EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN{PPE/95-28

14 March 1995

Inclusive Measurements of the

K� and p=p Productionin Hadronic Z0 Decays

DELPHI Collaboration

Abstract

This analysis, based on a sample of 170,000 hadronic Z0 decays, provides ameasurement of the K� and p=p di�erential cross-sections which is comparedto string- and cluster fragmentation models. The total multiplicities for K� andp=p per hadronic event were found to be: NK = 2:26�0:18 and Np = 1:07�0:14.The positions �� of the maxima of the di�erential cross-sections as a function of� = ln(1=xp) for K

� and p=p were determined to be 2:63� 0:07 and 2:96� 0:16respectively. A comparison of the �� values for various identi�ed particles mea-sured at LEP with the prediction of the Modi�ed Leading Logarithm Approx-imation with Local Parton Hadron Duality model has been performed. Themeasured �� position as a function of the hadron mass, after corrections due toparticle decays, is in agreement with the model calculation.

(To be submitted to Nuclear Physics B)

ii

P.Abreu21, W.Adam50, T.Adye37, E.Agasi31, I.Ajinenko42, R.Aleksan39, G.D.Alekseev16 , P.P.Allport22 ,

S.Almehed24 , S.J.Alvsvaag4, U.Amaldi9, S.Amato47, A.Andreazza28, M.L.Andrieux14 , P.Antilogus25 ,

W-D.Apel17 , Y.Arnoud39, B.�Asman44, J-E.Augustin19 , A.Augustinus31 , P.Baillon9 , P.Bambade19, F.Barao21,

R.Barate14, D.Y.Bardin16, G.J.Barker35, A.Baroncelli40 , O.Barring24, J.A.Barrio26, W.Bartl50 , M.J.Bates37,

M.Battaglia15 , M.Baubillier23 , J.Baudot39, K-H.Becks52, M.Begalli6 , P.Beilliere8 , Yu.Belokopytov9 , K.Belous42 ,

A.C.Benvenuti5, M.Berggren41 , D.Bertrand2, F.Bianchi45 , M.Bigi45 , M.S.Bilenky16 , P.Billoir23 , J.Bjarne24,

D.Bloch10 , M.Blume52 , S.Blyth35 , V.Bocci38, T.Bolognese39 , M.Bonesini28 , W.Bonivento28 , P.S.L.Booth22,

G.Borisov42 , C.Bosio40, B.Bostjancic43 , S.Bosworth35, O.Botner48, E.Boudinov42 , B.Bouquet19 , C.Bourdarios9 ,

T.J.V.Bowcock22, M.Bozzo13, P.Branchini40 , K.D.Brand36, R.A.Brenner15, C.Bricman2, L.Brillault23 ,

R.C.A.Brown9, P.Bruckman18, J-M.Brunet8, L.Bugge33, T.Buran33, A.Buys9, M.Caccia28, M.Calvi28 ,

A.J.Camacho Rozas41 , T.Camporesi9 , V.Canale38, M.Canepa13, K.Cankocak44, F.Cao2, F.Carena9,

P.Carrilho47 , L.Carroll22 , C.Caso13, V.Cassio45, M.V.Castillo Gimenez49 , A.Cattai9, F.R.Cavallo5, L.Cerrito38,

V.Chabaud9, Ph.Charpentier9 , L.Chaussard25 , J.Chauveau23 , P.Checchia36 , G.A.Chelkov16 , P.Chliapnikov42 ,

P.Chochula7 , V.Chorowicz9, V.Cindro43 , P.Collins9 , J.L.Contreras19, R.Contri13, E.Cortina49 , G.Cosme19,

F.Cossutti46, H.B.Crawley1, D.Crennell37 , G.Crosetti13, J.Cuevas Maestro34, S.Czellar15 , E.Dahl-Jensen29 ,

J.Dahm52, B.Dalmagne19 , M.Dam33, G.Damgaard29 , A.Daum17, P.D.Dauncey37 , M.Davenport9, W.Da Silva23 ,

C.Defoix8, G.Della Ricca46 , P.Delpierre27 , N.Demaria35 , A.De Angelis9 , H.De Boeck2, W.De Boer17,

S.De Brabandere2 , C.De Clercq2, C.De La Vaissiere23 , B.De Lotto46, A.De Min28 , L.De Paula47 ,

C.De Saint-Jean39 , H.Dijkstra9, L.Di Ciaccio38 , F.Djama10, J.Dolbeau8 , M.Donszelmann9 , K.Doroba51 ,

M.Dracos10, J.Drees52, K.-A.Drees52, M.Dris32 , Y.Dufour8, F.Dupont14 , D.Edsall1 , R.Ehret17, G.Eigen4 ,

T.Ekelof48, G.Ekspong44 , M.Elsing52 , J-P.Engel10, N.Ershaidat23 , M.Espirito Santo21 , V.Falaleev42 ,

D.Fassouliotis32 , M.Feindt9 , A.Ferrer49, T.A.Filippas32 , A.Firestone1, H.Foeth9, E.Fokitis32 , F.Fontanelli13 ,

F.Formenti9, B.Franek37, P.Frenkiel8 , D.C.Fries17, A.G.Frodesen4, R.Fruhwirth50 , F.Fulda-Quenzer19 ,

H.Furstenau9, J.Fuster49, D.Gamba45, M.Gandelman6 , C.Garcia49, J.Garcia41, C.Gaspar9, U.Gasparini36 ,

Ph.Gavillet9 , E.N.Gazis32, D.Gele10 , J-P.Gerber10, D.Gillespie9 , R.Gokieli51 , B.Golob43 , G.Gopal37 , L.Gorn1,

M.Gorski51 , V.Gracco13, F.Grard2, E.Graziani40 , G.Grosdidier19 , P.Gunnarsson44 , M.Gunther48, J.Guy37,

U.Haedinger17 , F.Hahn52, M.Hahn17, S.Hahn52, S.Haider31, Z.Hajduk18 , A.Hakansson24 , A.Hallgren48 ,

K.Hamacher52, W.Hao31, F.J.Harris35, V.Hedberg24, R.Henriques21 , J.J.Hernandez49, P.Herquet2, H.Herr9,

T.L.Hessing9, E.Higon49 , H.J.Hilke9, T.S.Hill1 , S-O.Holmgren44 , P.J.Holt35, D.Holthuizen31 , M.Houlden22 ,

