and Istituto di Fisica, UniÕersita` di Udine, IT-33100 Udine, Italy av UniÕ. Federal do Rio de Janeiro, C.P. 68528 Cidade UniÕ., Ilha do Fundao, ˜ BR-21945-970 Rio de Janeiro, Brazil aw Department of Radiation Sciences, UniÕersity of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden ax IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, AÕda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain ay ¨ Institut fur Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria ¨ Hochenergiephysik, Osterr. az Inst. Nuclear Studies and UniÕersity of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland ba Fachbereich Physik, UniÕersity of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany e
Received 21 June 2000; received in revised form 14 July 2000; accepted 18 July 2000 Editor: L. Montanet
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Abstract The rapidity-rank structure of p p pairs is used to analyze the mechanism of baryon production in hadronic Z 0 decay. The relative occurrence of the rapidity-ordered configuration p M p, where M is a meson, and that of p p adjacent pairs is compared. The data are found to be consistent with predictions from a mechanism producing adjacent-rank p p pairs, without requiring ‘string-ordered’ p M p configurations. An upper limit of 15% at 90% confidence is determined for the p M p contribution. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Baryon production from hadronic Z 0 decays, as interpreted in string-fragmentation models, is pictured in Fig. 1. Hadronisation results from breaks in the string formed from the colour-neutral system which stretches between the primary quarks w1x. Breaks occur between virtual flavour-neutral q q pairs, with mesons formed from string elements containing an adjacent q and q. Baryons are thought to be formed when breaks occur between diquark-antidiquark pairs, the baryon being made from adjacent diquark and quark w2x. A baryon and an antibaryon emerge as adjacent particles in rank along the string Ž‘string-rank’., or possibly separated in rank with a mesonic state between them. Fig. 1Ža. represents the case where the diquark is assumed to have a sufficiently large binding energy that it acts like a fundamental unit. Another possibility is to produce an ‘effective diquark’ through a step-wise process where two q q pairs are created, as shown in Fig. 1Žb.. In this case a mesonic state also can be produced between the baryon and antibaryon, seen in Fig. 1Žc.. This has been referred to as the ‘popcorn effect.’ In this paper, a novel method, using the rapidityrank structure of p p pairs, is used to study the mechanism of baryon production in hadronic Z 0 decay. A measurement of the relative frequency of occurrence of the rapidity-ordered configuration Ž i . p M p, where M is a charged meson, and Ž ii . p p adjacent in rapidity, is made to determine the magnitude of the popcorn effect. This approach provides
1
Now at DESY-Zeuthen, Platanenallee 6, D-15735 Zeuthen, Germany.
Fig. 1. Illustration of p p production in the string model. Each line represents a q q pair produced from potential energy in the string. Ža. Production by a diquark-antidiquark pair Žshown shaded. acting as a fundamental unit. Žb. Through a step-wise process with two q q pairs forming an effective diquark-antidiquark pair. Žc. Step-wise production with a mesonic state formed between the p p pair Žreferred to as the popcorn effect..
greater sensitivity than that used in previous studies w3x.
2. Data sample and event selection This analysis is based on data collected with the DELPHI detector w4x at the CERN LEP collider in 1994 and 1995 at the Z 0 centre-of-mass energy. The charged-particle tracking information relies on three cylindrical tracking detectors ŽInner Detector, Time Projection Chamber ŽTPC., and Outer Detector. all operating in a 1.2 T magnetic field.
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P. Abreu et al.r Physics Letters B 490 (2000) 61–70
The selection criteria for charged particles are: momentum above 0.3 GeVrc, polar angle between 158 and 1658, and track length above 30 cm. In addition, the impact parameters with respect to the beam axis and along the longitudinal coordinate at the origin, are required to be below 0.05 and 0.25 cm, respectively. These impact parameter cuts decrease the number of protons which result from secondary interactions in the detector. Also, protons from L and S decays are largely removed. Hadronic events are selected by requiring at least three charged particle tracks in each event hemisphere, and a total energy of all charged particles exceeding 15 GeV. The number of hadronic events is ; 2 million. Charged particle identification is provided by a tagging procedure which combines Cherenkov angle measurement from the RICH detector with ionization energy loss measured in the TPC. Details on the particle identification can be found in Ref. w4x. In the present analysis, the combined-probability tag is required to be at the ‘standard’ level w4x. In addition, the polar angle for identified particles is restricted to be in the barrel region, between 478 and 1338.
