Search for R-parity violating supersymmetry via the LL(E)over-bar couplings lambda(121), lambda(122) or lambda(133) in p(p)over-bar collisions at root s=1.96 TeV

(1)

www.elsevier.com/locate/physletb

Search for R-parity violating supersymmetry via the LL ¯

E

couplings λ

₁₂₁

,

λ

₁₂₂

or λ

₁₃₃

in p

¯p collisions at

√

s

= 1.96 TeV

D

∅ Collaboration

V.M. Abazov

aj

_{, B. Abbott}

bx

_{, M. Abolins}

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_{, B.S. Acharya}

ac

_{, M. Adams}

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_{, T. Adams}

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_{, M. Agelou}

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_,

J.-L. Agram

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_{, S.H. Ahn}

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_{, M. Ahsan}

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_{, G.D. Alexeev}

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_{, G. Alkhazov}

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_{, A. Alton}

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_{, G. Alverson}

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_,

G.A. Alves

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_{, M. Anastasoaie}

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_{, T. Andeen}

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_{, S. Anderson}

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_{, B. Andrieu}

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_{, M.S. Anzelc}

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_,

Y. Arnoud

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_{, M. Arov}

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_{, A. Askew}

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_{, B. Åsman}

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_{, A.C.S. Assis Jesus}

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_{, O. Atramentov}

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C. Autermann

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_{, C. Avila}

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_{, C. Ay}

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_{, F. Badaud}

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_{, A. Baden}

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_{, L. Bagby}

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_{, B. Baldin}

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_,

D.V. Bandurin

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_{, P. Banerjee}

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_{, S. Banerjee}

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_{, E. Barberis}

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_{, P. Bargassa}

cc

_{, P. Baringer}

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_,

C. Barnes

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_{, J. Barreto}

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_{, J.F. Bartlett}

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_{, U. Bassler}

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_{, D. Bauer}

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_{, A. Bean}

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_{, M. Begalli}

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M. Begel

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_{, C. Belanger-Champagne}

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_{, L. Bellantoni}

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_{, A. Bellavance}

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_{, J.A. Benitez}

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_{, S.B. Beri}

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G. Bernardi

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_{, R. Bernhard}

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_{, L. Berntzon}

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_{, I. Bertram}

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_{, M. Besançon}

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_{, R. Beuselinck}

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V.A. Bezzubov

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_{, P.C. Bhat}

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_{, V. Bhatnagar}

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_{, M. Binder}

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_{, C. Biscarat}

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_{, K.M. Black}

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I. Blackler

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_{, G. Blazey}

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_{, F. Blekman}

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_{, S. Blessing}

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_{, D. Bloch}

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_{, K. Bloom}

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_{, U. Blumenschein}

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A. Boehnlein

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_{, O. Boeriu}

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_{, T.A. Bolton}

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_{, F. Borcherding}

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_{, G. Borissov}

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_{, K. Bos}

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_{, T. Bose}

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A. Brandt

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_{, R. Brock}

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_{, G. Brooijmans}

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_{, A. Bross}

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_{, D. Brown}

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_{, N.J. Buchanan}

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D. Buchholz

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_{, M. Buehler}

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_{, V. Buescher}

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_{, S. Burdin}

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_{, S. Burke}

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_{, T.H. Burnett}

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_{, E. Busato}

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C.P. Buszello

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_{, J.M. Butler}

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_{, P. Calfayan}

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_{, S. Calvet}

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_{, J. Cammin}

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_{, S. Caron}

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_{, W. Carvalho}

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B.C.K. Casey

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_{, N.M. Cason}

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_{, H. Castilla-Valdez}

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_{, S. Chakrabarti}

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_{, D. Chakraborty}

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K.M. Chan

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_{, A. Chandra}

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_{, D. Chapin}

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_{, F. Charles}

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_{, E. Cheu}

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_{, F. Chevallier}

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_{, D.K. Cho}

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S. Choi

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_{, B. Choudhary}

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_{, L. Christofek}

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_{, D. Claes}

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_{, B. Clément}

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_{, C. Clément}

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_{, Y. Coadou}

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M. Cooke

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_{, W.E. Cooper}

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_{, D. Coppage}

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_{, M. Corcoran}

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_{, M.-C. Cousinou}

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_{, B. Cox}

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S. Crépé-Renaudin

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_{, D. Cutts}

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_{, M. ´}

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_{, H. da Motta}

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_{, A. Das}

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_{, M. Das}

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_{, B. Davies}

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G. Davies

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_{, G.A. Davis}

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_{, K. De}

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_{, P. de Jong}

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_{, S.J. de Jong}

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_{, E. De La Cruz-Burelo}

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C. De Oliveira Martins

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_{, J.D. Degenhardt}

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_{, F. Déliot}

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_{, M. Demarteau}

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_{, R. Demina}

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_{, P. Demine}

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D. Denisov

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_{, S.P. Denisov}

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_{, S. Desai}

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_{, H.T. Diehl}

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_{, M. Diesburg}

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_{, M. Doidge}

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A. Dominguez

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_{, H. Dong}

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_{, L.V. Dudko}

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_{, L. Duflot}

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_{, A. Duperrin}

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_{, J. Dyer}

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A. Dyshkant

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_{, M. Eads}

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_{, D. Edmunds}

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_{, T. Edwards}

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_{, J. Ellison}

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_{, J. Elmsheuser}

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V.D. Elvira

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_{, S. Eno}

