<figure><img src="image_1.png" /></figure>

Observation of short range three-particle correlations in \(e^{+}e^{-}\)

P. Abreu (et al), P.; Agasi, E.E.; Augustinus, A.; Hao, W.; Holthuizen, D.J.; Kluit, P.M.; Koene, B.K.S.; Nieuwenhuizen, M.; Ruckstuhl, W.; Siccama, I.; Timmermans, J.J.M.; Toet, D.Z.; van Apeldoorn, G.W.; van Dam, P.H.A.; van Eldik, J.E.

DOI

10.1016/0370-2693(95)00711-S

Publication date

1995

Published in

Physics Letters B

Link to publication

Citation for published version (APA):

P. Abreu (et al), P., Agasi, E. E., Augustinus, A., Hao, W., Holthuizen, D. J., Kluit, P. M., Koene, B. K. S., Nieuwenhuizen, M., Ruckstuhl, W., Siccama, I., Timmermans, J. J. M., Toet, D. Z., van Apeldoorn, G. W., van Dam, P. H. A., & van Eldik, J. E. (1995). Observation of short range three-particle correlations in \(e^{+}e^{-}\). *Physics Letters B*, *355*, 415.
https://doi.org/10.1016/0370-2693(95)00711-S

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# Observation of short range three-particle correlations in $e^{+}e^{−}$ annihilations at LEP energies

