Digital Object Identifier (DOI) 10.1140/epjc/s2002-01111-5Eur. Phys. J. C 26, 505–525 (2003) THE EUROPEAN

PHYSICAL JOURNAL C

Search for an LSP gluino at LEP with the DELPHI detectorThe DELPHI Collaboration

J. Abdallah24, P. Abreu22, W. Adam50, P. Adzic11, T. Albrecht17, T. Alderweireld2, R. Alemany-Fernandez8,T. Allmendinger17, P.P. Allport23, U. Amaldi28, N. Amapane44, S. Amato47, E. Anashkin35, A. Andreazza27,S. Andringa22, N. Anjos22, P. Antilogus26, W-D. Apel17, Y. Arnoud14, S. Ask25, B. Asman43, J.E. Augustin24,A. Augustinus8, P. Baillon8, A. Ballestrero45, P. Bambade20, R. Barbier26, D. Bardin16, G. Barker17, A. Baroncelli38,M. Battaglia8, M. Baubillier24, K-H. Becks52, M. Begalli6, A. Behrmann52, E. Ben-Haim20, N. Benekos31, A. Benvenuti5,C. Berat14, M. Berggren24, L. Berntzon43, D. Bertrand2, M. Besancon39, N. Besson39, D. Bloch9, M. Blom30, M. Bluj51,M. Bonesini28, M. Boonekamp39, P.S.L. Booth23, G. Borisov21, O. Botner48, B. Bouquet20, T.J.V. Bowcock23,I. Boyko16, M. Bracko42, R. Brenner48, E. Brodet34, P. Bruckman18, J.M. Brunet7, L. Bugge32, P. Buschmann52,M. Calvi28, T. Camporesi8, V. Canale37, F. Carena8, N. Castro22, F. Cavallo5, M. Chapkin41, Ph. Charpentier8,P. Checchia35, R. Chierici8, P. Chliapnikov41, J. Chudoba8, S.U. Chung8, K. Cieslik18, P. Collins8, R. Contri13,G. Cosme20, F. Cossutti46, M.J. Costa49, B. Crawley1, D. Crennell36, J. Cuevas33, J. D’Hondt2, J. Dalmau43,T. da Silva47, W. Da Silva24, G. Della Ricca46, A. De Angelis46, W. De Boer17, C. De Clercq2, B. De Lotto46,N. De Maria44, A. De Min35, L. de Paula47, L. Di Ciaccio37, A. Di Simone38, K. Doroba51, J. Drees52,8, M. Dris31,G. Eigen4, T. Ekelof48, M. Ellert48, M. Elsing8, M.C. Espirito Santo8, G. Fanourakis11, D. Fassouliotis11,3, M. Feindt17,J. Fernandez40, A. Ferrer49, F. Ferro13, U. Flagmeyer52, H. Foeth8, E. Fokitis31, F. Fulda-Quenzer20, J. Fuster49,M. Gandelman47, C. Garcia49, Ph. Gavillet8, E. Gazis31, T. Geralis11, R. Gokieli8,51, B. Golob42, G. Gomez-Ceballos40,P. Goncalves22, E. Graziani38, G. Grosdidier20, K. Grzelak51, J. Guy36, C. Haag17, A. Hallgren48, K. Hamacher52,K. Hamilton34, J. Hansen32, S. Haug32, F. Hauler17, V. Hedberg25, M. Hennecke17, H. Herr8, J. Hoffman51,S-O. Holmgren43, P.J. Holt8, M.A. Houlden23, K. Hultqvist43, J.N. Jackson23, G. Jarlskog25, P. Jarry39, D. Jeans34,E.K. Johansson43, P.D. Johansson43, P. Jonsson26, C. Joram8, L. Jungermann17, F. Kapusta24, S. Katsanevas26,E. Katsoufis31, G. Kernel42, B.P. Kersevan8,42, A. Kiiskinen15, B.T. King23, N.J. Kjaer8, P. Kluit30, P. Kokkinias11,C. Kourkoumelis3, O. Kouznetsov16, Z. Krumstein16, M. Kucharczyk18, J. Lamsa1, G. Leder50, F. Ledroit14,L. Leinonen43, R. Leitner29, J. Lemonne2, V. Lepeltier20, T. Lesiak18, W. Liebig52, D. Liko50, A. Lipniacka43,J.H. Lopes47, J.M. Lopez33, D. Loukas11, P. Lutz39, L. Lyons34, J. MacNaughton50, A. Malek52, S. Maltezos31,F. Mandl50, J. Marco40, R. Marco40, B. Marechal47, M. Margoni35, J-C. Marin8, C. Mariotti8, A. Markou11,C. Martinez-Rivero40, J. Masik12, N. Mastroyiannopoulos11, F. Matorras40, C. Matteuzzi28, F. Mazzucato35,M. Mazzucato35, R. Mc Nulty23, C. Meroni27, W.T. Meyer1, E. Migliore44, W. Mitaroff50, U. Mjoernmark25, T. Moa43,M. Moch17, K. Moenig8,10, R. Monge13, J. Montenegro30, D. Moraes47, S. Moreno22, P. Morettini13, U. Mueller52,K. Muenich52, M. Mulders30, L. Mundim6, W. Murray36, B. Muryn19, G. Myatt34, T. Myklebust32, M. Nassiakou11,F. Navarria5, K. Nawrocki51, R. Nicolaidou39, M. Nikolenko16,9, A. Oblakowska-Mucha19, V. Obraztsov41,A. Olshevski16, A. Onofre22, R. Orava15, K. Osterberg15, A. Ouraou39, A. Oyanguren49, M. Paganoni28, S. Paiano5,J.P. Palacios23, H. Palka18, Th.D. Papadopoulou31, L. Pape8, C. Parkes23, F. Parodi13, U. Parzefall8, A. Passeri38,O. Passon52, L. Peralta22, V. Perepelitsa49, A. Perrotta5, A. Petrolini13, J. Piedra40, L. Pieri38, F. Pierre39,M. Pimenta22, E. Piotto8, T. Podobnik42, V. Poireau39, M.E. Pol6, G. Polok18, P. Poropat†46, V. Pozdniakov16,N. Pukhaeva2,16, A. Pullia28, J. Rames12, L. Ramler17, A. Read32, P. Rebecchi8, J. Rehn17, D. Reid30, R. Reinhardt52,P. Renton34, F. Richard20, J. Ridky12, M. Rivero40, D. Rodriguez40, A. Romero44, P. Ronchese35, E. Rosenberg1,P. Roudeau20, T. Rovelli5, V. Ruhlmann-Kleider39, D. Ryabtchikov41, A. Sadovsky16, L. Salmi15, J. Salt49, A. Savoy-Navarro24, U. Schwickerath8, A. Segar34, R. Sekulin36, M. Siebel52, A. Sisakian16, G. Smadja26, O. Smirnova25,A. Sokolov41, A. Sopczak21, R. Sosnowski51, T. Spassov8, M. Stanitzki17, A. Stocchi20, J. Strauss50, B. Stugu4,M. Szczekowski51, M. Szeptycka51, T. Szumlak19, T. Tabarelli28, A.C. Taffard23, F. Tegenfeldt48, J. Timmermans30,L. Tkatchev16, M. Tobin23, S. Todorovova12, A. Tomaradze8, B. Tome22, A. Tonazzo28, P. Tortosa49, P. Travnicek12,D. Treille8, G. Tristram7, M. Trochimczuk51, C. Troncon27, M-L. Turluer39, I.A. Tyapkin16, P. Tyapkin16,S. Tzamarias11, V. Uvarov41, G. Valenti5, P. Van Dam30, J. Van Eldik8, A. Van Lysebetten2, N. van Remortel2,I. Van Vulpen30, G. Vegni27, F. Veloso22, W. Venus36, F. Verbeure2, P. Verdier26, V. Verzi37, D. Vilanova39, L. Vitale46,V. Vrba12, H. Wahlen52, A.J. Washbrook23, C. Weiser17, D. Wicke8, J. Wickens2, G. Wilkinson34, M. Winter9,M. Witek18, O. Yushchenko41, A. Zalewska18, P. Zalewski51, D. Zavrtanik42, N.I. Zimin16, A. Zintchenko16, M. Zupan11

