Interference of neutral kaons in the hadronic decays of the Z0

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UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)

Abreu, P.; Agasi, E.E.; van Apeldoorn, G.W.; Augustinus, A.; van Dam, P.H.A.; van Eldik,

J.E.; Hao, W.; van der Heijden, M.W.; Kluit, P.M.; Koene, B.K.S.; Los, M.; Ruckstuhl, W.;

Siccama, I.; Timmermans, J.J.M.; Toet, D.Z.

DOI

10.1016/0370-2693(94)90298-4

Publication date

1994

Published in

Physics Letters B

Link to publication

Citation for published version (APA):

Abreu, P., Agasi, E. E., van Apeldoorn, G. W., Augustinus, A., van Dam, P. H. A., van Eldik,

J. E., Hao, W., van der Heijden, M. W., Kluit, P. M., Koene, B. K. S., Los, M., Ruckstuhl, W.,

Siccama, I., Timmermans, J. J. M., & Toet, D. Z. (1994). Interference of neutral kaons in the

hadronic decays of the Z0. Physics Letters B, 323, 242.

https://doi.org/10.1016/0370-2693(94)90298-4

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Physics Letters B 323 (1994) 242-252

PHYSICS LETTERS B

North-Holland

242 Interference of neutral kaons in the hadronic decays of the Z °

D E L P H I Collaboration

P. Abreu t, W. A d a m g, T. Adye ak, E. Agasl ad, I. Ajlnenko aq, R. Aleksan am, G.D. Alekseev n,

A. Alger1 m, p. Allport u, S. A l m e h e d w, S.J. Alvsvaag d, U. Amaldl g, A. Andreazza

aa,

P Antilogus x, W.-D Apel o, R.J. A p s l m o n ak, y . A r n o u d

am,

B. A s m a n as, j -E. Augustln r

A. A u g u s t m u s ad, p. Balllon g, P. B a m b a d e r, F. Barao t, R. Barate e G. Barblelhm au,

D.Y. Bardln n, G.J. Barker ah, A. Baroncelh ao, O. Barring ~, J A. Barrio Y, W. Bartl ay,

M.J. Bates ak, M. Battaglla m, M. B a u b d h e r v, M. Begalli aj, p. Beflhere f, P. Beltran 1,

A.C. B e n v e n u t i e, M. Berggren r, D. Bertrand b, F. Blanch1 at, M. Big1 at, M.S Bllenky n,

P Bllloir v, J. Bjarne w, D. Bloch h, J. Blockl az, M. Blume ha, S. Blyth ah, V Bocci ae,

P.N. Bogolubov n, T. Bolognese

am,

M. Boneslni

aa

W. B o n l v e n t o

aa,

p S.L. Booth u,

G. B o n s o v aq, H. Borner g, C. Boslo ao, B. Bostjancic ar, S. Bosworth ah, O. Botner av, B Bouquet r,

C. Bourdarlos r T.J.V. Bowcock u, M. Bozzo k, S Bralbant b, p. Branchlnla°, K.D. Brand al,

T. Brenke ha, R.A Brennerg, H. Briand v, C. B r l c m a n b, L Brlllault v, R.C.A. Brown g,

P. B r u c k m a n P, J.-M. Brunet f, A. Budzlak P, L. Bugge

af,

T. Buran af, H. Burmelster g, A. Buys g,

J.A.M.A. Buytaert g, M Caccla

aa,

M. Calvlaa, A.J. C a m a c h o Rozas ap, R. C a m p i o n u

T. C a m p o r e s l g, V. Canale ae, K. C a n k o c a k as, F. Cao b F Carena g, L. Carroll u,

M.V. Castdlo G l m e n e z aw, A. Cattal g, F R. Cavallo e, L. Cerrlto ae, V C h a b a u d g, A. C h a n a,

M. C h a p k m aq, Ph. Charpentlerg, J. C h a u v e a u v, p Checchla a~, G.A. Chelkov n L. C h e v a h e r am

P. C h h a p n l k o v aq, V Chorowlcz v j T M. Chrin aw, V. C m d r o at, p. Colhns ah, j L. Contreras r,

R. Contrx k, E. Cortina aw, G. C o s m e r, F. C o u c h o t r, H.B. Crawley a, D. Crennell ak, G. Crosettl k,

J Cuevas Maestro ag, S. Czellar m, E. Dahl-Jensen ab, j D a h m ha, B. D a l m a g n e r, M D a m

af,

G. D a m g a a r d ab, E D a u b l e b, A. D a u m °, P.D. D a u n c e y g, M. D a v e n p o r t g, J. Davies u,

W. Da Silva v, C. Defoxx f, P. Delplerre z, N. D e m a r l a

at,

A De Angelis g, H. De Boeck b,

W. De Boer °, S. De Brabandere b, C. De Clercq b, M.D.M. De Fez Laso aw, C. De La Vaasslere v,

B. De Lotto au, A. De M l n aa, H. Dijkstra g, L. D1 Clacclo ae, F. D j a m a h, J. Dolbeau f,

M. D o n s z e l m a n n g, K. D o r o b a az, M. Dracos h, j. Drees ba, M Drls

ae,

y D u f o u r g, F. D u p o n t e,

D. Edsall a, L.-O Eek av, P.A -M. Eerola g, R. Ehret o, T Ekelof av, G. Ekspong as,

A. Elliot Pelsert g, M. Elsmg ha, j _p Engel h, N. Ershaldat v, M. Esplrlto Santo t, V. Falaleev aq,

D. Fassoulxotls ae, M. F e m d t g, A. F e n y u k aq, A. Ferrer aw, T.A. Ffllppas ae, A Firestone a,

H. F o e t h g, E. Fokltls

ae,

F. Fontanelll k, K.A.J. Forbes u, J.-L Fousset z, S. Francon x, B. F r a n e k ak,

P. Frenkiel f, D.C. Fries o, A.G. F r o d e s e n d, R. F r u h w l r t h

ay,

F. Fulda-Quenzer r, H. F u r s t e n a u o,

J. Fuster g, D. G a m b a at, M. G a n d e l m a n q, C. Garcaa aw, j Garcla ap C Gaspar g, U. Gasparlnlal,

Ph. Gawllet g, E.N. Gazls

ae,

j . . p . Gerber h, p. G l a c o m e l h 8 D. Glllesple g, R. G o k l e h az,

B. Golob at, V.M. G o l o v a t y u k n, J.J. G o m e z Y Cadenas g, G. Gopal ak, L G o r n a, M Gorskl az,

V. Gracco k, A. G r a n t g, F. G r a r d b, E. Grazlanl ao, G. Grosdldler r, E Gross g, B. Grossetete v,

P. G u n n a r s s o n as, j. G u y ak, U. Haedlnger o, F H a h n ba, M. H a h n as S. H a h n ba, S. Halder ad

Z. H a j d u k P , A. H a k a n s s o n w, A Hallgren av, K. H a m a c h e r ha, G. H a m e l De M o n c h e n a u l t am,