J.Hrubec50, K.Huet2, K.Hultqvist44 , P.Ioannou3 , J.N.Jackson22, R.Jacobsson44 , P.Jalocha18 , R.Janik7 ,

G.Jarlskog24 , P.Jarry39, B.Jean-Marie19, E.K.Johansson44 , L.Jonsson24, C.Joram9, P.Juillot10 , M.Kaiser17 ,

G.Kalmus37, F.Kapusta23, M.Karlsson44 , E.Karvelas11 , S.Katsanevas3, E.C.Katsou�s32, R.Keranen15 ,

B.A.Khomenko16, N.N.Khovanski16 , B.King22, N.J.Kjaer29, H.Klein9, A.Klovning4 , P.Kluit31, J.H.Koehne17,

B.Koene31, P.Kokkinias11 , M.Koratzinos9 , V.Kostioukhine42 , C.Kourkoumelis3 , O.Kouznetsov13 ,

P.-H.Kramer52, C.Kreuter17, J.Krolikowski51 , I.Kronkvist24, Z.Krumstein16 , W.Krupinski18 , P.Kubinec7 ,

W.Kucewicz18 , K.Kurvinen15 , C.Lacasta49, I.Laktineh25 , S.Lamblot23 , J.W.Lamsa1, L.Lanceri46 , D.W.Lane1,

P.Langefeld52 , V.Lapin42 , I.Last22, J-P.Laugier39, R.Lauhakangas15 , G.Leder50, F.Ledroit14 , V.Lefebure2,

C.K.Legan1, R.Leitner30, Y.Lemoigne39 , J.Lemonne2, G.Lenzen52, V.Lepeltier19 , T.Lesiak36, D.Liko50 ,

R.Lindner52 , A.Lipniacka19 , I.Lippi36 , B.Loerstad24, M.Lokajicek12 , J.G.Loken35, J.M.Lopez41,

A.Lopez-Fernandez9 , M.A.Lopez Aguera41, D.Loukas11, P.Lutz39, L.Lyons35, J.MacNaughton50, G.Maehlum17 ,

A.Maio21, V.Malychev16 , F.Mandl50 , J.Marco41, B.Marechal47 , M.Margoni36 , J-C.Marin9, C.Mariotti40 ,

A.Markou11, T.Maron52, C.Martinez-Rivero41 , F.Martinez-Vidal49 , S.Marti i Garcia49 , F.Matorras41,

C.Matteuzzi28, G.Matthiae38 , M.Mazzucato36, M.Mc Cubbin9 , R.Mc Kay1, R.Mc Nulty22, J.Medbo48,

C.Meroni28, W.T.Meyer1, M.Michelotto36 , E.Migliore45 , L.Mirabito25 , W.A.Mitaro�50 , U.Mjoernmark24,

T.Moa44, R.Moeller29 , K.Moenig9 , M.R.Monge13, P.Morettini13 , H.Mueller17 , L.M.Mundim6 , W.J.Murray37,

B.Muryn18 , G.Myatt35, F.Naraghi14 , F.L.Navarria5, S.Navas49, P.Negri28, S.Nemecek12, W.Neumann52 ,

N.Neumeister50, R.Nicolaidou3 , B.S.Nielsen29 , V.Nikolaenko25 , P.Niss44, A.Nomerotski36 , A.Normand35,

W.Oberschulte-Beckmann17 , V.Obraztsov42, A.G.Olshevski16 , A.Onofre21, R.Orava15, K.Osterberg15,

A.Ouraou39, P.Paganini19 , M.Paganoni28 , P.Pages10, H.Palka18 , Th.D.Papadopoulou32 , L.Pape9, F.Parodi13 ,

A.Passeri40, M.Pegoraro36 , J.Pennanen15 , H.Pernegger50, M.Pernicka50 , A.Perrotta5, C.Petridou46 ,

A.Petrolini13 , H.T.Phillips37 , G.Piana13 , F.Pierre39, M.Pimenta21 , S.Plaszczynski19 , O.Podobrin17 , M.E.Pol6,

G.Polok18 , P.Poropat46, V.Pozdniakov16 , M.Prest46, P.Privitera38 , A.Pullia28 , D.Radojicic35 , S.Ragazzi28 ,

H.Rahmani32 , J.Rames12, P.N.Rato�20, A.L.Read33, M.Reale52 , P.Rebecchi19 , N.G.Redaelli28 , M.Regler50 ,

D.Reid9 , P.B.Renton35, L.K.Resvanis3, F.Richard19 , J.Richardson22 , J.Ridky12, G.Rinaudo45 , I.Ripp39 ,

A.Romero45, I.Roncagliolo13 , P.Ronchese36, L.Roos14, E.I.Rosenberg1 , E.Rosso9, P.Roudeau19 , T.Rovelli5 ,

W.Ruckstuhl31 , V.Ruhlmann-Kleider39 , A.Ruiz41 , K.Rybicki18 , H.Saarikko15 , Y.Sacquin39 , A.Sadovsky16 ,

G.Sajot14, J.Salt49, J.Sanchez26, M.Sannino13 , H.Schneider17 , M.A.E.Schyns52, G.Sciolla45 , F.Scuri46 ,

Y.Sedykh16 , A.M.Segar35, A.Seitz17, R.Sekulin37 , R.C.Shellard6 , I.Siccama31 , P.Siegrist39 , S.Simonetti39 ,

F.Simonetto36 , A.N.Sisakian16 , B.Sitar7, T.B.Skaali33 , G.Smadja25, N.Smirnov42 , O.Smirnova16, G.R.Smith37 ,

R.Sosnowski51 , D.Souza-Santos6 , T.Spassov21 , E.Spiriti40 , S.Squarcia13 , H.Staeck52, C.Stanescu40, S.Stapnes33 ,

I.Stavitski36 , K.Stepaniak51 , F.Stichelbaut9 , A.Stocchi19 , J.Strauss50, R.Strub10, B.Stugu4 , M.Szczekowski51 ,

M.Szeptycka51 , T.Tabarelli28 , J.P.Tavernet23, O.Tchikilev42 , A.Tilquin27 , J.Timmermans31, L.G.Tkatchev16,

T.Todorov10, D.Z.Toet31, A.Tomaradze2, B.Tome21, E.Torassa45, L.Tortora40, G.Transtromer24, D.Treille9 ,

iii

W.Trischuk9 , G.Tristram8, A.Trombini19, C.Troncon28, A.Tsirou9, M-L.Turluer39, I.A.Tyapkin16, M.Tyndel37 ,