506 The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector

1 Department of Physics and Astronomy, Iowa State University, Ames, IA 50011-3160, USA2 Physics Department, Universiteit Antwerpen, Universiteitsplein 1, 2610 Antwerpen, Belgium

and IIHE, ULB-VUB, Pleinlaan 2, 1050 Brussels, Belgiumand Faculte des Sciences, Univ. de l’Etat Mons, Av. Maistriau 19, 7000 Mons, Belgium

3 Physics Laboratory, University of Athens, Solonos Str. 104, 10680 Athens, Greece4 Department of Physics, University of Bergen, Allegaten 55, 5007 Bergen, Norway5 Dipartimento di Fisica, Universita di Bologna and INFN, Via Irnerio 46, 40126 Bologna, Italy6 Centro Brasileiro de Pesquisas Fısicas, rua Xavier Sigaud 150, 22290 Rio de Janeiro, Brazil

and Depto. de Fısica, Pont. Univ. Catolica, C.P. 38071 22453 Rio de Janeiro, Braziland Inst. de Fısica, Univ. Estadual do Rio de Janeiro, rua Sao Francisco Xavier 524, Rio de Janeiro, Brazil

7 College de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, 75231 Paris Cedex 05, France8 CERN, 1211 Geneva 23, Switzerland9 Institut de Recherches Subatomiques, IN2P3 - CNRS/ULP - BP20, 67037 Strasbourg Cedex, France

10 Now at DESY-Zeuthen, Platanenallee 6, 15735 Zeuthen, Germany11 Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, 15310 Athens, Greece12 FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, 180 40, Praha 8, Czech Republic13 Dipartimento di Fisica, Universita di Genova and INFN, Via Dodecaneso 33, 16146 Genova, Italy14 Institut des Sciences Nucleaires, IN2P3-CNRS, Universite de Grenoble 1, 38026 Grenoble Cedex, France15 Helsinki Institute of Physics, HIP, P.O. Box 9, 00014 Helsinki, Finland16 Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, 101 000 Moscow, Russian Federation17 Institut fur Experimentelle Kernphysik, Universitat Karlsruhe, Postfach 6980, 76128 Karlsruhe, Germany18 Institute of Nuclear Physics,Ul. Kawiory 26a, 30055 Krakow, Poland19 Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, 30055 Krakow, Poland20 Universite de Paris-Sud, Lab. de l’Accelerateur Lineaire, IN2P3-CNRS, Bat. 200, 91405 Orsay Cedex, France21 School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK22 LIP, IST, FCUL - Av. Elias Garcia, 14-1o, 1000 Lisboa Codex, Portugal23 Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK24 LPNHE, IN2P3-CNRS, Univ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, 75252 Paris Cedex 05, France25 Department of Physics, University of Lund, Solvegatan 14, 223 63 Lund, Sweden26 Universite Claude Bernard de Lyon, IPNL, IN2P3-CNRS, 69622 Villeurbanne Cedex, France27 Dipartimento di Fisica, Universita di Milano and INFN-MILANO, Via Celoria 16, 20133 Milan, Italy28 Dipartimento di Fisica, Univ. di Milano-Bicocca and INFN-MILANO, Piazza della Scienza 2, 20126 Milan, Italy29 IPNP of MFF, Charles Univ., Areal MFF, V Holesovickach 2, 180 00, Praha 8, Czech Republic30 NIKHEF, Postbus 41882, 1009 DB Amsterdam, The Netherlands31 National Technical University, Physics Department, Zografou Campus, 15773 Athens, Greece32 Physics Department, University of Oslo, Blindern, 0316 Oslo, Norway33 Dpto. Fisica, Univ. Oviedo, Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain34 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK35 Dipartimento di Fisica, Universita di Padova and INFN, Via Marzolo 8, 35131 Padua, Italy36 Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK37 Dipartimento di Fisica, Universita di Roma II and INFN, Tor Vergata, 00173 Rome, Italy38 Dipartimento di Fisica, Universita di Roma III and INFN, Via della Vasca Navale 84, 00146 Rome, Italy39 DAPNIA/Service de Physique des Particules, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France40 Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, 39006 Santander, Spain41 Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation42 J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia and Laboratory for Astroparticle Physics,

Nova Gorica Polytechnic, Kostanjeviska 16a, 5000 Nova Gorica, Slovenia,and Department of Physics, University of Ljubljana, 1000 Ljubljana, Slovenia

43 Fysikum, Stockholm University, Box 6730, 113 85 Stockholm, Sweden44 Dipartimento di Fisica Sperimentale, Universita di Torino and INFN, Via P. Giuria 1, 10125 Turin, Italy45 INFN,Sezione di Torino, and Dipartimento di Fisica Teorica, Universita di Torino, Via P. Giuria 1, 10125 Turin, Italy46 Dipartimento di Fisica, Universita di Trieste and INFN, Via A. Valerio 2, 34127 Trieste, Italy

and Istituto di Fisica, Universita di Udine, 33100 Udine, Italy47 Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundao 21945-970 Rio de Janeiro, Brazil48 Department of Radiation Sciences, University of Uppsala, P.O. Box 535, 751 21 Uppsala, Sweden49 IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, 46100 Burjassot (Valencia), Spain50 Institut fur Hochenergiephysik, Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, 1050 Vienna, Austria51 Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, 00681 Warsaw, Poland52 Fachbereich Physik, University of Wuppertal, Postfach 100 127, 42097 Wuppertal, Germany† deceased

The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector 507

Received: 6 November 2002 /Published online: 15 January 2003 – c© Springer-Verlag / Societa Italiana di Fisica 2003

Abstract. In some supersymmetric models, the gluino (g) is predicted to be light and stable. In thatcase, it would hadronize to form R-hadrons. In these models, the missing energy signature of the lightestsupersymmetric particle is no longer valid, even if R-parity is conserved. Therefore, such a gluino is notconstrained by hadron collider results, which looked for the decay g → qqχ0

1.Data collected by the DELPHI detector in 1994 at 91.2 GeV have been analysed to search for qqggevents. No deviation from Standard Model predictions is observed and a gluino mass between 2 and18 GeV/c2 is excluded at the 95% confidence level in these models. Then, R-hadrons produced in thesquark decays were searched for in the data collected by DELPHI at the centre-of-mass energies of 189 to208 GeV, corresponding to an overall integrated luminosity of 609 pb−1. The observed number of eventsis in agreement with the Standard Model predictions. Limits at 95% confidence level are derived on thesquark masses from the excluded regions in the plane (mq1 ,mg):

mt1 > 90 GeV/c2, and mb1> 96 GeV/c2 for purely left squarks.

mt1 > 87 GeV/c2, and mb1> 82 GeV/c2 independent of the mixing angle.

1 Introduction

In minimal supergravity supersymmetry models(mSUGRA), the gaugino masses (Mi) are usually sup-posed to evolve from a common value m1/2 at the GUTscale. In such models, the Mi are proportional to the cor-responding coupling constants (gi) and the gluino is nat-urally heavier than the other gauginos at the electroweakscale.