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_{, P. Ermolov}

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_{, J. Estrada}

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_{, H. Evans}

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_{, A. Evdokimov}

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V.N. Evdokimov

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_{, S.N. Fatakia}

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_{, L. Feligioni}

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_{, A.V. Ferapontov}

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_{, T. Ferbel}

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_{, F. Fiedler}

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F. Filthaut

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_{, W. Fisher}

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_{, H.E. Fisk}

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_{, I. Fleck}

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_{, M. Ford}

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_{, M. Fortner}

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_{, H. Fox}

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_{, S. Fu}

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S. Fuess

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_{, T. Gadfort}

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_{, C.F. Galea}

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_{, E. Gallas}

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_{, E. Galyaev}

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_{, C. Garcia}

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_{, A. Garcia-Bellido}

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J. Gardner

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_{, V. Gavrilov}

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_{, A. Gay}

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_{, P. Gay}

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_{, D. Gelé}

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_{, R. Gelhaus}

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Y. Gershtein

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_{, D. Gillberg}

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_{, G. Ginther}

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_{, N. Gollub}

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_{, B. Gómez}

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_{, K. Gounder}

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_{, A. Goussiou}

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P.D. Grannis

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_{, H. Greenlee}

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_{, Z.D. Greenwood}

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_{, E.M. Gregores}

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_{, G. Grenier}

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_{, Ph. Gris}

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J.-F. Grivaz

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_{, S. Grünendahl}

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_{, M.W. Grünewald}

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_{, F. Guo}

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_{, J. Guo}

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_{, G. Gutierrez}

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(2)

P. Gutierrez

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_{, A. Haas}

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_{, N.J. Hadley}

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_{, P. Haefner}

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_{, S. Hagopian}

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_{, J. Haley}

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_{, I. Hall}

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R.E. Hall

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_{, L. Han}

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_{, K. Hanagaki}

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_{, K. Harder}

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_{, A. Harel}

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_{, R. Harrington}

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_{, J.M. Hauptman}

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R. Hauser

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_{, J. Hays}

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_{, T. Hebbeker}

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_{, D. Hedin}

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_{, J.G. Hegeman}

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_{, J.M. Heinmiller}

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A.P. Heinson

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_{, U. Heintz}

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_{, C. Hensel}

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_{, G. Hesketh}

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_{, M.D. Hildreth}

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_{, R. Hirosky}

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J.D. Hobbs

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_{, B. Hoeneisen}

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_{, H. Hoeth}

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_{, M. Hohlfeld}

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_{, S.J. Hong}

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_{, R. Hooper}

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_{, P. Houben}

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Y. Hu

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_{, Z. Hubacek}

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_{, V. Hynek}

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_{, S. Jabeen}

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_{, M. Jaffré}

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S. Jain

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_{, K. Jakobs}

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_{, C. Jarvis}

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_{, A. Jenkins}

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_{, C. Johnson}

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_{, M. Johnson}

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_{, E. Kajfasz}

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_{, A.M. Kalinin}

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_{, P. Kasper}

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_{, I. Katsanos}

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D. Kau

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_{, A. Khanov}

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A. Kharchilava

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_{, Y.M. Kharzheev}

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_{, D. Khatidze}

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_{, H. Kim}

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B. Klima

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_{, J.M. Kohli}

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_{, V.M. Korablev}

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_{, J. Kotcher}

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_{, A.V. Kozelov}

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_{, J. Kozminski}

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_{, A. Kryemadhi}

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_{, T. Kuhl}

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A. Kumar

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_{, J. Lazoflores}

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_{, A.-C. Le Bihan}

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_{, J. Leveque}

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_{, D. Lincoln}

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_{, J. Linnemann}

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_{, R. Lipton}

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_{, M. Lokajicek}

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_{, H.J. Lubatti}

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_{, M. Lynker}

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_{, A. Magerkurth}

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_{, N. Makovec}

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_{, P.K. Mal}

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_{, V.L. Malyshev}

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_{, H.S. Mao}

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_{, Y. Maravin}

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_{, M. Martens}

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_{, S.E.K. Mattingly}

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_{, R. McCroskey}

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_{, K.W. Merritt}

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_{, A. Meyer}

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_{, T. Millet}

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_{, J. Molina}

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_{, M. Mulhearn}

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_{, E. Nagy}

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_{, M. Naimuddin}

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_{, J.P. Negret}

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_{, S.F. Novaes}

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_{, V. Oguri}

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_{, N. Parua}

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_{, M. Petteni}

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_{, M.-A. Pleier}

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_{, Y. Pogorelov}

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_{, W.L. Prado da Silva}

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_{, P. Renkel}

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_{, F. Rizatdinova}

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_{, R. Ruchti}

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_{, T. Scanlon}

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_{, V. Sirotenko}

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_{, P. Skubic}

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_{, G.R. Snow}

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_{, J. Snow}

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_{, X. Song}

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_{, A. Sopczak}

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_{, M. Sosebee}

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_{, M. Souza}

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_{, B. Spurlock}

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_{, J. Steele}

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_{, K. Stevenson}

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_{, A. Stone}

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_{, D.A. Stoyanova}

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(3)