S.Tzamarias22 , B.Ueberschaer52 , S.Ueberschaer52 , O.Ullaland9 , V.Uvarov42, G.Valenti5 , E.Vallazza9 ,

C.Vander Velde2, G.W.Van Apeldoorn31 , P.Van Dam31, W.K.Van Doninck2 , J.Van Eldik31 , G.Vegni28 ,

L.Ventura36, W.Venus37, F.Verbeure2, M.Verlato36, L.S.Vertogradov16, D.Vilanova39 , P.Vincent25, L.Vitale46 ,

E.Vlasov42 , A.S.Vodopyanov16 , M.Voutilainen15 , V.Vrba12, H.Wahlen52 , C.Walck44 , F.Waldner46 , A.Wehr52,

M.Weierstall52 , P.Weilhammer9 , A.M.Wetherell9, D.Wicke52 , J.H.Wickens2, M.Wielers17 , G.R.Wilkinson35 ,

W.S.C.Williams35 , M.Winter10 , M.Witek9 , G.Wormser19, K.Woschnagg48 , K.Yip35, L.Yu35, O.Yushchenko42 ,

F.Zach25, A.Zaitsev42 , A.Zalewska18 , P.Zalewski51 , D.Zavrtanik43 , E.Zevgolatakos11 , N.I.Zimin16 , M.Zito39 ,

D.Zontar43 , R.Zuberi35 , G.C.Zucchelli44 , G.Zumerle36

1Ames Laboratory and Department of Physics, Iowa State University, Ames IA 50011, USA2Physics Department, Univ. Instelling Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgiumand IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgiumand Facult�e des Sciences, Univ. de l'Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece4Department of Physics, University of Bergen, All�egaten 55, N-5007 Bergen, Norway5Dipartimento di Fisica, Universit�a di Bologna and INFN, Via Irnerio 46, I-40126 Bologna, Italy6Centro Brasileiro de Pesquisas F�isicas, rua Xavier Sigaud 150, RJ-22290 Rio de Janeiro, Braziland Depto. de F�isica, Pont. Univ. Cat�olica, C.P. 38071 RJ-22453 Rio de Janeiro, Braziland Inst. de F�isica, Univ. Estadual do Rio de Janeiro, rua S~ao Francisco Xavier 524, Rio de Janeiro, Brazil7Comenius University, Faculty of Mathematics and Physics, Mlynska Dolina, SK-84215 Bratislava, Slovakia8Coll�ege de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, F-75231 Paris Cedex 05, France9CERN, CH-1211 Geneva 23, Switzerland10Centre de Recherche Nucl�eaire, IN2P3 - CNRS/ULP - BP20, F-67037 Strasbourg Cedex, France11Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece12FZU, Inst. of Physics of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic13Dipartimento di Fisica, Universit�a di Genova and INFN, Via Dodecaneso 33, I-16146 Genova, Italy14Institut des Sciences Nucl�eaires, IN2P3-CNRS, Universit�e de Grenoble 1, F-38026 Grenoble Cedex, France15Research Institute for High Energy Physics, SEFT, P.O. Box 9, FIN-00014 Helsinki, Finland16Joint Institute for Nuclear Research, Dubna, Head Post O�ce, P.O. Box 79, 101 000 Moscow, Russian Federation17Institut f�ur Experimentelle Kernphysik, Universit�at Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany18High Energy Physics Laboratory, Institute of Nuclear Physics, Ul. Kawiory 26a, PL-30055 Krakow 30, Poland19Universit�e de Paris-Sud, Lab. de l'Acc�el�erateur Lin�eaire, IN2P3-CNRS, Bat 200, F-91405 Orsay Cedex, France20School of Physics and Materials, University of Lancaster, Lancaster LA1 4YB, UK21LIP, IST, FCUL - Av. Elias Garcia, 14-1o, P-1000 Lisboa Codex, Portugal22Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK23LPNHE, IN2P3-CNRS, Universit�es Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, F-75252 Paris Cedex 05, France24Department of Physics, University of Lund, S�olvegatan 14, S-22363 Lund, Sweden25Universit�e Claude Bernard de Lyon, IPNL, IN2P3-CNRS, F-69622 Villeurbanne Cedex, France26Universidad Complutense, Avda. Complutense s/n, E-28040 Madrid, Spain27Univ. d'Aix - Marseille II - CPP, IN2P3-CNRS, F-13288 Marseille Cedex 09, France28Dipartimento di Fisica, Universit�a di Milano and INFN, Via Celoria 16, I-20133 Milan, Italy29Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen 0, Denmark30NC, Nuclear Centre of MFF, Charles University, Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic31NIKHEF-H, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands32National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece33Physics Department, University of Oslo, Blindern, N-1000 Oslo 3, Norway34Dpto. Fisica, Univ. Oviedo, C/P. P�erez Casas, S/N-33006 Oviedo, Spain35Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK36Dipartimento di Fisica, Universit�a di Padova and INFN, Via Marzolo 8, I-35131 Padua, Italy37Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK38Dipartimento di Fisica, Universit�a di Roma II and INFN, Tor Vergata, I-00173 Rome, Italy39Centre d'Etude de Saclay, DSM/DAPNIA, F-91191 Gif-sur-Yvette Cedex, France40Istituto Superiore di Sanit�a, Ist. Naz. di Fisica Nucl. (INFN), Viale Regina Elena 299, I-00161 Rome, Italy41C.E.A.F.M., C.S.I.C. - Univ. Cantabria, Avda. los Castros, S/N-39006 Santander, Spain, (CICYT-AEN93-0832)42Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation43J. Stefan Institute and Department of Physics, University of Ljubljana, Jamova 39, SI-61000 Ljubljana, Slovenia44Fysikum, Stockholm University, Box 6730, S-113 85 Stockholm, Sweden45Dipartimento di Fisica Sperimentale, Universit�a di Torino and INFN, Via P. Giuria 1, I-10125 Turin, Italy46Dipartimento di Fisica, Universit�a di Trieste and INFN, Via A. Valerio 2, I-34127 Trieste, Italyand Istituto di Fisica, Universit�a di Udine, I-33100 Udine, Italy

47Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fund~ao BR-21945-970 Rio de Janeiro, Brazil48Department of Radiation Sciences, University of Uppsala, P.O. Box 535, S-751 21 Uppsala, Sweden49IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain50Institut f�ur Hochenergiephysik, �Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, A-1050 Vienna, Austria51Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland52Fachbereich Physik, University of Wuppertal, Postfach 100 127, D-42097 Wuppertal 1, Germany

1

1 Introduction

The way quarks and gluons transform into hadrons is complex and not entirely under-stood by present theories. In the current picture the hadronization of a qq pair from thedecay of a Z0 is split into 3 phases [1]. In a �rst phase, gluon emission and parton branch-ing of the original qq pair take place. It is believed that this phase can be described byperturbative QCD, although most of the calculations performed today are only to secondorder. In a second phase, quarks and gluons produced in phase 1 are clustered in coloursinglets and transform into mesons and baryons. Only phenomenological models, whichneed to be tuned to the data, are available to describe this process of fragmentation.The models most frequently used in e+e� annihilations are those using string and clusterfragmentation. Most of the primary produced hadrons have very short lifetimes. In thethird phase the unstable hadrons decay into hadrons which can be observed or identi�edby the detector.