M1

g21

=M2

g22

=M3

g23

that is, M1 : M2 : M3 ∼ 1 : 2 : 7

Nevertheless, models exist where the Mi do not followthis relation. M3 could be lighter than the other gaug-ino masses [1], and in this case, the gluino is the Light-est Supersymmetric Particle (LSP). For example there isa particular Gauge Mediated Supersymmetry Breakingmodel (GMSB) [2] where the gluino can either be the LSPor the next to lightest supersymmetric particle (NLSP)with a gravitino LSP. In the latter case, the lifetime ofthe gluino would ever be sufficiently large to consider thegluino as a stable particle for collider physic. If R-parityis assumed, the gluino is stable in all these models andit should hadronize to form R-hadrons because of colorconfinement.

The gluino has been intensively searched for in hadroncollisions in various decay channels [3]. However, the limitobtained (mg > 173 GeV/c2 for mg = mq) does not applyto a stable gluino. For this model, it has been shown thatCDF run I data could not constrain a stable gluino withmass lower than 35 GeV/c2[1,2]. On the other hand, thegluino mass could be much larger than it is in the so-calledlight gluino scenario [4], which seems to be excluded bythe measurement of the triple gluon coupling and of thefour-jet rates at LEP [5].

A pair of gluinos can be produced in the splitting ofa gluon. Figure 1 shows the Feynman diagram of thisprocess and the corresponding cross-sections at centre-of-mass energies of 91.2 GeV (LEP1) and of 200 GeV(LEP2). The production rate is too low at LEP2, andLEP1 data must be analysed to be sensitive to this pro-cess. In this channel, the gluino does not originate from

the decay of another sparticle, so it can be produced evenif the other supersymmetric particles are not accessible.

Gluinos can also be produced from other sparticle de-cays. qL and qR are the supersymmetric partners of theleft-handed and right handed quarks. With large Yukawacoupling running and important off-diagonal terms thesupersymmetric partners of top and bottom quarks arethe most probable candidates for the charged lightest su-persymmetric particle. The squark mass eigenstates areparametrised by a mixing angle θq. The lighter squark isgiven by q1 = qL sin θq + qR cos θq. The stop (t1) and thesbottom (b1) could be pair-produced at LEP via e+e−annihilation into Z0/γ. A squark mixing angle equal tozero leads to the maximal squark pair production cross-section, while the minimal cross-sections are obtained fora mixing angle of 56◦ for the stop and of 68◦ for the sbot-tom. For these particular angles, the Z0 − q1 − ¯q1 cou-pling is suppressed. This paper also describes the searchfor R-hadrons from stop and sbottom decays at LEP2.The dominant decay of the stop and of the sbottom aret1 → cg and b1 → bg [6] when the gluino is lighterthan the squarks, as in the stable gluino scenario. Thebranching ratios of these decay channels were taken to be100%. Figure 2 shows the squark production and decaydiagrams.

DELPHI data collected in 1994 at a centre-of-massenergy of 91.2 GeV were used to search for the processe+e− → qqgg. Then, stop and sbottom squarks weresearched for in DELPHI data collected from 1998 to 2000at centre-of-mass energies ranging from 189 to 208 GeV.The three analyses presented in this paper are thereforesearches for:

e+e− → qqg → qqgge+e− → t1¯t1 → cgcge+e− → b1

¯b1 → bgbg

all giving the same topology of two standard jets plus twogluino jets. The gluino could either fragment to neutralR◦ states (gg, guu,...) or to charged R± states (gud,...). IfP is the probability that a gluino fragments to a charged

508 The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector

Fig. 1. a Gluon splitting into a pair of gluinos. b Compari-son of the cross-section (pb) of this process at centre-of-massenergies of 91.2 GeV (LEP1) and of 200 GeV (LEP2)

e+

e−

γ,Z0

¯t1

t1

c

g

c

g

e+

e−

γ,Z0

¯b1

b1

b

g

b

ga b

Fig. 2a,b. Stop a and sbottom b production and decay atLEP2

R-hadron, then for P = 1, R-hadrons are identified by ananomalous ionizing energy loss in the tracking chambers,and for P = 0, the gluino hadronizes into neutral stateswhich reach the calorimeters where they deposit a part oftheir energy. The missing energy carried away by the LSPis reduced compared with usual SUSY models with R-parity conservation. For neutral R-hadrons, the estimateof the experimental sensitivity depends on the model usedto calculate the energy loss in the calorimeters.

2 The DELPHI detector

The description of the DELPHI detector and its perfor-mance can be found in references [7,8]. We only summarizehere the parts relevant to the analysis.

Charged particles are reconstructed in a 1.2 T mag-netic field by a system of cylindrical tracking detectors.The closest to the beam is the Vertex Detector (VD) whichconsists of three cylindrical layers of silicon detectors atradii 6.3 cm, 9.0 cm and 11.0 cm. They measure coor-

dinates in the Rφ plane1. In addition, the inner and theouter layers are double-sided giving also a z measurement.VD is the barrel part of the Silicon Tracker (ST), whichextends the polar angle acceptance down to 10 degrees.The Inner Detector (ID) is a drift chamber with inner ra-dius 12 cm and outer radius 22 cm covering polar anglesbetween 15◦ and 165◦. The principal tracking detector ofDELPHI is the Time Projection Chamber (TPC). It is acylinder of 30 cm inner radius, 122 cm outer radius and2.7 m length. Each end-plate is divided into 6 sectors, with192 sense wires to allow the dE/dx measurement, and with16 circular pad rows which provide 3-dimensional trackreconstruction. The TPC covers polar angles from 20◦ to160◦. Finally, the Outer Detector (OD) consists of driftcells at radii between 192 cm and 208 cm, covering polarangles between 43◦ and 137◦. In addition, two planes ofdrift chambers perpendicular to the beam axis (ForwardChambers A and B) are installed in the endcaps coveringpolar angles 11◦ < θ < 33◦ and 147◦ < θ < 169◦.

The electromagnetic calorimeters are the High densityProjection Chamber (HPC) in the barrel region (40◦ <θ < 140◦) and the Forward Electromagnetic Calorime-ter (FEMC) in the endcaps (11◦ < θ < 36◦ and 144◦ <θ < 169◦). In the forward and backward regions, theScintillator TIle Calorimeter (STIC) extends the coveragedown to 1.66◦ from the beam axis. The number of radi-ation lengths are respectively 18, 20 and 27 in the HPC,the FEMC and the STIC. In the gap between the HPCand the FEMC, hermeticity taggers made of single layerscintillator-lead counters are used to veto events with elec-tromagnetic particles which would otherwise escape detec-tion. Between the HPC modules, gaps at θ = 90◦ and gapsin φ are also instrumented with such taggers. Finally, thehadron calorimeter (HCAL) covers polar angle between11◦ < θ < 169◦. The iron thickness in the HCAL is 110 cmwhich corresponds to 6.6 nuclear interaction lengths.

3 Data and Monte Carlo samples

The total integrated luminosity collected by the DELPHIdetector in 1994 at the Z0 peak (

√s = 91.2 GeV) was

46 pb−1. It corresponded to around 1.6 million hadronicZ0 events. The Standard Model hadronic background wasestimated with the JETSET 7.3 [9] program tuned to re-produce LEP1 data [10]. The program described in [1] wasused to simulate the e+e− → qqgg signal.