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_{, N. Xuan}

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_{, J. Yu}

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_{, A. Yurkewicz}

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_{, A. Zatserklyaniy}

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_{, C. Zeitnitz}

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_{, D. Zhang}

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_{, T. Zhao}

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_{, J. Zhu}

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_{, D. Zieminska}

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_{, A. Zieminski}

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_{, V. Zutshi}

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_{, E.G. Zverev}

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a_{Universidad de Buenos Aires, Buenos Aires, Argentina} b_{LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil}

c_{Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil} d_{Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil}

e_{University of Alberta, Edmonton, Alberta, Canada, Simon Fraser University, Burnaby, British Columbia, and}

York University, Toronto, Ontario, Canada, and McGill University, Montreal, Quebec, Canada

f_{Institute of High Energy Physics, Beijing, People’s Republic of China} g_{University of Science and Technology of China, Hefei, People’s Republic of China}

h_{Universidad de los Andes, Bogotá, Colombia}

i_{Center for Particle Physics, Charles University, Prague, Czech Republic} j_{Czech Technical University, Prague, Czech Republic}

k_{Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic} l_{Universidad San Francisco de Quito, Quito, Ecuador}

m_{Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Université Blaise Pascal, Clermont-Ferrand, France} n_{Laboratoire de Physique Subatomique et de Cosmologie, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France}

o_{CPPM, IN2P3-CNRS, Université de la Méditerranée, Marseille, France} p_{IN2P3-CNRS, Laboratoire de l’Accélérateur Linéaire, Orsay, France}

q_{LPNHE, IN2P3-CNRS, Universités Paris VI and VII, Paris, France} r_{DAPNIA/Service de Physique des Particules, CEA, Saclay, France}

s_{IReS, IN2P3-CNRS, Université Louis Pasteur, Strasbourg, France, and Université de Haute Alsace, Mulhouse, France} t_{Institut de Physique Nucléaire de Lyon, IN2P3-CNRS, Université Claude Bernard, Villeurbanne, France}

u_{III. Physikalisches Institut A, RWTH Aachen, Aachen, Germany} v_{Physikalisches Institut, Universität Bonn, Bonn, Germany} w_{Physikalisches Institut, Universität Freiburg, Freiburg, Germany}

x_{Institut für Physik, Universität Mainz, Mainz, Germany} y_{Ludwig-Maximilians-Universität München, München, Germany} z_{Fachbereich Physik, University of Wuppertal, Wuppertal, Germany}

aa_{Panjab University, Chandigarh, India} ab_{Delhi University, Delhi, India}

ac_{Tata Institute of Fundamental Research, Mumbai, India} ad_{University College Dublin, Dublin, Ireland}

ae_{Korea Detector Laboratory, Korea University, Seoul, South Korea} af_{SungKyunKwan University, Suwon, South Korea}

ag_{CINVESTAV, Mexico City, Mexico}

ah_{FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands} ai_{Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands}

aj_{Joint Institute for Nuclear Research, Dubna, Russia} ak_{Institute for Theoretical and Experimental Physics, Moscow, Russia}

al_{Moscow State University, Moscow, Russia} am_{Institute for High Energy Physics, Protvino, Russia} an_{Petersburg Nuclear Physics Institute, St. Petersburg, Russia}

ao_{Lund University, Lund, Sweden, Royal Institute of Technology and Stockholm University, Stockholm, and}

Uppsala University, Uppsala, Sweden

ap_{Physik Institut der Universität Zürich, Zürich, Switzerland} aq_{Lancaster University, Lancaster, United Kingdom}

ar_{Imperial College, London, United Kingdom} as_{University of Manchester, Manchester, United Kingdom}

at_{University of Arizona, Tucson, AZ 85721, USA}

au_{Lawrence Berkeley National Laboratory and University of California, Berkeley, CA 94720, USA} av_{California State University, Fresno, CA 93740, USA}

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aw_{University of California, Riverside, CA 92521, USA} ax_{Florida State University, Tallahassee, FL 32306, USA} ay_{Fermi National Accelerator Laboratory, Batavia, IL 60510, USA}

az_{University of Illinois at Chicago, Chicago, IL 60607, USA} ba_{Northern Illinois University, DeKalb, IL 60115, USA}

bb_{Northwestern University, Evanston, IL 60208, USA} bc_{Indiana University, Bloomington, IN 47405, USA} bd_{University of Notre Dame, Notre Dame, IN 46556, USA} be_{Purdue University Calumet, Hammond, IN 46323, USA}

bf_{Iowa State University, Ames, IA 50011, USA} bg_{University of Kansas, Lawrence, KS 66045, USA} bh_{Kansas State University, Manhattan, KS 66506, USA}

bi_{Louisiana Tech University, Ruston, LA 71272, USA} bj_{University of Maryland, College Park, MD 20742, USA}

bk_{Boston University, Boston, MA 02215, USA} bl_{Northeastern University, Boston, MA 02115, USA} bm_{University of Michigan, Ann Arbor, MI 48109, USA} bn_{Michigan State University, East Lansing, MI 48824, USA}

bo_{University of Mississippi, University, MS 38677, USA} bp_{University of Nebraska, Lincoln, NE 68588, USA} bq_{Princeton University, Princeton, NJ 08544, USA} br_{State University of New York, Buffalo, NY 14260, USA}