DELPHI Collaboration

P. Abreu<sup>u</sup>, W. Adam<sup>ay</sup>, T. Adye<sup>ak</sup>, E. Agasi<sup>ae</sup>, I. Ajinenko<sup>ap</sup>, R. Aleksan<sup>am</sup>, G.D. Alekseev<sup>p</sup>, P.P. Allport<sup>v</sup>, S. Almehed<sup>x</sup>, S.J. Alvsaag<sup>d</sup>, U. Amaldi<sup>i</sup>, S. Amato<sup>au</sup>, A. Andreazza<sup>ab</sup>, M.L. Andrieux<sup>n</sup>, P. Antilogus<sup>y</sup>, W-D. Apel<sup>q</sup>, Y. Arnoud<sup>am</sup>, B. Åsman<sup>ar</sup>, J-E. Augustin<sup>s</sup>, A. Augustinus<sup>ae</sup>, P. Baillon<sup>i</sup>, P. Bambade<sup>s</sup>, F. Barao<sup>u</sup>, R. Barate<sup>n</sup>, G. Barbiellini<sup>at</sup>, D.Y. Bardin<sup>p</sup>, G.J. Barker<sup>ai</sup>, A. Baroncelli<sup>an</sup>, O. Barring<sup>x</sup>, J.A. Barrio<sup>z</sup>, W. Bartl<sup>ay</sup>, M.J. Bates<sup>ak</sup>, M. Battaglia<sup>o</sup>, M. Baubillier<sup>w</sup>, J. Baudot<sup>am</sup>, K-H. Becks<sup>ba</sup>, M. Begalli<sup>f</sup>, P. Beilliere<sup>h</sup>, Yu. Belokopytov<sup>i</sup>, K. Belous<sup>ap</sup>, A.C. Benvenuti<sup>e</sup>, M. Berggren<sup>ao</sup>, D. Bertrand<sup>b</sup>, F. Bianchi<sup>as</sup>, M. Bigi<sup>as</sup>, M.S. Bilenky<sup>p</sup>, P. Billoir<sup>w</sup>, D. Bloch<sup>j</sup>, M. Blume<sup>ba</sup>, S. Blyth<sup>ai</sup>, V. Bocci<sup>al</sup>, T. Bolognese<sup>am</sup>, M. Bonesini<sup>ab</sup>, W. Bonivento<sup>ab</sup>, P.S.L. Booth<sup>v</sup>, G. Borisov<sup>ap</sup>, C. Bosio<sup>an</sup>, S. Bosworth<sup>ai</sup>, O. Botner<sup>av</sup>, B. Bouquet<sup>s</sup>, C. Bourdarios<sup>i</sup>, T.J.V. Bowcock<sup>v</sup>, M. Bozzo<sup>m</sup>, P. Branchini<sup>an</sup>, K.D. Brand<sup>aj</sup>, R.A. Brenner<sup>o</sup>, C. Bricman<sup>b</sup>, L. Brillault<sup>w</sup>, R.C.A. Brown<sup>i</sup>, P. Bruckman<sup>r</sup>, J-M. Brunet<sup>h</sup>, L. Bugge<sup>ag</sup>, T. Buran<sup>ag</sup>, A. Buys<sup>i</sup>, M. Caccia<sup>ab</sup>, M. Calvi<sup>ab</sup>, A.J. Camacho Rozas<sup>ao</sup>, T. Camporesi<sup>i</sup>, V. Canale<sup>al</sup>, M. Canepa<sup>m</sup>, K. Cankocak<sup>ar</sup>, F. Cao<sup>b</sup>, F. Carena<sup>i</sup>, P. Carrilho<sup>au</sup>, L. Carroll<sup>v</sup>, C. Caso<sup>m</sup>, M.V. Castillo Gimenez<sup>aw</sup>, A. Cattai<sup>i</sup>, F.R. Cavallo<sup>e</sup>, L. Cerrito<sup>al</sup>, V. Chabaud<sup>i</sup>, Ph. Charpentier<sup>i</sup>, L. Chaussard<sup>y</sup>, J. Chauveau<sup>w</sup>, P. Checchia<sup>aj</sup>, G.A. Chelkov<sup>p</sup>, R. Chierici<sup>as</sup>, P. Chochula<sup>g</sup>, V. Chorowicz<sup>i</sup>, V. Cindro<sup>aq</sup>, P. Collins<sup>i</sup>, J.L. Contreras<sup>s</sup>, R. Contri<sup>m</sup>, E. Cortina<sup>aw</sup>, G. Cosme<sup>s</sup>, F. Cossutti<sup>at</sup>, H.B. Crawley<sup>a</sup>, D. Crennell<sup>ak</sup>, G. Crosetti<sup>m</sup>, J. Cuevas Maestro<sup>ah</sup>, S. Czellar<sup>o</sup>, E. Dahl-Jensen<sup>ac</sup>, J. Dahm<sup>ba</sup>, B. Dalmagne<sup>s</sup>, M. Dam<sup>ag</sup>, G. Damgaard<sup>ac</sup>, A. Daum<sup>q</sup>, P.D. Dauncey<sup>ak</sup>, M. Davenport<sup>i</sup>, W. Da Silva<sup>w</sup>, C. Defoix<sup>h</sup>, G. Della Ricca<sup>at</sup>, P. Delpierre<sup>aa</sup>, N. Demaria<sup>ai</sup>, A. De Angelis<sup>i</sup>, H. De Boeck<sup>b</sup>, W. De Boer<sup>q</sup>, S. De Brabandere<sup>b</sup>, C. De Clercq<sup>b</sup>, C. De La Vaissiere<sup>w</sup>, B. De Lotto<sup>at</sup>, A. De Min<sup>ab</sup>, L. De Paula<sup>au</sup>, C. De Saint-Jean<sup>am</sup>, H. Dijkstra<sup>i</sup>, L. Di Ciaccio<sup>al</sup>, F. Djama<sup>j</sup>, J. Dolbeau<sup>h</sup>, M. Donszelmann<sup>i</sup>, K. Doroba<sup>az</sup>, M. Dracos<sup>j</sup>, J. Drees<sup>ba</sup>, K.-A. Drees<sup>ba</sup>, M. Dris<sup>af</sup>, Y. Dufour<sup>h</sup>, F. Dupont<sup>n</sup>, D. Edsall<sup>a</sup>, R. Ehret<sup>q</sup>, G. Eigen<sup>d</sup>, T. Ekelof<sup>av</sup>, G. Ekspong<sup>ar</sup>, M. Elsing<sup>ba</sup>, J-P. Engel<sup>j</sup>, N. Ershaidat<sup>w</sup>, B. Erzen<sup>aq</sup>, M. Espirito Santo<sup>u</sup>, E. Falk<sup>x</sup>, D. Fassouliotis<sup>af</sup>, M. Feindt<sup>i</sup>, A. Fenyuk<sup>ap</sup>, A. Ferrer<sup>aw</sup>, T.A. Filippas<sup>af</sup>, A. Firestone<sup>a</sup>, P.-A. Fischer<sup>j</sup>, H. Foeth<sup>i</sup>, E. Fokitis<sup>af</sup>, F. Fontanelli<sup>m</sup>,
F. Formenti<sup>i</sup>, B. Franek<sup>ak</sup>, P. Frenkiel<sup>h</sup>, D.C. Fries<sup>q</sup>, A.G. Frodesen<sup>d</sup>, R. Fruhwirth<sup>ay</sup>,
F. Fulda-Quenzer<sup>s</sup>, H. Furstenau<sup>i</sup>, J. Fuster<sup>aw</sup>, A. Galloni<sup>v</sup>, D. Gamba<sup>as</sup>, M. Gandelman<sup>f</sup>,