A di�erent and purely analytical approach giving quantitative predictions of hadronicspectra are QCD calculations using the so called Modi�ed Leading Logarithmic Approx-imation (MLLA) under the assumption of Local Parton Hadron Duality (LPHD) [2]. Inthis model the particle yield is described as function of the variable � where � = ln(1=xp)and xp is the normalized momentum Phadron=Pbeam.

1

�

d�

d�= KLPHD � f(�; Y; �) (1)

with

Y = ln

ps

Q0

; � = lnQ0

�eff(2)

The MLLA+LPHD predictions involve three parameters: an e�ective scale parameter�eff , Q0 as the cut-o� parameter in the quark-gluon cascade and an overall normalizationfactor KLPHD that depends on the particle mass.

In this analysis the K� and p=p spectra from Z0 hadronic decays were measured usingthe Cherenkov signal from the liquid and gas radiator of the DELPHI barrel Ring ImagingCHerenkov (RICH) detector. The measurements were compared to the MLLA+LPHDcalculations and to the JETSET 7.3 and HERWIG 5.6 model predictions which use stringand cluster fragmentation respectively [3,4].

2 Event and Charged Particle Selection

The analysis presented is based on about 170,000 Z0 decays, collected with the DEL-PHI detector equipped with a barrel RICH detector allowing particle identi�cation. Thedata were taken at a centre-of-mass energy of 91.2 GeV. Apart from the barrel RICHdetector the relevant detector components for this analysis were the following trackingchambers: the vertex detector, the inner detector, the time projection chamber and theouter detector. A description of the DELPHI detector and a detailed illustration of theDELPHI RICH detectors can be found in [5,6].

For the event selection charged particles were accepted in the momentum region 0:2 <P < 50 GeV/c, requiring that the relative momentum error, �P

P, was less than 1 and a

minimum length of 50 cm was measured in the DELPHI tracking detectors. The chargedparticle polar angle � had to be between 20� and 160�. The track impact parameter was

2

required to be smaller than 5 cm in the plane transverse to the beam and less than 10cm in the direction of the beam.

A hadronic event was selected by requiring a charged particle multiplicity greater than4, a total energy deposited by charged particles of at least 15 GeV with at least 3 GeVin each hemisphere. The background, mainly coming from �+�� events, was estimatedto be less than 0.2 %.

For the analysis particle identi�cation is essential therefore the charged particle mo-mentum was required to be bigger than 0.7 GeV/c and the polar angle was restrictedto the region 41� < � < 139�, which corresponds to the active area of the barrel RICHdetector.

3 Evaluation of the Mean Cherenkov Angle

The input for the analysis of the mean Cherenkov angle were single space points mea-sured in the photon detector of the barrel RICH. They correspond to the coordinatesof the Cherenkov photo-electrons which were detected and associated to a track. Themeasured space points were transformed to a plane orthogonal to the track. In this coor-dinate system the Cherenkov photons from the signal form a ring with the track crossingpoint in its centre. To perform particle identi�cation a mean Cherenkov angle per track,re ecting the best possible choice from the original single photo-electron distribution wascalculated. One of the main di�culties is an e�cient separation between noise and signalpoints. The algorithm to evaluate the mean angle developed for this analysis does notmake use of any mass hypothesis [7].

To recognize a circle without making any assumption on its centre, at least three pointsare needed. Given three points the ring centre and the radius can easily be determined, byconstructing a triangle out from the three points and taking the normal at the middle ofeach side of the triangle. The unique crossing point of the three perpendicular bisectors isthe centre of the ring passing through the three original points. This simple triangulationprocedure was repeated for all possible three point combinations. For each triangle thering centre and the radius were recorded. The combinations originating from the signalaccumulate their ring centres near the crossing point of the track. Triangles containingnoise points spread their centres arbitrarily in position. The mean angle was extractedby �tting the radius distribution of all combinations which have the ring centre in asmall cell around the track crossing point. Noise points were e�ciently rejected by thecombinatorial dominance of the signal. Given n points on a circle the density in the cellaround the centre grows as n(n � 1)(n � 2)=6 [7].

After the calculation of the mean Cherenkov angle the number of signal photo-electrons(nsig) was determined for this track, as the number of photo-electrons which satisfy:j�j � �j < 3 � ��j, where �j is the Cherenkov angle of the individual photo-electron j,��j is the error of �j and � is the mean Cherenkov angle for this track. The error onthe mean angle �� is obtained from the width of the corresponding radius distributiondivided by

pnsig.

Further cuts were applied in order to optimize particle identi�cation. It was requiredthat the photon detector traversed by the particle recorded its ionization, thus assuringthat the corresponding sector of the detector was operational. The number of signalphoto-electrons assigned to the ring was required to be greater than 5 in the liquidradiator and greater than 3 in the gas radiator. The error of the mean angle �� wasrequired to be less than 0.011 rad for rings from the liquid radiator. With these additionalquality cuts between 57 % and 93 % of the tracks crossing the barrel RICH in the liquid

3

and between 45 % and 65 % in the gas were retained, where the e�ciencies rise withincreasing momenta.

4 Measurement of Inclusive K� and p=p Rates

(a) (b)

Figure 1: Cherenkov angle versus the charged particle momentum in (a) the liquid radi-ator and (b) the gas radiator.

