Searches for prompt light gravitino signatures in e ...krieger/... · 14 OPAL Collaboration / Physics Letters B 501 (2001) 12–27 v Department of Physics and Astronomy, Tel Aviv

1 March 2001

Physics Letters B 501 (2001) 12–27www.elsevier.nl/locate/npe

Searches for prompt light gravitino signaturesin e+e− collisions at

√s = 189 GeV

OPAL Collaboration

G. Abbiendib, K. Ackerstaffh, C. Ainsleye, P.F. Akessonc, G. Alexanderv, J. Allisonp,K.J. Andersoni, S. Arcelliq, S. Asaiw, S.F. Ashbya, D. Axenaa, G. Azuelosr,1,I. Baileyz, A.H. Ball h, E. Barberioh, R.J. Barlowp, J.R. Batleye, S. Baumannc,T. Behnkey, K.W. Bell t, G. Bellav, A. Bellerivei, S. Bentvelsenh, S. Bethken,9,

O. Biebeln,9, I.J. Bloodwortha, P. Bockk, J. Böhmen,8, O. Boeriuj, D. Bonacorsib,M. Boutemeurae, S. Braibanth, P. Bright-Thomasa, L. Brigliadori b, R.M. Brownt,

H.J. Burckharth, J. Camminc, P. Capiluppib, R.K. Carnegief, A.A. Carterm,J.R. Cartere, C.Y. Changq, D.G. Charltona,2, C. Cioccab, P.E.L. Clarkeo, E. Clayo,

I. Cohenv, O.C. Cookeh, J. Couchmano, C. Couyoumtzelism, R.L. Coxei,M. Cuffianib, S. Dadou, G.M. Dallavalleb, S. Dallisonp, A. de Roeckh, P. Dervano,K. Deschy, B. Dienesad,8, M.S. Dixit g, M. Donkersf, J. Dubbertae, E. Duchovnix,G. Duckeckae, I.P. Duerdothp, P.G. Estabrooksf, E. Etzionv, F. Fabbrib, M. Fantib,

L. Feldj, P. Ferraril, F. Fiedlerh, I. Fleckj, M. Forde, A. Freyh, A. Fürtjesh,D.I. Futyanp, P. Gagnonl, J.W. Garyd, G. Gayckeny, C. Geich-Gimbelc,

G. Giacomellib, P. Giacomellih, D. Glenzinskii, J. Goldbergu, C. Grandib,K. Grahamz, E. Grossx, J. Grunhausv, M. Gruwéy, P.O. Güntherc, C. Hajduac,

G.G. Hansonl, M. Hansroulh, M. Hapkem, K. Hardery, A. Harelu, C.K. Hargroveg,M. Harin-Diracd, A. Haukec, M. Hauschildh, C.M. Hawkesa, R. Hawkingsy,

R.J. Hemingwayf, C. Hensely, G. Hertenj, R.D. Heuery, M.D. Hildrethh, J.C. Hille,P.R. Hobsony, A. Hockeri, K. Hoffmanh, R.J. Homera, A.K. Honmah, D. Horváthac,3,

K.R. Hossainab, R. Howardaa, P. Hüntemeyery, P. Igo-Kemenesk, D.C. Imriey,K. Ishii w, F.R. Jacobt, A. Jawaheryq, H. Jeremier, C.R. Jonese, P. Jovanovica,

T.R. Junkf, N. Kanayaw, J. Kanzakiw, G. Karapetianr, D. Karlenf, V. Kartvelishvili p,K. Kawagoew, T. Kawamotow, R.K. Keelerz, R.G. Kelloggq, B.W. Kennedyt,

D.H. Kim s, K. Klein k, A. Klier x, T. Kobayashiw, M. Kobelc, T.P. Kokottc,S. Komamiyaw, R.V. Kowalewskiz, T. Kressd, P. Kriegerf, J. von Kroghk, T. Kuhl c,M. Kupperx, P. Kyberdm, G.D. Laffertyp, H. Landsmanu, D. Lansken, I. Lawsonz,

J.G. Layterd, A. Leinsae, D. Lellouchx, J. Lettsl, L. Levinsonx, R. Liebischk,J. Lillich j, B. List h, C. Littlewoode, A.W. Lloyd a, S.L. Lloydm, F.K. Loebingerp,

0370-2693/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PII: S0370-2693(01)00101-0

OPAL Collaboration / Physics Letters B 501 (2001) 12–27 13

G.D. Longz, M.J. Lostyg, J. Luaa, J. Ludwigj, A. Macchiolor, A. Macphersonab,W. Maderc, M. Mannellih, S. Marcellinib, T.E. Marchantp, A.J. Martinm, J.P. Martinr,

G. Martinezq, T. Mashimow, P. Mättigx, W.J. McDonaldab, J. McKennaaa,T.J. McMahona, R.A. McPhersonz, F. Meijersh, P. Mendez-Lorenzoae, F.S. Merritti,

H. Mesg, A. Michelini b, S. Miharaw, G. Mikenbergx, D.J. Millero, W. Mohrj,A. Montanarib, T. Mori w, K. Nagaih, I. Nakamuraw, H.A. Neall,6, R. Nisiush,