C. Garcia<sup>aw</sup>, J. Garcia<sup>ao</sup>, C. Gaspari<sup>i</sup>, U. Gasparini<sup>aj</sup>, Ph. Gavillet<sup>i</sup>, E.N. Gazis<sup>af</sup>, D. Gele<sup>j</sup>,
J-P. Gerber<sup>j</sup>, M. Gibbs<sup>v</sup>, D. Gillespie<sup>i</sup>, R. Gokieli<sup>az</sup>, B. Golob<sup>aq</sup>, G. Gopal<sup>ak</sup>, L. Gorn<sup>a</sup>,
M. Gorski<sup>az</sup>, Yu. Gouz<sup>ap</sup>, V. Gracco<sup>m</sup>, E. Graziani<sup>an</sup>, G. Grosdidier<sup>s</sup>, P. Gunnarsson<sup>ar</sup>,
M. Gunther<sup>av</sup>, J. Guy<sup>ak</sup>, U. Haedinger<sup>q</sup>, F. Hahn<sup>ba</sup>, M. Hahn<sup>q</sup>, S. Hahn<sup>ba</sup>, Z. Hajduk<sup>r</sup>,
A. Hallgren<sup>av</sup>, K. Hamacher<sup>ba</sup>, W. Hao<sup>ae</sup>, F.J. Harris<sup>ai</sup>, V. Hedberg<sup>x</sup>, R. Henriques<sup>u</sup>,
J.J. Hernandez<sup>aw</sup>, P. Herquet<sup>b</sup>, H. Herr<sup>i</sup>, T.L. Hessing<sup>i</sup>, E. Higon<sup>aw</sup>, H.J. Hilke<sup>i</sup>, T.S. Hill<sup>a</sup>,
S-O. Holmgren<sup>ar</sup>, P.J. Holt<sup>ai</sup>, D. Holthuizen<sup>ae</sup>, M. Houlden<sup>v</sup>, K. Huet<sup>b</sup>, K. Hultqvist<sup>ar</sup>,
P. Ioannou<sup>c</sup>, J.N. Jackson<sup>v</sup>, R. Jacobsson<sup>ar</sup>, P. Jalocha<sup>r</sup>, R. Janik<sup>g</sup>, G. Jarlskog<sup>x</sup>, P. Jarry<sup>am</sup>,
B. Jean-Marie<sup>s</sup>, E.K. Johansson<sup>ar</sup>, L. Jonsson<sup>x</sup>, P. Jonsson<sup>x</sup>, C. Joram<sup>i</sup>, P. Juillot<sup>j</sup>,
M. Kaiser<sup>q</sup>, G. Kalmus<sup>ak</sup>, F. Kapusta<sup>w</sup>, M. Karlsson<sup>ar</sup>, E. Karvelas<sup>k</sup>, A. Katargin<sup>ap</sup>,
S. Katsanevas<sup>c</sup>, E.C. Katsoufis<sup>af</sup>, R. Keranen<sup>o</sup>, B.A. Khomenko<sup>p</sup>, N.N. Khovanski<sup>p</sup>,
B. King<sup>v</sup>, N.J. Kjaer<sup>ac</sup>, H. Klein<sup>i</sup>, A. Klovning<sup>d</sup>, P. Kluit<sup>ac</sup>, J.H. Koehne<sup>q</sup>, B. Koene<sup>ac</sup>,
P. Kokkinias<sup>k</sup>, M. Koratzinos<sup>i</sup>, V. Kostioukhine<sup>ap</sup>, C. Kourkoumelis<sup>c</sup>, O. Kouznetsov<sup>m</sup>,
P.-H. Kramer<sup>ba</sup>, M. Krammer<sup>ay</sup>, C. Kreuter<sup>q</sup>, J. Krolikowski<sup>az</sup>, I. Kronkvist<sup>x</sup>,
Z. Krumstein<sup>p</sup>, W. Krupinski<sup>r</sup>, P. Kubinec<sup>g</sup>, W. Kucewicz<sup>r</sup>, K. Kurvinen<sup>o</sup>, C. Lacasta<sup>aw</sup>,
I. Laktineh<sup>y</sup>, S. Lamblot<sup>w</sup>, J.W. Lamsa<sup>a</sup>, L. Lanceri<sup>at</sup>, D.W. Lane<sup>a</sup>, P. Langefeld<sup>ba</sup>,
V. Lapin<sup>ap</sup>, I. Last<sup>v</sup>, J-P. Laugier<sup>am</sup>, R. Lauhakangas<sup>o</sup>, G. Leder<sup>ay</sup>, F. Ledroit<sup>n</sup>,
V. Lefebure<sup>b</sup>, C.K. Legan<sup>a</sup>, R. Leitner<sup>ad</sup>, Y. Lemoigne<sup>am</sup>, J. Lemonne<sup>b</sup>, G. Lenzen<sup>ba</sup>,
V. Lepeltier<sup>s</sup>, T. Lesiak<sup>aj</sup>, D. Liko<sup>ay</sup>, R. Lindner<sup>ba</sup>, A. Lipniacka<sup>s</sup>, I. Lippi<sup>aj</sup>, B. Loerstad<sup>x</sup>,
M. Lokajicek<sup>l</sup>, J.G. Loken<sup>ai</sup>, J.M. Lopez<sup>ao</sup>, A. Lopez-Fernandez<sup>i</sup>, M.A. Lopez Aguera<sup>ao</sup>,
D. Loukas<sup>k</sup>, P. Lutz<sup>am</sup>, L. Lyons<sup>ai</sup>, J. MacNaughton<sup>ay</sup>, G. Maehlum<sup>q</sup>, A. Maio<sup>u</sup>,
V. Malychev<sup>p</sup>, F. Mandl<sup>ay</sup>, J. Marco<sup>ao</sup>, B. Marechal<sup>au</sup>, M. Margoni<sup>aj</sup>, J-C. Marin<sup>i</sup>,
C. Mariotti<sup>an</sup>, A. Markou<sup>k</sup>, T. Maron<sup>ba</sup>, C. Martinez-Rivero<sup>ao</sup>, F. Martinez-Vidal<sup>aw</sup>,
S. Marti i Garcia<sup>aw</sup>, F. Matorras<sup>ao</sup>, C. Matteuzzi<sup>ab</sup>, G. Matthiae<sup>al</sup>, M. Mazzucato<sup>aj</sup>,
M. Mc Cubbin<sup>i</sup>, R. Mc Kay<sup>a</sup>, R. Mc Nulty<sup>v</sup>, J. Medbo<sup>av</sup>, C. Meroni<sup>ab</sup>, W.T. Meyer<sup>a</sup>,
A. Miagkov<sup>ap</sup>, M. Michelotto<sup>aj</sup>, E. Migliore<sup>as</sup>, L. Mirabito<sup>y</sup>, W.A. Mitaroff<sup>ay</sup>,
U. Mjoernmark<sup>x</sup>, T. Moa<sup>ar</sup>, R. Moeller<sup>ac</sup>, K. Moenig<sup>i</sup>, M.R. Monge<sup>m</sup>, P. Morettini<sup>m</sup>,
H. Mueller<sup>q</sup>, L.M. Mundim<sup>f</sup>, W.J. Murray<sup>ak</sup>, B. Muryn<sup>r</sup>, G. Myatt<sup>ai</sup>, F. Naraghi<sup>n</sup>,
F.L. Navarria<sup>e</sup>, S. Navas<sup>aw</sup>, P. Negri<sup>ab</sup>, S. Nemecek<sup>l</sup>, W. Neumann<sup>ba</sup>, N. Neumeister<sup>ay</sup>,
R. Nicolaidou<sup>c</sup>, B.S. Nielsen<sup>ac</sup>, M. Nieuwenhuizen<sup>ae</sup>, V. Nikolaenko<sup>j</sup>, P. Niss<sup>ar</sup>,
A. Nomerotski<sup>aj</sup>, A. Normand<sup>ai</sup>, W. Oberschulte-Beckmann<sup>q</sup>, V. Obraztsov<sup>ap</sup>,