bs_{Columbia University, New York, NY 10027, USA} bt_{University of Rochester, Rochester, NY 14627, USA} bu_{State University of New York, Stony Brook, NY 11794, USA}

bv_{Brookhaven National Laboratory, Upton, NY 11973, USA} bw_{Langston University, Langston, OK 73050, USA} bx_{University of Oklahoma, Norman, OK 73019, USA} by_{Oklahoma State University, Stillwater, OK 74078, USA}

bz_{Brown University, Providence, RI 02912, USA} ca_{University of Texas, Arlington, TX 76019, USA} cb_{Southern Methodist University, Dallas, TX 75275, USA}

cc_{Rice University, Houston, TX 77005, USA} cd_{University of Virginia, Charlottesville, VA 22901, USA}

ce_{University of Washington, Seattle, WA 98195, USA}

Received 30 April 2006; received in revised form 26 May 2006; accepted 29 May 2006 Available online 12 June 2006

Editor: L. Rolandi

Abstract

A search for gaugino pair production with a trilepton signature in the framework of R-parity violating supersymmetry via the couplings λ121,

λ122, or λ133 is presented. The data, corresponding to an integrated luminosity ofL ≈ 360 pb−1, were collected from April 2002 to August 2004 with the D∅ detector at the Fermilab Tevatron Collider, at a center-of-mass energy of√s= 1.96 TeV. This analysis considers final states with

three charged leptons with the flavor combinations ee, μμ, and eeτ (= e or μ). No evidence for supersymmetry is found and limits at the 95% confidence level are set on the gaugino pair production cross section and lower bounds on the masses of the lightest neutralino and chargino are derived in two supersymmetric models.

Keywords: Supersymmetry; Supergravity; Supersymmetric models

Supersymmetry (SUSY)[1]predicts the existence of a new particle for each standard model (SM) particle, differing by half a unit in spin but otherwise sharing the same quantum numbers.

* _{Corresponding author.}

E-mail address:[email protected](D. Käfer).

1 _{On leave from IEP SAS Kosice, Slovakia.}

2 _{Visitor from Helsinki Institute of Physics, Helsinki, Finland.}

The new scalar particles, known as squarks and sleptons, carry baryon (B) or lepton (L) quantum numbers, potentially leading to interactions violating B or L conservation. In the supersym-metric Lagrangian, there is a continuous R-invariance, which prevents lepton and baryon number violation, but also prevents gluinos and gravitinos from being massive.

In a supergravity scenario, the gravitino will acquire mass through the spontaneous breaking of local SUSY. The

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SUSY-breaking is then communicated to the so-called observable sec-tor so that, in particular, the gluino acquires its mass[2]. This breaks the continuous R-invariance, leaving only a discrete ver-sion, which is called R-parity[3]. Each particle is characterized by an R-parity quantum number defined as Rp= (−1)3B+L+2S

(S being the spin), such that SM particles have Rp= 1 and

SUSY particles Rp = −1. The gauge symmetry allows

R-parity violating (/Rp) terms to be included in the

superpoten-tial[4]. These terms are:

WR/p=

1

2λij kLiLj ¯Ek+ λ

ij kLiQjDk¯ + μiLiHu (1) +1 2λ ij k ¯UiD¯jD¯k,

where L and Q are the lepton and quark SU(2) doublet super-fields, while ¯E, ¯U, and ¯Ddenote the weak isospin singlet fields and the indices i, j , k refer to the fermion families. The cou-pling strengths in the trilinear terms are given by the Yukawa coupling constants λ, λ and λ. Terms appearing in the first line of Eq.(1)violate lepton number by one unit, and the last term in the second line leads to baryon number violation. The bilinear term μiLiHumixes lepton and Higgs (Hu) superfields.

This Letter reports on a search for chargino and neutralino pair production under the hypothesis that /Rpcan only occur via

a term of the type λij kLiLj ¯Ek. A non-zero /Rp coupling λij k

thus enables a slepton to decay into a lepton pair, as shown in

Fig. 1for the /Rp-decay of the lightest neutralino. The so-called LL ¯E couplings λij k specifically studied here, are λ121, λ122,

and λ133. One coupling is assumed to be dominant at a time,

with any other /Rp-coupling negligibly small.

The initial state at the Fermilab Tevatron Collider consists of hadrons, so the production of a single SUSY particle could only occur through a trilinear term including at least one baryon field, i.e. via λor λterms. Consequently, since only the LL ¯E

term (λ) is considered here, SUSY particles are produced pair-wise in an R-parity conserving process[5], with /Rpmanifesting

itself in the decay only. Even though direct decays of heavy gauginos (˜χ_2,3,40 , ˜χ₂±) are possible, they predominantly cascade decay into the lightest supersymmetric particle (LSP), which in turn decays into SM particles via /Rp. In all scenarios studied

here, the lightest neutralino (˜χ₁0) is assumed to be the LSP. Two SUSY models are investigated. In the minimal super-gravity model (mSUGRA)[6], the universal soft breaking mass

Fig. 1. Two examples ofR/p-decays of the lightest neutralino via LL ¯E

cou-plings λ1j k. In each decay, two charged leptons and one neutrino are produced.

