Higgs boson searches in CP-conserving and CP-violating MSSM scenarios with the DELPHI detector

CERN–PH–EP/2007–029

DAPNIA–07–150

9 July 2007

DELPHI Collaboration

Abstract


This paper presents the final interpretation of the results from DELPHI on the searches for Higgs bosons in the Minimal Supersymmetric extension of the Standard Model (MSSM). A few representative scenarios are considered, that include CP conservation and explicit CP violation in the Higgs sector. The experimental results encompass the searches for neutral Higgs bosons at LEP1 and LEP2 in final states as expected in the MSSM, as well as LEP2 searches for charged Higgs bosons and for neutral Higgs bosons decaying into hadrons independent of the quark flavour. The data reveal no significant excess with respect to background expectations. The results are translated into excluded regions of the parameter space in the various scenarios. In the CP-conserving case, these lead to limits on the masses of the lightest scalar and pseudoscalar Higgs bosons, h and A, and on . The dependence of these limits on the top quark mass is discussed. Allowing for CP violation reduces the experimental sensitivity to Higgs bosons. It is shown that this effect depends strongly on the values of the parameters responsible for CP violation in the Higgs sector.

(Accepted by Eur. Phys. J. C)

J.Abdallah

, P.Abreu, W.Adam, P.Adzic, T.Albrecht, R.Alemany-Fernandez, T.Allmendinger, P.P.Allport, U.Amaldi, N.Amapane, S.Amato, E.Anashkin, A.Andreazza, S.Andringa, N.Anjos, P.Antilogus, W-D.Apel, Y.Arnoud, S.Ask, B.Asman, J.E.Augustin, A.Augustinus, P.Baillon, A.Ballestrero, P.Bambade, R.Barbier, D.Bardin, G.J.Barker, A.Baroncelli, M.Battaglia, M.Baubillier, K-H.Becks, M.Begalli, A.Behrmann, E.Ben-Haim, N.Benekos, A.Benvenuti, C.Berat, M.Berggren, L.Berntzon, D.Bertrand, M.Besancon, N.Besson, D.Bloch, M.Blom, M.Bluj, M.Bonesini, M.Boonekamp, P.S.L.Booth, G.Borisov, O.Botner, B.Bouquet, T.J.V.Bowcock, I.Boyko, M.Bracko, R.Brenner, E.Brodet, P.Bruckman, J.M.Brunet, B.Buschbeck, P.Buschmann, M.Calvi, T.Camporesi, V.Canale, F.Carena, N.Castro, F.Cavallo, M.Chapkin, Ph.Charpentier, P.Checchia, R.Chierici, P.Chliapnikov, J.Chudoba, S.U.Chung, K.Cieslik, P.Collins, R.Contri, G.Cosme, F.Cossutti, M.J.Costa, D.Crennell, J.Cuevas, J.D’Hondt, J.Dalmau, T.da Silva, W.Da Silva, G.Della Ricca, A.De Angelis, W.De Boer, C.De Clercq, B.De Lotto, N.De Maria, A.De Min, L.de Paula, L.Di Ciaccio, A.Di Simone, K.Doroba, J.Drees, G.Eigen, T.Ekelof, M.Ellert, M.Elsing, M.C.Espirito Santo, G.Fanourakis, D.Fassouliotis, M.Feindt, J.Fernandez, A.Ferrer, F.Ferro, U.Flagmeyer, H.Foeth, E.Fokitis, F.Fulda-Quenzer, J.Fuster, M.Gandelman, C.Garcia, Ph.Gavillet, E.Gazis, R.Gokieli, B.Golob, G.Gomez-Ceballos, P.Goncalves, E.Graziani, G.Grosdidier, K.Grzelak, J.Guy, C.Haag, A.Hallgren, K.Hamacher, K.Hamilton, S.Haug, F.Hauler, V.Hedberg, M.Hennecke, H.Herr, J.Hoffman, S-O.Holmgren, P.J.Holt, M.A.Houlden, J.N.Jackson, G.Jarlskog, P.Jarry, D.Jeans, E.K.Johansson, P.D.Johansson, P.Jonsson, C.Joram, L.Jungermann, F.Kapusta, S.Katsanevas, E.Katsoufis, G.Kernel, B.P.Kersevan, U.Kerzel, B.T.King, N.J.Kjaer, P.Kluit, P.Kokkinias, C.Kourkoumelis, O.Kouznetsov, Z.Krumstein, M.Kucharczyk, J.Lamsa, G.Leder, F.Ledroit, L.Leinonen, R.Leitner, J.Lemonne, V.Lepeltier, T.Lesiak, W.Liebig, D.Liko, A.Lipniacka, J.H.Lopes, J.M.Lopez, D.Loukas, P.Lutz, L.Lyons, J.MacNaughton, A.Malek, S.Maltezos, F.Mandl, J.Marco, R.Marco, B.Marechal, M.Margoni, J-C.Marin, C.Mariotti, A.Markou, C.Martinez-Rivero, J.Masik, N.Mastroyiannopoulos, F.Matorras, C.Matteuzzi, F.Mazzucato, M.Mazzucato, R.Mc Nulty, C.Meroni, E.Migliore, W.Mitaroff, U.Mjoernmark, T.Moa, M.Moch, K.Moenig, R.Monge, J.Montenegro, D.Moraes, S.Moreno, P.Morettini, U.Mueller, K.Muenich, M.Mulders, L.Mundim, W.Murray, B.Muryn, G.Myatt, T.Myklebust, M.Nassiakou, F.Navarria, K.Nawrocki, R.Nicolaidou, M.Nikolenko, A.Oblakowska-Mucha, V.Obraztsov, A.Olshevski, A.Onofre, R.Orava, K.Osterberg, A.Ouraou, A.Oyanguren, M.Paganoni, S.Paiano, J.P.Palacios, H.Palka, Th.D.Papadopoulou, L.Pape, C.Parkes, F.Parodi, U.Parzefall, A.Passeri, O.Passon, L.Peralta, V.Perepelitsa, A.Perrotta, A.Petrolini, J.Piedra, L.Pieri, F.Pierre, M.Pimenta, E.Piotto, T.Podobnik, V.Poireau, M.E.Pol, G.Polok, V.Pozdniakov, N.Pukhaeva, A.Pullia, J.Rames, A.Read, P.Rebecchi, J.Rehn, D.Reid, R.Reinhardt, P.Renton, F.Richard, J.Ridky, M.Rivero, D.Rodriguez, A.Romero, P.Ronchese, P.Roudeau, T.Rovelli, V.Ruhlmann-Kleider, D.Ryabtchikov, A.Sadovsky, L.Salmi, J.Salt, C.Sander, A.Savoy-Navarro, U.Schwickerath, R.Sekulin, M.Siebel, A.Sisakian, G.Smadja, O.Smirnova, A.Sokolov, A.Sopczak, R.Sosnowski, T.Spassov, M.Stanitzki, A.Stocchi, J.Strauss, B.Stugu, M.Szczekowski, M.Szeptycka, T.Szumlak, T.Tabarelli, A.C.Taffard, F.Tegenfeldt, J.Timmermans, L.Tkatchev, M.Tobin, S.Todorovova, B.Tome, A.Tonazzo, P.Tortosa, P.Travnicek, D.Treille, G.Tristram, M.Trochimczuk, C.Troncon, M-L.Turluer, I.A.Tyapkin, P.Tyapkin, S.Tzamarias, V.Uvarov, G.Valenti, P.Van Dam, J.Van Eldik, N.van Remortel, I.Van Vulpen, G.Vegni, F.Veloso, W.Venus, P.Verdier, V.Verzi, D.Vilanova, L.Vitale, V.Vrba, H.Wahlen, A.J.Washbrook, C.Weiser, D.Wicke, J.Wickens, G.Wilkinson, M.Winter, M.Witek, O.Yushchenko, A.Zalewska, P.Zalewski, D.Zavrtanik, V.Zhuravlov, N.I.Zimin, A.Zintchenko, M.Zupan