At LEP2, the total integrated luminosity collected bythe DELPHI detector at centre-of-mass energies from 189to 208 GeV was 609 pb−1. In September 2000, one ofthe twelve TPC sectors (sector 6) stopped functioning.About 60 pb−1 of data were collected without that sec-tor until the end of the data taking. The reconstructionprograms were modified to allow the analysis of the datataken with the DELPHI TPC not fully operational. Af-ter this modification, there was only a small degradation

1 The DELPHI coordinate system is defined with z along thee− beam direction; θ and φ are the polar and azimuthal anglesand R is the radial distance from the z axis

The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector 509

Table 1. Total integrated luminosity as a function of thecentre-of-mass energy of the LEP2 analysed data samples. Thethird column shows the centre-of-mass energy of the simulatedevents. (*) indicates the data collected by DELPHI in 2000without the sector 6 of the TPC

Year 〈√s〉 (GeV)√

s (GeV) Integrated luminosityData Simulated MC (pb−1)

1998 188.6 189 158.01999 191.6 192 25.9

195.6 196 76.4199.6 200 83.4201.6 202 40.6

2000 204.8 204 78.1206.6 206 78.5208.1 208 7.3

2000(*) 206.5 206.7 60.6

of the performance of the tracking. The data collected inyear 2000 were divided in centre-of-mass energy windowsto optimize the analysis sensitivity. Table 1 summarizesthe LEP2 data samples used in the analysis.

The e+e− interactions leading to four-fermion finalstates were generated using EXCALIBUR [11]. GRC4F[12] was used to simulate the processes e+e− → eνqqand e+e− → Zoee with electrons emitted at polar an-gles lower than the cut imposed in EXCALIBUR. Thetwo-fermion final states were generated with PYTHIA [9]for e+e− → qq(nγ), KORALZ [13] for e+e− → τ+τ−(γ),e+e− → µ+µ−(γ), e+e− → νν(γ), and BHWIDE [14] fore+e− → e+e−(γ). PYTHIA 6.143 [15] was used to simulateγγ interactions leading to hadronic final states. BDKRC[16] was used for γγ interactions leading to leptonic finalstates. In all cases, the final hadronization of the particleswas performed with JETSET [9].

The flavour changing decay t1 → cg goes through one-loop diagrams. Therefore, t1 is expected to be long-livedand to hadronize before its decay. A modified version ofthe SUSYGEN [17] generator was used to simulate thisprocess. Special care was taken to introduce hard gluonradiation off the scalar stop at the matrix-element leveland to treat the stop hadronization as a non-perturbativestrong interaction effect. A detailed description of thishadronization model can be found in [18]. Such a model,based on the Peterson function [19], was also used to per-form the gluino hadronization into R-hadrons. SUSYGENhas also been modified to perform the sbottom decay intobg. Figure 3 summarizes the stop and sbottom productionand the fragmentation steps. The final hadronization wasperformed using JETSET [9].

The Monte Carlo samples used to simulate the Stan-dard Model processes and the supersymmetric signalswere passed through DELSIM [20], the program simulat-ing the full DELPHI detector response. They were subse-quently processed with the same reconstruction programas the real data. The number of generated events was al-ways several times higher than the number expected forthe integrated luminosity collected.

t∼

1

t∼−

1

g∼

g∼

g

g

gg

u−

u−

u

u

c

c−

u−

u

Ro

Ro

t∼

1

t∼−

1

g∼

g∼

g

g

gg

u−

u−

u

u

c

c−

u−

u

Ro

Ro

b∼

1

b∼−

1

g∼

b

g∼

b−

g

g

g

g

R0

R0

b∼

1

b∼−

1

g∼

b

g∼

b−

g

g

g

g

R0

R0

Fig. 3. Production and decay of the stop and sbottom squarks.Ellipses indicate the color singlet and the color string stretchedbetween the partons

4 R-hadron simulation

In the analysis, two generic R-hadron states were consid-ered: one charged denoted R± and one neutral, R◦, whichcorresponds to the glueballino, a gg state. It is importantto understand how an R◦ would manifest itself in the de-tector. We refer to the results of reference [1]. The energyloss in the scattering on a nucleon R◦N → R◦X is givenby:

∆E =m2

X − m2N + |t|

2mN

where |t| is the usual momentum transfer invariant forthe R◦ and mX is the mass of the system produced inthe R◦N → R◦X collision. The average energy loss in thereaction R◦N → R◦X is then given by:

〈∆E〉 =

∫ √s−mR◦

mNdmX

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d|t|dmX

where s = M2R◦ +m2

N +2γMR◦mN describes the collisionenergy. The following functions are defined:

γ = (1 − β2)−1/2

|t|min,max(mX) = 2[E(mN )E(mX) ∓ p(mN )p(mX) − M2R◦ ]

E(m) = (s + M2R◦ − m2)/(2

√s)

p(m) = λ1/2(s, M2R◦ , m2)/(2

√s)

λ(a, b, c) = a2 + b2 + c2 − 2(ab + ac + bc)

From the results of studies in [1], the differential cross-section dσ

d|t|dmXis taken as:

dσ

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{1, if |t| ≤ 1 GeV 2

0, if |t| > 1 GeV 2

The average number of collisions of an R◦ particle inthe calorimeters is given by the depth of the calorime-ter in units of equivalent iron interaction lengths, λT . InDELPHI, the electromagnetic calorimeter’s thickness rep-resents around 1 λT while this value is 6.6 λT for the

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hadronic calorimeter. We have adopted a correction factorfor the interaction length of 9/16 as suggested in reference[1]: a factor CA/CF = 9/4 comes from the colour octet na-ture of the R◦ constituents increasing the σR◦N cross-sec-tion as compared to σπN , while a factor 〈r2

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takes into account the relative size of the R-hadrons ascompared to standard hadrons. On average, neutral R-hadrons should undergo 4.3 collisions in DELPHI calori-meters. Figure 4 shows the total energy loss by an R◦ after4 collisions in iron.

The difficulty in separating the signal of a neutral R-hadron from the background increases with the amountof energy lost in the calorimeters. The choice of the in-teraction model made here is conservative in this respect.The R◦ scatters were subsequently treated in the DEL-PHI detector simulation as K0

L with the energy that theR◦ should deposit in four collisions according to the aboveformula.

The charged R-hadrons were treated as heavy muonsto reproduce the anomalous dE/dx signature. In this case,only the tracking information was used to calculate the R-hadron momentum.

5 Particle identification and analysis method

5.1 Particle identification and event preselection

Particle selection was identical for LEP1 and LEP2 data.Reconstructed charged particles were required to have mo-menta above 100 MeV/c with ∆p/p < 1, where ∆p is themomentum error, and impact parameter below 5 cm in thetransverse plane and below 10 cm/ sin θ in the beam direc-tion. More stringent cuts were applied for tracks withoutTPC information. A cluster in the calorimeters was se-lected as a neutral particle if not associated to a chargedparticle and if the cluster energy was greater than 500 MeVin the HPC, 400 MeV in the FEMC, 300 MeV in the STIC

or 900 MeV in the HAC. Particles were then clusteredinto jets with the DURHAM algorithm [21]. b-quarks weretagged using a probabilistic method based on the impactparameters of tracks with respect to the main vertex. Acombined b-tagging variable was defined by including theproperties of secondary vertices [22].

Events were then kept if there were at least two chargedparticles, and at least one with a transverse momentumabove 1.5 GeV/c, and if the transverse energy2 exceeded4 GeV.

5.2 Neural networks

A neural network allows one discriminating variable tobe constructed from the set of variables given as input.The form used here contains three layers of nodes: theinput layer where each neuron corresponds to a discrim-inating variable, the hidden layer, and the output layerwhich is the response of the neural network. The lay-ers were connected in a “feed forward” architecture. Theback-propagation algorithm was used to train the networkwith simulated events. This entails minimising a χ2 to ad-just the neurons’ weights and connections. An indepen-dent validation sample was also used not to overtrain thenetwork. The outputs of neural networks were used to iso-late events containing two neutral R-hadrons at LEP2.