parameter for all scalars at the unification scale, m0, is set to

100 GeV or 1 TeV. At low m0, the stau can be lighter than the

second lightest neutralino (˜χ₂0) and the lightest chargino (˜χ₁±), leading to a larger number of final states with taus. By contrast, a high value of m0prevents complex cascade decays involving

sleptons. The universal trilinear coupling, A0, has only a small

influence on the gaugino pair production cross section and is set to zero as in the previous Run I analysis[7]. Searches for supersymmetric Higgs bosons at LEP[8]imply that tan β 2 is excluded, where tan β is the ratio of the vacuum expectation values of the two neutral Higgs fields. Since the cross section for gaugino pair production increases with increasing tan β due to decreasing masses, a value of tan β = 5 (close to the LEP limit) is chosen to ensure conservative results. A higher value of tan β= 20 is studied exclusively in the eeτ analysis, because the stau mass decreases with increasing tan β, leading to an en-hanced signal efficiency for this particular analysis. Both signs of the higgsino mixing mass parameter, μ, are considered and the common gaugino mass, m1/2, is varied.

In the specific minimal supersymmetric standard model (MSSM) [9] considered here, heavy squarks and sleptons (1 TeV) are assumed, while the GUT relation between M1and M2, the masses of the superpartners of the U (1)Y and SU(2)L

gauge bosons, is relaxed. The value of tan β is set to 5, and M1

and M2 are varied independently. The higgsino mixing mass

parameter μ is set to 1 TeV, so that ˜χ₃0, ˜χ₄0, and ˜χ₂±are heavy. Within the domain of the SUSY parameters explored in this analysis, pair production of ˜χ₁±˜χ₁∓ and ˜χ₂0˜χ₁± are the domi-nant processes, leading to final states with at least four charged leptons and two neutrinos. They come from either the decay of the ˜χ₁0, with the lepton flavors depending on λij k, or from

cascade decays of ˜χ₁± and ˜χ₂0. The strengths of the couplings are set to 0.01 (λ121 and λ122) and 0.003 (λ133). These values

are well below the current limits of λ121<0.5, λ122<0.085,

and λ133<0.005 for a slepton mass of 1 TeV, which have

been derived from the upper limits λ121<0.05, λ122<0.027,

and λ133<0.0016 obtained for a slepton mass of 100 GeV in

Refs.[4,10]. Additionally, only neutralinos with a decay length of less than 1 cm are considered, which results in a cut-off at low neutralino masses[11], i.e. 30 GeV for λ121and λ122, and

50 GeV for λ133, again for slepton masses of 1 TeV. As the ˜χ10

can be light, the leptons can have small transverse (w.r.t. the beam axis) momentum and thus be difficult to detect. For this reason, only three charged leptons with the flavor combinations

ee, μμ, or eeτ (= e or μ) are required.

The analysis is based on a dataset recorded with the D∅ detector between April 2002 and August 2004, corresponding to an integrated luminosity of L = 360 ± 23 pb−1. Previous searches with the hypothesis of a LL ¯E coupling have been performed by the D∅ Collaboration with Tevatron Run I data collected at a center-of-mass energy√s= 1.8 TeV[7].

The D∅ detector consists of a central tracking system sur-rounded by a uranium/liquid-argon sampling calorimeter and a system of muon detectors[12]. Charged particles are recon-structed using multiple layers of silicon detectors, as well as eight double layers of scintillating fibers in the 2 T axial mag-netic field of a superconducting solenoid. The D∅

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calorime-ter provides hermetic coverage up to pseudorapidities |η| = |− ln[tan(θ/2)]| ≈ 4 in a semi-projective tower geometry with longitudinal segmentation. The polar angle θ is measured from the geometric center of the detector with respect to the proton-beam direction. The muon system covers|η| < 2 and consists of a layer of tracking detectors and scintillation trigger coun-ters in front of 1.8 T toroidal magnets, followed by two more similar layers of detectors outside the toroids[13].

Events containing electrons or muons are selected for off-line analysis by a real-time three-stage trigger system. A set of single and dilepton triggers is used to tag the presence of electrons or muons based on their characteristic energy deposits in the calorimeter, the presence of high-momentum tracks in the tracking system, and hits in the muon detectors.

R-parity violating supersymmetry events are modeled using

SUSYGEN[14], with CTEQ5L [15] parton distribution func-tions (PDFs). The package SUSYGEN is interfaced with the program SUSPECT[16] for the evolution of masses and

cou-plings from the renormalization group equations. Leading order (LO) cross sections of signal processes, obtained withSUSY

-GEN, are multiplied by a K factor computed with GAUGI

-NOS [17]. Standard model processes are generated using the Monte Carlo (MC) generatorPYTHIA[18]. All MC events are processed through a detailed simulation of the detector geome-try and response based onGEANT3[19]. Multiple interactions per crossing as well as detector pile-up are included in the sim-ulations. The SM background predictions are normalized us-ing cross-section calculations at next-to-leadus-ing order (NLO) and next-to-NLO (for Drell–Yan production) with CTEQ6.1M PDFs[20]. Background from multijet production is estimated from data similar to the search samples, however, the lepton identification and isolation criteria are inverted (ee and eeτ ) or loosened (μμ). These samples are scaled at an early stage of the analysis where multijet production still dominates.

Electrons are identified based on their characteristic en-ergy deposition in the calorimeter [21]. The fraction of en-ergy deposited in the electromagnetic part of the calorime-ter and the transverse shower profile inside a cone of radius

R =( η)2_{+ ( ϕ)}2_{= 0.4 around the cluster direction are}

considered (where ϕ is the azimuthal angle). In addition, a track must point to the energy deposition in the calorimeter and its momentum and the calorimeter energy must be consistent with each other. Remaining backgrounds from jets are suppressed based on the track multiplicity within R = 0.4 around the track direction.