S.W. O’Nealea, F.G. Oakhamg, F. Odoricib, H.O. Ogrenl, A. Ohh, A. Okparak,M.J. Oregliai, S. Oritow, G. Pásztorh,10, J.R. Paterp, G.N. Patrickt, J. Pattj,

P. Pfeifenschneidern, J.E. Pilcheri, J. Pinfoldab, D.E. Planeh, B. Polib, J. Polokh,O. Poothh, M. Przybycienh,4, A. Quadth, C. Rembserh, H. Rickd, S.A. Robinsu,N. Rodningab, J.M. Roneyz, S. Rosatic, K. Roscoep, A.M. Rossib, Y. Rozenu,

K. Rungej, O. Runolfssonh, D.R. Rustl, K. Sachsf, T. Saekiw, O. Sahrae, W.M. Sangy,E.K.G. Sarkisyanv, C. Sbarraz, A.D. Schaileae, O. Schaileae, P. Scharff-Hansenh,

S. Schmittk, M. Schröderh, M. Schumachery, C. Schwickh, W.G. Scottt, R. Seustern,8,T.G. Shearsh, B.C. Shend, C.H. Shepherd-Themistocleouse, P. Sherwoodo,

G.P. Sirolib, A. Skujaq, A.M. Smithh, G.A. Snowq, R. Sobiez, S. Söldner-Remboldj,5,S. Spagnolot, M. Sprostont, A. Stahlc, K. Stephensp, K. Stoll j, D. Stroms,

R. Ströhmerae, B. Surrowh, S.D. Talbota, S. Taremu, R.J. Tayloro, R. Teuscheri,M. Thiergenj, J. Thomaso, M.A. Thomsonh, E. Torrencei, S. Towersf, T. Trefzgerae,I. Triggerh, Z. Trócsányiad,7, E. Tsurv, M.F. Turner-Watsona, I. Uedaw, P. Vanneremj,

M. Verzocchih, H. Vossh, J. Vossebeldh, D. Wallerf, C.P. Warde, D.R. Warde,P.M. Watkinsa, A.T. Watsona, N.K. Watsona, P.S. Wellsh, T. Wenglerh, N. Wermesc,

D. Wetterlingk, J.S. Whitef, G.W. Wilsonp, J.A. Wilsona, T.R. Wyattp, S. Yamashitaw,V. Zacekr, D. Zer-Zionh

a School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UKb Dipartimento di Fisica dell’ Università di Bologna and INFN, I-40126 Bologna, Italy

c Physikalisches Institut, Universität Bonn, D-53115 Bonn, Germanyd Department of Physics, University of California, Riverside CA 92521, USA

e Cavendish Laboratory, Cambridge CB3 0HE, UKf Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada

g Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canadah CERN, European Organisation for Nuclear Research, CH-1211 Geneva 23, Switzerland

i Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60637, USAj Fakultät für Physik, Albert Ludwigs Universität, D-79104 Freiburg, Germany

k Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germanyl Indiana University, Department of Physics, Swain Hall West 117, Bloomington IN 47405, USA

m Queen Mary and Westfield College, University of London, London E1 4NS, UKn Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany

o University College London, London WC1E 6BT, UKp Department of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UK

q Department of Physics, University of Maryland, College Park, MD 20742, USAr Laboratoire de Physique Nucléaire, Université de Montréal, Montréal, Quebec H3C 3J7, Canada

s University of Oregon, Department of Physics, Eugene OR 97403, USAt CLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UKu Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel

14 OPAL Collaboration / Physics Letters B 501 (2001) 12–27

v Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israelw International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113-0033,

and Kobe University, Kobe 657-8501, Japanx Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel

y Universität Hamburg/DESY, II Institut für Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germanyz University of Victoria, Department of Physics, PO Box 3055, Victoria BC V8W 3P6, Canada

aaUniversity of British Columbia, Department of Physics, Vancouver BC V6T 1Z1, Canadaab University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada

ac Research Institute for Particle and Nuclear Physics, H-1525 Budapest, PO Box 49, Hungaryad Institute of Nuclear Research, H-4001 Debrecen, PO Box 51, Hungary

aeLudwigs-Maximilians-Universität München, Sektion Physik, Am Coulombwall 1, D-85748 Garching, Germany

Received 28 May 2000; accepted 9 January 2001Editor: K. Winter

Abstract

Searches for final states expected in models with light gravitinos have been performed, including experimental topologieswith multi-leptons with missing energy, leptons and photons with missing energy, and jets and photons with missing energy.No excess over the expectations from the Standard Model has been observed. Limits are placed on production cross-sectionsin the different experimental topologies. Additionally, combining with searches for the anomalous production of lepton andphoton pairs with missing energy, results are interpreted in the context of minimal models of gauge mediated SUSY breaking.Exclusion limits at the 95% confidence level on the supersymmetric particle masses ofm

�> 83 GeV andm

χ01> 85 GeV for

tanβ = 2, andmτ > 69 GeV,me,µ > 88 GeV andmχ0

1> 76 GeV for tanβ = 20, are established. 2001 Elsevier Science B.V.

All rights reserved.