W. H a o ad, F.J. Harris ah, V. Hedberg w, T. Henkes g, R Henrlques t, j . j H e r n a n d e z aw,

J.A. H e r n a n d o aw, p. Herquet b, H Herr g, T.L. Hesslng u, I. H l e t a n e n m, C O. Hlggms u,

E. Higon aw, H.J. Hllke g, T.S Hill a, S.D. H o d g s o n ah, T. H o f m o k l az, S -O. H o l m g r e n as,

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P.J Holt ah, D. H o l t h u l z e n ad, P.F. H o n o r e f, M. H o u l d e n u, j. Hrubec ay, K. Huet b,

K. Hultqvlst as, p. I o a n n o u e, P.-S. Iversen d, J.N. Jackson u, R Jacobsson as, p. Jalocha P,

G. Jarlskog w, P Jarry am, B J e a n - M a n e r, E.K J o h a n s s o n as, M. Jonkerg, L. Jonsson w,

P. Jmllot h, G. Kalkanls c, G. K a l m u s ak, F. Kapusta v, M. Karlsson as, E. Karvelas l,

S. Katsanevas c, E.C. Katsoufis ae, R. Keranen g, B.A K h o m e n k o n, N.N. K h o v a n s k l n, B. King u,

N J. Kjaer g, H. Klein g, A K l o v n l n g d, P. Klult ad, A K o c h - M e h r m ha, J.H. K o e h n e °, B. K o e n e aa,

P. Kokklnlas ~, M. Koratzlnos af, A.V. Korytov n, V. K o s t l o u k h l n e aq, C. K o u r k o u m e h s c,

O. K o u z n e t s o v n, P.H K r a m e r ba, M. K r a m m e r ay, C Kxeuter o, j. Krohkowskm az, I. Kronkvlst w,

W Kucewlcz P, K Kulka av, K. K u r v m e n m, C Lacasta aw, C. L a m b r o p o u l o s ~, J.W. L a m s a a,

L Lancerl au, p. Langefeld ha, V. Lapin aq, I. Last u j._p. Laugmer am, R. Lauhakangas m,

G. Leder ay, F. Ledrolt t, R. Leltner ac, y . L e m o l g n e am, j. L e m o n n e b, G. Lenzen ba, V. Lepeltler r,

J.M Levy h, E. Lleb ha, D. Llko ay, J. L m d g r e n m, R L l n d n e r ba, A Llpnlacka r, I. Llppl ax,

B. Loerstad w, M. Lokajlcek J, J.G L o k e n ah, A. Lopez-Fernandez g, M.A. Lopez Aguera ap,

M. Los ad, D. Loukas ~, J.J Lozano aw, p Lutz f, L. Lyons ah, G. M a e h l u m af, j. Maillard f,

A. Malo t, A. Maltezos ~, J. Marco ap, M. Margonl a~, J.-C. Marin g, C Marlottla°, A. M a r k o u ~,

T. M a r o n ba, S Martl aw, C M a r t m e z - R l v e r o ap, F. Martmez-Vldal aw, F. Matorras ap,

C. Matteuzzl aa, G. Matthlae a~, M. Mazzucato a~, M. Mc C u b b m u, R. Mc Kay a, R. Mc Nulty u,

J. M e d b o av, C. Meronl aa W.T. Meyer a, M. Mlchelotto a~, I Mlkulec ay, L. Mlrablto x,

W.A. M l t a r o f f ay, G.V M l t s e l m a k h e r n, U. M j o e r n m a r k w, T. M o a as, R. Moeller ab, K. Moenigg,

M.R. M o n g e k, p. Morettlnlk, H. Mueller o, W.J Murray ak, B. M u r y n P, G. Myatt an, F. Naraghl l,

F.L Navarrla e, p. Negrl aa, S. NemecekJ, W N e u m a n n ba, N. N e u m e l s t e r ay, R. N l c o l m d o u c,

B.S. Nielsen ab P.E S. N d s e n d, p Nlss as, A N o m e r o t s k l a,, V. Obraztsov aq, A.G. Olshevskln,

R. Orava m A. O s t a n k o v aq, K. Osterberg m, A. O u r a o u am, p. Paganini r, M. Paganonm aa,

R. Pare v, H. Palka P, T h . D P a p a d o p o u l o u ae, L Pape g, F Parodl k, A. Passerl ao, M. Pegoraro a~,

J P e n n a n e n m, L Peraltat, H. Pernegger ay, M P e r m c k a ay, A Perrottae, C. P e t n d o u au

A Petrohnm k, G. Pinna k, F. Pierre am, M. P l m e n t a t, S. Plaszczynski r, O P o d o b r i n o, M.E Pol q,

G. Polok P, P. P o r o p a t au V. Pozdnaakov n, M. Prest au, p. P r l w t e r a ae, A. Pulha aa

D. RadojlClC ah, S. Ragazzm aa, H R a h m a m ae, j. RamesJ, P.N. R a t o f f s, A.L. R e a d af, M. Reale ha,

P Rebecchi r, N . G Redaelli aa, M. Regler ay, D Reid g, P B. R e n t o n ah, L.K. R e s v a m s c,

F. R i c h a r d r, j. R i c h a r d s o n u, j RldkyJ, G. R l n a u d o at, A. R o m e r o at, I. R o n c a g h o l o k,

P R o n c h e s e a~, C. R o n n q v l s t m, E.I. Rosenberg a, E. Rossog, P. R o u d e a u r, T. Rovelh e,

W R u c k s t u h l ad, V. R u h l m a n n - K l e l d e r am, A. RUlZ ap, K. Ryblcki P, A. Rybln aq, H. Saarlkko m,

Y. Sacquln am, G Sajot e, J. Salt aw, J. Sanchez Y, M. Sannlno TM, S. Schael g, H Schneider °,

M.A.E. Schyns ha, G. Sclolla at, F. Scurl au, A.M. Segar ah, A. Seltz °, R. S e k u h n ak, M Sessa au,

R. Seufert o, R.C. Shellard aj, I. Slccama ad, p. Saegrlst am, S. Slmonettl k, F S i m o n e t t o a~,

A.N. Slsaklan n, G. Skjevlang af, G. Smadja am,x, N S m l r n o v aq, O S m l r n o v a n, G R. Smith ak,

R. Sosnowskl az, D. Souza-Santos aj, T. Spassov t, E Splrltl ao, S. Squarcaa k, C. Stanescu ao,

S Stapnes af, G Stavropoulos ~, F. Stlchelbaut b, A Stocchl r, J Strauss ay, J. Straverg, R. Strub h,

B. Stugu d, M. Szczekowski g, M Szeptycka az, p Szymanskl az, T. Tabarelll aa, O. Tchikilev aq,

G.E. T h e o d o s l o u l, A T d q u l n ~, J T i m m e r m a n s aa, V.G T l m o f e e v n, L.G. T k a t c h e v n,