Muons are reconstructed using track segments in the muon system, and each muon is required to have a matched central track measured with the tracking detectors[21]. Furthermore, muons are required to be isolated in both the tracking detec-tors and the calorimeter, which is essential for rejecting muons associated with heavy-flavor jets. The sum of the track trans-verse momenta (pT) inside a cone of R = 0.5 around the

muon direction should be less than 2.5 GeV and less than 6% of the muon pT. For the calorimeter isolation, a transverse energy

(ET) of less than 2.5 GeV in a hollow cone of 0.1 < R < 0.4

around the muon direction is required and less than 8% of the muon’s transverse energy should be deposited in the

calorime-ter inside this hollow cone. For both isolation cricalorime-teria, the pT

(ET) of the muon track itself is excluded from the sum.

Electrons and muons are required to be isolated from each other ( Reμ >0.2), among themselves ( Ree >0.4,

Rμμ>0.2), and from hadronic jets ( Rj>0.5).

Taus decaying hadronically (τhad) are detected as narrow,

isolated jets with a specific ratio of electromagnetic to hadronic energy. Two neural networks (NN) are used to identify one-prong tau decays according to the calorimeter information: either with no subclusters in the electromagnetic section of the calorimeter (π -like) or with EM subclusters (ρ-like)[22]. Muons misidentified as taus are removed by taking the shower shape of the hadronic cluster into account.

Jets are defined using an iterative seed-based cone algorithm

[23], clustering calorimeter energy within R = 0.5. The jet energy calibration is determined from the transverse momtum balance in photon plus jet events. Missing transverse en-ergy (/ET) is calculated as the negative vector sum of energy deposits in the calorimeter cells, taking into account energy cor-rections for reconstructed electrons, muons, and jets.

Electron, muon, and tau reconstruction efficiencies and res-olutions are determined using measured Z boson decays. They are parametrized as functions of pT, η, and φ and applied to the

simulated MC events. The electron and muon trigger efficien-cies are measured in data and translate to signal event trigger efficiencies close to 100% for ee and eeτ , and around 94% for

μμ.

To achieve the best sensitivity for each /Rp-coupling, three

different analyses are used depending on the flavors of the lep-tons in the final state: ee, μμ, and eeτ (= e or μ). The criteria are summarized inTable 1. Each analysis requires three identified leptons with minimum transverse momenta pi_T. In the ee and eeτ analyses, the same lepton quality criteria are applied to each lepton, independent of its transverse momen-tum. The μμ analysis, however, uses looser quality criteria for the lowest-pT lepton to increase the selection efficiency.

Dielectron and dimuon backgrounds from Drell–Yan, Υ , and

Z boson production are suppressed using cuts on /ET and on

the invariant dilepton mass M(for the μμ and eeτ

analy-ses). All three analyses are optimized separately using SM and signal MC simulations.

Cuts I and II of the ee analysis (Table 1) are used to select a dielectron control sample for data and MC comparison, while cuts III and IV define the trilepton ee analysis. Cut III requires three leptons to be identified, two of which must be electrons. Cut IV, the photon conversion veto, which requires that a track associated with an electron has hits in the innermost layers of the silicon detector, is extended to all identified electrons in an event. Contrary to this, cut II only applies to the two electrons of the control sample. In the μμ and eeτ analyses all cuts presented inTable 1serve as selection cuts for the respective trilepton sample and are applied successively to all MC sam-ples and the data. Two-dimensional cuts in the (/ET, Mμμ) and

( ϕ(μμ), /ET) planes are defined in the μμ analysis to veto

events from Υ and Z boson production. In the eeτ analysis, hadronic tau decays are identified by requiring the transverse energy deposited in a calorimeter cone of radius R = 0.5 to

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Table 1

Summary of the selection criteria for ee, μμ, and eeτ analyses and num-bers of events observed in data and expected from SM background, including statistical and systematic uncertainties

ee(= e or μ) analysis

Cut Data Background

I pe_T1>20 GeV, pe_T2>20 GeV 20170 20534± 55 ± 1484 II γ-conversion veto (lead. 2 e)

andE/T>15 GeV 1247 1241± 21 ± 668

III p_T1>20 GeV, p_T2>20 GeV

p_T3>10 GeV, at least 2 e 5 5.5+0.8_−0.5± 0.6 IV γ-conversion veto (all e)

andE/T>15 GeV 0 0.9+0.4_−0.1± 0.1

μμ(= μ or e) analysis

Cut Data Background

I p_T1>12 GeV, p_T2>8 GeV 19283 19588± 81 ± 3332 II ϕ(μi,E/T) >0.1 14918 15275± 72 ± 2598

III Υand Z veto (E/T, Mμμ) plane

ϕ(μμ) <2.53 forE/T <44 GeV 564 506± 13 ± 86 IV pμ_T3>4 GeV or pe_T >5 GeV ϕ(e,E/T) >0.1 pi_T >50 GeV 0 0.4± 0.1 ± 0.1 eeτanalysis

Cut Data Background

I pe_T1>10 GeV, pe_T2>10 GeV

Mee>18 GeV 20437 20905± 70 ± 1555

II Mee<80 GeV 2831 2531± 32 ± 329

III τ: ET >10 GeV, NN > 0.9 16 11.0± 2.8 ± 2.0

IV E/T/√ST>1.5 GeV1/2 0 1.3± 1.7 ± 0.5

be above 10 GeV and an NN output of more than NN > 0.9, corresponding to cut III inTable 1. To select events with real

/

ET, which is expected due to neutrinos in the final state, a cut on /ET/

√

ST is applied, where ST is the total scalar transverse

energy. It allows discrimination against events with fake /ET,

which may arise through statistical fluctuations in jet energy measurements.