11footnotetext: Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA 22footnotetext: IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium 33footnotetext: Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece 44footnotetext: Department of Physics, University of Bergen, Allégaten 55, NO-5007 Bergen, Norway 55footnotetext: Dipartimento di Fisica, Università di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy 66footnotetext: Centro Brasileiro de Pesquisas Físicas, rua Xavier Sigaud 150, BR-22290 Rio de Janeiro, Brazil 77footnotetext: Inst. de Física, Univ. Estadual do Rio de Janeiro, rua São Francisco Xavier 524, Rio de Janeiro, Brazil 88footnotetext: Collège de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France 99footnotetext: CERN, CH-1211 Geneva 23, Switzerland 1010footnotetext: Institut de Recherches Subatomiques, IN2P3 - CNRS/ULP - BP20, FR-67037 Strasbourg Cedex, France 1111footnotetext: Now at DESY-Zeuthen, Platanenallee 6, D-15735 Zeuthen, Germany 1212footnotetext: Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece 1313footnotetext: FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, CZ-180 40, Praha 8, Czech Republic 1414footnotetext: Dipartimento di Fisica, Università di Genova and INFN, Via Dodecaneso 33, IT-16146 Genova, Italy 1515footnotetext: Institut des Sciences Nucléaires, IN2P3-CNRS, Université de Grenoble 1, FR-38026 Grenoble Cedex, France 1616footnotetext: Helsinki Institute of Physics and Department of Physical Sciences, P.O. Box 64, FIN-00014 University of Helsinki,   Finland 1717footnotetext: Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federation 1818footnotetext: Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany 1919footnotetext: Institute of Nuclear Physics PAN,Ul. Radzikowskiego 152, PL-31142 Krakow, Poland 2020footnotetext: Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, PL-30055 Krakow, Poland 2121footnotetext: Université de Paris-Sud, Lab. de l’Accélérateur Linéaire, IN2P3-CNRS, Bât. 200, FR-91405 Orsay Cedex, France 2222footnotetext: School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK 2323footnotetext: LIP, IST, FCUL - Av. Elias Garcia, 14-, PT-1000 Lisboa Codex, Portugal 2424footnotetext: Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK 2525footnotetext: Dept. of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ, UK 2626footnotetext: LPNHE, IN2P3-CNRS, Univ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris Cedex 05, France 2727footnotetext: Department of Physics, University of Lund, Sölvegatan 14, SE-223 63 Lund, Sweden 2828footnotetext: Université Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France 2929footnotetext: Dipartimento di Fisica, Università di Milano and INFN-MILANO, Via Celoria 16, IT-20133 Milan, Italy 3030footnotetext: Dipartimento di Fisica, Univ. di Milano-Bicocca and INFN-MILANO, Piazza della Scienza 3, IT-20126 Milan, Italy 3131footnotetext: IPNP of MFF, Charles Univ., Areal MFF, V Holesovickach 2, CZ-180 00, Praha 8, Czech Republic 3232footnotetext: NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands 3333footnotetext: National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece 3434footnotetext: Physics Department, University of Oslo, Blindern, NO-0316 Oslo, Norway 3535footnotetext: Dpto. Fisica, Univ. Oviedo, Avda. Calvo Sotelo s/n, ES-33007 Oviedo, Spain 3636footnotetext: Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK 3737footnotetext: Dipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, IT-35131 Padua, Italy 3838footnotetext: Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK 3939footnotetext: Dipartimento di Fisica, Università di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy 4040footnotetext: Dipartimento di Fisica, Università di Roma III and INFN, Via della Vasca Navale 84, IT-00146 Rome, Italy 4141footnotetext: DAPNIA/Service de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-Yvette Cedex, France 4242footnotetext: Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, ES-39006 Santander, Spain 4343footnotetext: Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation 4444footnotetext: J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia 4545footnotetext: Laboratory for Astroparticle Physics, University of Nova Gorica, Kostanjeviska 16a, SI-5000 Nova Gorica, Slovenia 4646footnotetext: Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia 4747footnotetext: Fysikum, Stockholm University, Box 6730, SE-113 85 Stockholm, Sweden 4848footnotetext: Dipartimento di Fisica Sperimentale, Università di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy 4949footnotetext: INFN,Sezione di Torino and Dipartimento di Fisica Teorica, Università di Torino, Via Giuria 1, IT-10125 Turin, Italy 5050footnotetext: Dipartimento di Fisica, Università di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy 5151footnotetext: Istituto di Fisica, Università di Udine and INFN, IT-33100 Udine, Italy 5252footnotetext: Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundão BR-21945-970 Rio de Janeiro, Brazil 5353footnotetext: Department of Radiation Sciences, University of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden 5454footnotetext: IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain 5555footnotetext: Institut für Hochenergiephysik, Österr. Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria 5656footnotetext: Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland 5757footnotetext: Now at University of Warwick, Coventry CV4 7AL, UK 5858footnotetext: Fachbereich Physik, University of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany
 deceased