3. Rapidity-rank configurations p p and p M p This analysis studies p p correlations in the rapidity variable with respect to the ‘thrust’ direction. The thrust direction approximates the directions of the primary q and q, especially for two-jet events. The rapidity, y, of a given particle is defined as 1 2 ln Ž Ž E q pL . r Ž E y pL . . , where pL is the momentum component parallel to the thrust axis, and E is the energy calculated using the particle mass as determined from RICH and the measured momentum. The restriction is made that events have only ‘one p and one p’ in a given hemisphere. Hemispheres are defined, one for positive y and one for negative y, with respect to the thrust direction. Each hemisphere is considered independently. The number of events with this selection is 27.6 thousand. The background to this event sample can be determined from the number of events that have two p’s or two p’s in a given hemisphere. These events, 10.1 thousand, result mainly from p or p misidentifications
and also from non-correlated baryon-antibaryon pairs Ži.e., a p and p from different B B pairs.. This yields a 63% purity, Ž27.6k–10.1k.r27.6k, for the p p sample. A study of events from Jetset 7.3 w5x, including detector simulation, determined the p p pair detection efficiency to be ; 35%, and the p p pair purity to be ; 60%, consistent with the above-mentioned value. These values are nearly constant over the range of the analysis variable D ymin defined later. The efficiency is computed from the ratio of Jetset p p pairs detected, to the total number of p p pairs generated. The purity is obtained from the ratio of Jetset p p pairs detected and congruous with a generated p p pair, to the total number of p p pairs detected. The charged particles in each event are ordered according to their rapidity values as defined above. The rapidity-rank is defined as the position that a particle has in the rapidity chain. In the following, two types of rapidity-rank configurations for p p pairs are considered, and are shown in Fig. 2. The first is when the p and p are adjacent in rapidity Žranks differ by one unit.. The second is when the p and p have one or more mesons between them. The number of mesons is restricted to be at most three Žthe ranks differ by two to four units.. This reduces the probability that the p and p may have come from different baryon-antibaryon pairs. It should be
Fig. 2. Ža. An event hemisphere configuration with p and p adjacent in rapidity. The rapidity-gap, D ymin , indicates the distance to the nearest particle external to the p p pair. Žb. An event configuration with a particle, M, between the p and p. The rapidity-gap, D ymin , denotes the distance of the particle, M, to the nearest of p or p.
P. Abreu et al.r Physics Letters B 490 (2000) 61–70
noted that the rapidity configurations only approximately portray the string-rank patterns as shown in Fig. 1. This is because of the softness of the fragmentation function and of resonance decays which can mix the rapidity-ranks. Since adjacent particles separated by a small rapidity gap have a high probability to have ‘crossedover’ Žreversed rank., this study is performed as a function of the rapidity gap size. For p p adjacent pairs, the concern is that a meson close in rapidity to the p or p may have crossed-over from an original ‘string position’ which was between the p p pair. Correspondingly, for the p M p configuration, a meson on the outside of a p p pair on the ‘string’ may have crossed-over to be between the p and p in the rapidity variable. To determine the relative amount of p p and p M p configurations in the data the following ratio is calculated: R Ž D ymin . s N Ž p M p .
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case includes a multiplicative factor of 2r3. This is arbitrary but it provides for a better balance of the two contributions when studying the ratio R over a range of D ymin . Excluded from the analysis are events where the particle with the largest rank Ži.e., smallest rapidity. is a p or p. This is to avoid the possibility that a low momentum particle may not have been detected Žor reconstructed. and could have formed a small D ymin that was not considered. The above treatments are applied to both data and model. The ratio RŽ D ymin . for the data is plotted in Fig. 3, as solid circles. Also shown are the predictions from Jetset 7.3 for the case when the relative fraction of the p M p string-rank configuration is zero and when it is 100%, indicated by open circles and squares, respectively. The errors are statistical. A background subtraction of like-sign pairs Ž p p and p p . has been applied to the data and model to remove contributions from uncorrelated baryon pairs
Ž NŽ p p. qNŽ p M p. . , Ž 1.