Fig. 2 shows (a) the dielectron invariant mass in the ee analysis after cut I ofTable 1, (b) the missing transverse en-ergy distribution in the μμ analysis after cut III ofTable 1, and (c) the neural network output for a loose Z→ ττ → τhadμ

selection, which is used as an identification criterion for taus in the eeτ analysis. The μ+ jet opposite-sign data sample (OS) represents the control sample, while the μ+ jet like-sign data sample (LS) is used to model the multijet background. The dif-ferent contributions are scaled to the control sample by fitting the ET spectrum of the tau candidate. While in (a), (b) the

sig-nal is scaled by a factor of 50, an arbitrary scale is used in (c), since the search and control samples are completely indepen-dent of each other and no meaningful scale can be defined for the signal contribution w.r.t. Z→ ττ or μ + jet data.

The number of observed events in data and the expected background from SM processes with its respective statistical and systematic uncertainties are given inTable 1. The back-ground composition at the final stage of the ee and μμ analy-ses is similar. Diboson production constitutes the largest back-ground fraction (ee: 86%, μμ: 61%), followed by multijet

(a)

(b)

(c)

Fig. 2. (a) The dielectron invariant mass distribution of the ee analysis af-ter cut I,Table 1; (b) theE/T distribution of the μμ analysis after cut III,

Table 1; and (c) the combination of the π and ρ-like NN outputs of a loose Z→ ττ → τhadμselection used as the τ identification criterion in the eeτ

analysis. In (c) like-sign (opposite-sign) μ+ jet data is abbreviated LS (OS) and signal refers to the mSUGRA point m0= 1 TeV, tan β = 5, μ > 0, A0= 0,

and m1/2= 280 GeV, scaled by a factor of 50 in (a), (b) and arbitrarily in (c),

details in the text.

(ee: 11%), or t¯t production (μμ: 36%). In case of the eeτ analysis, the main background is Z/γ∗→ ee (44%). Events from diboson, multijet and Z/γ∗→ ττ contribute 20%, 16%

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and 14%, respectively. The number of events observed in data is in good agreement with the expectation from SM processes at all stages of the three analyses.

The numbers of events expected from SM background and from signal depend on several quantities, each one introducing a systematic uncertainty. The relative uncertainty due to the lumi-nosity measurement is 6.5%. The relative uncertainty on trigger efficiencies ranges from about 11% for Drell–Yan (DY) back-ground with low dilepton invariant masses (15 GeV < M<

60 GeV) to about 1% for the signal. Lepton identification and reconstruction efficiencies give 3% (e), 4% (μ), and 12% (τ ) per lepton candidate, and the photon conversion veto adds an-other 0.4%. The relative systematic uncertainties due to the resolution of the electron or muon energies and /ET are

esti-mated by varying the resolutions in the MC simulation and are found to be less than 1% (e), 1.5% (μ), and 2% (/ET).

Further systematic uncertainties on the experimental cross-section limits concern the theoretical uncertainties on SM back-ground MC cross sections, ranging from 3% to 17%, depending on the process, and including PDF uncertainties. SincePYTHIA

does not model the Z boson pT accurately, a relative

uncer-tainty of 3% to 15%, depending on the dilepton mass, is added for MC Drell–Yan events. The influence of PDF uncertainties on the signal acceptance is estimated to be 4%.

Theoretical uncertainties on the signal cross sections are due to variations of the renormalization and factorization scales (5%), the LO cross section (2%), the K factor (3%), and the choice of PDF (9%). As gaugino pair production mostly pro-ceeds via s-channel exchange of virtual γ , W , or Z bosons, the latter uncertainty is deduced from studies of the DY cross section at similar masses. The uncertainty on the DY cross sec-tion due to the choice of PDF is estimated to be 6%, using the CTEQ6.1M uncertainty function set[20]. An additional 3% is added linearly to account for the lower DY cross section if calculated with CTEQ6 PDFs, compared to its estimation with CTEQ5 PDFs, which are used for the signal MC generation. An additional, conservative, systematic uncertainty of +10/−0% is added to account for the lower LO cross section fromSUSY

-GENcompared to the one obtained withPYTHIA. All of these uncertainties are assumed to be independent, and are added in quadrature. The total systematic uncertainty of−11% and +15% is represented by the grey-shaded bands of the signal cross-section curve inFig. 3.