T. T o d o r o v h, D.Z. Toet ad, O. T o k e r m, A. T o m a r a d z e b, B. T o m e t, E. Torassa at, L. Tortora a°,

D Trellle g, W. Trlschuk g, G. Trxstram f, C. T r o n c o n aa, A. Tslrou g, E.N Tsyganov ~,

M. Turala P, M.-L Turluer am, T T u u v a m, I.A. Tyapkan v, M. Tyndel ak, S. Tzamarlas u,

ba

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B. Ueberschaer ba, S. Ueberschaer

, O. Ullaland , G. Valent~ , E. Vallazza , J.A. Vails Ferrer

,

C. V a n d e r Velde b, G.W. Van A p e l d o o r n ad, p. Van D a m aa, M. Van Der Heljden ad,

W.K. Van D o n m c k b, J. Van Eldlk ad, P Vazg, G Vegnl aa, L Ventura a~, W. Venus ak,

F. Verbeure b, M. Verlato a~, L.S Vertogradov n, D. Valanova am, p. Vincent x, L. Vxtale au,

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Volume 323, number 2

PHYSICS LETTERS B

10 March 1994

E. V l a s o v aq, A.S. V o d o p y a n o v n, M . V o l l m e r ha, M . V o u t d a m e n m, V. V r b a ao, H . W a h l e n ha,

C. W a l c k as, F. W a l d n e r au, A. W e h r ha, M . W e l e r s t a l l ha, P W e l l h a m m e r g, A . M . W e t h e r e l l g,

J . H . W i c k e n s b, M . W w l e r s

o,

G . R . W i l k i n s o n

ah,

W . S . C . W i l l i a m s ah, M. W i n t e r h, G . W o r m s e r r,

K. Woschnagg av, A. Zaltsev aq, A. Zalewska P, D. Zavrtanlk ar, E. Zevgolatakos ~, N.I. Z l m m n,

M. Zlto

am,

D. Zontar

ar,

R. Zuberl ah, G. Zumerle

a~

and J. Zunlga aw

a Ames Laboratory and Department of Physws, Iowa State Umverstty, Ame~ IA 50011, USA b Physics Department, Untv Instelhng Antwerpen, Umversttett~plem 1, B-2610 Wtlrtjk, Belggum

and IIHE, ULB-VUB, Pletnlaan 2, B-1050 Brussels, Belgtum

and FacultO des Sctences, Umv de l'Etat Mons, Av Matstrtau 19, B-7000 Mons, Belgtum c Physics Laboratory, Untverstty of Athens, Solonos Str 104, GR-10680 Athens, Greece d Department of Physlcs, Untverstty of Bergen, Allbgaten 55, N-5007 Bergen, Norway

e Dlparttmento dt Ftstca, Untversttit dt Bologna and INFN, Vta Irnerto 46, 1-40126 Bologna, Italy f Collkge de France, Lab de Phystque Corpusculatre, IN2P3-CNRS, F-75231 Parts Cedex 05, France g CERN, CH-1211 Geneva 23, Swttzerland

h Centre de Recherche Nuclbatre, IN2P3 - CNRS/ULP- BP20, F-67037 Strasbourg Cedex, France 1 Institute of Nuclear Phystcs, N C S R Demokrttos, P 0 Box 60228, GR-15310 Athens, Greece

J FZU, lnst of Phystcs of the CA S Htgh Energy Phystcs Dtvtston, Na Slovance 2, CS-180 40, Praha 8, Czechoslovakia k Dtparttmento dt Flslca, Untvers,tit dt Genova and INFN, Via Dodecaneso 33, 1-16146 Genova, Italy

e Instttut des Sctences Nuclbatres, IN2P3-CNRS, Untversttk de Grenoble 1, F-38026 Grenoble, France m Research Instgtutefor Htgh Energy Phystcs, SEFT, P 0 Box 9, F1N-O0014 Umverstty ofHelsmkt, Ftnland n Jomt Instttutefor Nuclear Research, Dubna, Head Post Office, P 0 Box 79, 101 000 Moscow, Russian Federatton o Instttut fur Expertmentelle Kernphystk, Umversttat Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany P High Energy Phystcs Laboratory, Instttute of Nuclear Phystcs, UI Kawtory 26a, PL-30055 Krakow 30, Poland q Centro Brastletro de Pesqutsas Fistcas, rua Xavter Stgaud 150, RJ-22290 Rto de Janetro, Braztl

r Untversttb de Parts-Sud, Lab de l'Accblkrateur Lmkatre, IN2P3-CNRS, Bat 200, F-91405 Orsay, France s School of Phystcs and Matertals, Untverstty of Lancaster, GB-Lancaster LA1 4YB, UK

t LIP, IST, FCUL - Av Ehas Garcta, 14-1 °, P-IO00 Ltsboa Codex, Portugal

u Department ofPhystcs, Untverstty ofLtverpool, P 0 Box 147, GB-Ltverpool L69 3BX, UK

v LPNHE, IN2P3-CNRS, Untversttbs Parts II1 et VII, Tour 33 (RdC), 4 place Jussteu, F-75252 Parts Cedex 05, France w Department ofPhystcs, Umverstty of Lurid, Solvegatan 14, S-22363 Lund, Sweden

x Untversttb Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Vdleurbanne Cedex, France Y Umverstdad Complutense, Avda Complutense s/n, E-28040 Madrtd, Spam

z Umv d'Atx- Marsetlle H - CPP, IN2P3-CNRS, F-13288 Marsetlle Cedex 09, France

a a Dtparttmento dt Ftstca, Untverstt~ dt Mtlano and INFN, Vta Celorta 16, 1-20133 Mtlan, Italy

ab

Ntels Bohr Instttute, Blegdamsve) 17, DK-2100 Copenhagen O, Denmark

a c NC, Nuclear Centre of MFF, Charles Umverstty, Areal MFF, V Holesovtckach 2, CS-180 00, Praha 8, Czechoslovakta

ad

NIKHEF-H, Postbus 41882, NL-IO09 DB Amsterdam, The Netherlands

a e Nattonal Techmcal Umverstty, Phystcs Department, Zografou Campus, GR-15773 Athens, Greece

a f Phystcs Department, Untverstty of Oslo, Bhndern, N-IO00 Oslo 3, Norway

ag Dpto Ftstca, Untv Ovtedo, C/P Jtmenez Casa~, S/N-33006 Ovtedo, Spam

an

Department of Phystcs, Umverstty of Oxford, Keble Road, Oxford OX1 3RH, UK

a~ Dtparttmento dt Ftstca, Untverstt~ dt Padova and INFN, Vta Marzolo 8, 1-35131 Padua, Italy