A.G. Olshevski<sup>p</sup>, A. Onofre<sup>u</sup>, R. Orava<sup>o</sup>, K. Osterberg<sup>o</sup>, A. Ouraou<sup>am</sup>, P. Paganini<sup>s</sup>,
M. Paganoni<sup>ab</sup>, P. Pages<sup>j</sup>, H. Palka<sup>r</sup>, Th.D. Papadopoulou<sup>af</sup>, L. Pape<sup>i</sup>, C. Parkes<sup>ai</sup>,
F. Parodi<sup>m</sup>, A. Passeri<sup>an</sup>, M. Pegoraro<sup>aj</sup>, L. Peralta<sup>u</sup>, H. Pernegger<sup>ay</sup>, M. Pernicka<sup>ay</sup>,
A. Perrotta<sup>e</sup>, C. Petridou<sup>at</sup>, A. Petrolini<sup>m</sup>, H.T. Phillips<sup>ak</sup>, G. Piana<sup>m</sup>, F. Pierre<sup>am</sup>,
M. Pimenta<sup>u</sup>, S. Plaszczynski<sup>s</sup>, O. Podobrin<sup>q</sup>, M.E. Pol<sup>f</sup>, G. Polok<sup>r</sup>, P. Poropat<sup>at</sup>,
V. Pozdniakov<sup>p</sup>, M. Prest<sup>at</sup>, P. Privitera<sup>al</sup>, N. Pukhaeva<sup>p</sup>, A. Pullia<sup>ab</sup>, D. Radojicic<sup>ai</sup>,
S. Ragazzi<sup>ab</sup>, H. Rahmani<sup>af</sup>, J. Rames<sup>l</sup>, P.N. Ratoff<sup>t</sup>, A.L. Read<sup>ag</sup>, M. Reale<sup>ba</sup>,
P. Rebecchi<sup>s</sup>, N.G. Redaelli<sup>ab</sup>, M. Regler<sup>ay</sup>, D. Reid<sup>i</sup>, P.B. Renton<sup>ai</sup>, L.K. Resvanis<sup>c</sup>, F. Richard<sup>s</sup>, J. Richardson<sup>v</sup>, J. Ridky<sup>l</sup>, G. Rinaudo<sup>as</sup>, I. Ripp<sup>am</sup>, A. Romero<sup>as</sup>, I. Roncagliolo<sup>m</sup>, P. Ronchese<sup>aj</sup>, L. Roos<sup>n</sup>, E.I. Rosenberg<sup>a</sup>, E. Rosso<sup>i</sup>, P. Roudeau<sup>s</sup>, T. Rovelli<sup>e</sup>, W. Ruckstuhl<sup>ae</sup>, V. Ruhlmann-Kleider<sup>am</sup>, A. Ruiz<sup>ao</sup>, H. Saarikko<sup>o</sup>, Y. Sacquin<sup>am</sup>, A. Sadovsky<sup>p</sup>, G. Sajot<sup>n</sup>, J. Salt<sup>aw</sup>, J. Sanchez<sup>z</sup>, M. Sannino<sup>m</sup>, H. Schneider<sup>q</sup>, M.A.E. Schyns<sup>ba</sup>, G. Sciolla<sup>as</sup>, F. Scuri<sup>at</sup>, Y. Sedykh<sup>p</sup>, A.M. Segar<sup>ai</sup>, A. Seitz<sup>q</sup>, R. Sekulin<sup>ak</sup>, R.C. Shellard<sup>f</sup>, I. Siccama<sup>ae</sup>, P. Siegrist<sup>am</sup>, S. Simonetti<sup>am</sup>, F. Simonetto<sup>aj</sup>, A.N. Sisakian<sup>p</sup>, B. Sitar<sup>g</sup>, T.B. Skaali<sup>ag</sup>, G. Smadja<sup>y</sup>, N. Smirnov<sup>ap</sup>, O. Smirnova<sup>p</sup>, G.R. Smith<sup>ak</sup>, A. Sokolov<sup>ap</sup>, R. Sosnowski<sup>az</sup>, D. Souza-Santos<sup>f</sup>, T. Spassov<sup>u</sup>, E. Spiriti<sup>an</sup>, S. Squarcia<sup>m</sup>, H. Staeck<sup>ba</sup>, C. Stanescu<sup>an</sup>, S. Stapnes<sup>ag</sup>, I. Stavitski<sup>aj</sup>, K. Stepaniak<sup>az</sup>, F. Stichelbaut<sup>i</sup>, A. Stocchi<sup>s</sup>, J. Strauss<sup>ay</sup>, R. Strub<sup>j</sup>, B. Stugu<sup>d</sup>, M. Szczekowski<sup>az</sup>, M. Szeptycka<sup>az</sup>, T. Tabarelli<sup>ab</sup>, J.P. Tavernet<sup>w</sup>, A. Tilquin<sup>aa</sup>, J. Timmermans<sup>ae</sup>, L.G. Tkatchev<sup>p</sup>, T. Todorov<sup>j</sup>, D.Z. Toet<sup>ae</sup>, A. Tomaradze<sup>b</sup>, B. Tome<sup>u</sup>, L. Tortora<sup>an</sup>, G. Transtromer<sup>x</sup>, D. Treille<sup>i</sup>, W. Trischuk<sup>i</sup>, G. Tristram<sup>h</sup>, A. Trombini<sup>s</sup>, C. Troncon<sup>ab</sup>, A. Tsirou<sup>i</sup>, M-L. Turluer<sup>am</sup>, I.A. Tyapkin<sup>p</sup>, M. Tyndel<sup>ak</sup>, S. Tzamarias<sup>v</sup>, B. Ueberschaer<sup>ba</sup>, S. Ueberschaer<sup>ba</sup>, O. Ullaland<sup>i</sup>, G. Valenti<sup>e</sup>, E. Vallazza<sup>i</sup>, C. Vander Velde<sup>b</sup>, G.W. Van Apeldoorn<sup>ae</sup>, P. Van Dam<sup>ae</sup>, J. Van Eldik<sup>ae</sup>, N. Vassilopoulos<sup>ai</sup>, G. Vegni<sup>ab</sup>, L. Ventura<sup>aj</sup>, W. Venus<sup>ak</sup>, F. Verbeure<sup>b</sup>, M. Verlato<sup>aj</sup>, L.S. Vertogradov<sup>p</sup>, D. Vilanova<sup>am</sup>, P. Vincent<sup>y</sup>, L. Vitale<sup>at</sup>, E. Vlasov<sup>ap</sup>, A.S. Vodopyanov<sup>p</sup>, V. Vrba<sup>l</sup>, H. Wahlen<sup>ba</sup>, C. Walck<sup>ar</sup>, A. Wehr<sup>ba</sup>, M. Weierstall<sup>ba</sup>, P. Weilhammer<sup>i</sup>, A.M. Wetherell<sup>i</sup>, D. Wicke<sup>ba</sup>, J.H. Wickens<sup>b</sup>, M. Wielers<sup>q</sup>, G.R. Wilkinson<sup>ai</sup>, W.S.C. Williams<sup>ai</sup>, M. Winter<sup>j</sup>, M. Witek<sup>i</sup>, K. Woschnagg<sup>av</sup>, K. Yip<sup>ai</sup>, O. Yushchenko<sup>ap</sup>, F. Zach<sup>y</sup>, C. Zacharatou<sup>x</sup>, A. Zaitsev<sup>ap</sup>, A. Zalewska<sup>r</sup>, P. Zalewski<sup>az</sup>, D. Zavrtanik<sup>aq</sup>, E. Zevgolatakos<sup>k</sup>, N.I. Zimin<sup>p</sup>, M. Zito<sup>am</sup>, D. Zontar<sup>aq</sup>, R. Zuberi<sup>ai</sup>, G.C. Zucchelli<sup>ar</sup>, G. Zumerle<sup>aj</sup>