For a given momentum, the Cherenkov angle depends on the mass of the particle andthe refractive index of the radiator. Figures 1 to 3 show the Cherenkov angles recon-structed with the triangulation method for liquid and gas radiator. For the gas radiator(see Figure 1(b)) an accumulation of background at large angles and small momenta isobserved which is mainly due to scattered tracks, especially electrons, and veto particlesaccompanied with noise points. A veto particle is such that its velocity is below thethreshold for Cherenkov light emission in the relevant medium. The fraction of K� andp=p were extracted using a maximum likelihood �t for the Cherenkov angle distribu-tion in discrete momentum intervals. For each track satisfying the selection criteria, theprobability density \li" of observing the measured angle �i was calculated.

li =1

C�24(1� fK � fp)

���i� e�

(�i���)2

2(���i)2 +

fK

��Ki� e�

(�i��K)2

2(��Ki)2 +

fp

��pi� e�

(�i��p)2

2(��p

i)2 + b

35 (3)

with

�i : measured Cherenkov angle of track i��;K;p : expected Cherenkov angle for a piony, kaon and proton

���;K;pi : =q��2 + ( @�

@P�P )2 error on the Cherenkov angle of track i for

a pion, kaon and proton

4

Pion

Kaon

Proton

Figure 2: Cherenkov angle distribution in multi-hadronic events for the momentum in-terval 2:0 < P < 2:5 GeV/c. Plotted is �meas� �kaonexp of the liquid radiator signal, the fulllines corresponds to a �t of three Gaussians plus a at background.

5

(a) (b)

(c)

Figure 3: Distribution of the normalized an-gle ���exp

��using (a) identi�ed pions from K0

decays for the liquid radiator signal, (b) iden-ti�ed protons from �0 decays for the liquidradiator signal and (c) identi�ed pions fromK0 decays for the gas radiator signal. In (b)the background on the right hand side of thedistribution is due to residual pion contami-nation in the proton sample.

6

fK : fraction of kaons estimated by the �tfp : fraction of protons estimated by the �tb : constant for the backgroundC : normalization constant

Normally particles which do not have an appropriate Cherenkov angle measurement wereremoved by the quality cuts, but badly measured tracks may sometimes have passed thecuts and contributed to the background. Hence the background term b contains apartfrom real background such as veto particles or digitizations from multiple scattering alsosome ��, K� and p=p. But Figures 2 and 3 show that the �tted distributions containonly little background which justi�es the approach b = constant.

The normalization constant C was determined through the integral

1 =Z �2(P up)

�1(P low)li(fK; fp; �i;��i; b) d� (4)

where the integration limits �1 and �2 cover, for the liquid radiator, the range from�1(P low) = �prot: � 0:060 rad and �2(P up) = �elec: + 0:060 rad, taking for P low(P up) thelower (upper) limit of each �tted momentum interval. For the gas radiator the integrationcovers the entire active � range from 0 to 70 mrad.

The extended likelihood function LE in eqn.(5) is derived from the product of the liover all tracks and an additional Poissonian factor estimating the probability of obtaininga sample of size [8].

LE = m � e� m!

mYi=1

li(fK; fp; �i;��i; b) (5)

m : total number of entries in the given momentum bin : total number of tracks (including background) estimated by the �t

LE describes the probability to obtain the observed sample of measurements. The pa-rameters ; fK; fp and b were estimated by maximizing the logarithm of the likelihoodfunction in equation (5).

The upper kinematical limit to which the di�erent particle types can be separated de-pends crucially on the distances ����Kp

2��and �K��pp

2��, which are shown in Figure 4. Requiring

a minimal separation of��(K)��K(p)p

2��& 0:8 and taking into account the behaviour of the

systematic errors (see section 4.1) the kaon fraction was extracted from the measurementup to 4.0 GeV/c in the liquid and up to 23 GeV/c in the gas radiator. For the protonfraction, the limit in the liquid radiator was 5 GeV/c.

In this analysis a �t for the measured Cherenkov angle was used, therefore the lower

kinematical limit is given by the Cherenkov threshold P �q

M2

n2�1which depends on the

mass M and the refractive index n. To keep e�ciency corrections small (discussed insection 4.1), the following lower momentum limits were used: in the liquid P kaon

low = 0:8GeV/c and P proton

low = 1:4 GeV/c, in the gas only the kaon yield for P kaonlow = 10:0 GeV/c

was evaluated. In order to estimate the proton fraction at high momenta it is favorable totake advantage of the veto signal. This requires an extension in eqn.(3) for the probabilityof observing no light at all, which was not done for this analysis. The veto signal wouldallow a determination of the proton rate for P & 10 GeV/c.

yPion stands for pion, electron or muon since they cannot be distinguished in most cases.

7

(a) (b)

Figure 4: The hadron separation capacities ����K�

and �K��p�

with � =p2�� are shown

for (a) the liquid and (b) for the gas radiator. Full curve is pion/kaon separation anddashed curve is kaon/proton separation.

In some of the low momentumintervals the proton is below or very close to its thresholdfor emitting Cherenkov light (veto particle). Protons are therefore excluded from theprobability density in eqn.(3). In this case a correction factor to the number of tracksmeasured was applied using the proton yield predicted by JETSET. Using the protonyield measured in [9], which is signi�cantly lower than the JETSET fraction at highmomenta, would change the results by an amount much smaller than the experimentalerrors.

4.1 E�ciency and Acceptance Corrections and Systematic Er-

ror Evaluation

Some long lived particles such as K0S, K

0L or �0 may or may not decay inside the

detector. The measurements were corrected such that all K0S and �0 decay products were

included and all K0L were counted as stable particles. Furthermore the fractions were

corrected bin by bin for detector e�ects and particles produced in secondary interactions.Both corrections were evaluated using the full DELPHI detector simulation [10].

It is important to take account of any relative e�ciency di�erences between particlespecies. The number of photo-electrons in a ring is proportional to sin2 �. Considering amomentum interval where particles with di�erent masses have distinct Cherenkov angles,less photo-electrons are expected for heavier particles than for lighter ones. This leadsto a lower ring detection e�ciency in some of the lower momentum bins for kaons orprotons with respect to pions. Since eqn.(3) does not include a term which corrects fore�ciency di�erences depending on the number of photo-electrons, this e�ect was treated

8

separately. The procedure to correct the measured fractions was di�erent for rings fromthe liquid and from the gas radiator.