where N Ž p p . and N Ž p M p . represent the number of rapidity-rank configurations of each type in the data sample, and are implicitly a function of D ymin , defined as follows. For the p p case, Fig. 2Ža., D ymin is defined as the absolute rapidity difference between the nearest adjacent meson to either p or p, whichever is smaller. In the p M p case, Fig. 2Žb., D ymin is defined as the absolute rapidity difference between either p or p and the particle in-between them, whichever is smaller. If there is more than one particle in-between, then the particle which is closest to being in the exact middle of the p p pair Žand therefore least likely to have crossed over. is the one considered. With these definitions for D ymin , the probability that a given rapidity configuration will represent the actual rank order on the string will be enhanced as D ymin is made larger. If the production of p and p are correlated, the rapidity gaps between a p p pair are expected to be smaller than the gaps external to the pair. In the present data the average size of rapidity gaps between the p and p for the p M p case Ž0.18 units. is ; 2r3 the size of the adjacent rapidity gaps for the p p case Ž0.26 units.. To put the two cases on a more equal footing, the definition of D ymin for the p p
Fig. 3. The relative amount, RŽ D ymin ., of the p M p configuration as a function of D ymin . The data points are indicated by solid circles. The predictions from Jetset for two cases: no contribution from the popcorn effect Žopen circles. and all popcorn effect Žopen squares..
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x 2 is minimum over the range below 5% popcorn contribution; and, an upper-limit contribution of 15% is determined at 90% confidence level. For completeness, the distributions, N Ž p p . and N Ž p M p ., of the number of rapidity-rank configurations of each type as a function of D ymin , are displayed in Fig. 4. The data are shown by the solid circles. The predictions for the case when the relative fraction of the p M p string-rank configuration is zero and when it is 100%, are indicated by open circles and squares, respectively. In accord with the analysis above, consistency between the data and the prediction for no-popcorn is evident for these distributions.
4. The p p rapidity difference Fig. 4. Distributions, N Ž p p . and N Ž p M p ., of the number of rapidity-rank configurations of each type as a function of D ymin , in Ža. and Žb., respectively. The data points are indicated by solid circles. The predictions from Jetset for two cases: no contribution from the popcorn effect Žopen circles. and all popcorn effect Žopen squares..
and from particle misidentifications. The possible effect of variations Žof order " 30%. in the fraction of protons coming from resonances Žlike Deltas. was investigated, and found to be negligible. Standard DELPHI detector simulation along with charged particle reconstruction and hadronic event selection are applied to the events from Jetset 7.3 with parameters tuned as in Ref. w6x. Since Jetset was run with a 50% popcorn contribution, p p pairs were separated into string-rank p M p Žpopcorn. and p p Žnon-popcorn. components using the information on rank-order stored with the Monte Carlo events. The prediction for the case with no contribution from p M p is seen to fall for large D ymin , as expected. The case with 100% contribution might be thought to rise to the maximum value 1.0, but it flattens out possibly because contributions, for example, from p p pairs with a p 0 ŽX s . in between become relatively more important for large D ymin . As seen in Fig. 3, the data are consistent with no contribution Žor little. from p M p string configurations. The x 2 between data and model was calculated as a function of the relative amount of p p and p M p configurations. The
Previous studies of baryon-antibaryon Žin particular, L L. rapidity correlations have claimed evi-
Fig. 5. The distribution of D y Ž pp . for the data Žsolid circles., and the predictions of Jetset for no-contribution from the popcorn effect Žopen circles., and for an all-popcorn effect Žopen squares..
P. Abreu et al.r Physics Letters B 490 (2000) 61–70
dence for the popcorn effect w3x. In these studies, distributions of the L L rapidity difference were compared to predictions from the string-model Jetset. To test the sensitivity of this method for the p p case, the distribution of the p p rapidity difference, D y Ž pp ., for the data was compared to the Jetset predictions for 100% popcorn and for no-popcorn contribution, as shown in Fig. 5. The thrust value was required to be greater than 0.96. A background subtraction of like-sign pairs Ž p p and p p . has been applied to the data and model. The all-popcorn assumption yields a mean value for D y Ž pp . that is 11% larger than that for no-popcorn; without the thrust requirement the difference is 5.5%. These values are in accordance with what is predicted in Ref. w7x. Even though this method is clearly not as sensitive as the one above-mentioned, it can be seen that the data prefer the no-popcorn prediction. The difference between the present result and that from L L experiments might indicate the importance of dynamical effects not incorporated in Jetset or simply the inadequacy of the popcorn model, although no firm conclusion can be drawn yet.