<footnote><sup>a</sup> Ames Laboratory and Department of Physics, Iowa State University, Ames IA 50011, USA</footnote>

<footnote><sup>b</sup> Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgium and IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium</footnote>

<footnote>and Faculté des Sciences, Univ. de l'Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium</footnote>

<footnote><sup>c</sup> Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece</footnote>

<footnote><sup>d</sup> Department of Physics, University of Bergen, Allégaten 55, N-5007 Bergen, Norway</footnote>

<footnote><sup>e</sup> Dipartimento di Fisica, Università di Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy</footnote>

<footnote><sup>f</sup> Centro Brasileiro de Pesquisas Físicas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Brazil and Depto. de Física, Pont. Univ. Católica, C.P. 38071 RJ-22453 Rio de Janeiro, Brazil</footnote>

<footnote>and Inst. de Física, Univ. Estadual do Rio de Janeiro, rua São Francisco Xavier 524, Rio de Janeiro, Brazil</footnote>

<footnote><sup>g</sup> Comenius University, Faculty of Mathematics and Physics, Młynska Dolina, SK-84215 Bratislava, Slovakia</footnote>

<footnote><sup>h</sup> Collège de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, F-75231 Paris Cedex 05, France</footnote>

<footnote><sup>i</sup> CERN, CH-1211 Geneva 23, Switzerland</footnote>

<footnote><sup>j</sup> Centre de Recherche Nucléaire, IN2P3 - CNRS/ULP - BP20, F-67037 Strasbourg Cedex, France</footnote>

<footnote><sup>k</sup> Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece</footnote>

<footnote><sup>l</sup> FZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic</footnote>

<footnote><sup>m</sup> Dipartimento di Fisica, Università di Genova and INFN, Via Dodecaneso 33, I-16146 Genova, Italy</footnote>

<footnote><sup>n</sup> Institut des Sciences Nucléaires, IN2P3-CNRS, Université de Grenoble 1, F-38026 Grenoble Cedex, France</footnote>

<footnote><sup>o</sup> Research Institute for High Energy Physics, SEFT, P.O. Box 9, FIN-00014 Helsinki, Finland</footnote>

<footnote><sup>p</sup> Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian Federation</footnote>

<footnote><sup>q</sup> Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany</footnote>
† High Energy Physics Laboratory, Institute of Nuclear Physics, Ul. Kawiory 26a, PL-30055 Krakow 30, Poland

s Université de Paris-Sud, Lab. de l'Accélérateur Linéaire, IN2P3-CNRS, Bât. 200, F-91405 Orsay Cedex, France

† School of Physics and Materials, University of Lancaster, Lancaster LA1 4YB, UK

u LIP, IST, FCUL - Av. Elías Garcia, 14-1(o), P-1000 Lisboa Codex, Portugal

v Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK

w LPNHE, IN2P3-CNRS, Universités Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France

x Department of Physics, University of Lund, Sölvegatan 14, S-22363 Lund, Sweden

y Université Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France

z Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain

aa Univ. d'Aix - Marseille II - CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France

ab Dipartimento di Fisica, Università di Milano and INFN, Via Celoria 16, I-20133 Milan, Italy

ac Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen 0, Denmark

ad NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic

ae NIKHEF-H, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands

af National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece

ag Physics Department, University of Oslo, Blindern, N-1000 Oslo 3, Norway

ah Dpto. Fisica, Univ. Oviedo, C/P. Pérez Casas, S/N-33006 Oviedo, Spain

ai Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK

aj Dipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, I-35131 Padua, Italy

ak Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK

a2 Dipartimento di Fisica, Università di Roma II and INFN, Tor Vergata, I-00173 Rome, Italy

am Centre d'Etudes de Saclay, DSM/DAPNIA, F-91191 Gif-sur-Yvette Cedex, France

an Istituto Superiore di Sanità, Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, I-00161 Rome, Italy

ao C.E.A.F.M., C.S.I.C. - Univ. Cantabria, Avda. los Castros, (CICYT-AEN93-0832), S/N-39006 Santander, Spain

ap Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation

aq J. Stefan Institute and Department of Physics, University of Ljubljana, Jamova 39, SI-61000 Ljubljana, Slovenia

ar Fysikum, Stockholm University, Box 6730, S-113 85 Stockholm, Sweden

as Dipartimento di Fisica Sperimentale, Università di Torino and INFN, Via P. Giuria 1, I-10125 Turin, Italy

at Dipartimento di Fisica, Università di Trieste and INFN, Via A. Valerio 2, I-34127 Trieste, Italy
and Istituto di Fisica, Università di Udine, I-33100 Udine, Italy

au Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundão BR-21945-970 Rio de Janeiro, Brazil

av Department of Radiation Sciences, University of Uppsala, P.O. Box 535, S-751 21 Uppsala, Sweden

aw IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain

ay Institut für Hochenergiephysik, Österr. Akad. d. Wissenschaft., Nikolsdorfergasse 18, A-1050 Vienna, Austria

az Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland

ba Fachbereich Physik, University of Wuppertal, Postfach 100 127, D-42097 Wuppertal 1, Germany

Received 31 May 1995

Editor: L. Montanet

## Abstract

Measurements are presented of short range three-particle correlations in $e^{+}e^{-}$ annihilations at LEP using data collected by the DELPHI detector. At small values of the four-momentum difference, strong three-particle correlations are observed for like-sign (+++ and ---) and for unlike-sign (++- and +-- ) pion combinations which are not a consequence of two-particle correlations. A possible explanation of the observed effects in like-sign combinations is the existence of higher order Bose-Einstein interference, which significantly changes the particle distributions in jets.

## 1. Introduction

Studies of the properties of hadronic events in $e^{+}e^{-}$ annihilations and tests of QCD generators are usually

performed using global event shape variables and single particle distributions. As the multiplicity of particles increases with increasing initial energy, correlations between particles change their distributions in
jets and an understanding of these correlations becomes important. Studies of correlations at high energy are thus related to the composition of jets and tests of QCD models. A clear example of the influence of correlations on particle distributions is the distortion of the Breit-Wigner shape for oppositely charged pions from the decay of broad resonances by residual Bose-Einstein (BE) correlations, which was observed at LEP energies [1] (see also [2]). Recently, it was also shown that the observed W mass at LEP200 is likely to be affected by BE correlations [3]. A better understanding of these correlations, as well as comparisons of BE algorithms with experimental data at high energies, becomes necessary for high precision measurements of the W mass.

Two-particle correlations have been studied extensively in hadron-hadron interactions [4,5] and in $e^+e^-$ annihilations at LEP energies [6]. However, very few experimental results are available on three-particle correlations which can be generated either by two-particle correlations or by genuine three-particle correlations. Identifying the latter is complicated because of the need for high statistics of large multiplicity events and the problem of subtracting the direct consequences of two-particle correlations. Obvious $\pi^+\pi^+\pi^-$ and $\pi^+\pi^-\pi^-$ correlations are generated in the decays of many resonances. The most prominent example at low masses is the $\eta'$ decay into $\eta\pi^+\pi^-$ with subsequent decay of the $\eta$ into $\pi^+\pi^-\pi^0$ or $\pi^+\pi^-\gamma$. At higher three-pion masses there are many contributions from the decays of charm and beauty particles.