aj

Depto de Ftstca, Ponttficta Untv Catbltca, C P 38071 RJ-22453 Rto de Janetro, Braztl

ak Rutherford Appleton Laboratory, Chtlton, GB - Dtdcot 0 X l l OQX, UK

at Dtparttmento dt Ftstca, Umverstth dt Roma H and INFN, Tor Vergata, 1-00173 Rome, Italy

am

Centre d'Etude de Saclay, DSM/DAPNIA, F-91191 Gtf-sur-Yvette Cedex, France

an

Dtparttmento dt Ftstca-Untverstth dt Salerno, 1-84100 Salerno, Italy

ao

Istttuto Supertore ch Santtiz, Ist Naz dt Ftstca Nucl (INFN), Vtale Regma Elena 299, 1-00161 Rome, Italy

ap

C E A F M , C S I C - Untv Cantabrta, Avda los Castros, S/N-39006 Santander, Spam

aq

Inst for Htgh Energy Phystcs, Serpukov P 0 Box 35, Protvtno Moscow Regton, Russtan Federatton

a r j Stefan Instttute and Department of Phystcs, Umverstty of Ljubljana, Jamova 39, $1-61000 Ljubljana, Slovema

as Fystkum, Stockholm Untverstty, Box 6730, S-113 85 Stockholm, Sweden

at

Dtparttmento dt Ftstca Spertmentale, Umversttit dt Tormo and INFN, Vta P Gturta 1, 1-10125 Turtn, Italy

au

Dtparttmento dt Ftstca, Untverstt& dt Trwste and INFN, Vta A Valerto 2, 1-34127 Trteste, Italy and lstttuto dt Ftstca, Untverstt& dt Udtne, 1-33100 Udme, Italy

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av Department of Radtatlon Sctences, Umverstty of Uppsala, P 0 Box 535, S-751 21 Uppsala, Sweden

aw IFIC, Valencta-CSIC, and D F A M N , U de Valencta, Al'da Dr Mohner 50, E-46100 Burjassot (Valencta), Spain ay Insntut fur Hochenergwphystk, Osterr Akad d Wtssensch, Nzkolsdorfergasse 18, A-1050 Vwnna, Austria

az Inst Nuclear Studtes and Umverstty of Warsaw, UI Hoza 69, PL-00681 Warsavt; Poland

ba Fachberetch

ehyslk,

Umverstty of Wuppertal, Postfach 100 127, D-5600 Wuppertal 1, Germany

Received 14 January 1994 Editor K Winter

K~K~ correlations have been studied in a sample of 717 511 hadronic events collected by the DELPHI detector at LEP during 1992 An enhancement is found in the production of pairs of K~ of similar momenta, as compared with a Monte Carlo simulated reference sample The measured values for the strength of the correlation and the radius of the emitting source of kaons are 2 = 1 13 + 0 54 (stat) + 0 23 (syst) and r = 0 90 ± 0 19 (stat) ± 0 10 (syst) fm This enhancement is consistent with the hypothesis that K~K ° pairs display an enhancement, regardless of whether they come from a K ° [ ° or from a K ° K ° ( [ o ~ 0 ) system

1. Introduction

A n e n h a n c e m e n t in the p r o d u c t i o n o f i d e n t i c a l b o s o n s w i t h s i m i l a r m o m e n t a p r o d u c e d in high energy c o l h s l o n s is o b s e r v e d in any type o f r e a c t i o n (see r e f [1] for a r e v i e w ) , a n d a t t r i b u t e d to B o s e - E i n s t e i n ( B E ) statistics a p p r o p r i a t e to i d e n t i c a l bo- son pairs T o study t h e e n h a n c e d p r o b a b i l i t y for e m i s s i o n o f t w o i d e n t i c a l b o s o n s it is useful to d e f i n e a c o r r e l a t i o n f u n c t i o n R

R ( p l , p 2 ) - P(Pl,P2) P(Pl ) P ( P z ) '

w h e r e P(Pl,P2) is t h e t w o - p a r t i c l e p r o b a b i l i t y den- sity, subject to BE s y m m e t r l z a t i o n , a n d P ( p , ) is the c o r r e s p o n d i n g single p a r t i c l e q u a n t i t y for a p a r t i c l e w i t h f o u r - m o m e n t u m Pz In practice, P ( P l ) P ( P 2 ) is o f t e n r e p l a c e d by a r e f e r e n c e 2-particle d i s t r i b u t i o n Po (pl, P2 ), which, ideally, r e s e m b l e s P (Pl, P2 ) in all

respects, apart from

t h e lack o f BE s y m m e t r l z a t i o n

BE c o r r e l a t i o n s c a n be used to study t h e s p a c e - t i m e s t r u c t u r e o f t h e h a d r o n l z a t l o n s o u r c e [2]

T h e effect can be d e s c r i b e d using the v a r i a b l e Q, d e f i n e d by Q2 = M 2 _ 4 m 2, w h e r e M is t h e l n v a r I a n t m a s s o f t h e t w o particles, a n d m is t h e p a r t i c l e mass T h e c o r r e l a t i o n f u n c t i o n is usually p a r a m e t r l z e d as R ( Q ) = 1 + 2 e -r202, (1) w h e r e t h e p a r a m e t e r r gives t h e size o f t h e s o u r c e a n d 2 m e a s u r e s t h e strength o f t h e c o r r e l a t i o n b e t w e e n t h e i d e n t i c a l bosons, b e i n g 1 for a c o m p l e t e l y i n c o h e r e n t ( " c h a o t i c " ) s o u r c e

T h i s letter describes a study o f Ks°Ks ° c o r r e l a t i o n s In

0 0

h a d r o n l c Z ° decays W h e n a K s K s p a i r is p r o d u c e d , there are t w o possIblhtles

(a) T h e Ks°K ° p a i r c o m e s f r o m a K ° K ° (or [ 0 ~ 0 ) system In this case, the Ks°Ks ° p a i r originates f r o m an i d e n t i c a l b o s o n pair, a n d is t h u s subject to BE sym- m e t r i z a t l o n At low Q values, w h e r e t h e BE effect is o b s e r v e d , the f r a c t i o n o f K ° K s ° c o m i n g f r o m identical b o s o n pairs is a b o u t 28% o f the w h o l e d a t a sample T h i s f r a c t i o n was e v a l u a t e d using the J E T S E T 7 3 [3] M o n t e C a r l o p r o g r a m b a s e d on a p a r t o n s h o w e r m o d e l ( J E T S E T PS in t h e f o l l o w i n g )

0 0

(b) T h e K s K s p a i r c o m e s f r o m a K ° K ° system In this case, the original system is a b o s o n - a n t l b o s o n pair, a n d thus is n o t subject to BE s y m m e t r l z a t l o n H o w e v e r , as d e s c r i b e d in detail in r e f [4], an en- h a n c e m e n t is e x p e c t e d in the low Q region i f o n e se- lects the C = + 1 elgenstate o f the charge c o n j u g a t i o n o p e r a t o r C T h e w a v e f u n c t i o n o f the