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operating the DELPHI detector. We acknowledge in particular the support of Austrian Federal Ministry of Science and Traffics, GZ 616.364r2-IIIr2ar98, FNRS–FWO, Belgium, FINEP, CNPq, CAPES, FUJB and FAPERJ, Brazil, Czech Ministry of Industry and Trade, GA CR 202r96r0450 and GA AVCR A1010521, Danish Natural Research Council, Commission of the European Communities ŽDG XII., Direction des Sciences de la Matiere, ` CEA, France, Bundesministerium fur ¨ Bildung, Wissenschaft, Forschung und Technologie, Germany, General Secretariat for Research and Technology, Greece, National Science Foundation ŽNWO. and Foundation for Research on Matter ŽFOM., The Netherlands, Norwegian Research Council, State Committee for Scientific Research, Poland, 2P03B06015, 2P03B1116 and SPUBrP03r178r98, JNICT–Junta e Tecnologica, Nacional de Investigac¸ao ˜ Cientıfica ´ ´ Portugal, Vedecka grantova agentura MS SR, Slovakia, Nr. 95r5195r134, Ministry of Science and Technology of the Republic of Slovenia, CICYT, Spain, AEN96–1661 and AEN96-1681, The Swedish Natural Science Research Council, Particle Physics and Astronomy Research Council, UK, Department of Energy, USA, DE–FG02–94ER40817.
5. Conclusions The rapidity-rank structure of p p pairs was used to analyze the mechanism of baryon production in hadronic Z 0 decay. By comparing the relative occurrence in the data of the rapidity-ordered configuration p M p, where M is a meson, to that of p p adjacent pairs with predictions from Jetset, it is found that the data can be explained without requiring ‘string-ordered’ p M p configurations. The production of adjacent-rank p p pairs is sufficient to describe the data.
Acknowledgements We are greatly indebted to our technical collaborators, to the members of the CERN-SL Division for the excellent performance of the LEP collider, and to the funding agencies for their support in building and
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a Department of Physics and Astronomy, Iowa State UniÕersity, Ames IA 50011-3160, USA Physics Department, UniÕ. Instelling Antwerpen, UniÕersiteitsplein 1, B-2610 Antwerpen, Belgium, and IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium, and Faculte´ des Sciences, UniÕ. de l’Etat Mons, AÕ. Maistriau 19, B-7000 Mons, Belgium c Physics Laboratory, UniÕersity of Athens, Solonos Str. 104, GR-10680 Athens, Greece
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d Department of Physics, UniÕersity of Bergen, Allegaten 55, NO-5007 Bergen, Norway ´ Dipartimento di Fisica, UniÕersita` di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy f Centro Brasileiro de Pesquisas Fısicas, rua XaÕier Sigaud 150, BR-22290 Rio de Janeiro, Brazil, ´ and Depto. de Fısica, Pont. UniÕ. Catolica, C.P. 38071 BR-22453 Rio de Janeiro, Brazil, ´ ´ and Inst. de Fısica, UniÕ. Estadual do Rio de Janeiro, rua Sao ´ ˜ Francisco XaÕier 524, Rio de Janeiro, Brazil g Comenius UniÕersity, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 BratislaÕa, SloÕakia h College ` de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France i CERN, CH-1211 GeneÕa 23, Switzerland j Institut de Recherches Subatomiques, IN2P3 - CNRSr ULP - BP20, FR-67037 Strasbourg Cedex, France k Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece l FZU, Inst. of Phys. of the C.A.S. High Energy Physics DiÕision, Na SloÕance 2, CZ-180 40 Praha 8, Czech Republic m Dipartimento di Fisica, UniÕersita` di GenoÕa and INFN, Via Dodecaneso 33, IT-16146 GenoÕa, Italy n Institut des Sciences Nucleaires, IN2P3-CNRS, UniÕersite´ de Grenoble 1, FR-38026 Grenoble Cedex, France ´ o Helsinki Institute of Physics, HIP, P.O. Box 9, FI-00014 Helsinki, Finland p Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federation q Institut fur ¨ Experimentelle Kernphysik, UniÕersitat ¨ Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany r Institute of Nuclear Physics and UniÕersity of Mining and Metalurgy, Ul. Kawiory 26a, PL-30055 Krakow, Poland s UniÕersite´ de Paris-Sud, Lab. de l’Accelerateur Lineaire, IN2P3-CNRS, Bat. ´´ ´ ˆ 200, FR-91405 Orsay Cedex, France t School of Physics and Chemistry, UniÕersity of Lancaster, Lancaster LA1 4YB, UK u LIP, IST, FCUL - AÕ. Elias Garcia, 14-1o , PT-1000 Lisboa Codex, Portugal v Department of Physics, UniÕersity of LiÕerpool, P.O. Box 147, LiÕerpool L69 3BX, UK w LPNHE, IN2P3-CNRS, UniÕ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris Cedex 05, France x Department of Physics, UniÕersity of Lund, SolÕegatan 14, SE-223 63 Lund, Sweden ¨ y UniÕersite´ Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France z UniÕ. d’Aix - Marseille II - CPP, IN2P3-CNRS, FR-13288 Marseille Cedex 09, France aa Dipartimento di Fisica, UniÕersita` di Milano and INFN-MILANO, Via Celoria 16, IT-20133 Milan, Italy ab Dipartimento di Fisica, UniÕ. di Milano-Bicocca and INFN-MILANO, Piazza delle Scienze 2, IT-20126 Milan, Italy ac Niels Bohr Institute, BlegdamsÕej 