Short-range rapidity correlations are observed for $(++)$ and $(--)$ combinations in several experiments [7-10]. In contrast to the unlike-sign combinations, no genuine correlations were found for the like-sign $(++)$ and $(--)$ configuration. Furthermore, in the three-particle Bose-Einstein effect studied in [8,10,11], no evidence was found for three-particle correlations beyond those generated from pairs in the triplet. Only one hadron-proton experiment recently reported the observation of positive short-range higher order like-sign correlations [12].

Experimental evidence for genuine like-sign three-particle correlations has still to be reported; it constitutes an important theoretical issue for the understanding of BE correlations [13].

In this paper, the first evidence is presented for genuine

three particle correlations at LEP using data collected by the DELPHI detector. We discuss like-sign and unlike-sign three-particle correlations after subtraction of the two-particle ones. It is demonstrated that positive short range correlations exist for both like-sign and unlike-sign configurations. Both these correlations can be understood, at least partly, as following from higher order Bose-Einstein correlations, which change the event shape at small relative momenta. Experimental data are compared with various modifications of the JETSET PS model [14].

## 2. Analysis

The single-particle density is defined as

$$ \rho_1(q_a) = \frac{E_a}{N_{ev}} \frac{d^3 n}{d^3 p_a}, \quad (1) $$

the two-particle density as

$$ \rho_2(q_a, q_b) = \frac{E_a E_b}{N_{ev}} \frac{d^6 n}{d^3 p_a d^3 p_b} \quad (2) $$

and the three-particle density as

$$ \rho_3(q_a, q_b, q_c) = \frac{E_a E_b E_c}{N_{ev}} \frac{d^9 n}{d^3 p_a d^3 p_b d^3 p_c}, \quad (3) $$

where $q_i$ and $p_i$ are the four vector and three vector momentum, respectively, and $E_i$ the energy of the particle; $n$ is the number of particles (in Eq. (1)), of doublets (in Eq. (2)) or triplets (in Eq. (3)) and $N_{ev}$ is the number of events. For $n$ identical particles, these densities are normalized to $<n>$, $<n(n-1)>$ and $<n(n-1)(n-2)>$, respectively. We study the normalized three-body correlation function written as [15]

$$ R_3 = R_3'' - R_3' + 1 \quad (4) $$

where the quantity

$$ R_3'' = [\rho_3(q_a, q_b, q_c) - \rho_1(q_a)\rho_1(q_b)\rho_1(q_c)] / \rho_1(q_a)\rho_1(q_b)\rho_1(q_c) \quad (5) $$

is the full three-particle correlation function and

$$ R_3' = [\rho_2(q_a, q_b)\rho_1(q_c) + \rho_2(q_a, q_c)\rho_1(q_b) + \rho_2(q_b, q_c)\rho_1(q_a) - 3\rho_1(q_a)\rho_1(q_b)\rho_1(q_c)] / \rho_1(q_a)\rho_1(q_b)\rho_1(q_c) \quad (6) $$
is the three-particle correlation arising from correlations in the pairs of the triplet. The $\rho_1(q_a)\rho_1(q_b) \times \rho_1(q_c)$ term represents uncorrelated production of the three particles, each to be taken with its density defined in Eq. (1). The $\rho_2(q_a, q_b)\rho_1(q_c)$ term, as well as the next two terms in Eq. (6), contain the two-body correlations. The genuine three-particle correlation function $R_3$ is then given by

$$R_3 = [\rho_3 + 3\rho_1\rho_1\rho_1 - 3\rho_2\rho_1]/\rho_1\rho_1\rho_1 \quad (7)$$

where the q-variables have been omitted for clarity and $3\rho_2\rho_1$ is the sum of the three $\rho_2\rho_1$ terms in Eq. (6). The quantity $R_3$ therefore does not contain three-particle correlations which arise from two-body correlations nor is it sensitive to possible bias in two-particle combinations due to Dalitz pairs, $\gamma$-conversions, or particle or resonance decays.

The kinematical variable used in this analysis is

$$Q^2 = q_{12}^2 + q_{23}^2 + q_{31}^2 \quad (8)$$

with $q_{ij}^2 = -(q_i - q_j)^2$. For three-pion systems, $Q^2 = M_{123}^2 - 9m_\pi^2$, with $M_{123}$ the invariant mass of the pion triplet. It has been shown [5] that this Lorentz invariant variable is more sensitive to correlations than the rapidity variable.

### 3. Experimental procedure

This study is based on a sample of about 1.5 million hadronic events collected with the DELPHI detector during the 1992 and 1993 running periods, at a center of mass energy at and around the $Z^0$ peak. The detector has been described in [16]. The analysis uses the same methodology as in [17]. All charged particles were considered to be pions and only charged particles satisfying the following requirements were used:
- polar angle $\theta$ with respect to the beam axis between 25° and 155°;

- momentum greater than 0.2 GeV/c and less than 50 GeV/c;

- measured track length in the TPC, the main tracking chamber, greater than 50 cm;

- measured impact parameter with respect to the event vertex less than 5 cm in the transverse plane and 10 cm along the beam direction.

Hadronic events were selected by requiring that:

- there were at least 5 charged particles in the event;

- the total energy of the charged particles exceeded 3 GeV in each of the two hemispheres defined with respect to the beam direction;

- the total energy of all charged particles was larger than 15 GeV;

- the total momentum imbalance was less than 30 GeV/c;

- the polar angle of the thrust axis $\theta_{th}$, defined with respect to the beam direction, satisfied $|\cos\theta_{th}| < 0.75$.

The contamination from events due to beam-gas scattering, $\gamma\gamma$ interactions and $\tau^+\tau^-$ events was estimated to be less than 0.3% of the selected events. Only charged particles with an impact parameter less than 0.1 cm in the transverse plane and 1 cm in the beam direction were used in the calculation of the $Q$ distribution. Thus only particles originating from the primary vertex were included. These strict cuts on both transverse and longitudinal impact parameters removed most tracks from $K_S^0$ and $\Lambda$ decays. To select clean two-jet events, a cut on the thrust variable $T > 0.97$ was imposed. A sample of 327,162 events was available after all cuts.