IK°~ °)

state is a s u p e r p o s i t i o n o f C = + 1 a n d C = - 1 elgenstates I K ° E ° ) c =±1 = ~ ( I K ° ( p ) K ° ( - P ) )

+ I ~ ° ( p ) K ° ( - p ) ) ) ,

w h e r e p is t h e three m o m e n t u m o f o n e o f the kaons in t h e i r c e n t r e o f mass f r a m e

In the l i m i t o f [Pl = 0 ( Q = 0), the p r o b a b i l i t y a m - 0 0

p l l t u d e for t h e C = - 1 state ( K s K L p a i r ) d i s a p p e a r s

0 0 0 0

w h e r e a s that for the C = + 1 state ( K s K s or K L K L pair) is m a x i m a l T h i s s h o u l d cause an e n h a n c e m e n t

0 0

for K s K s ( a n d K L K e) pairs at l o w Q values, b u t this 0 0 is exactly c o m p e n s a t e d by the l o w Q s u p p r e s s i o n o f

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Volume 323, number 2 PHYSICS LETTERS B l0 March 1994 the K ° K ° state. This m e a n s that no BE effect would be

observed (as expected for a b o s o n - a n t l b o s o n system) If all the possible final states of K ° K ° system were detected Since this analysis uses only K ° K ° pairs, one expects to observe a full BE-hke e n h a n c e m e n t in the low Q region

I n reahty the selected K ° K ° sample will not display a full BE correlation due to the presence of K ° coming from sources which are not BE correlated I n this analysis we correct for n o n - p r o m p t kaons a n d for the decays of the j~ (975) scalar meson

Although there are m a n y m e a s u r e m e n t s of BE correlations between pions in the literature Including three studies by LEP experaments [5-7 ], only OPAL has pubhshed results on K ° K ° interference in e+e - interactions [ 8 ]

• there were at least 5 charged particles with mo- m e n t a above 0.2 G e V / c

In the calculation of the energies, all charged particles have been assumed to have the pion mass A total of 717 511 events satisfied these criteria. The background due to b e a m - g a s scattenng, yy interactions a n d r + r - events has been estimated to be less t h a n 0 3% of the sample.

The influence of the detector on the analysis was studied with the simulation program DELSIM [10] Events were generated using JETSET PS, with parameters t u n e d as in ref. [ 11 ]. The particles were followed through the detailed geometry of D E L P H I giving simulated digitizations in each detector These data were processed with the same reconstruction a n d analysis programs as the real data

2. Experimental procedure

This study is based on the sample o f h a d r o n l c events collected with the D E L P H I detector at the centre of mass energy a r o u n d x/s = 91 2 GeV in the 1992 run- ning period of LEP. The D E L P H I detector has been d e s c n b e d in detail elsewhere [9] The analysis rehes on the i n f o r m a t i o n provided by the central tracking detectors: the Micro Vertex Detector (VD), the I n n e r Detector, the T i m e Projection C h a m b e r ( T P C ) , a n d the Outer Detector.

The central tracking system of D E L P H I covers the region between 25 ° a n d 155 ° in the polar angle 0, with reconstruction efficiency close to unity. The average m o m e n t u m resolution for the charged particles in h a d r o n m final states is in the range A p / p ~_ 0 001p to 0.01p (p in G e V / c ) , depending on which detectors are included in the track fit

Charged particles were used in the analysis if they had

• m o m e n t u m larger than 0 1 G e V / c ,

• measured track length in the T P C above 30 cm, • O between 25 ° a n d 155 °

H a d r o m c events were then selected by r e q u i n n g that"

• the total energy o f the charged particles exceeded 15 GeV;

• the total energy of the charged particles in each of the two hemispheres defined with respect to the b e a m axis exceeded 3 GeV,

3. Analysis

The K ° are detected by their decay i n flight into + n - Such decays are normally separated in space from the Z ° decay point (primary vertex), measured for each fill using the VD data.

Candidates for secondary decays, V0, were found by considering all pairs of tracks with opposite charge The vertex of each pair was d e t e r m i n e d by m i n i m i z i n g the Z 2 obtained from the distance of the vertex to the extrapolated tracks

The K ° decay vertex candidates were required to satisfy the following

• The probablhty from the Z 2 of the fit was larger t h a n 0.001

• In the R~b plane (perpendicular to the b e a m di- rection), the angle between the vector sum of the charged particle m o m e n t a a n d the line j o i n i n g the ~on- mary to the secondary vertex was less than (10 +

2 0 / p t ( K ° ) ) mrad, where pt (K °) is the transverse mo-

m e n t u m of the K ° candidate relative to the b e a m axis, in G e V / c

• The radial separation rR~ of the primary a n d secondary vertex in the R~b plane was larger than four times the error on rR~ from the fit if VD hits were included in the track fit, six times the error otherwise.

• W h e n the reconstructed decay point of the K ° was b e y o n d the radius of the VD, there were no signals in the VD associated to the decay tracks.

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t - 1 0 0 0 0 8 0 0 0 6 0 0 0 4 0 0 0 2 0 0 0 0 I I f I I I i '4 (a) - I ~ I ~ I ~ I ~ I 0 4 0 4 2 5 0 4 5 0 4 7 5 0 5 0 5 2 5 0 . 5 5 0 5 7 5 Z n+n" i n v a r i a n t m a s s ( G e V / c ) 1200 1000 8 0 0 6 0 0 4OO 2 0 0 A m 1 O.OS 0 1 - -- Am 2 O l

Fig 1 (a) n+n - mvarlant mass spectrum for the ac- cepted secondary vertices used m the present analysis (b) Two-dimensional plot of the absolute value of the differ- ence from the nominal K~ mass Am (GeV/c 2) when two or more I ~ candidates are present in the same event

The n + n - i n v a r l a n t mass spectrum from the ac- cepted K ° candidates is shown in fig l a A clear signal of about 111 000 K ° is seen over a background of about 17% within 4-10 M e V / c 2 from the peak. In a n interval of 4-10 M e V / c 2 a r o u n d the n o m i n a l K ° mass, the average detection efficiency for K ° to n + n - , weighted by the m o m e n t u m spectrum predicted by JETSET PS, is about 28O/o

The background from A decays Into p n - was found to be flat in the n + n - mass spectrum The level of this background is about 2% u n d e r the peak The con- t r l b u t l o n from p h o t o n conversions was found to be neghglble

I n order to evaluate the n u m b e r of Ks ° pairs, the following procedure was used First a search was carried out for events with at least two K ° candidates (com- m o n tracks were not allowed) with mvarxant mass within ± 100 M e V / c 2 of the K ° peak To evaluate the background in this sample, the absolute values Aml a n d Am2 of the differences between the m v a n a n t mass of the K ° candidate a n d the known Ks ° mass was computed The correlation between Aml and Am2 is shown in fig. l b