1. Introduction

Supersymmetry (SUSY) provides a method of solv-ing the “naturalness” or “hierarchy” problem by intro-ducing a set of new particles which cancel the large ra-diative corrections to the Higgs mass. The cancellationis achieved by assuming that, for each Standard Model(SM) particle chirality state, there is one additionalparticle, identical to its SM partner except that its spindiffers by 1/2 unit. If SUSY were an exact symmetry,

1 And at TRIUMF, Vancouver, Canada V6T 2A3.2 And Royal Society University Research Fellow.3 And Institute of Nuclear Research, Debrecen, Hungary.4 And University of Mining and Metallurgy, Cracow.5 And Heisenberg Fellow.6 Now at Yale University, Dept. of Physics, New Haven, USA.7 And Department of Experimental Physics, Lajos Kossuth

University, Debrecen, Hungary.8 And MPI München.9 Now at MPI für Physik, 80805 München.

10 And Research Institute for Particle and Nuclear Physics,Budapest, Hungary.

the new SUSY particles would have the same massesas their SM partners. Since this scenario is experimen-tally excluded, SUSY must be a broken symmetry. It istypically assumed that SUSY is broken in some “hid-den” sector of new particles, and is “communicated”(or mediated) to the “visible” sector of SM and SUSYparticles by one of the known interactions. Two sce-narios for this mediation have been widely investi-gated: gravity and gauge mediation. In gauge mediatedSUSY breaking (GMSB), the hidden11 sector can lieat energies as low as about 104 GeV. In most currentGMSB theoretical work [1–3], it is assumed that thishidden sector is coupled to a messenger sector, whichin turn couples to the visible sector through normalSM gauge interactions. The advantage of GMSB overgravity mediated models is that flavour changing neu-tral currents cannot be induced by SUSY breaking be-cause the normal gauge interactions are flavour blind.

11 In some GMSB Letters this is called the “secluded” sector, toavoid confusion with the hidden sector of gravity mediated SUSYbreaking models.


A feature which distinguishes gravity from gauge me-diated models is the mass of the gravitino,G. In grav-ity mediated models,G is usually too heavy to have asignificant effect on SUSY phenomenology, while inGMSB models, theG is typically light (< 1 GeV) andis the lightest SUSY particle, the LSP. WhileG is aspin 3/2 particle, only its spin 1/2 component (whichhas “absorbed” the goldstino associated with sponta-neous SUSY breaking via the “superhiggs” mecha-nism) interacts with weak, rather than gravitational,strength interactions, and contributes to phenomenol-ogy.

The next-to-lightest SUSY particle (NLSP) is usu-ally either the lightest neutralino (χ0

1) or the lightestscalar lepton (�±1 ), and in a significant fraction of theparameter space the NLSP is the lightest scalar taulepton (τ1). The coupling of the SUSY particles toG is small, and typically SUSY particles will decayto the NLSP, which then decays to the gravitino viaχ0

1 → γ G or � → �G. If the decay to the gravitinooccurs with a small lifetime, the distinguishing fea-ture is events with energetic leptons or photons, plussignificant missing energy due to the missing grav-itinos. OPAL has considered scalar lepton and light-est neutralino pair creation in these scenarios in pre-vious publications [4,5]. This Letter reports the firstOPAL results on the systematic search for experimen-tal topologies expected in SUSY models with a lightgravitino, assuming prompt decays of the NLSP intothe G. It is also possible for the NLSP lifetime to besignificant and it may decay near the interaction point,at an observably macroscopic distance, or outside thedetector. Many signatures expected with long NLSPlifetimes have been considered in other OPAL publi-cations [4,6,7], and the case of arbitrary lifetime willbe considered in a subsequent publication. In additionto the new experimental searches which have sensitiv-ity to general SUSY models with light gravitinos, theresults reported in this Letter are also combined withthose from previous publications to constrain minimalGMSB models. Results from searches for GMSB havealso been reported by other collaborations [8,9].

2. OPAL detector and event simulation

The OPAL detector is described in detail in Ref. [10].The SUSYGEN [11] event generator was used to sim-

ulate most of the signal events. Forχ01 pair creation

in the χ01 NLSP case, 1000 events were simulated for

eachχ01 mass, using 6mχ0

1points from 50 GeV to

94 GeV. For� pair production in theχ01 NLSP case,

1000 events were generated for each (m�, mχ01), using

a grid of 48 different points for each� flavour. Simi-lar one- or two-dimensional mass grids were used for� andχ0

1 pair production in the� (andτ ) NLSP cases.For chargino pair production,χ+

1 χ−1 , and the associ-

ated pair production of the lightest and second lightestneutralino,χ0

2 χ01 , in the χ0

1 NLSP case, the W and Zboson widths can play an important role and are notfully treated in SUSYGEN. The DFGT generator [12]is used to simulate these signal events. It includes spincorrelations and allows for a proper treatment of theW boson and the Z boson width effects in the charginoand heavy neutralino decays. Both SUSYGEN andDFGT include initial-state radiation. The JETSET 7.4package [13] is used for the hadronization. The grav-itino mass is set identically to zero in the generation,since a small mass in the range favoured by the modelshas a negligible effect on the detection efficiencies.