17, DK-2100 Copenhagen Ø, Denmark ad IPNP of MFF, Charles UniÕ., Areal MFF, V HolesoÕickach 2, CZ-180 00 Praha 8, Czech Republic ae NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands af National Technical UniÕersity, Physics Department, Zografou Campus, GR-15773 Athens, Greece ag Physics Department, UniÕersity of Oslo, Blindern, NO-1000 Oslo 3, Norway ah Dpto. Fisica, UniÕ. OÕiedo, AÕda. CalÕo Sotelo s r n, ES-33007 OÕiedo, Spain ai Department of Physics, UniÕersity of Oxford, Keble Road, Oxford OX1 3RH, UK aj Dipartimento di Fisica, UniÕersita` di PadoÕa and INFN, Via Marzolo 8, IT-35131 Padua, Italy ak Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK al Dipartimento di Fisica, UniÕersita` di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy am Dipartimento di Fisica, UniÕersita` di Roma III and INFN, Via della Vasca NaÕale 84, IT-00146 Rome, Italy an DAPNIAr SerÕice de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-YÕette Cedex, France ao Instituto de Fisica de Cantabria (CSIC-UC), AÕda. los Castros s r n, ES-39006 Santander, Spain ap Dipartimento di Fisica, UniÕersita` degli Studi di Roma La Sapienza, Piazzale Aldo Moro 2, IT-00185 Rome, Italy aq Inst. for High Energy Physics, SerpukoÕ P.O. Box 35, ProtÕino (Moscow Region), Russian Federation ar J. Stefan Institute, JamoÕa 39, SI-1000 Ljubljana, SloÕenia and Laboratory for Astroparticle Physics, NoÕa Gorica Polytechnic, KostanjeÕiska 16a, SI-5000 NoÕa Gorica, SloÕenia, and Department of Physics, UniÕersity of Ljubljana, SI-1000 Ljubljana, SloÕenia as Fysikum, Stockholm UniÕersity, Box 6730, SE-113 85 Stockholm, Sweden at Dipartimento di Fisica Sperimentale, UniÕersita` di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy au Dipartimento di Fisica, UniÕersita` di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy, and Istituto di Fisica, UniÕersita` di Udine, IT-33100 Udine, Italy av UniÕ. Federal do Rio de Janeiro, C.P. 68528 Cidade UniÕ., Ilha do Fundao, ˜ BR-21945-970 Rio de Janeiro, Brazil aw Department of Radiation Sciences, UniÕersity of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden ax IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, AÕda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain ay ¨ Institut fur Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria ¨ Hochenergiephysik, Osterr. az Inst. Nuclear Studies and UniÕersity of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland ba Fachbereich Physik, UniÕersity of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany e
Received 21 June 2000; received in revised form 14 July 2000; accepted 18 July 2000 Editor: L. Montanet
P. Abreu et al.r Physics Letters B 490 (2000) 61–70
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Abstract The rapidity-rank structure of p p pairs is used to analyze the mechanism of baryon production in hadronic Z 0 decay. The relative occurrence of the rapidity-ordered configuration p M p, where M is a meson, and that of p p adjacent pairs is compared. The data are found to be consistent with predictions from a mechanism producing adjacent-rank p p pairs, without requiring ‘string-ordered’ p M p configurations. An upper limit of 15% at 90% confidence is determined for the p M p contribution. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Baryon production from hadronic Z 0 decays, as interpreted in string-fragmentation models, is pictured in Fig. 1. Hadronisation results from breaks in the string formed from the colour-neutral system which stretches between the primary quarks w1x. Breaks occur between virtual flavour-neutral q q pairs, with mesons formed from string elements containing an adjacent q and q. Baryons are thought to be formed when breaks occur between diquark-antidiquark pairs, the baryon being made from adjacent diquark and quark w2x. A baryon and an antibaryon emerge as adjacent particles in rank along the string Ž‘string-rank’., or possibly separated in rank with a mesonic state between them. Fig. 1Ža. represents the case where the diquark is assumed to have a sufficiently large binding energy that it acts like a fundamental unit. Another possibility is to produce an ‘effective diquark’ through a step-wise process where two q q pairs are created, as shown in Fig. 1Žb.. In this case a mesonic state also can be produced between the baryon and antibaryon, seen in Fig. 1Žc.. This has been referred to as the ‘popcorn effect.’ In this paper, a novel method, using the rapidityrank structure of p p pairs, is used to study the mechanism of baryon production in hadronic Z 0 decay. A measurement of the relative frequency of occurrence of the rapidity-ordered configuration Ž i . p M p, where M is a charged meson, and Ž ii . p p adjacent in rapidity, is made to determine the magnitude of the popcorn effect. This approach provides
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Now at DESY-Zeuthen, Platanenallee 6, D-15735 Zeuthen, Germany.