In the rings from the liquid radiator, for pions and protons, the e�ciencies can bemeasured using identi�ed tracks from K0 or � decays. In Figure 5 (a) the e�ciencyto �nd a ring at the expected position with the selection criteria used in this analysis isplotted as a function of the momentum. The di�erence between pion and proton e�ciencyat low momenta is due to the reduced number of photo-electrons in the proton ring. Theproton e�ciency correction can be extracted bin by bin from the ratio of

"p"�. Very good

agreement is observed for the extracted e�ciency ratio between data and simulation. (seeFigure 5 (b)). The e�ciency corrections for kaons and protons were therefore estimatedusing detector simulation. A minimal error of � 5% on the e�ciency correction wasassumed if the statistical error from the simulation was smaller (Table 1).

In the rings from the gas radiator, particles with an equal number of photo-electronsare expected to have the same ring detection e�ciency. However, there are argumentsfor a kaon at 12 GeV/c not to have the same e�ciency as a pion at 3.5 GeV/c: they havedi�erent momentum errors, they have di�erent densities of surrounding tracks and thetrack curvature in the radiator is di�erent. Despite these additional factors, the simulationpredicts similar reconstruction e�ciencies for pions and kaons with equal number ofphoto-electrons. This result is because the ring detection e�ciency does not dependstrongly on the resolution of the Cherenkov angle but rather on the number of photo-electrons. In Figure 5 (c) the e�ciencies are shown versus the relative number of photo-electrons in the ring, which is de�ned as the measured number divided by the number ofphoto-electrons obtained in a ring with the maximal Cherenkov angle. In the data, thering detection e�ciency can be measured for pions from K0 decays (Figure 5 (d)). Usingthe above arguments, the kaon e�ciency was assumed to be equal to the pion e�ciencyfor the same number of photo-electrons ("K(nK) = "�(n�) for n� = nK). The correctionsare given in Table 2. They are in agreement with the relative e�ciency corrections whichwere extracted from the simulation directly.

Momentum Correction FactorInterval [GeV/c] Kaon Proton

0.8 - 1.1 1.18 � 0.06 -1.1 - 1.4 1.02 � 0.05 -1.4 - 1.7 1.00 � 0.05 1.96 � 0.151.7 - 2.0 1.00 � 0.05 1.27 � 0.092.0 - 2.5 1.00 � 0.05 1.17 � 0.072.5 - 3.0 1.00 � 0.05 1.09 � 0.08

Table 1: E�ciency correction factors in the Cherenkov liquid for kaons and protons dueto di�erences in the number of photo-electrons.

The uncertainties due to di�erences in e�ciency between di�erent particles were di-rectly obtained from the errors on the correction factors given in Tables 1 and 2 and theyappear in column 5 of Tables 3 and 4. Where no e�ciency correction was applied, a 5%relative systematic error was assumed.

The expected Cherenkov angles for the di�erent particles were used as input to the�tting procedure and kept constant during the �t. Errors in these quantities contributeto the systematic error. To evaluate this contribution the �tting procedure was repeatedwith a systematic shift in the expected Cherenkov angle of �0:5 mrad in the liquid, and�0:2 mrad in the gas. These variations were computed for all momentum bins and the

9

(a) (b)

(c) (d)

Figure 5: Ring detection e�ciencies in (a,b) the liquid radiator and (c,d) the gas radiator.(a) E�ciencies for pions and protons measured in the data, (b) e�ciency ratios "K

"�and

"p"�

in the simulation (shaded areas) and in the data (points), (c) e�ciencies as a function

of the relative number of photo-electrons and (d) pion e�ciency measured in the data.

10

Momentum Correction FactorInterval [GeV/c] Kaon

10.0 - 12.0 1.70 � 0.2912.0 - 14.0 1.28 � 0.0814.0 - 16.0 1.15 � 0.0716.0 - 18.0 1.11 � 0.0518.0 - 20.0 1.07 � 0.0520.0 - 23.0 1.03 � 0.05

Table 2: E�ciency correction factors in the Cherenkov gas for kaons due to di�erencesin the number of photo-electrons.

change in the fraction observed was taken as the contribution to the systematic errorwhich is given in column 6 of Tables 3 and 4. This error is negligible in the region wherethe angular separation is large.

In the liquid radiator signal, in some cases, a small non-Gaussian tail towards smallervalues in the Cherenkov angle distribution was observed. This tail was caused by a fewpoorly measured particles. The procedure used to evaluate the systematic errors shown incolumn 7 of Tables 3 and 4 uses pions identi�ed in the gas radiator. Tight identi�cationcuts on the gas radiator signal allow pion selection with a purity near 100 % in themomentum range from 2.5 to 8.0 GeV/c. This pion sample allows to �t single particledistribution in the liquid with the likelihood function in all momentum bins above 2.5GeV/c. The number of kaons determined from the �t were used to extract the systematicerror contribution on the kaon fraction due to pions. For the protons the main in uencecomes from the tail originating from the nearby kaon distribution. Therefore the measuredpion angle was shifted such that it appears on the position of the kaon peak and the sameprocedure was repeated. The shape errors for P < 2:5 GeV/c can be neglected since thepion, kaon and proton curves have very little overlap in this kinematical range.

5 Results

With the methods described in the previous section a large fraction of the possible errorsources are covered and a conservative error estimation on the inclusive kaon and protonfractions is obtained. In Tables 3 and 4, a complete summary of the measured fractionswith their statistical and systematic errors is given. The three sources of systematic errorswhich were discussed before and the error resulting from the likelihood �t are listed inall relevant momentum intervals. The �t error is essentially the statistical error. Thetotal systematic error, which is calculated from the quadratic sum of the three singlesystematic errors, is also given. In Figure 6 the K� and p=p fractions are shown andcompared to the JETSET 7.3 and HERWIG 5.6 models. The kaon fraction in the lowmomentum region is well represented by the JETSET model, while at higher momentathere is some indication of a higher kaon yield in the data. The proton fraction in theJETSET model is up to 15 % higher than in the data, while the HERWIG model is ingood agreement with the proton yield in the measured kinematical region.

The di�erential K� and p=p cross-sections were obtained by multiplying the measuredfraction with the total cross-section for charged particles. Figure 7 shows that the totalcharged spectrum is in excellent agreement with the predictions from JETSET 7.3. Thedi�erential cross-sections for K� and p=p are summarized in Table 5 as functions of xp

11

Inclusive Particle Fractions

Figure 6: The measured percentages of K� and p=p among all charged particles are shownwith their total errors.