The sources of background include two-photon,lepton-pair, multihadronic, and four-fermion proces-ses. The Monte Carlo generators PHOJET [14] (forQ2 < 4.5 GeV2) and HERWIG [15] (for Q2 �4.5 GeV2) are used to simulate hadronic events fromtwo-photon processes. The Vermaseren [16] programis used to simulate leptonic two-photon processes(e+e−e+e−, e+e−µ+µ− and e+e−τ+τ−). Four-ferm-ion processes were simulated using KORALW [17],and with the grc4f [18] generator, both of which takeinto account all interfering four-fermion diagrams.The improved simulation of the transverse momentumof photons from initial-state radiation makes the useof KORALW essential for events including photonsin the final states. Lepton pairs were simulated usingthe KORALZ [19] generator forτ+τ−(γ ), µ+µ−(γ )andννγ (γ ) events, and the BHWIDE [20] (when boththe electron and positron scatter at least 12.5◦ fromthe beam axis) and TEEGG [21] (for the remainingphase space) programs for e+e− → e+e−(γ ) events.Multihadronic, qq(γ ), events were simulated usingPYTHIA [13].

Generated signal and background events were pro-cessed through the full simulation of the OPAL detec-tor [22] and the same event analysis chain was applied


to the simulated events as to the data. A data set of ap-proximately 182 pb−1 at a luminosity weighted centreof mass energy of

√s = 188.7 GeV was used for the

analysis.

3. Analysis

For all the selections, after the event reconstruc-tion, double-counting of energy between tracks andcalorimeter clusters is corrected by reducing the calor-imeter cluster energy by the expected energy deposi-tion from aligned tracks [23]. The selections for eventswith leptons or hadronic jets plus photons and miss-ing energy described in Section 3.1, as well as four orsix leptons plus missing energy in Section 3.2, use thesame lepton identification and isolation requirementsand preselection as the OPAL Chargino/Neutralinoanalysis [6]. The most significant preselection cuts re-quire that there is no significant energy in the OPALforward calorimeters.

3.1. χ01 NLSP

3.1.1. χ01 χ

01 production withχ0

1 NLSPThe search for lightest neutralino pair production

followed by the decaysχ01 → γ G uses the OPAL se-

lection of events with photon pairs and missing en-ergy [5]. The analysis selects events with at leasttwo photon candidates and significant missing energy,along with no other significant energy in the event.A total of 24 events are selected, which is consistentwith the expectation of 26.9±1.2 events from StandardModel e+e− → ννγ γ (γ ) production and 0.11±0.04from all other sources. The selection efficiency fore+e− → ννγ γ (γ ) within the kinematic acceptance ofthe analysis is (66.4±2.9)%. One can calculate [24]the maximum neutralino mass,Mmax

χ01

, which is con-

sistent with the measured three-momenta of the twophotons. A cut onMmax

χ01

provides further suppression

of the ννγ γ (γ ) background while retaining high ef-ficiency for the signal hypothesis. We require that themaximum kinematically allowed mass be greater thanmχ0

1− 5 GeV, which retains(95.5+2.0

−1.0)% relative ef-ficiency for signal at all values ofmχ0

1while sup-

pressing much of the remainingννγ γ (γ ) background.The number of selected events consistent with a given

value ofmχ01

varies from 14 formχ01

� 45 GeV to 3events at the kinematic limit. The expected number ofSM background events decreases from 13.67±0.20 atmχ0

1� 45 GeV to 1.34± 0.07 consistent withmχ0

1�

94 GeV.

3.1.2. �+�−, χ+1 χ

−1 andχ0

2 χ01 production withχ0

1NLSP

With a χ01 NLSP, scalar lepton, charginos and

neutralinos may be observed via

e+e− → �+�− → (�+χ0

1

)(�−χ0

1

)→ (

�+γ G)(�−γ G

),

e+e− → χ+1 χ

−1 → (

W(∗)+χ01

)(W(∗)−χ0

1

)→ (

W(∗)+γ G)(

W(∗)−γ G)

and

e+e− → χ02 χ

01 → Z(∗)χ0

1 χ01 → (

Z(∗)γ G)(γ G

).

In all cases, the signature is events with two photonsplus missing energy, plus other activity in the detector.Scalar lepton production will always lead to a lowmultiplicity final state, and only events with at mostsix tracks are considered in the analysis. Chargino pairproduction and neutralino associated pair productionmay lead to either low or high multiplicity finalstates depending on the decays of the W(∗)± and Z(∗)bosons. For charginos and neutralinos, the analysis is,therefore, divided into two categories:

(HM) High-multiplicity topologies, withNch −Nconv> 4, whereNch is the total number of tracks in theevent, andNconv is the number of tracks originatingfrom identified photon conversions,

(LM) Low-multiplicity topologies, withNch −Nconv� 4.

The background composition depends on the eventkinematics, which are functions of the mass differencebetween the produced particles and the lightest neu-tralino, �m = m − mχ0

1. The analysis is, therefore,

separately optimized for different�m regions, listedin Table 1.

The analyses select events with significant miss-ing energy and two photons. Cuts are applied on theevent acoplanarity12 (φacop), polar angle of the miss-

12 After forcing the event into two jets, the acoplanarity angleis 180◦ minus the opening angle between the jets in the planetransverse to the beam axis.