Fig. 1. Illustration of p p production in the string model. Each line represents a q q pair produced from potential energy in the string. Ža. Production by a diquark-antidiquark pair Žshown shaded. acting as a fundamental unit. Žb. Through a step-wise process with two q q pairs forming an effective diquark-antidiquark pair. Žc. Step-wise production with a mesonic state formed between the p p pair Žreferred to as the popcorn effect..
greater sensitivity than that used in previous studies w3x.
2. Data sample and event selection This analysis is based on data collected with the DELPHI detector w4x at the CERN LEP collider in 1994 and 1995 at the Z 0 centre-of-mass energy. The charged-particle tracking information relies on three cylindrical tracking detectors ŽInner Detector, Time Projection Chamber ŽTPC., and Outer Detector. all operating in a 1.2 T magnetic field.
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The selection criteria for charged particles are: momentum above 0.3 GeVrc, polar angle between 158 and 1658, and track length above 30 cm. In addition, the impact parameters with respect to the beam axis and along the longitudinal coordinate at the origin, are required to be below 0.05 and 0.25 cm, respectively. These impact parameter cuts decrease the number of protons which result from secondary interactions in the detector. Also, protons from L and S decays are largely removed. Hadronic events are selected by requiring at least three charged particle tracks in each event hemisphere, and a total energy of all charged particles exceeding 15 GeV. The number of hadronic events is ; 2 million. Charged particle identification is provided by a tagging procedure which combines Cherenkov angle measurement from the RICH detector with ionization energy loss measured in the TPC. Details on the particle identification can be found in Ref. w4x. In the present analysis, the combined-probability tag is required to be at the ‘standard’ level w4x. In addition, the polar angle for identified particles is restricted to be in the barrel region, between 478 and 1338.
3. Rapidity-rank configurations p p and p M p This analysis studies p p correlations in the rapidity variable with respect to the ‘thrust’ direction. The thrust direction approximates the directions of the primary q and q, especially for two-jet events. The rapidity, y, of a given particle is defined as 1 2 ln Ž Ž E q pL . r Ž E y pL . . , where pL is the momentum component parallel to the thrust axis, and E is the energy calculated using the particle mass as determined from RICH and the measured momentum. The restriction is made that events have only ‘one p and one p’ in a given hemisphere. Hemispheres are defined, one for positive y and one for negative y, with respect to the thrust direction. Each hemisphere is considered independently. The number of events with this selection is 27.6 thousand. The background to this event sample can be determined from the number of events that have two p’s or two p’s in a given hemisphere. These events, 10.1 thousand, result mainly from p or p misidentifications
and also from non-correlated baryon-antibaryon pairs Ži.e., a p and p from different B B pairs.. This yields a 63% purity, Ž27.6k–10.1k.r27.6k, for the p p sample. A study of events from Jetset 7.3 w5x, including detector simulation, determined the p p pair detection efficiency to be ; 35%, and the p p pair purity to be ; 60%, consistent with the above-mentioned value. These values are nearly constant over the range of the analysis variable D ymin defined later. The efficiency is computed from the ratio of Jetset p p pairs detected, to the total number of p p pairs generated. The purity is obtained from the ratio of Jetset p p pairs detected and congruous with a generated p p pair, to the total number of p p pairs detected. The charged particles in each event are ordered according to their rapidity values as defined above. The rapidity-rank is defined as the position that a particle has in the rapidity chain. In the following, two types of rapidity-rank configurations for p p pairs are considered, and are shown in Fig. 2. The first is when the p and p are adjacent in rapidity Žranks differ by one unit.. The second is when the p and p have one or more mesons between them. The number of mesons is restricted to be at most three Žthe ranks differ by two to four units.. This reduces the probability that the p and p may have come from different baryon-antibaryon pairs. It should be
Fig. 2. Ža. An event hemisphere configuration with p and p adjacent in rapidity. The rapidity-gap, D ymin , indicates the distance to the nearest particle external to the p p pair. Žb. An event configuration with a particle, M, between the p and p. The rapidity-gap, D ymin , denotes the distance of the particle, M, to the nearest of p or p.