5.3 General description of the analyses

The LEP1 and LEP2 data analyses have all the same finalstates which consists of two jets and two gluino jets. De-pending on the probability P that the gluino hadronizesinto a charged R-hadron, three topologies are possible:

– charged: e+e− → qqR±R±– mixed: e+e− → qqR±R◦– neutral: e+e− → qqR◦R◦

For LEP1 data, the search analyses corresponding tothe charged and the mixed topologies were identical, whilethey were optimised separately for LEP2 data. For thesetwo topologies, the LEP1 and LEP2 analyses were onlybased on anomalous ionizing energy loss, and no quarktagging was applied.

For the neutral topology, LEP1 data were analyzed us-ing sequential cuts without trying to tag the quark flavor.Since there are b-quarks in the final state of the sbottomdecay, the b-quark tagging improves the isolation of thissignal from the Standard Model backgrounds. Therefore,the b-tagging variable was used in the stop and sbottomsearch analyses at LEP2 in the neutral topology. This vari-able was included into the neural networks which wereused to isolate the stop and the sbottom signals.

2 The transverse energy is defined as the sum of√

p2T + m2

over all particles; pT is the transverse momentum

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6 Search for a stable gluino at LEP1

6.1 Search for qqR±R± and qqR±R◦ events

The same analysis based on the dE/dx measurement wasperformed to identify qqR±R± and qqR±R◦ events.

In the preselection step, events were required to con-tain at least 5 charged particles. At least one of these hadto satisfy the following conditions. The track was requiredto be reconstructed including a TPC track element andto have a momentum above 10 GeV/c. At least 80 wiresof the TPC were required to have been included in thedE/dx measurement. The dE/dx had to be either greater

than 1.8 mip (units of energy loss for a minimum ionizingparticle), or less than the dE/dx expected for a particle ofmass equal to 1 GeV/c2. The Y23 variable is the ycut valuein the DURHAM algorithm for which the number of jetschanges between two and three. qqR±R± and qqR±R◦events contain three or four jets. Thus, Y23 was requiredto be less than 0.01. Figure 5 shows a comparison betweensimulated and real data at this level.

A R± candidate had to satisfy the following conditions:it had to be reconstructed with the VD, the ID and theTPC detectors, and the dE/dx measurement had to bebased on at least 80 wires of the TPC. In addition, theenergy of the other particles in a 15◦ cone around the R±

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√s =200 GeV, while

the stars and the triangles correspond to R± tracks with massof 10 and 70 GeV/c2respectively. The dE/dx is expressed inunits of energy loss for a minimum ionizing particle

candidate had to be less than 2 GeV. Finally, its associatedelectromagnetic energy had to be less than 5 GeV.

The final selection was performed by cuts in the plane(P,dE/dx). Figure 6 shows the expected dE/dx as a func-tion of the particle momentum. The analysis was sepa-rated into two mass windows:

– mg < 14 GeV/c2:Here, charged R-hadrons were identified by low dE/dxvalues. The R± candidates were selected if their mo-mentum was greater than 15 GeV/c, and if their dE/dxwas less than the dE/dx expected for a particle of massequal to 3 GeV/c2.

– mg ≥ 14 GeV/c2:In this mass window, R-hadrons were identified by highdE/dx values. The R± candidates were selected if theirdE/dx was greater than 2 mip.

The final selection was performed by requiring at leastone charged R-hadron candidate in either mass window.Table 2 contains the number of events selected after eachcut of this analysis. For mg < 14 GeV/c2, 5 events wereselected when 4.2 were expected. These numbers are 12and 13.5 in the mg ≥ 14 GeV/c2 mass window. Unlike theexpected signal, all selected candidates in the data haveonly one particle with anomalous dE/dx. Figure 7 showsthe signal detection efficiencies. For qqR±R±, they rangedfrom a few percent for gluino masses close to 2 GeV/c2 toaround 50% for gluino masses of the order of 25 GeV/c2.qqR±R◦ efficiencies were about half of the qqR±R± ones.

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Table 2. Number of events selected after each cut of thecharged R-hadron analysis at LEP1

Data Z0 → qqbackground

anomalous dE/dx 99322 97170 ± 200Y23 24566 25794 ± 1041 R± candidate 421 464 ± 14

low dE/dx (mg< 14) 5 4.2 ± 1.3high dE/dx (mg≥ 14) 12 13.5 ± 2.4

Table 3. Number of events selected after each cut of theqqR◦R◦ analysis at LEP1

Data Z0 → qqbackground

Acolinearity 41231 34853 ± 120NTPC 38977 33807 ± 120%EV D−ID 36877 32419 ± 120E40/Evis 19309 15311 ± 80E20/Evis 16664 13480 ± 75Et 16317 13453 ± 75Mvis 5932 6353 ± 52| cos θthrust| 5384 5725 ± 49| cos θPmis| 2527 2294 ± 31Y23 214 194 ± 9Nchar. 183 161 ± 8Acoplanarity 134 115 ± 7Thrust 105 81.7 ± 5.9Acol. vs Mjet1/Ejet1 + Mjet2/Ejet2 12 10.6 ± 2.1

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6.2 Search for qqR◦R◦events

The search for qqR◦R◦ events was performed at LEP1with a sequential cut analysis. It was based on the searchfor the small part of missing energy carried away by theneutral R-hadrons. Hadronic events were first selected byrequiring at least 5 charged particles. After forcing theevents into two jets, the acollinearity3 was required to begreater than 20◦ to reduce the huge number of backgroundStandard Model Z0 → qq events.

The following cuts were applied to reduce the num-ber of hadronic γγ interactions. The number of tracks re-constructed with the TPC had to be greater than 4, and

3 The acollinearity of two jets is defined as the complementof the angle between their directions

the energy of the particles with tracks reconstructed usingonly the VD and ID detectors had to be less than 20% ofthe total energy. The energies in 40◦ and 20◦ cones aroundthe beam axis were required to be less than 40% and 10%of the total energy respectively. The transverse energy hadto be greater than 20 GeV.

Hadronic events with missing energy were then se-lected in the barrel region of the detector. The visiblemass was required to be less than 60 GeV/c2. The thrustaxis and the missing momentum had to point in the polarregions [37◦, 143◦] and [45◦, 135◦] respectively. Figure 8shows a comparison between data and simulation at thislevel of the selection.

The Y23 quantity was then required to be less than0.01 and events had to contain less than 20 charged par-ticles. In order to reduce the number of events with two

514 The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector

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Fig. 9. Momentum and dE/dx of the charged R-hadron candidates selected by the qqR±R± analysis at LEP2. Data takenin the centre-of-mass energy range between 189 and 208 GeV were included. Right-hand side histograms show the expecteddistributions for one possible stop and sbottom signal (mq1 = 90 GeV/c2, mg = 60 GeV/c2) at

√s = 200 GeV with arbitrary

normalization

back-to-back jets, the acoplanarity4 was required to begreater than 10◦ and the thrust to be less than 0.95. Thefinal cut was bi-dimensional. The value of the variableMjet1/Ejet1 + Mjet2/Ejet2 was calculated from the twojets reconstructed with the DURHAM algorithm. Eventswere rejected if this variable was greater than 0.45 andif the acollinearity was less than 50◦. Table 3 shows thenumber of events after each cut of the qqR◦R◦ analysis. 12events were selected in the data while 10.6 were expectedin the hadronic background. Signal efficiencies as a func-tion of the gluino mass are shown in figure 7. They ranged

4 The acoplanarity of two jets is defined as the complementof the angle between their directions projected onto the planeperpendicular to z

from a few percent for low gluino masses to around 20%for mg = 18 GeV/c2.