Table 1Analysis requirements on quantities used in the differentχ0

1 NLSP selections

Region pmissT

/Ebeam Evis/√s M2jet Eγ1 Eγ2

(GeV) (GeV) (GeV)

�+�−

3 GeV<�m< 10 GeV > 0.10 [0.30,0.80] – > 15 > 10

10 GeV<�m<m�/2 > 0.08 [0.40,0.85] – > 15 > 10

m�/2<�m<m

�> 0.08 [0.45,0.95] – >10 > 5

χ+1 χ

−1

HM 3 GeV<�m< 10 GeV > 0.06 [0.30,0.80] < 60 > 20 > 3

10 GeV<�m<mχ±/2 > 0.05 [0.30,0.80] – [15,70] > 3

mχ±/2<�m<mχ± − 20 GeV > 0.04 [0.40,0.90] – [10,70] > 3

mχ± − 20 GeV<�m<mχ± > 0.03 [0.40,0.95] – [5,50] > 3

LM 3 GeV<�m< 10 GeV > 0.05 [0.30,0.80] – > 20 > 3

10 GeV<�m<m�/2 > 0.05 [0.30,0.80] – [15,70] > 3

mχ±/2<�m<mχ± − 20 GeV > 0.05 [0.30,0.80] – [10,70] > 3

mχ± − 20 GeV<�m<mχ± > 0.05 [0.30,0.80] – [5,50] > 3

χ02 χ

01

HM 3 GeV<�m< 10 GeV > 0.05 [0.25,0.75] < 50 > 20 > 3

10 GeV<�m< 30 GeV > 0.04 [0.30,0.80] < 60 > 20 > 3

30 GeV<�m< 80 GeV > 0.035 [0.40,0.85] – [10,70] > 3

80 GeV<�m<Mχ0

2> 0.025 [0.50,0.90] – [5,60] > 3

LM 3 GeV<�m< 10 GeV > 0.05 [0.25,0.75] – > 20 > 3

10 GeV<�m< 30 GeV > 0.04 [0.30,0.80] – [20,70] > 3

30 GeV<�m< 80 GeV > 0.035 [0.35,0.85] – [10,70] > 3

80 GeV<�m<Mχ0

2> 0.025 [0.35,0.90] – [10,60] > 3

ing momentum (cosθmiss), missing transverse momen-tum scaled by the beam energy (pmiss

T /Ebeam) andvisible energy scaled by the centre-of-mass energy(Evis/

√s ). Additionally, unlike other SUSY searches,

the LSP gravitino is essentially massless, and the back-grounds can be further reduced while retaining highefficiency by also imposing a minimum requirementon Evis/

√s. In the HM analyses, there is significant

background from e+e− → W+W− in some of thekinematic regions. This background is reduced by re-moving the most energetic photon and forcing theevent into two jets, and then cutting on the two-jet

mass (M2jet). In the scalar lepton search, it is also re-quired that there be at least one identified, isolated lep-ton in each event. To maintain a general search, if twoleptons are found they are not required to be of thesame flavour.

Finally, in all channels, it is required that there beat least two energetic photons in each event. Photonsare identified by selecting unassociated clusters inthe electromagnetic calorimeter, with the followingisolation requirements in a cone centred on the cluster(15◦ half-angle for the highest energy photon and 10◦half-angle for the second photon):


Fig. 1. The distribution of the event visible energy,Evis, and energy of the most energetic photon,Eγ , for events in the�+�−γ γ analysisin Section 3.1.2. In (a) and (c) are shown the data (filled circles with error bars) and the prediction from different background processes,normalized to the acquired luminosity for the data: dilepton events (double hatched area), two-photon processes (negative slope hatching) andfour-fermion processes (positive slope hatching). In (b) and (d) the prediction for simulated selectron events are shown forme = 94 GeV andwith m

χ01

= 49 GeV. The normalization of the signal distribution is arbitrary. The arrows indicate the region accepted by the analysis.

• scalar momentum sum< 1 GeV;• additional electromagnetic calorimeter energy sum< 5 GeV;

• hadronic calorimeter energy< 5 GeV.

The energies of the most (Eγ1) and second most (Eγ2)energetic photon are also used to select signal events.

In the�+�− selections,φacop> 5◦ is required, whilethe cut is tightened toφacop> 10◦ for the χ+

1 χ−1 and

χ02 χ

01 selections. In all channels,|cosθmiss| < 0.95

is required. The values of all other analysis cuts aresummarized in Table 1, for the different�m regions.

Examples distributions of the event visible energyand the energy of the most energetic photon areshown in Fig. 1. The selection results are summarizedin Table 2, and the numbers of selected events areconsistent with Standard Model sources.

The detection efficiencies for events from�+�−production assuming the decays�→ �χ0

1 and χ01 →


Table 2Remaining numbers of events after all cuts for sleptons, charginos and neutralinos. There are large correlations among both the selected eventsand expected background in the different analyses

Channel Region Data Total bkg.