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noted that the rapidity configurations only approximately portray the string-rank patterns as shown in Fig. 1. This is because of the softness of the fragmentation function and of resonance decays which can mix the rapidity-ranks. Since adjacent particles separated by a small rapidity gap have a high probability to have ‘crossedover’ Žreversed rank., this study is performed as a function of the rapidity gap size. For p p adjacent pairs, the concern is that a meson close in rapidity to the p or p may have crossed-over from an original ‘string position’ which was between the p p pair. Correspondingly, for the p M p configuration, a meson on the outside of a p p pair on the ‘string’ may have crossed-over to be between the p and p in the rapidity variable. To determine the relative amount of p p and p M p configurations in the data the following ratio is calculated: R Ž D ymin . s N Ž p M p .
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case includes a multiplicative factor of 2r3. This is arbitrary but it provides for a better balance of the two contributions when studying the ratio R over a range of D ymin . Excluded from the analysis are events where the particle with the largest rank Ži.e., smallest rapidity. is a p or p. This is to avoid the possibility that a low momentum particle may not have been detected Žor reconstructed. and could have formed a small D ymin that was not considered. The above treatments are applied to both data and model. The ratio RŽ D ymin . for the data is plotted in Fig. 3, as solid circles. Also shown are the predictions from Jetset 7.3 for the case when the relative fraction of the p M p string-rank configuration is zero and when it is 100%, indicated by open circles and squares, respectively. The errors are statistical. A background subtraction of like-sign pairs Ž p p and p p . has been applied to the data and model to remove contributions from uncorrelated baryon pairs
Ž NŽ p p. qNŽ p M p. . , Ž 1.
where N Ž p p . and N Ž p M p . represent the number of rapidity-rank configurations of each type in the data sample, and are implicitly a function of D ymin , defined as follows. For the p p case, Fig. 2Ža., D ymin is defined as the absolute rapidity difference between the nearest adjacent meson to either p or p, whichever is smaller. In the p M p case, Fig. 2Žb., D ymin is defined as the absolute rapidity difference between either p or p and the particle in-between them, whichever is smaller. If there is more than one particle in-between, then the particle which is closest to being in the exact middle of the p p pair Žand therefore least likely to have crossed over. is the one considered. With these definitions for D ymin , the probability that a given rapidity configuration will represent the actual rank order on the string will be enhanced as D ymin is made larger. If the production of p and p are correlated, the rapidity gaps between a p p pair are expected to be smaller than the gaps external to the pair. In the present data the average size of rapidity gaps between the p and p for the p M p case Ž0.18 units. is ; 2r3 the size of the adjacent rapidity gaps for the p p case Ž0.26 units.. To put the two cases on a more equal footing, the definition of D ymin for the p p
Fig. 3. The relative amount, RŽ D ymin ., of the p M p configuration as a function of D ymin . The data points are indicated by solid circles. The predictions from Jetset for two cases: no contribution from the popcorn effect Žopen circles. and all popcorn effect Žopen squares..
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x 2 is minimum over the range below 5% popcorn contribution; and, an upper-limit contribution of 15% is determined at 90% confidence level. For completeness, the distributions, N Ž p p . and N Ž p M p ., of the number of rapidity-rank configurations of each type as a function of D ymin , are displayed in Fig. 4. The data are shown by the solid circles. The predictions for the case when the relative fraction of the p M p string-rank configuration is zero and when it is 100%, are indicated by open circles and squares, respectively. In accord with the analysis above, consistency between the data and the prediction for no-popcorn is evident for these distributions.