The "signal region", defined by Aml,Am2 < 10 M e V / c 2, contains 14741 pairs coming from 12408 events. The n u m b e r N of selected pmrs is a sum of four contributions

• Nit, the n u m b e r of pairs of true K °,

• Ntf, the n u m b e r of pairs in which the first can- dldate is a true Ks °, while the second is fake,

• Nut, the n u m b e r of pairs in which the first candidate is a fake K °, while the second is true,

• NTj, the n u m b e r of pairs in which neither candidate is a true K °,

where m the ideal case N i t = Ntf

It was verified by simulation that, in the region of Am used for the extrapolation, the background u n d e r the Am, peak is flat for each Ks ° candidate The three background contributions Ntf, Nit a n d NiT can thus be estimated from the n u m b e r s of pairs N1, N2 a n d N3, m three "control regions" defined m the Am t, Am2

correlation plot N~ = k N t f + k N i T , Am~ < a , b < A m 2 < 1 0 0 M e V / c 2, N2 = k N f t + k N f f , b < Aml < 100 M e V / c 2 Am2 < a X 3 = k 2 N f f , b < Arn~ < 1 0 0 M e V / c 2 , b < A m 2 < 1 0 0 M e V / c 2, where

k = width of the control region = 100 - b width of the signal region a

The upper limit a = l 0 M e V / c 2 of the signal region a n d the lower limit b = 20 M e V / c 2 of the interval defining the control region (from b to 100 M e V / c 2)

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Volume 323, number 2 PHYSICS LETTERS B 10 March 1994 3 0 0 2 0 0 0 . , l i d 0 A 7 0 0 ' ' I ' i I ' ' ' I

t

I , , , I , , , I , ~ , I L ~ 0 4 0 6 0 8 I l ' ' ' I ' ' ' l ' ' ' I ' '

DELPHI

+

+ +

1 2 114 ' 1 1 6 ' ' ' I 1 8 ' ' K o o Q(,K~) (GeV/c) Fig 2 Distribution of K~ paxrs m data (points) and simulation without Bose-Einstein interference (solxd line), as a function of Q The contents of the s~mulated sample ~s nor- mahzed to be equal to the data sample m the range 0 5-2 0 GeV/c 2

were chosen to have a stable signal to background ratm a n d to match the hypothesis of a fiat background b e h a v l o u r for the extrapolation procedure.

The n u m b e r of true pairs m the signal region can then be estimated as

N, = N - (Ntf + Nft + NSS)

= N - (N1 +

N2)/k + N3/k 2,

gwmg finally after background subtraction 10943 + 124(star) Ks°K ° pairs a m o n g which 4956 ± 82(star) have Q < 2 G e V / c

F~g. 2 shows the d i s t r i b u t i o n as a function of Q of the pairs of K ° for data a n d simulated events Simu- lated events were generated w~thout BE s y m m e t n z a - t m n A n excess m the experimental data can be observed at low Q

To give a first estxmate of the correlatmn function, we define the ratio Rmeas(O) =

.MNR(Q)/Ns(Q),

where

Nn

a n d

Ns

are the n u m b e r of K ° pmrs per interval of Q for real a n d simulated data respectively after background subtractmn, a n d A / i s a normahzatlon factor computed as the ratio of

Ns

a n d NR m the

2 1 8

~

' I ' ' ' I ' ' I I 1 ' ' E ' ' b D ' ' I ' ' ' ~ ' ' ' I ' ~

ELPHI

I I I I L I I L 0 2 0 4 0 6 0 8 I 1 . 2 1 4 1 6 1 . 8 2 0 K°K% --1 s s-(GeV/c} Fig 3 Ratio Rmeas (Q) The best fit to ( 1 ) is superimposed as a sohd line

range between 0.5 G e V / c a n d 2 G e V / c

I n the case of K ° pairs there is no obvious way to extract a good reference sample from the data atself [8], as It is the case of the charged plons [7], so in this analysis a sample of 754 000 samulated events was used as a reference sample

The correlation function Rmeas (Q) IS plotted m fig 3 An e n h a n c e m e n t is clearly visible in the region Q < 0.4 G e V / c

The best fit to expression (1) gives 2 = 0 88 + 0 35 (star) + 0 16 (syst), r = 0 82 + 0 16 (stat) + 0 12 (syst) f m ,

with ~2 = 8 5 for 10 degrees of freedom a n d correlation coefficient 0.62 The evaluatmn of systematic errors is explained m section 3 2

In fig 4, the contour plot of the 68% a n d 90% confidence levels for the fit of Rmeas to ( 1 ) IS shown. Re- sults from OPAL [8] on K°Ks ° correlations a n d results from LEP [5-7] on two-plon correlations are also shown

3 1 Corrections for non-mterfermg kaons

Due to the presence of K ° not coming from the pta- mary interaction, the measured correlatmn between

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, - . 1 8 t- 1 6 1 4 1 2 1 08 06 0 4 02 0 ' ~ ' D : ; P " I ' ~ ' ' ' [ ' ~ rDIE;pltlK*~KI ' I ' ' ' I ' ' t 0 OPALnx • OPALK,°K] ~. ALEPH ~

1

' '012 ' ' '0L4 ' ' '016 ' ' '018 ' ' 1 ' ' 'll2 ' ' 'It4 ' ' '116 ' ' 18 k Table 1

Correlation function before and after corrections

Rmeas (Q)

is the measured value, R* (Q) is the value after correcting for the contribution of non-prompt kaons Jbc (Q), and in R** (Q) the f0 correction is also applied

Q (GeV/c) Rmeas(Q)

fbc(Q) R(Q)*

*R**(Q)*

0 0 0 0 - 0 1 6 7 1 694-0 34 0328 2 0 3 + 0 5 1 1 864-0 50 0 1 6 7 - 0 3 3 3 1 34±0 12 0 2 8 7 1 48-I-0 17 1 374-0 18 0 333-0 500 1 01-4-0 07 0 243 1 024-0 09 0 974-0 10 0 5 0 0 - 0 6 6 7 0994-006 0238 0984-008 0 9 6 + 0 0 8 0 6 6 7 - 0 8 3 3 1 0 5 ± 0 0 6 0232 1 0 7 ± 0 0 8 1064-008 0 8 3 3 - 1 0 0 0 0934-006 0223 0914-007 0 9 1 ± 0 0 7 1 000-1 167 1024-006 0211 1034-008 1 034-0 08 1 1 6 7 - 1 3 3 3 0 9 1 ± 0 0 6 0235 0 8 9 ± 0 0 8 0894-008 1 333-1 500 1 144-0 08 0246 1 194-010 1 204-010 1 500-1 667 0984-008 0236 0974-010 0 9 8 + 0 1 0 1 6 6 7 - 1 8 3 3 0 9 9 ± 0 0 8 0231 0984-010 1 0 0 + 0 1 0 1 8 3 3 - 2 0 0 0 1014-008 0246 1014-011 1024-011