In order to calculate the terms $\rho_2\rho_1$ and $\rho_1\rho_1\rho_1$ in Eqs. (5)-(7), the following mixing technique was used. A pool of particle four-vectors with momentum components calculated with respect to the thrust axis, was constructed from a large number of events. To calculate $\rho_1\rho_1\rho_1$, three tracks were randomly drawn from the pool and the term was calculated in the same way as in real events; to calculate $\rho_2\rho_1$, two particles were taken from the same event and the third one from another event.

The analysis was limited to $Q > 0.15$ GeV/c in order to avoid the region where the three tracks could be geometrically confused. This value for triplets corresponds, on average, to $q_{ij} > 0.09$ GeV/c for pairs. Moreover, if false two-body correlations are introduced they are subtracted in the quantity $R_3$. The correction for geometrical acceptance, kinematical cuts, particle interactions with the detector material and other detector imperfections, was made by using the Monte Carlo simulation program DELSIM [18]. A sample of $Z^0$ hadronic events was generated with JET-SET and all tracks were followed through the full detector. After application of the same cuts as on the data, including the thrust cut, about 1,000,000 events
<figure><img src="image_3.png" /><figcaption>Fig. 1. Q-dependence of $R_3''$, the total three-particle correlation, and $R_3'$, the three-particle correlation arising from two-body correlations, (a) for like-sign and (b) for unlike-sign triplets.</figcaption></figure>

remained. Bin by bin correction factors were calculated for $\rho_3$, $\rho_2\rho_1$, and $\rho_1\rho_1\rho_1$. In the following, only corrected distributions will be presented. However, it was checked that the same features are present at the level of the uncorrected distributions.

## 4. Results and discussion

Fig. 1a shows $R_3''$, the full three-particle correlation function for like-sign triplets using the normalization of the density functions as given above. A strong correlation is observed at small Q-values. However, $R_3'$, the background three-particle correlation arising from two-particle correlations between particles in the triplet, also shows a strong rise towards Q = 0. Fig. 1a demonstrates that most of the three-particle correlations are due to two-particle correlations, but also that some excess of $R_3''$ over $R_3'$ is present at small Q. The three-particle correlation functions $R_3''$ and $R_3'$ for unlike-sign triplets are presented in Fig. 1b. A difference between the $R_3''$ and $R_3'$ functions at small Q is also present for unlike-sign triplets.

The genuine three-particle correlations for like-sign

<figure><img src="image_4.png" /><figcaption>Fig. 2. The three-particle correlation function $R_3$ for (a) like-sign triplets and (b) for unlike-sign triplets, compared to the JETSET prediction with no Bose-Einstein correlations included. The dot-dashed curve in (a) is the result of a fit with Eq. (10).</figcaption></figure>

triplets, $R_3$, are shown in Fig. 2a. A clear signal is observed at $Q < 0.5$ GeV/c, corresponding to a short-range three-particle correlation. A reference sample such as the one of unlike-sign pion combinations is inadequate because of the presence of correlations in this sample. This is clearly seen from Fig. 2b where the function $R_3(Q)$ is plotted for unlike-sign triplets.

The predictions of JETSET 7.3 PS [14] with no BE correlations included, are shown in Fig. 2 (full lines). Here and in the following, the JETSET events are subject to the same cuts and contributions to $\rho_3$ calculated from single events and the other terms with the same mixing technique as the experimental data. The statistical errors on the JETSET are about three times smaller than those on the data points. At small Q-values, strong differences are observed between JETSET and the data for both like-sign and unlike-sign triplets. For like-sign triplets the model does not show any increase of the correlation function for $Q \to 0$, compatible with no like-sign three-particle correlations in the model. A steep increase of the correlation function at small Q-values is observed in the model without BE correlations for $(++)$ and $(-^-)$ combinations (full line in Fig. 2b). In the model, the
$\eta'$ production rate was reduced by a factor 4, based on a measurement of $\eta'$ production at LEP [19] which is about 4 times smaller than the one predicted by the original version of JETSET. It was checked that this modification has little effect on the (++++) and (---) correlations but changes the (++-) and (+--)) correlations (dashed line in Fig. 2b). The larger Q value of the first data point for (++-) and (+--)) correlations (0.25 GeV/c as compared to 0.15 GeV/c for like-sign triplets) and the larger errors on the first two data points, are due to the large uncertainty on $\eta'$ production in JETSET and consequent uncertainties in the correction factors. Simulations based on JETSET show that $R_3$ for like-sign combinations is only slightly affected if $b\bar{b}$ events are removed from the sample whereas the change in $R_3$ for unlike-sign combinations is comparable to the effect of reducing $\eta'$ production. All modifications of JETSET yield expected results, supporting the method used.

Higher-order BE correlations are a natural source of like-sign three-particle correlations. The shape of $R_3(Q)$ for (++++) and (---) combinations is reminiscent of the shape of the two-body BE correlations [20-22]. In analogy to the latter it can be parametrized by [23]

$$R_3(Q) \sim [1 + 2\lambda_3 \exp(-r_3^2 Q^2)]. \quad (9)$$

The factor two before the $\lambda_3$ parameter arises from the presence of two possible diagrams with exchange of identical pions within a triplet [13]. The total three-particle BE correlation is built up from three diagrams with interchange of two particles in the triplet, plus two diagrams of interchange of the three particles. The latter correspond to the quantity $R_3$ mentioned above, and the former to the “background” term $R_3'$.

A modification of Eq. (9) is often used to parametrize the experimental data:

$$R_3(Q) = N(1 + \delta Q)[1 + 2\lambda_3 \exp(-r_3^2 Q^2)], \quad (10)$$

where N is a normalization factor and the term (1 + $\delta Q$) is an empirical term which takes into account the rise of the correlation function at large Q-values. A fit of Eq. (10) to the data with $Q < 1.35$ GeV/c yielded the parameter values given in Table 1 ($\chi^2$/DF = 5.2/8). The fitted form is shown in Fig. 2a as a dot-dashed curve. The experimental resolution for Q at

<table><caption>Table 1
Results of the fit of the three-particle correlation function $R_3(Q)$ for (++++) and (---) combinations with Eq. (10).</caption><tr><td>$N$</td><td>0.92 ± 0.01</td></tr><tr><td>$\delta$</td><td>0.11 ± 0.01 (GeV/c)<sup>-1</sup></td></tr><tr><td>$\lambda_3$</td><td>0.28 ± 0.05 (stat) ± 0.07 (syst)</td></tr><tr><td>$r_3$</td><td>3.33 ± 0.20 (stat) ± 0.16 (syst) (GeV/c)<sup>-1</sup></td></tr></table>