When setting limits, the ee, μμ, and eeτ analyses are combined for each coupling (λ121, λ122, λ133) in order to

en-hance the signal sensitivity. All signal and background sam-ples, as well as the data are processed by all analyses accord-ing to the three channels. Events selected in multiple channels are assigned only to the analysis with the largest signal-to-background ratio, and are removed from all other analyses. The percentage of common signal events for any two analy-ses is less than 13%, while no common data or SM background events are found.Table 2shows the efficiencies of the analyses for a typical mSUGRA point (m0= 1 TeV, tan β = 5, μ > 0, A0= 0, and m1/2= 280 GeV). Correlations between the signal

efficiencies in the three channels are taken into account in the calculation of the systematic uncertainties.

Fig. 3. mSUGRA (m0= 1 TeV, tan β = 5, μ > 0, A0= 0): The σNLOcross

section and the σ95% C.L.limits for the λ121, λ122, and λ133analyses as

func-tions of the˜χ₁0mass (lower horizontal axis) and the˜χ₁±mass (upper horizontal axis). The exclusion domains, indicated by the hatched regions, lie above the respective observed limit curve.

Table 2

Efficiencies (in %) of the ee, μμ, and eeτ analyses and of the combined analyses for a typical mSUGRA point (m0= 1 TeV, tan β = 5, μ > 0, A0= 0,

and m1/2= 280 GeV). The first uncertainty is statistical and the second one

systematic Analysis λ121 λ122 λ133 ε(ee) 18.9±0.3±1.2 4.5±0.2 ± 0.3 2.6±0.2±0.1 ε(μμ) 2.1±0.1±0.3 16.1±0.1 ± 1.9 0.8±0.1±0.1 ε(eeτ ) 1.1±0.1±0.1 0.23±0.04 ± 0.03 2.0±0.2±0.2 εcomb 22.1±0.3±1.6 20.8±0.2 ± 2.2 5.4±0.3±0.4 Since no evidence for gaugino pair production is observed, upper limits on the cross sections are extracted in two models: in mSUGRA (with m0= 100 GeV or 1 TeV, tan β = 5 or 20, μ >0, and A0= 0) and in an MSSM model assuming no GUT

relation between M1and M2and assuming heavy squarks and

sleptons, i.e. the higgsino mixing mass parameter, μ, and all sfermion masses are set to 1 TeV. Limits are calculated at the 95% C.L. using the LEP CLS method[24]taking into account

correlated uncertainties between SM and signal processes. For mSUGRA (m0= 1 TeV and tan β = 5), the expected

and observed cross-section limits (σ95% C.L.) are shown in Fig. 3as functions of the ˜χ₁0and ˜χ₁±masses.

Studies for m0= 100 GeV and tan β = 5 and 20 are done for λ133. Particularly interesting is the region of high tan β values,

where the stau is the next-to-lightest supersymmetric particle. In such a case, decays of SUSY particles into final states with stau leptons can be dominant and consequently increase the ef-ficiency of the eeτ channel. Lower bounds on the masses of the

˜χ0

1 and the ˜χ1±are given inTable 3.

In the MSSM, the exclusion domain is presented in the (˜χ₁0, ˜χ1±) mass plane inFig. 4. The cut-off of the exclusion domain

towards low neutralino masses, i.e. at m_˜χ0

1 = 30 GeV for λ121 and λ122, and at m_˜χ0

1 = 50 GeV for λ133, is due to the combined effect of the mean decay length of the lightest neutralino

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(cho-Table 3

The combined lower limits at the 95% C.L. on the masses of ˜χ₁0and ˜χ₁±(in GeV) obtained using the mSUGRA model with different parameters Coupling sign(μ) m(˜χ₁0) m(˜χ₁±) λ121(m0= 1 TeV, tan β = 5) >0 119 231 λ122 >0 118 229 λ133 >0 86 166 λ121(m0= 1 TeV, tan β = 5) <0 117 234 λ122 <0 115 230 λ133(m0= 100 GeV, tan β = 5) >0 105 195 λ133(m0= 100 GeV, tan β = 20) >0 115 217

Fig. 4. Observed and expected exclusion domains at the 95% C.L. in the (˜χ₁0, ˜χ1±) mass plane of the considered MSSM model for the λ121, λ122, and λ133

couplings with their strengths set to 0.01 (λ121, λ122) and 0.003 (λ133).

sen to lie below one cm) and the values of the λ121, λ122, and λ133couplings.

In summary, no evidence for /Rp-SUSY is observed in

trilep-ton events. Upper limits on the chargino and neutralino pair production cross section are set in the case of one dominant coupling: λ121, λ122, or λ133. Lower bounds on the masses of

the lightest neutralino and the lightest chargino are derived in mSUGRA and in an MSSM scenario with heavy sfermions, but assuming no GUT relation between M1and M2. All limits

sig-nificantly improve previous results obtained at LEP[4]and with the D∅ Run I dataset[7]and are the most restrictive to date.

Acknowledgements

We wish to thank M. Klasen for providing us with the

GAUGINOSpackage for the calculation of the K factors for the SUSY signal. We thank the staffs at Fermilab and collaborat-ing institutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); FASI, Rosatom and RFBR (Russia); CAPES, CNPq, FAPERJ, FAPESP and

FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); KRF and KOSEF (Korea); CONICET and UBACyT (Argentina); FOM (The Netherlands); PPARC (United Kingdom); MSMT (Czech Republic); CRC Program, CFI, NSERC and WestGrid Project (Canada); BMBF and DFG (Germany); SFI (Ireland); The Swedish Research Council (Sweden); Research Corporation; Alexander von Hum-boldt Foundation; and the Marie Curie Program.

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