Fig 4 The inner line shows the 68% and the outer line shows the 90% confidence level for the fit of Rmeas to ( 1 ), statistical error only OPAL results [8] on Rmeas from K~3K ~ correlations are also shown Note that for Rmeas, corrections for non-prompt K~ and for f0 (975) and a0(980) production have not been applied Results from LEP [5-7] on two-plon correlations, displayed in the same plot, have different correction procedures for non-lnterfenng pairs, and different reference samples The extra dotted error bars cor- respond to the systematic errors added in quadrature

K ° pairs is e x p e c t e d to be s m a l l e r t h a n t h e b a r e cor- r e l a t i o n b e t w e e n p r o m p t K ° In p a r t i c u l a r , a n o n - n e g l i g i b l e f r a c t i o n o f K ° is ex- p e c t e d to c o m e f r o m t h e d e c a y o f c h a r m e d a n d b o t - t o m p a r t i c l e s In o r d e r to p e r f o r m this c o r r e c t i o n we n e e d to e s t i m a t e t h e f r a c t i o n

fbc(Q)

o f K ° K s ° pairs i n c l u d i n g at least o n e K ° c o m i n g f r o m the decays o f c h a r m e d o r b o t t o m p a r t i c l e s

fbc (Q)

was c o m p u t e d b y m e a n s o f J E T S E T PS, a n d is & s p l a y e d in table

1 #1

D u e to t h e c o r r e c t i o n

fbc (Q),

t h e c o r r e l a t i o n func- t i o n b e c o m e s

# 1 _{The rise}

_{offb, (Q)}

_{at low Q values is due to pairs from}

the same decay For most of these pairs the decay am- plitude is highly constrained and thus they should not display BE enhancement (coherent source) [ 12] Under the extreme assumption that

all

pairs from a common ancestor would fully interfere, 2 would be decreased by 20% This is anyway an overestimate of the effect

R* ( Q ) = 1 + Rmeas(Q) - 1

1 - f a c ( Q )

A f i t o f R * t o e q (1) y i e l d e d 2* = 1 31 ± 0 53 (stat) ± 0 22 ( s y s t ) , r* = 0 84 ± 0 16 (stat) ± 0 10 (syst) f m A c o r r e c t i o n to R* ( Q ) is n e e d e d d u e to the absence o f decays o f m e s o n s like j~ (975 ) a n d a0 ( 9 8 0 ) in t h e s i m u l a t e d s a m p l e Such decays can fake t h e correla- t i o n effect, p r o d u c i n g t w o K ° v e r y close in m o m e n - t u m T h e p r o d u c t i o n cross section at L E P energies is p r e s e n t l y k n o w n o n l y for J~ [13] T h e m e a n m u l t i - p h c l t y o f J~ p e r h a d r o n i c e v e n t has b e e n m e a s u r e d to be 0 10 ± 0 04 m t h e r e g i o n o f m o m e n t u m o f t h e j~ larger t h a n 4 5 G e V / c W e c o u l d t h u s correct o n l y for this s o u r c e

T h e Q d i s t r i b u t i o n for K K pairs c o m i n g f r o m y~ d e c a y was c a l c u l a t e d by using t h e c o u p l e d c h a n n e l B r e l t - W l g n e r f o r m u l a [ 14 ] I n c l u d i n g t h e KI~ thresh- o l d effects T h e J~ b r a n c h i n g ratio to kaons was t a k e n f r o m ref. [ 15 ] T h e c o r r e l a t i o n f u n c t i o n R** ( Q ) after s u b t r a c t i o n o f these pairs is h s t e d in table 1

A fit o f R** to eq (1) y i e l d e d #2

# 2 _{A rough estimate of the a 0 (980) contribution (assuming}

that the a 0 multlphclty is the average of the predictions from JETSET PS and HERWIG, and that the a 0 behaves like the f0) would decrease 2** by approximately 10%

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Volume 323, number 2 PHYSICS LETTERS B 10 March 1994 Table 2

Systematic errors from different sources contnbutmg to the uncertainty due to the reference sample Contributions to the corrected correlation functions are shown m the four last columns

Source Uncorr data After fbc corr After fbc and 3~ corr

AA Ar(fm) A2* Ar*(fm) AA** Ar**(fm)

aq -4-0 073 4-0 084 4-0 092 4-0 063 :t:0 107 4-0 066 a 4-0 037 4-0 020 4-0 046 4-0 016 4-0 053 4-0 020 A 4-0 021 -t-0 005 4-0 026 4-0 003 4-0 025 4-0 005 Q0 4-0 048 +0 029 +0 059 +0 023 ±0 053 ±0 022 7s/Yu +0 014 4-0 014 +0 017 4-0 O11 4-0 019 4-0 009 V / ( V + P) 4-0 039 4-0 066 +0 048 4-0 050 4-0 044 4-0 049 total 4-0 11 4-0 11 4-0 13 4-0 09 4-0 14 4-0 09 2** = 1 13 4- 0 54 (stat) 4- 0 23 (syst), r** = 0 90 4- 0 19 (stat) 4- 0.10 (syst) fm

3 2 Evaluatton o f the systemattc error

The following sources of systematic error were con- sldered.

• Reference sample I n order to estimate the sys- tematics of the reference sample, we v a n e d the physical parameters of the simulation Relevant parameters for the p a r t o n shower evolution of JETSET PS are the Q C D parameter A, a n d the cut-off parameter Q0- Their ranges of variations were established as in ref. [16]: A was allowed to vary between 0.25 a n d 0 32 GeV, a n d Q0 in the range between 0 6 a n d 1.4 GeV The fragmentation in JETSET PS is governed by the L u n d symmetric fragmentation function, with essen- tially only one free parameter, a Its value was f o u n d in ref. [16] to be between 0.14 a n d 0.26 (the b parameter was fixed at 0 34 GeV - 2 ) The transverse m o m e n - t u m of p r i m a r y hadrons is parametrlzed by a Gaus- sian, whose width aq was v a n e d between 355 M e V / c a n d 415 MeV/c.

I n addition, the following were varied:

- the probability of generating a p r o m p t spin 1 me-

son, V / ( V + P ) , between 0.47 a n d 0 67 This range was calculated from the K ° a n d K* average multlphc- lties measured previously by D E L P H I [ 17,13 ]

- the probability of exciting a s~ pair from the

vacuum, ?'s/~'u, between 0 28 a n d 0 32 This range was derived [17] from the K ° differential cross section

The uncertainties due to these sources are shown in table 2

• Selectton o f t h e p a w s The systematlcs were eval- uated by a variation of the signal region upper limit from a = 8 M e V / c 2 to 20 M e V / c 2, a n d of the control region from the range between 10 a n d 100 M e V / c 2 off the mass peak, to the range between 40 a n d 100 M e V / c 2 off the mass peak. D u n n g the variation the upper limit of the signal region was required to be less than the lower limit of the control region

• Normahzatton o f R This source was estimated by varying the range of Q used for the normalization; the intervals of Q between 0 333 a n d 2 GeV/c, a n d between 1 a n d 2 G e V / c were studied

• Non-prompt kaons A relative systematic error of + 10% was assigned to Jbc (Q), to account for uncertainties in the decay modes of charmed a n d b o t t o m particles.