�+�− 3 GeV<�m< 10 GeV 0 1.1±0.2

10 GeV<�m<m�/2 0 1.3±0.2

m�/2<�m<m

�0 2.6±0.4

χ+1 χ

−1 3 GeV<�m< 10 GeV HM 0 0.6±0.1

LM 0 1.5±0.4

10 GeV<�m<mχ±/2 HM 3 3.2±0.8

LM 0 2.1±0.5

mχ±/2<�m<mχ± − 20 GeV HM 4 5.5±1.7

LM 0 1.4±0.4

mχ± − 20 GeV<�m<mχ± HM 5 7.2±3.4

LM 0 0.8±0.3

χ02 χ

01 3 GeV<�m< 10 GeV HM 0 0.3±0.05

LM 0 1.8±0.4

10 GeV<�m< 30 GeV HM 0 0.7±0.05

LM 0 1.5±0.4

30 GeV<�m< 80 GeV HM 4 4.5±1.5

LM 0 1.7±0.5

80 GeV<�m< 180 GeV HM 3 4.6±1.6

LM 0 1.3±0.4

γ G are typically 30–50% for scalar electrons andmuons, and 20–40% for scalar tau leptons. Summingthe high- and low-multiplicity selections, the detec-tion efficiencies for events fromχ+

1 χ−1 production as-

suming the decaysχ±1 → W(∗)±χ0

1 and χ01 → γ G

range from 20–50%, depending on the masses of thechargino and lightest neutralino. Summing the high-and low-multiplicity selections, the detection efficien-cies for events fromχ0

2 χ01 production assuming the

decaysχ02 → Z(∗)χ0

1 andχ01 → γ G are typically 20–

50%, depending on the mass of the two neutralinos.

3.2. � NLSP

3.2.1. �+�− production with� NLSPThe search for lightest scalar lepton pair production

followed by the decays�± → �±G uses the OPALselection of events with lepton pairs and missing

energy [4]. The analysis selects events with two leptoncandidates and significant missing energy, along withno other significant energy in the event. A total of301 events were observed in the data, consistent withthe 303.3±1.9 events expected from all backgroundsources. A likelihood selection using informationabout the leptons’ energies, charges and polar anglesis used to maximize the sensitivity of the analysisto slepton production for each slepton mass. Anoptimized cut for each scalar lepton mass on thelikelihood is applied, as described in Ref. [25]. Noevidence for anomalous production of lepton pairswith missing energy is observed.

3.2.2. χ01 χ

01 production with� NLSP and�+�− with

τ NLSPWith a � NLSP, the large neutralino pair pro-

duction cross-section may make the 4-lepton plus


Fig. 2. The event transverse momentum,pmissT

, for events in the 4 leptons plus missing energy analysis after the preselection and requiringbetween 4 and 10 tracks for (a) data and Standard Model backgrounds (as for Fig. 1) and (b) predictions from simulated neutralino events form�

= 50 GeV and withmχ0

1= 60 GeV (solid line),m

χ01

= 90 GeV (dashed line) and withmχ0

1= 94 GeV (dotted line), assuming equal

branching fractions for all three lepton generations. Also shown are the distributions of the number of identified, isolated leptons after themissing energy cuts for events in the 6 leptons plus missing energy analysis for (c) data and Standard Model backgrounds (with an additionalcontribution from multihadronic events shown by the open area) and (d) scalar electron signal Monte Carlo withme = 94 GeV and withmτ = 85 GeV (solid line) andmτ = 60 GeV (dashed line). The normalizations of the signal distributions are arbitrary. The arrows indicate theregion accepted by the analysis.

missing energy signature e+e− → χ01 χ

01 → ��′�′ →

(�+�−G)(�′+�′−G) the GMSB discovery channel. Be-cause the scalar tau lepton may be the lightest slepton,the signature may predominantly include tau leptons.The selection is sensitive to all 4-lepton plus missingenergy final states. Additionally, with aτ NLSP, ifthe neutralinos are too heavy to be produced and the

scalar tau lepton is significantly lighter than the scalarelectron and muon, then the 6-lepton plus missing en-ergy final state may contribute via e+e− → �+�− →(�+τ τ )(�−τ τ )→ (�+τ+τ−G)(�−τ+τ−G).

The analyses select low multiplicity events byallowing at most 10 tracks. The events are requiredto have significant missing energy by applying cuts


Table 3Analysis requirements on quantities used in the different� or τNLSP selections

Channel φacop cosθmiss pmissT

/Ebeam Evis/√s

χ01 χ

01 > 10◦ < 0.90 > 0.10 [0.10,0.90]

�+�− – > 0.12 [0.10,0.80]

Table 4The numbers of events remaining after all cuts in the search forneutralinos and sleptons with a� NLSP

Channel Data Bkg.

χ01 χ

01 → (��G)(�′�′G) 2 1.9±0.2

�+ �− → (�+ττ G)(�−ττ G) 5 5.2±0.4

on φacop, cosθmiss, pmissT /Ebeam andEvis/

√s, listed

in Table 3. In the 4-lepton analysis, we require twoidentified, isolated leptons in the event and removeStandard Modelτ+τ−γ events by vetoing events withphotons with more than half the beam energy. In the6-lepton analysis, only one identified, isolated leptonis required. This is because these events typically haveonly two high energy leptons, both taus, and they oftenhave nearby tracks from the other decay products andare, therefore, not isolated. If the event is consistentwith one lepton plus two hadronic jets an additionalveto on e+e− → W+W− → qq�ν is applied: eventsare removed if the invariant mass of the most energeticlepton and missing momentum is greater than 60 GeV,or if the mass of the two hadronic jets is greater than60 GeV. Examples distributions of the event transversemomentum and the number of identified, isolatedleptons are shown in Fig. 2. The selection results aresummarized in Table 4, and the numbers of selectedevents are consistent with Standard Model sources.