Momentum < P > Kaon Fit Systematic ErrorsInterval [GeV/c] [GeV/c] Fraction [%] Error E�. Angle Shape Total

0.8 - 1.1 0.95 7.5 �0:14 �0:4 < 0:1 � �0:41.1 - 1.4 1.25 9.3 �0:24 �0:4 < 0:1 � �0:41.4 - 1.7 1.55 10.2 �0:29 �0:5 < 0:1 � �0:51.7 - 2.0 1.85 11.1 �0:32 �0:6 < 0:3 < 0:5 �0:82.0 - 2.5 2.25 12.3 �0:35 �0:6 �0:5 < 0:5 �0:92.5 - 3.0 2.75 13.5 �0:40 �0:6 �1:1 �0:7 �1:43.0 - 3.5 3.25 14.3 �0:48 �0:6 �1:9 �1:5 �2:53.5 - 4.0 3.75 15.9 �0:60 �0:8 �3:0 �2:3 �3:910 - 12 11.0 22.9 �1:5 �5:5 < 0:5 - �5:512 - 14 13.0 28.4 �0:5 �2:1 < 0:5 - �2:214 - 16 15.0 27.4 �0:7 �2:2 �0:7 - �2:316 - 18 17.0 28.2 �0:9 �1:5 �1:5 - �2:118 - 20 19.0 31.3 �1:1 �1:6 �2:2 - �2:720 - 23 21.5 30.3 �1:2 �1:6 �3:0 - �3:4

Table 3: Inclusive kaon percentages and their errors measured in the liquid (low momenta)and in the gas (high momenta).

12

Momentum < P > Proton Fit Systematic ErrorsInterval [GeV/c] [GeV/c] Fraction [%] Error E�. Angle Shape Total

1.4 - 1.7 1.55 5.3 �0:20 �0:8 < 0:1 � �0:81.7 - 2.0 1.85 5.8 �0:22 �0:4 < 0:1 � �0:42.0 - 2.5 2.25 6.5 �0:25 �0:3 �0:1 � �0:32.5 - 3.0 2.75 6.8 �0:25 �0:3 �0:1 < 0:1 �0:33.0 - 3.5 3.25 7.0 �0:25 �0:4 �0:1 �0:4 �0:63.5 - 4.0 3.75 7.1 �0:27 �0:4 �0:1 �0:3 �0:54.0 - 4.5 4.25 8.0 �0:30 �0:4 �0:7 �2:0 �2:24.5 - 5.0 4.75 9.9 �0:38 �0:5 �1:3 �2:5 �2:9

Table 4: Inclusive proton percentages and their errors measured in the liquid.

and momentum, P . The mean K� multiplicity per hadronic event was evaluated usinga �t through the data in the range of 0:018 < xp < 0:5 which corresponds to 79 % ofthe full integral. In the unmeasured region the kaon fraction was extrapolated using theJETSET prediction. This leads to a mean multiplicity per Z0 decay of:

< NK� >= 2:26 � 0:01 (stat:) � 0:16 (sys:) � 0:09 (extrapol:) (6)

The error is split in 3 parts: statistical error, systematic error from the measurementand a systematic error from the extrapolation which was assumed to be � 20%. For thep=p the measured range of 0:031 < xp < 0:11 covers only � 50% of the full integral.In the measured region alone the multiplicity is � 10:5% lower than in JETSET. Theextrapolation to the full xp range assuming a total production which is 10.5% lower thanJETSET leads to a value of:

< Np=p >= 1:07 � 0:01 (stat:) � 0:05 (sys:) � 0:13 (extrapol:) (7)

The results are consistent with a measurement from the OPAL collaboration [9], wherethe �� , K� and p=p yields were obtained from an energy loss measurement in the OPALjet chamber. By overlaying the p=p measurements from DELPHI, the proton yield isdetermined over the full kinematical range. Both measurements see a lower p=p yield,than given by JETSET 7.3.

QCD calculations within the framework of the Modi�ed Leading Logarithm Approxi-mation (MLLA) and Local Parton Hadron Duality (LPHD) make predictions of inclusivehadronic spectra in � = ln(1=xp) [2]. The calculation predicts that the momentum frac-tion distribution has the form of a \humped-backed-plateau", which is approximatelyGaussian in � [11]. In order to compare the MLLA predictions with the data, the datacan be �tted with a simple Gaussian in the peak region only or with a distorted Gaussianover the entire spectrum, as proposed in [12]. The formula for the distorted gaussianused was

D(N;< � >; �; �; s; k) =N

�p2�

exp(1

8k � 1

2s� � 1

4(2 + k)�2 +

1

6s�3 +

1

24k�4) (8)

where N is an overall normalization factor, � = ��<�>�

with < � > being the peak positionin leading order, � is the width, s the skewness and k the kurtosis of the distribution.

In Figure 8 the measured distributions 1�had

d�d�

for K� and p=p are shown. The maxima

(��) of the distributions were determined to be 2:63 � 0:07 and 2:96 � 0:16 for K� andp=p respectively. The kaon distribution was �tted with a distorted Gaussian function. AGaussian function was used to determine the ��-value for the proton distribution.

13

Figure 7: Di�erential cross-sections for inclusive K� and p=p production as functionsof normalized momentum xp. Points are measured values, also showing errors, lines arepredictions of the JETSET 7.3 model.

14

Momentum< xp >

1�had

d�Kdxp

1�had

d�KdP

[GeV/c]�1 1�had

d�pdxp

1�had

d�pdP

[GeV/c]�1[GeV/c]

0.8 - 1.1 0.021 23.9 � 1.27 0:524 � 0:0281.1 - 1.4 0.028 22.8 � 1.23 0:500 � 0:0271.4 - 1.7 0.034 19.1 � 1.13 0:419 � 0:025 10.0 � 1.50 0:219 � 0:0331.7 - 2.0 0.041 16.7 � 1.36 0:366 � 0:030 8.69 � 0.76 0:191 � 0:0172.0 - 2.5 0.050 14.5 � 1.18 0:318 � 0:026 7.63 � 0.47 0:167 � 0:0102.5 - 3.0 0.061 12.1 � 1.35 0:265 � 0:030 6.06 � 0.36 0:133 � 0:0083.0 - 3.5 0.072 10.0 � 1.82 0:219 � 0:040 4.91 � 0.45 0:108 � 0:0103.5 - 4.0 0.083 8.8 � 2.16 0:193 � 0:047 3.95 � 0.33 0:087 � 0:0074.0 - 4.5 0.094 3.60 � 0.99 0:079 � 0:0224.5 - 5.0 0.106 3.66 � 1.07 0:080 � 0:02310 - 12 0.241 1.833 � 0.456 0:0402 � 0:010012 - 14 0.285 1.483 � 0.115 0:0325 � 0:002514 - 16 0.329 0.960 � 0.084 0:0211 � 0:001816 - 18 0.373 0.663 � 0.054 0:0145 � 0:001218 - 20 0.417 0.507 � 0.047 0:0111 � 0:001020 - 23 0.471 0.303 � 0.036 0:0067 � 0:0008

Table 5: K� and p=p cross-sections depending on xp and P .