• fo productton The multiplicity of J~-mesons per hadronic event was varied within errors of the DEL- P H I m e a s u r e m e n t (0 l 0 i 0.04)

The total systematic errors were calculated by adding in quadrature all the contributions (see table

3)

4 . C o n c l u s i o n s

Low-Q correlations between pairs of K ° from the decay of the Z ° have been observed with the D E L P H I detector at LEP, using a sample of about 11 000 pairs coming from 717 511 selected hadronlc events The results show a BE-hke e n h a n c e m e n t which can be

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Table 3 Systematic errors

Source Uncorr data After

fbc

corr

AA Ar(fm)

After

fbc

and f0 corr

A2* Ar* (fm) A2** Ar** (fro)

reference sample (see table 2) 20 11 2 0 11 selection of the parrs 4-0 11 4-0 04

normahzatlon of R 20 01 20 01

10% relative error of Jbc (Q) - -

( r t f 0 ( 9 7 5 ) ) = 0 1 0 ± 0 0 4 - -

total systematic error 20 16 2 0 12

+0 13 +0 09 4-0 14 +0 09 +0 17 4-0 04 +0 16 +0 04 +0 05 +0 01 +0 01 20 01 4-0 06 20 00 20 06 2 0 00 - - 20.07 20 03 20 22 20 10 20 23 20 10 r2 Q 2 p a r a m e t n z e d by the expression R (Q) = 1 + 2 e - , where, without any correction for n o n - p r o m p t K ° pairs, it = 0 8 8 ± 0 3 5 ( s t a r ) + 0 1 6 ( s y s t ) a n d r = 0.82 + 0 16(stat) J: 0 12(syst) fm

Taking into account the c o n t r i b u t i o n from non- p r o m p t K ° pairs coming from the decays of charmed a n d b o t t o m hadrons changes the values above to it = 1.31 ± 0.53(stat) & 0 22(syst) a n d r = 0 84 + 0 16(stat) ± 0 10(syst) fm. Taking into account in addition the decay of the J~ into K K pairs gives 2 = 1 13 - 4 - 0 5 4 ( s t a t ) + 0 2 3 ( s y s t ) a n d r = 0 90 + 0.19(stat) -t- 0 10(syst) fm

The radius o f the region of emission of the kaons compares with that measured by D E L P H I for the pions [7], r = 0 62 + 0 04(stat) + 0 20(syst) fm The physical interpretation of a comparison of the strength of the correlations is more difficult, since the results in ref [ 7 ] were not corrected for particles coming from long-living secondary sources (like B a n d D mesons) A new analysis by D E L P H I [ 18] makes a correction for all these sources, o b t a i n i n g a value of 2 consistent with 1

According to JETSET PS, 28% of the low Q KsKs0 0 pairs come from identical K ° K ° (or ~ 0 ~ 0 ) pairs, about 70% of them originate from p r o m p t sources If the positive interference at low Q would affect only the K ° K ° (or ~ 0 ~ 0 ) pairs, a value of 2 -~ 3-5 would be required to explain our data Assuming that the strength of the Bose-Einstein effect can be parametrized by it ~< l, it is then unlikely that only identical neutral kaons are responsible for the observed e n h a n c e m e n t at low Q O u r results support the hypothesis that K ° coming from K ° K ° pairs also exhibit constructive interference at Q -~ 0

We are greatly indebted to our technical staffs a n d collaborators a n d funding agencies for their support in building the D E L P H I detector and to the m a n y members of the CERN-SL division for the excellent performance of the LEP machine We would like to thank M G Bowler a n d N Tornqvlst for useful dis- cusslons

References

[ I ] B Lorstad, Int J Mod Phys A 4 (1989)2861, W A Zajc, m Hadronlc Mult:pamcle Productmn, ed P Carruthers (World Scientific, 1988) 235,

B De Lotto, Contributed talk at the XXVI International Conference on High Energy Physics

(Dallas, August 1992)

[2] G I Kopylov and M I Podgoretskn, Sov J Nucl Phys 19 (1974) 215,

G I Kopylov, Phys Lett B 50 (1974) 472, G Coccom, Phys Lett B 49 (1974)459,

M Deutschmann et al, Nucl Phys B 204 (1982) 333, A Glovanmm and G Venezlano, Nucl Phys B 130

(1977) 61,

M G Bowler, Z Phys C 29 (1985) 617

[3]T Sjostrand, Comp Phys Comm 27 (1982)243, 28 (1983) 229,

T Sjostrand and M Bengtsson, Comp Phys Comm 43 (1987) 367,

T Sjostrand, CERN-TH 6488/92 (May 1992) [4] H Llpkln, Phys Lett B 219 (1989) 474, Phys Rev

Lett 69 (1992) 3700

[5] OPAL Collab, P D Acton et al, Phys Lett B 267 (1991) 143

[6] ALEPH Collab, D Decamp et al, Z Plays C 54 (1992) 75

[7] DELPHI Collab, P Abreu et al, Phys Lett B 286 (1992) 201

[8] OPAL Collab, P D Acton et al, Plays Lett B 298 (1993) 456

(12)

Volume 323, number 2 PHYSICS LETTERS B 10 March 1994 [9] DELPHI Collab, P Aarnlo et al, Nucl Instr and

Meth A 303 (1991) 233

[10]DELSIM User Manual, DELPHI 87-96 PROG-99 (Geneva, July 1989),

DELSIM Reference Manual, DELPHI 87-98 PROG- 100 (Geneva, July 1989)

[11] W de Boer and H Furstenau, IEKP-KA/91-07 (Karlsruhe, June 1991)

[ 1 2 ] M G Bowler, Z Phys C 46 (1990) 305

[13] DELPHI Collab, P Abreu et al, Phys. Lett B 298 (1993) 236

[14] WA 76 Collab, T A Armstrong et al, Z Phys C 51 (1991) 351

[15] Particle Data Group, M Agudar-Bemtez et al, Phys Rev D 45 (1992)

[16] DELPHI Collab, P Abreu et al, Phys Lett B 295 (1992) 383

[17] DELPHI CoUab, P Abreu et al, Phys Lett B 275 (1992) 231

[18] DELPHI Collab, P Abreu et al, Invanant Mass Dependence of Particle Correlations, m Hadromc Final States from the Decay of the Z, to be pubhshed