The detection efficiencies for events fromχ01 χ

01 pair

production assuming the decaysχ01 → ��→ ��G are

fairly uniform for differentχ01 and�masses, and about

50% if the neutralino decays into all three sleptongenerations with equal branching ratios, and 35% ifit decays via staus with 100% branching ratio. Thedetection efficiencies for events from selectron andsmuon pair production assuming decays into staus arealso fairly uniform for different sparticle masses, andare typically about 50%.

4. Systematic errors and corrections

Systematic errors on the number of expected signalevents arise from the following sources: the measure-ment of the integrated luminosity (0.5%); Monte Carlostatistics for the signal samples (1–2%), and interpola-tion errors when determining the efficiencies at arbi-trary masses (typically 5%); gaugino field content ofthe χ± andχ0 which can lead to different productionand decay angular distributions (< 5%); modelling ofthe cut variables in the Monte Carlo simulations (5–10%). The cut variable modelling error is determinedby shifting each cut by an amount estimated by com-paring data and Monte Carlo in high statistics samples.

The systematic errors on the expected number ofbackground events are determined from: Monte Carlostatistics in the simulated background events (typically5%); modelling of the cut variables (from 10–20%,depending on the analysis and kinematic region).

In the analyses in Sections 3.1.2 and 3.2.2, a com-mon veto on energy deposition in the forward detec-tors was applied in the preselection. The rate of eventsin which accidental energy depositions in the forwarddetectors exceeds the veto thresholds used in the prese-lection is estimated from luminosity weighted randombeam crossing events to be 2.9%. Since this effect isnot included in the Monte Carlo simulations, the lu-minosity is reduced accordingly by this factor whenderiving limits using the data.

5. Results

No significant excesses are observed in any chan-nels, so limits are derived using the search results.Limits are derived using the method from Ref. [26],including the effects of systematic errors on the sig-nal detection efficiencies and background expectationusing the method from Ref. [27].

5.1. Model independent interpretations

For a χ01 NLSP, assuming the prompt decayχ0

1 →γ G, production cross-section limit contours are calcu-lated in the mass plane of the particle produced vs.the mass of theχ0

1 . In this scenario, limits on theproduction cross-sections for the processes e+e− →µ+µ−, e+e− → τ+τ−, e+e− → χ+

1 χ−1 and e+e− →


Fig. 3. Limits at the 95% confidence level for the production cross-section of e+e− → (a) µ+µ−, (b) τ+τ−, (c) χ+1 χ

−1 and (d) χ0

2 χ01 ,

assuming decays viaχ01 followed by the prompt decaysχ0

1 → γ G. The limits one+e− are essentially identical to those forµ+µ−. Thedashed lines indicate the kinematic limit.

χ02 χ

01 are shown in Fig. 3. Typically, production cross-

sections in excess of about 0.03–0.1 pb are excludedat the 95% confidence level.

For a � NLSP, assuming the prompt decay� →�G, production cross-section limit contours can becalculated in the mass plane of the particle producedvs. the mass of the�, shown in Fig. 4. Typically,cross-sections for e+e− → χ0

1 χ01 larger than 0.05–

0.06 pb are excluded at the 95% confidence level forthe degenerate slepton case, while cross-section largerthan 0.07–0.15 pb are excluded for the stau NLSP

case. For scalar electron or muon pair production witha scalar tau NLSP, the cross-section limits are typically0.06–0.13 pb.

5.2. GMSB model dependent interpretations

While there is no single GMSB model, there aretypically [1–3] six new parameters in addition to thoseof the SM:

(1)F,Λ,M,N, tanβ and sign(µ).


Fig. 4. Limits at the 95% confidence level for the production cross-section of e+e− → (a) χ01 χ

01 assuming the decaysχ0

1 → �� with equal

branching ratios to all three generations, (b)χ01 χ

01 assuming the decaysχ0

1 → τ τ , (c) e+e− assuming the decayse→ τ τe and (d)µ+µ−assuming the decaysµ→ τ τµ. The limits assume that these decays are followed by the prompt decays�→ �G. The dashed lines indicate thekinematic limit.

The intrinsic SUSY breaking scale is√F , which

also determines theG mass according tomG � 2.5 ×F/(100 TeV)2 eV. Since

√F affects primarily the

lifetime of the NLSP we do not vary it for this Letter,but simply assume that this lifetime is short enoughto have no effect on our detection efficiencies. TheparameterΛ sets the overall mass scale for SUSYparticles,M is the mass of the messenger particles,

N is the number of sets13 of messenger particles,

13 N is technically the Dynkin index of the gauge representationof the messenger fields. To preserve gauge coupling unification,the messengers are assumed to form a GUT representation. Inthe simplest form, each of theN messenger particle sets has thequantum numbers of an5 + 5 of SU(5). The maximum numberof messengers can be bounded by requiring the gauge interactions


Fig. 5. Excluded regions at the 95% C.L. in theΛ vs. tanβ plane forN = 1,2,3 and 4, and forµ < 0. The areas above and to the left of thesolid line are excluded forM = 106 TeV, the dashed line forM = 250 TeV, and the dotted line forM = 1.01×Λ. The shaded regions aretheoretically inaccessible forM = 106 TeV (the inaccessible region is larger for smaller values ofM). The exclusions forµ> 0 are somewhatstronger.