4. The p p rapidity difference Fig. 4. Distributions, N Ž p p . and N Ž p M p ., of the number of rapidity-rank configurations of each type as a function of D ymin , in Ža. and Žb., respectively. The data points are indicated by solid circles. The predictions from Jetset for two cases: no contribution from the popcorn effect Žopen circles. and all popcorn effect Žopen squares..
and from particle misidentifications. The possible effect of variations Žof order " 30%. in the fraction of protons coming from resonances Žlike Deltas. was investigated, and found to be negligible. Standard DELPHI detector simulation along with charged particle reconstruction and hadronic event selection are applied to the events from Jetset 7.3 with parameters tuned as in Ref. w6x. Since Jetset was run with a 50% popcorn contribution, p p pairs were separated into string-rank p M p Žpopcorn. and p p Žnon-popcorn. components using the information on rank-order stored with the Monte Carlo events. The prediction for the case with no contribution from p M p is seen to fall for large D ymin , as expected. The case with 100% contribution might be thought to rise to the maximum value 1.0, but it flattens out possibly because contributions, for example, from p p pairs with a p 0 ŽX s . in between become relatively more important for large D ymin . As seen in Fig. 3, the data are consistent with no contribution Žor little. from p M p string configurations. The x 2 between data and model was calculated as a function of the relative amount of p p and p M p configurations. The
Previous studies of baryon-antibaryon Žin particular, L L. rapidity correlations have claimed evi-
Fig. 5. The distribution of D y Ž pp . for the data Žsolid circles., and the predictions of Jetset for no-contribution from the popcorn effect Žopen circles., and for an all-popcorn effect Žopen squares..
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dence for the popcorn effect w3x. In these studies, distributions of the L L rapidity difference were compared to predictions from the string-model Jetset. To test the sensitivity of this method for the p p case, the distribution of the p p rapidity difference, D y Ž pp ., for the data was compared to the Jetset predictions for 100% popcorn and for no-popcorn contribution, as shown in Fig. 5. The thrust value was required to be greater than 0.96. A background subtraction of like-sign pairs Ž p p and p p . has been applied to the data and model. The all-popcorn assumption yields a mean value for D y Ž pp . that is 11% larger than that for no-popcorn; without the thrust requirement the difference is 5.5%. These values are in accordance with what is predicted in Ref. w7x. Even though this method is clearly not as sensitive as the one above-mentioned, it can be seen that the data prefer the no-popcorn prediction. The difference between the present result and that from L L experiments might indicate the importance of dynamical effects not incorporated in Jetset or simply the inadequacy of the popcorn model, although no firm conclusion can be drawn yet.
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operating the DELPHI detector. We acknowledge in particular the support of Austrian Federal Ministry of Science and Traffics, GZ 616.364r2-IIIr2ar98, FNRS–FWO, Belgium, FINEP, CNPq, CAPES, FUJB and FAPERJ, Brazil, Czech Ministry of Industry and Trade, GA CR 202r96r0450 and GA AVCR A1010521, Danish Natural Research Council, Commission of the European Communities ŽDG XII., Direction des Sciences de la Matiere, ` CEA, France, Bundesministerium fur ¨ Bildung, Wissenschaft, Forschung und Technologie, Germany, General Secretariat for Research and Technology, Greece, National Science Foundation ŽNWO. and Foundation for Research on Matter ŽFOM., The Netherlands, Norwegian Research Council, State Committee for Scientific Research, Poland, 2P03B06015, 2P03B1116 and SPUBrP03r178r98, JNICT–Junta e Tecnologica, Nacional de Investigac¸ao ˜ Cientıfica ´ ´ Portugal, Vedecka grantova agentura MS SR, Slovakia, Nr. 95r5195r134, Ministry of Science and Technology of the Republic of Slovenia, CICYT, Spain, AEN96–1661 and AEN96-1681, The Swedish Natural Science Research Council, Particle Physics and Astronomy Research Council, UK, Department of Energy, USA, DE–FG02–94ER40817.
5. Conclusions The rapidity-rank structure of p p pairs was used to analyze the mechanism of baryon production in hadronic Z 0 decay. By comparing the relative occurrence in the data of the rapidity-ordered configuration p M p, where M is a meson, to that of p p adjacent pairs with predictions from Jetset, it is found that the data can be explained without requiring ‘string-ordered’ p M p configurations. The production of adjacent-rank p p pairs is sufficient to describe the data.
Acknowledgements We are greatly indebted to our technical collaborators, to the members of the CERN-SL Division for the excellent performance of the LEP collider, and to the funding agencies for their support in building and
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