7 Search for a stable gluino at LEP2

7.1 Preselection

A common preselection for the charged and neutral R-hadron analyses was applied to reduce the backgroundcoming from soft γγ interactions. The cuts are the samefor the stop and sbottom analysis at all centre-of-massenergies ranging from 189 to 208 GeV.

First, events were forced into two jets. To selecthadronic events, the number of charged particles recon-

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structed with the TPC was required to be greater thanthree, and the energy in the STIC to be less than 70% ofthe total visible energy. The polar angle of the thrust axishad to be in the interval [20◦, 160◦]. Then, quality cutswere applied. The fraction of good tracks was defined asthe ratio between the number of charged particles remain-ing after the track selection divided by this number beforethe selection. It had to be greater than 35%. In addition,the scalar sum of particle momenta reconstructed with theTPC was required to be greater than 55% of the total re-constructed energy and the number of charged particlesto be greater than six. To remove radiative events, the en-ergy of the most energetic neutral particle had to be lessthan 40 GeV. Table 4 contains the number of events aftereach of these cuts.

For the qqR±R± and qqR±R◦ analyses, charged R-hadron candidates were defined at this level. They hadto be reconstructed with the VD, ID and TPC detec-tors and their momentum was required to be greater than10 GeV/c. At least 80 sense wires of the TPC were re-quired to have contributed to the measurement of theirdE/dx. Their associated electromagnetic energy was re-quired to be less than 5 GeV, and the energy of the othercharged particles in a 15◦ cone around a candidate had tobe less than 5 GeV. In 2000, the dE/dx could not be usedin sector 6 of the TPC for almost any of the data. For thissample, charged R-hadron candidates in this sector wereremoved.

7.2 Search for qqR±R± events

The search for qqR±R± events was exactly the same forthe stop and the sbottom analyses. Events were selected if

they contained at least two charged R-hadron candidates.Figure 9 shows the momentum and the dE/dx distributionof the selected R± candidates. Table 4 shows the numberof selected events.

The analysis was then separated into three windows ingluino mass, and cuts in the plane (P,dE/dx) were applied:

– mg ≤ 30 GeV/c2:events had to contain at least one charged R-hadroncandidate with momentum greater than 20 GeV/c, andwith dE/dx less than the dE/dx expected for a particleof mass equal to 3 GeV/c2.

– 30 GeV/c2 < mg < 60 GeV/c2:events were selected if they contained at least twocharged R-hadron candidates with dE/dx both greaterthan the dE/dx expected for a particle of mass equalto 30 GeV/c2, and less than the dE/dx expected fora particle of mass equal to 60 GeV/c2. Moreover, thisdE/dx had also to be either less than the dE/dx ex-pected for a particle of mass equal to 1 GeV/c2, orgreater than 1.8 mip.

– mg ≥ 60 GeV/c2:events were kept if they contained at least two chargedR-hadron candidates with dE/dx greater than the dE/dx expected for a particle of mass equal to 60 GeV/c2.

In all LEP2 data which were analysed, no events wereselected in any of these windows. The number of expectedStandard Model background events were 0.115, 0.009 and0.011 in the analyses for mg ≤ 30 GeV/c2, 30 GeV/c2 <mg < 60 GeV/c2 and mg ≥ 60 GeV/c2 respectively. Ta-ble 5 contains the number of events expected for the dif-ferent centre-of-mass energies. Figure 10 shows the signaldetection efficiencies near the kinematical limit (mq1 =90 GeV/c2). The difference between stop and sbottom ef-

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Table 4. Number of events after each cut of the LEP2 preselection. 189 to 208 GeV data are added

Cuts Data Simulation 4-fermions 2-fermions γγ

NTPC 175436 164146 ± 105 12418 ± 13 50391 ± 24 101338 ± 102

ESTIC/Evis. 145810 141362 ± 95 12062 ± 13 48170 ± 24 81131 ± 91

θthrust 54838 54933 ± 45 9739 ± 10 31510 ± 23 13685 ± 38

PTPC 48475 48846 ± 43 9141 ± 10 27580 ± 23 12126 ± 35

Ncha. 45816 46227 ± 37 9040 ± 9 26969 ± 16 10219 ± 32

Emax.neu. 41880 42113 ± 37 8802 ± 9 23108 ± 16 10203 ± 32

1 R± candidate 2187 2279.1 ± 6.3 1746.8 ± 4.6 470.3 ± 3.4 62.6 ± 2.6

2 R± candidates 74 79.2 ± 0.8 75.2 ± 0.7 3.4 ± 0.3 0.5 ± 0.2

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Table 5. Number of events selected by the qqR±R± analysis at LEP2. (*) indicates 2000data taken without sector 6 working

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s Data Simulation Data Simulation Data Simulation

188.7 0 0.029±0.016 0 0.001±0.001 0 0.003±0.003191.6 0 0.005±0.004 0 0.001±0.001 0 0.001±0.001195.6 0 0.025±0.020 0 0.001±0.001 0 0.001±0.001199.6 0 0.007±0.007 0 0.001±0.001 0 0.001±0.001201.7 0 0.011±0.007 0 0.001±0.001 0 0.001±0.001204.8 0 0.009±0.009 0 0.001±0.001 0 0.001±0.001206.7 0 0.012±0.009 0 0.001±0.001 0 0.001±0.001208.1 0 0.000±0.000 0 0.001±0.001 0 0.001±0.001206.5(*) 0 0.017±0.013 0 0.001±0.001 0 0.001±0.001

total 0 0.115±0.033 0 0.009±0.003 0 0.011±0.004

ficiencies is not large. The highest efficiencies were alwaysobtained for high gluino masses, where the dE/dx is veryhigh.

7.3 Search for qqR±R◦ events

The search for qqR±R◦ events was also the same for thestop and sbottom analyses. Events were selected if theycontained at least one charged R-hadron candidate. Fig-ure 11 shows the momentum and the dE/dx distributionof the selected R± candidates. Table 4 shows the numberof selected events.

The analysis was then separated into three gluino masswindows, and cuts in the plane (P,dE/dx) were applied:

– mg ≤ 30 GeV/c2:events had to contain at least one charged R-hadroncandidate with momentum greater than 20 GeV/c, and

with dE/dx less than the dE/dx expected for a particleof mass equal to 3 GeV/c2.

– mg ≥ 60 GeV/c2:events were kept if they contained at least one chargedR-hadron candidate with dE/dx greater than the dE/dx expected for a particle of mass equal to 60 GeV/c2,and greater than 2 mip.

– 30 GeV/c2 < mg < 60 GeV/c2:events selected in either of the above windows (higheror lower mg) were accepted.Three, nine and six events were selected in the mass

windows mg ≤ 30 GeV/c2, 30 GeV/c2 < mg < 60 GeV/c2

and mg ≥ 60 GeV/c2 respectively. The number of ex-pected background events were 1.6, 8.2 and 6.6. All se-lected events in the data are more likely Standard Modelinstead than signal like. In particular, they do not followany mass iso-curve in the (P,dE/dx) plane. Table 6 con-tains the number of selected events as a function of the

518 The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector

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vent

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Fig. 13. Data-simulation comparison at the preselection level of the LEP2 qqR◦R◦ analysis. Data taken in the centre-of-mass energy range between 189 and 208 GeV were included. Right-hand side histograms show the expected distributions witharbitrary normalization for the stop and the sbottom signal at 200 GeV when all simulated samples are added together

centre-of-mass energy. Figure 12 shows the signal detec-tion efficiencies near the kinematical limit (mq1 =90 GeV/c2). The highest efficiencies were obtained for high gluinomasses where the dE/dx is very high.