<table><caption>Table 2
Values of the parameters $\lambda_3$ and $r_3$ with different analysis methods (see text).</caption><thead><tr><th></th><th>λ<sub>3</sub></th><th>r<sub>3</sub> (GeV/c)<sup>-1</sup></th></tr></thead><tbody><tr><td>$T > 0.95$</td><td>0.34±0.05</td><td>3.29±0.19</td></tr><tr><td>$\theta > 2°$</td><td>0.35±0.06</td><td>3.48±0.20</td></tr><tr><td>Data/JETSET ($T > 0.97$)</td><td>0.24±0.04</td><td>3.32±0.25</td></tr><tr><td>Data/JETSET ($T > 0.95$)</td><td>0.26±0.04</td><td>3.17±0.22</td></tr><tr><td>Uncorrected data</td><td>0.25±0.04</td><td>4.16±0.30</td></tr><tr><td>Data/DELSIM</td><td>0.19±0.03</td><td>3.55±0.24</td></tr></tbody></table>

$Q < 0.5$ GeV/c is less than 25 MeV/c, i.e. four times smaller than the bin size, and was neglected.

To estimate the systematic errors on the parameters $\lambda_3$ and $r_3$:

- the cut on the thrust variable was chosen to be $T > 0.95$; this increased the data sample by 60%;

- a cut was made of minimum $2°$ on the opening angle $\theta$ between pairs of tracks in the triplet;

- $R_3$ for the corrected data was divided by $R_3$ of JETSET in order to reduce possible residual correlations which are not due to BE correlations.

The values obtained are given in Table 2. The maximal deviation of the $\lambda_3$ and $r_3$ values was used as an estimate of the systematic errors given in Table 1. The results were checked by relaxing the impact parameter requirements to 5 and 10 cm respectively. The conclusions of this analysis are not affected by these cuts. In order to check detector influences Eq. (10) was also fit to the uncorrected data of $R_3$ and to the uncorrected data of $R_3$ divided by $R_3$ of simulated events, fully tracked through the detector by means of DELSIM. The values of $\lambda_3$ and $R_3$ obtained with this procedure are presented in Table 2.

It should be remarked that calculation with JETSET shows that the fraction of pure $\pi\pi\pi$ triplets in all charge combinations is 72% for the interval $0.15 < Q < 0.5$ GeV/c. The values of $\lambda_3$ and $r_3$ in Table 1 are
not corrected for the contamination by triplets where (at least) one of the particles is not a pion. Correcting for this effect would increase the value of $\lambda_3$ by 39%, in the hypothesis that non-$\pi\pi\pi\pi$ triplets are uncorrelated.

Bose-Einstein correlations can be included in JETSET where they are introduced as a final state intcraction. Practically, after the generation of the pion momenta the generated values of the momenta of all identical pions are modified in such a way that their momentum vector differences are reduced with a quantity determined by the chosen form of parametrization and given parameters of correlation strength $\lambda$ and radius $r$ [14] in order to describe the like-sign two-pion distribution for $R(Q)$. In [17], DELPHI demonstrated that JETSET reproduces well the two-particle correlations if BE correlations are switched on in the model with Gaussian parametrisation for pions which are produced promptly or are decay products of short-lived resonances<fnref n="1" />. The maximal correlation strength $\lambda = 1$ and a radius $r = 0.50$ fm were used. This method of including Bose-Einstein correlations in the model moves all direct like-sign pions closer together in momentum space and therefore also yields genuine higher-order correlations with, however, some arbitrary form and correlation strength [3]. Another weakness of the model for BE correlations is that JETSET does not take into account the lifetime of resonances. Consequently, the model can only give a qualitative picture of these final state effects and provide evidence that genuine higher order Bose-Einstein correlations are present at small $Q$ for $R_3(Q)$.

In Fig. 3, the three-particle correlation functions $R_3$ are shown with the predictions of JETSET with and without BE correlations included. The parameters used to include the BE correlations are the same as in the two-particle correlation study of DELPHI [17]. The model is in reasonable agreement with the data for the $(++-)$ and $(+--)$ configurations and gives an enhancement for the $(+++)$ and $(- --)$ correlations. Even if the enhancement in $R_3$ at low $Q$ values would be partly due to two-particle correlations, arising from the method used, the $\lambda_3$ value obtained from the ratio $R_3$ of the data to $R_3$ of JETSET with

<figure><img src="image_5.png" /><figcaption>Fig. 3. The function $R_3(Q)$ for (a) like-sign triplets and (b) unlike-sign triplets. The predictions of JETSET without BE (dashed line) and with BE correlations included for direct pions (full line) are also shown, using parameters $\lambda = 1$ and $r = 0.50$ fm in the Gaussian parametrization. In both versions of the model $\eta'$ production was reduced by a factor four.</figcaption></figure>

BE effects included would give a lower limit of $\lambda_3$. The value obtained by a fit to Eq. (10) is $0.14\pm0.03$.

Bose-Einstein interference in JETSET not only changes the distribution of like-sign correlations (Fig. 3a), but also the unlike-sign ones (Fig. 3b) and leads to better agreement with the data. Due to BE correlations, particle distributions and invariant masses of jets are changed [3]. This observation is important for studies at high energies, particularly for the W mass measurement at LEP200.

## 5. Conclusions

The first observation is reported of genuine three-like-sign particle correlations in $e^+e^-$ annihilations at the $Z^0$ mass. These correlations can be explained as a higher order Bose-Einstein enhancement. The JETSET model with BE correlations included, with the same $\lambda$ and $r$ parameters which are used for describing the two-particle correlations, yields reasonable agreement for the $(++-)$ and $(+--)$ correlations and gives an enhancement for $(+++)$ and $(- --)$ cor-

<footnote n="1">¹ All resonances with lifetime larger than the $K^*(890)$ were considered as long-lived.</footnote>
relations. One possible explanation of the inadequacy
to describe the (+++) and (---) configurations
could be an incomplete treatment of Bose-Einstein
correlations in the model.

Acknowledgements

We thank T. Sjöstrand for very useful discussions on
Bose-Einstein correlations in JETSET. We are greatly
indebted to our technical collaborators and to the fund-
ing agencies for their support in building and operat-
ing the DELPHI detector, and to the members of the
CERN-SL Division for the excellent performance of
the LEP collider.

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