The peak values from single particle distributions and their dependence on the hadronmass are of interest. In the framework of MLLA+LPHD smaller peak values are expectedfor more massive particles [15]. A complete list of the measured ��-values with their errorsis given in Table 6. Most ��-values were directly taken from the references given in thelast column, for the rows marked with an \*" the �t of the �-distribution, determiningthe ��-value, was carried out in the presented analysis. The errors contain the quadraticsum of the statistical error from the �t and the systematic error from variations of the �tconditions. The data indicate a di�erent mass dependence of �� for mesons and baryons.Figure 9 shows the measured ��-position for K� and p=p combined with various othermeasurements at LEP.

At LEP energies the majority of the observed hadrons come from secondary decaysof heavier primary hadrons. Using the latest (1994) DELPHI tuning of the JETSET7.3 model, which generally reproduces well the known particle spectra, the in uence ofparticle decays on the observed ��-positions was estimated. This was done by comparingthe peak values with and without inhibiting all particles decays. The quantity ���decays,de�ned in equation 9, was added to the measured ��-values.

��prim = �� +���decays (9)

In Figure 10 (a) the corrected ��prim-positions for primary hadrons are shown. The fullline is a �t proportional to � log(Mhadron) which describes the data satisfactorily. Inthe MLLA calculations the peak position moves linearly with � log(Q0

�) [17] with Q0

being the cut-o� parameter in the parton cascade and � an e�ective QCD scale. Q0 isrelated to the hadron mass, where the most simple approach is Q0 � Mhadron [2], thusleading to a linear dependence between ��prim and � log(Mhadron). The errors on the decaycorrections (���decays) were estimated through variation of relevant JETSET parametersand are typically 10-20% of the applied correction. Figure 10 (b) shows that the decaycorrections vary quantitatively for the di�erent particle species and are relatively largefor K�, K0 and K�0. The corrected ��prim-values show a smooth decrease with increasing

15

hadron mass, which is in good agreement with the expectation of the MLLA+LPHDmodel (Figure 10).

Particle �� ���decays Fit Function Experiment Reference

�0 3.96 � 0.13 -0.22 limited spectrum L3 [18]�� 3.81 � 0.02

-0.22OPAL [9]

�� 3.78 � 0.02 Gaussian ALEPH [20]

K� 2.70 � 0.09 Gaussian ALEPH [20]K� 2.63 � 0.07

0.54distorted Gaussian * DELPHI this paper

K� 2.63 � 0.04 OPAL [9]

K0 2.65 � 0.05 distorted Gaussian * ALEPH [19]K0 2.57 � 0.08

0.41distorted Gaussian * DELPHI [13]

K0 2.89 � 0.05 limited spectrum L3 [18]K0 2.77 � 0.05 distorted Gaussian * OPAL [21]� 2.52 � 0.10 0.13 limited spectrum L3 [18]

K�0 2.51 � 0.20 0.58 Gaussian OPAL [22]p=p 2.85 � 0.18 Gaussian ALEPH [20]p=p 2.96 � 0.16 0.11 Gaussian * DELPHI this paperp=p 3.00 � 0.09 OPAL [9]�0 2.87 � 0.13 distorted Gaussian * ALEPH [19]�0 2.79 � 0.06

0.18distorted Gaussian * DELPHI [14]

�0 2.83 � 0.13 limited spectrum L3 [18]�0 2.77 � 0.05 Gaussian OPAL [23]�� 2.60 � 0.16

0.16Gaussian * DELPHI [16]

�� 2.57 � 0.11 Gaussian OPAL [23]

Table 6: Position of the maximum in the �-distribution and their decay corrections(���decays) for di�erent particles measured at LEP.

6 Summary and Conclusion

In the present paper the measurements of the Cherenkov angles in two radiator media(gas and liquid) were used for the identi�cation of charged particles. The di�erentialcross-sections for the production of K� and p=p were measured as a function of xp (xp =P=P beam) in the kinematical regions:

K� 0:018 < xp < 0:078 and 0:22 < xp < 0:50p=p 0:031 < xp < 0:11

The average K� and p=p multiplicities per hadronic event were determined to be: NK =2:26�0:18 and Np = 1:07�0:14. Compared to the measurements, the JETSET model forthe K� spectrum is a little softer at high momenta and the p=p rate is 10.5 % higher in themeasured momentum region. The measured spectra are in agreement with measurementsfrom OPAL [9] and ALEPH [20].

The di�erential cross-sections as a function of � (� = ln(1=xp)) are approximatelyGaussian shaped. The maxima �� of the measured distributions are: ��K = 2:63 � 0:07and ��p = 2:96� 0:16.

The measured �-distributions for various identi�ed particles indicate a di�erent massdependence of �� for mesons and baryons. The di�erences between mesons and baryons

16

(a) K� (b) p=p

Figure 8: Kaon and proton � distributions (� = ln(1=xp)). The full curves show the �tthrough the data.

DELPHI

L3

OPAL

ALEPH

Figure 9: The maximum �� of the �-distribution is shown as function of the particlemass. The full lines are separated �ts for the meson and baryon distribution with�� / � log(Mhadron).

17

DELPHI

L3

OPAL

ALEPH

Figure 10: The maximum ��prim of the � distribution for primary hadrons is shown asfunction of the particle mass. The full line is a �t ��prim / � log(Mhadron) through thedata points. The peak position is corrected for shifts coming from particle decays usingthe JETSET 7.3 model (1994 DELPHI tuning). The errors drawn do not include anycontribution for the decay corrections. Figure (b) shows the size of the applied decaycorrection.

18

can be explained by shifts in the ��-values due to particle decays which were extractedusing the JETSET model. The observed mass dependence for the corrected ��prim-valuesis in agreement with the prediction of the MLLA+LPHD model.

Acknowledgements

We are greatly indebted to our technical collaborators and to the funding agencies fortheir support in building and operating the DELPHI detector, and to the members ofthe CERN-SL Division for the excellent performance of the LEP collider.

19

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