and tanβ is the usual ratio of the Higgs vacuumexpectation values. The final parameter is just thesign of the Higgs sector mixing parameter,µ, whichintroduces a two-fold ambiguity (the magnitude ofµis calculable from the other parameters in the minimalmodel by imposing radiative electroweak symmetrybreaking). The messenger scale gaugino masses can

remain perturbative up the GUT scale, although this bound dependsonM . ForM = 100 TeV,N � 5, while forM = 1010 TeV,N � 10.

be calculated using the relation

(2)Mi =Nαi

4πΛg(Λ/M),

where the indexi refers to theU(1), SU(2) orSU(3) gauge group, and theαi are the SM gaugecouplings. The functiong(Λ/M) is always slightlygreater than 1, but its effect is only significant whenΛ ≈ M. It is also possible to calculate all of themessenger scale scalar SUSY particle masses usingΛ


Fig. 6. Excluded regions at the 95% C.L. in them�

vs.mχ0

1plane for (a) tanβ = 2 (approximately degenerate slepton case) and (b) tanβ = 20

(lighter stau case). Also shown are the regions exclusively excluded by (A)χ01 χ

01 → γ Gγ G, (B) τ+τ− → τ+Gτ−G, (C)µ+µ− →µ+Gµ−G

and (D)χ01 χ

01 → 4 lepton final states. The other search channels do not contribute significantly to the exclusion regions in the minimal model.

The shaded regions are theoretically inaccessible.

andN via

(3)m2 = 2NΛ2f (Λ/M)

3∑i=1

ki

(αi

4π

)2

,

whereki are multiplicative factors determined by theparticle’s SM charge, hypercharge and colour charge.The functionf (Λ/M) is usually near 1, except whenΛ≈M. The electroweak scale particle masses may becalculated from the messenger scale masses using therenormalization group equations.

We will work in a theoretical framework based onRef. [1], extending it by including a full mass treat-ment for all three generations of sparticles. The the-oretical calculations are embedded in the SUSYGEN[11] generator. The complete interpretation frameworkis described in Ref. [28]. The SUSY breaking scale(or equivalently gravitino mass) is not considered ex-plicitly in this section, although it is assumed thatMG < 1 GeV for the selection efficiencies to remainvalid. The values of the parameters considered in ourscan are shown in Table5.

In Fig. 5, 95% C.L. exclusion limits in theΛ vs.tanβ plane are shown for different values ofN . Theχ0

1 NLSP signatures tend to be dominant for smallN

and low tanβ , while the� NLSP signatures are more

Table 5Parameter ranges considered in GMSB scans

Parameter Lower value Upper value

tanβ 2 50

Λ 5 TeV 200 TeV

M 1.01×Λ 106 TeV

N 1 4

sign(µ) −1 +1

important for either largerN or larger tanβ . Absolute95% C.L. lower limits onΛ of 48, 31, 22 and 19 TeVare established forN = 1,2,3 and 4, respectively.In Fig. 6(a), the excluded region in theM� vs.Mχ0

1plane is shown for tanβ = 2, corresponding to the casewhere the three sleptons are degenerate in mass. Thedominant exclusion channels in the minimal model areχ0

1 χ01 → γ Gγ G and�+�− → �+G�−G. In Fig. 6(b),

the excluded region in theMτ vs.Mχ01

plane is shownfor tanβ = 20, corresponding to the case where theτ is significantly lighter than the other sleptons. Theχ0

1 χ01 → γ Gγ G channel remains powerful in this

case, but the lightτ means that only theτ+τ− →


τ+Gτ−G channel contributes to the significance fromlepton pair final states.

Finally, 95% C.L. limits can be derived on theNLSP mass ofM� > 83 GeV andMχ0

1> 85 GeV

for tanβ = 2, andMτ > 69 GeV,Me,µ > 88 GeV andMχ0

1> 76 GeV for tanβ = 20.

6. Conclusion

We have searched for signatures expected in modelswith gauge mediated SUSY breaking at a centre-of-mass energy of

√s = 189 GeV with the OPAL

detector at LEP. No evidence in any search channelover the expectations from the Standard Model wasobserved. Limits are placed on the production cross-sections for a number of processes for the promptdecays of the next-to-lightest SUSY particle to agravitino. The results are used to constrain minimalmodels of gauge mediated supersymmetry breaking.

Acknowledgements

We particularly wish to thank the SL Division forthe efficient operation of the LEP accelerator at allenergies and for their continuing close cooperationwith our experimental group. We thank our colleaguesfrom CEA, DAPNIA/SPP, CE-Saclay for their effortsover the years on the time-of-flight and trigger sys-tems which we continue to use. In addition to the sup-port staff at our own institutions we are pleased to ac-knowledge the Department of Energy, USA; NationalScience Foundation, USA; Particle Physics and As-tronomy Research Council, UK; Natural Sciences andEngineering Research Council, Canada; Israel Sci-ence Foundation, administered by the Israel Academyof Science and Humanities, Minerva Gesellschaft;Benoziyo Center for High Energy Physics; JapaneseMinistry of Education, Science and Culture (the Mon-busho) and a grant under the Monbusho Interna-tional Science Research Program; Japanese Societyfor the Promotion of Science (JSPS); German IsraeliBi-national Science Foundation (GIF); Bundesminis-terium für Bildung und Forschung, Germany; NationalResearch Council of Canada; Research Corporation,USA; Hungarian Foundation for Scientific Research,OTKA T-029328, T023793 and OTKA F-023259.

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