7.4 Search for qqR◦R◦ events

After the preselection described in Sect. 7.1, the trans-verse missing momentum was required to be greater than4 GeV/c, the angle of the missing momentum had to pointin the polar angle region [20◦, 160◦], and the energy in a40◦ cone around the beam axis was required to be lessthan 40% of the event energy. A veto algorithm was thenapplied based on the hermeticity taggers at polar angles

close to 40◦ and 90◦. Figures 13 and 14 show data MonteCarlo comparisons following this selection and Table 7gives the observed and expected event numbers at the dif-ferent steps.

The stop and sbottom analyses were then separatedfor different ranges of the mass difference ∆m betweenthe squark and the gluino:

– ∆m ≤ 20 GeV/c2 :For high gluino masses, the energy deposited by theneutral R-hadrons is quite small. In this respect, thegluino is not so different from a neutralino, and theq1 → qg events resemble q1 → qχ0

1 events.– ∆m > 20 GeV/c2 :

In this case, the gluino deposits more energy.

The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector 519

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Fig. 14. Data-simulation comparison at the preselection level of the LEP2 qqR◦R◦ analysis. Data taken in the centre-of-mass energy range between 189 and 208 GeV were included. Right-hand side histograms show the expected distributions witharbitrary normalization for the stop and the sbottom signal at 200 GeV when all simulated samples are added together

The neural networks were trained to isolate the qqR◦R◦signal in both ∆m windows. They were trained separatelyon stop signals or sbottom signals. The neural networkstructure was the same for the stop and the sbottomsearches. It consisted of 10 input nodes, 10 hidden nodesand 3 output nodes.

For ∆m ≤ 20 GeV/c2, the 10 input variables were:the ratio between the transverse missing momentum andthe visible energy, the transverse energy, the visible mass,the softness defined as Mjet1/Ejet1 + Mjet2/Ejet2, theacollinearity, the quadratic sum of transverse momenta of

the jets√

(P jet1t )2 + (P jet2

t )2, the acoplanarity, the sumof the first and third Fox-Wolfram moments, the polar

angle of the missing momentum and finally the combinedb-tagging probability [22].

For ∆m > 20 GeV/c2, the 10 input variables were: thecharged energy, the transverse charged energy, the visiblemass, the thrust, the effective centre-of-mass energy [23],the acollinearity, the acoplanarity, the sum of the first andthird Fox-Wolfram moments, the sum of the second andfourth Fox-Wolfram moments, and finally the combinedb-tagging probability.

The neural networks were trained to discriminate thesignal from the combined two-fermion and four-fermionbackgrounds, and from the γγ interactions leading tohadronic final states. The first output node was trained toidentify both Z0 → qq and four-fermion events. The sec-ond node identified the γγ interactions leading to hadronic

520 The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector

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a b

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c d

Fig. 15a–d. Numbers of events as a function of the signal efficiencies for the stop and sbottom analysis. Data taken inthe centre-of-mass energy range between 189 and 208 GeV were included. a stop analysis for ∆m > 20 GeV/c2 and b for∆m ≤ 20 GeV/c2, c sbottom analysis for ∆m > 20 GeV/c2 and b for ∆m ≤ 20 GeV/c2. The squark and gluino mass valuesused for the signal detection efficiencies are indicated on the x axis, (mq,mg)

final states. And the third node was trained to select thesignal. The three output nodes were useful in the train-ing of the network, but the selection was made accordingto the output of the signal node only. Figure 15 showsthe number of events as a function of the signal efficiencyfor the two mass analysis windows of the stop and thesbottom analysis. The number of real events was in agree-ment with the Standard Model predictions over the fullrange of the neural network outputs. The optimisations ofthe final cuts were performed by minimising the expectedconfidence level of the signal hypothesis [24].

Tables 8 and 9 contain the numbers of events selectedin the stop and sbottom analyses. Combining all datafrom 189 to 208 GeV, 32 and 11 events were selected

in the stop analysis for ∆m > 20 GeV/c2 and ∆m ≤20 GeV/c2, while the expected number of events were 30.1and 11.1. In the sbottom analysis, no candidates were ob-served for ∆m > 20 GeV/c2 and five were selected for∆m ≤ 20 GeV/c2. The expected number of events were3.0 and 5.3. Figure 16 shows the signal detection efficien-cies for the stop and for the sbottom (mq1 = 90 GeV/c2).They are very low when the gluino mass is close to zero.

8 Results

No excess of events was observed in any analysis per-formed at LEP1 or at LEP2 in the stable gluino scenario.

The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector 521

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Eff

icie

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∼1) = 90 GeV/c2

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∆m ≤ 20 GeV/c2

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∆m ≤ 20 GeV/c2

∆m =

20

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5 G

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2

a b

Fig. 16a,b. Signal detection efficiencies at√

s =200 GeV for the stop a and sbottom b qqR◦R◦ analysis as a function of thegluino mass (mq1 = 90 GeV/c2)

Table 6. Number of events selected by the qqR±R◦ analysis at LEP2. (*) indicates 2000data taken without sector 6 working

mg ≤ 30 GeV/c2 30 GeV/c2 < mg < 60 GeV/c2 mg ≥ 60 GeV/c2

√s Data Simulation Data Simulation Data Simulation

188.7 0 0.577±0.101 0 2.514±0.264 0 1.937±0.243191.6 0 0.030±0.011 1 0.454±0.132 1 0.425±0.131195.6 2 0.135±0.042 2 0.783±0.097 0 0.648±0.088199.6 0 0.266±0.071 1 1.333±0.158 1 1.068±0.141201.7 0 0.097±0.025 2 0.489±0.056 2 0.392±0.050204.8 1 0.208±0.051 1 0.961±0.106 0 0.753±0.093206.6 0 0.187±0.040 1 0.848±0.089 1 0.661±0.079208.1 0 0.011±0.005 0 0.095±0.014 0 0.085±0.013206.5(*) 0 0.083±0.025 1 0.679±0.074 1 0.596±0.070

total 3 1.59±0.15 9 8.16±0.39 6 6.57±0.36

Table 7. qqR◦R◦ analysis at LEP2: number of events aftereach selection cut. Data with

√s in the range 189 GeV-208 GeV

are included

Cuts Data simulation 4-fermions 2-fermions γγ

P mis.t 26423 26938 ± 20 8117 ± 8 18012 ± 15 809 ± 9

θPmis.16379 16821 ± 15 7191 ± 6 9088 ± 12 542 ± 8

E400/Evis. 14694 15231 ± 14 6395 ± 6 8471 ± 12 364 ± 6Hermeticity 14422 14651 ± 14 6150 ± 6 8140 ± 12 361 ± 6

Results were therefore combined to obtain excluded re-gions at 95% confidence level in the parameter space. Thelimits were computed using the likelihood ratio methoddescribed in [24]. For different values of the parameter Pdescribing the probability that the gluino hadronizes to a

charged R-hadron, the relative cross-sections for the dif-ferent channels were given by:

σ(R±R±) = P 2σ

σ(R±R◦) = 2P (1 − P )σσ(R◦R◦) = (1 − P )2σ

where σ was either the e+e− → qqgg cross section atLEP1, the t1¯t1 or the b1

¯b1 cross-section at LEP2.For the LEP1 analysis, results were interpreted in terms

of excluded gluino masses for different P. Figure 17 showsthe excluded region at 95% confidence level. From this fig-ure, a stable gluino with mass between 2 and 18 GeV/c2

is excluded regardless of the charge of the R-hadrons. Theminimum upper limit, 18 GeV/c2, is obtained for interme-

522 The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector

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P(g∼ →

R+

/-)

DELPHI91.2 GeV - L=46 pb-1

Observed

Expected

Fig. 17. Results of the LEP1 analysis: excluded region at 95%confidence level in the plane (mg,P). P is the probability thatthe gluino hadronizes to a charged R-hadron. The shaded re-gion corresponds to the observed exclusion and the line to theexpected one

Table 8. Number of events selected by the stop qqR◦R◦ anal-ysis. (*) indicates 2000 data taken without sector 6 working

∆M > 20 GeV/c2 ∆M ≤ 20 GeV/c2

√s Data Simulation Data Simulation

188.7 4 6.634±0.741 6 3.685±1.158191.6 4 1.054±0.115 0 0.482±0.097195.6 5 3.532±0.236 3 1.408±0.256199.6 7 4.324±0.270 0 1.617±0.280201.7 1 2.055±0.140 0 0.836±0.138204.8 4 4.432±0.302 0 1.197±0.268206.6 5 4.287±0.290 2 1.227±0.272208.1 0 0.418±0.031 0 0.117±0.026206.5(*) 2 3.411±0.203 0 0.556±0.072

total 32 30.2±1.0 11 11.1±1.3

diate values of P (between 0.2 and 0.45), while an upperlimit of 23 GeV/c2 is obtained for P=1.

For the LEP2 analysis, excluded regions in the planes(mt1 ,mg) and (mb1

,mg) were derived for five different val-ues of P: 0., 0.25, 0.5, 0.75 and 1. Moreover, the stop andsbottom cross-sections were calculated for two cases. Inthe first case, the squark mixing angle was set to zerowhich corresponds to the maximal cross-sections. In thesecond case, the mixing angle was equal to 56◦ for thestop and to 68◦ for the sbottom, which gives the mini-mal cross-sections. Squark masses below 50 GeV/c2 werenot taken into account in these analyses. Figures 18 and19 show the excluded regions thus obtained. In the case

Table 9. Number of events selected by the sbottom qqR◦R◦

analysis. (*) indicates 2000 data taken without sector 6 working

∆M > 20 GeV/c2 ∆M ≤ 20 GeV/c2

√s Data Simulation Data Simulation

188.7 0 1.038±0.657 3 2.475±1.139191.6 0 0.085±0.026 0 0.180±0.058195.6 0 0.314±0.088 1 0.571±0.178199.6 0 0.295±0.094 0 0.663±0.195201.7 0 0.225±0.049 1 0.319±0.096204.8 0 0.295±0.040 0 0.428±0.174206.6 0 0.312±0.05 0 0.379±0.175208.1 0 0.022±0.005 0 0.037±0.017206.5(*) 0 0.417±0.054 0 0.281±0.160

total 0 3.0±0.7 5 5.3±1.2

Table 10. Upper limits on the stop and sbottom masses asa function of the probability P that the gluino hadronizes tocharged R-hadrons. Limits are set for ∆m ≥ 10 GeV/c2 and fora gluino mass greater than 2 GeV/c2. Mixing angles equal tozero corresponds to purely left-handed squarks, while θt = 56◦

and θb = 68◦ corresponds to minimal cross-section case

Stop SbottomP θt = 0◦ θt = 56◦ θb = 0◦ θb = 68◦

0.00 92 87 98 860.25 90 87 96 820.50 92 89 94 820.75 94 92 94 841.00 95 94 95 87

of minimal cross-sections, a hole appears in the sbottomexclusion histograms around (60 GeV/c2, 50GeV/c2) inthe plane (mb1

,mg) for intermediate values of P. It can beexplained by different effects:

– In the analyses searching for charged R-hadrons, thesignal detection efficiencies are small in this region ofthe (mq1 ,mg) plane, because the dE/dx distributionof the charged R-hadrons as a function of the mo-mentum crosses the band corresponding to StandardModel particles (cf Fig. 6).

– When the Z0 − q1 − ¯q1 coupling is suppressed, thesquark pair production cross-section is much more re-duced for the sbottom than for the stop.

– The visible energy of qqR◦R◦ events becomes smallfor low values of ∆M . At ∆M = 5 GeV/c2, this hasno effect on the stop exclusion results, because of thec-quark which is lighter than the b-quark.

Lower limits on the stop and sbottom masses are givenin Table 10 for ∆m ≥ 10 GeV/c2 and for a gluino massgreater than 2 GeV/c2 for different values of P.

The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector 523

0

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ino

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LEP2

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Glu

ino

Mas

s (G

eV/c

2 )

DELPHIt∼ → c g

∼ P=0.

MixedLeft

Fig. 18. Results of the LEP2+LEP1 stop analysis: excluded regionat 95% confidence level in the plane (mt1 ,mg). The line correspondsto the exclusion for purely left stop, and the shaded region to exclu-sion obtained for the mixing angle giving the minimal cross-section.Excluded regions are given for different values of P, the probabilitythat the gluino hadronizes to charged R-hadron: 0, 0.25, 0.5, 0.75and 1

524 The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector

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Mas

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∼ P=1.00

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DELPHIb∼ → b g

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Fig. 19. Results of the LEP2+LEP1 sbottom analysis: excludedregion at 95% confidence level in the plane (mb1

,mg). The line cor-responds to the exclusion for purely left sbottom, and the shadedregion to exclusion obtained for the mixing angle giving the mini-mal cross-section. Excluded regions are given for different values ofP, the probability that the gluino hadronizes to charged R-hadron:0, 0.25, 0.5, 0.75 and 1

The DELPHI Collaboration: Search for an LSP gluino at LEP with the DELPHI detector 525

9 Conclusion

The analysis of the LEP1 data collected in 1994 excludesat 95% confidence level a stable gluino with mass between2 and 18 GeV/c2. These limits are valid for any charge ofthe produced R-hadrons.

Stop and sbottom squarks have been searched for inthe 609 pb−1 collected by DELPHI at centre-of-mass en-ergies ranging from 189 to 208 GeV. In the stable gluinoscenario, the dominant decays are t1 → cg and b1 → bg.No deviation from Standard Model predictions was ob-served. The observed limits at 95% confidence level are:

– mt1 > 90 GeV/c2, and mb1> 96 GeV/c2 for purely

left squarks.– mt1 > 87 GeV/c2, and mb1

> 82 GeV/c2 independentof the mixing angle.

Acknowledgements. We are greatly indebted to our technicalcollaborators, to the members of the CERN-SL Division for theexcellent performance of the LEP collider, and to the fundingagencies for their support in building and operating the DEL-PHI detector. We acknowledge in particular the support ofAustrian Federal Ministry of Science and Traffics, GZ 616.364/2-III/2a/98, FNRS–FWO, Belgium, FINEP, CNPq, CAPES,FUJB and FAPERJ, Brazil, Czech Ministry of Industry andTrade, GA CR 202/96/0450 and GA AVCR A1010521, Dan-ish Natural Research Council, Commission of the EuropeanCommunities (DG XII), Direction des Sciences de la Matiere,CEA, France, Bundesministerium fur Bildung, Wissenschaft,Forschung und Technologie, Germany, General Secretariat forResearch and Technology, Greece, National Science Foundation(NWO) and Foundation for Research on Matter (FOM), TheNetherlands, Norwegian Research Council, State Committeefor Scientific Research, Poland, 2P03B06015, 2P03B1116 andSPUB/P03/178/98, JNICT–Junta Nacional de InvestigacaoCientıfica e Tecnologica, Portugal, Vedecka grantova agenturaMS SR, Slovakia, Nr. 95/5195/134, Ministry of Science andTechnology of the Republic of Slovenia, CICYT, Spain, AEN96-1661 and AEN96-1681, The Swedish Natural Science ResearchCouncil, Particle Physics and Astronomy Research Council,UK, Department of Energy, USA, DE–FG02–94ER40817.

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