1 Introduction

This paper presents the final interpretation of the Higgs boson search results from DELPHI in the framework of representative scenarios of the Minimal Supersymmetric Standard Model (MSSM). With respect to the previous MSSM interpretation published in Ref. [1], this analysis uses an enlarged set of experimental results, updated calculations of MSSM radiative corrections and covers more scenarios, including models with CP violation in the Higgs sector.

As compared with the Standard Model, the MSSM has an extended Higgs sector with two doublets of complex Higgs fields, leading to five physical Higgs bosons, of which three are neutral.

Figure 1: Main production processes of MSSM neutral Higgs bosons at LEP. Left: associated production of a Z and a Higgs boson, which must be one of the CP-even scalars (h or H) if CP is conserved or any Higgs boson (H, H, H) in the contrary case. At LEP1, the intermediate Z is on-shell and the final Z is off-shell, while it is the reverse at LEP2. Right: pair-production of neutral Higgs bosons. If CP is conserved, one of them must be CP-even (h or H) and the other one is the CP-odd pseudo-scalar A. If CP is not conserved, the pair can be any couple of different scalars among H, H and H. The intermediate Z is on-shell at LEP1.

If CP is conserved, two of the three neutral Higgs bosons are CP-even. They are denoted h, for the lighter one, and H. The third one is a CP-odd pseudo-scalar, denoted A. In  collisions, the dominant production mechanisms are the s-channel processes described in Fig. 1, that is the associated production of a Z and a CP-even Higgs boson and the pair production of either CP-even boson together with the CP-odd scalar. These processes are complemented by additional t-channel diagrams in the final states where a CP-even Higgs boson is produced with neutrinos or electrons, which proceed through  and  fusions, respectively. These diagrams and their interference with the  process have an impact on the production cross-section at masses around the  kinematic threshold. At LEP2 energies, the only significant effect is from  fusion which doubles the neutrino  cross-section at the kinematic threshold. Finally, charged Higgs bosons,  and , are produced in pairs through a diagram similar to that in Fig. 1, right, via exchange of a Z boson or a photon.

Although CP is conserved at tree level in the MSSM, radiative corrections can introduce CP violation through stop and sbottom loops, leading to changes in the neutral Higgs boson sector [2]. If CP is not conserved, the three neutral Higgs bosons are no longer pure CP eigenstates but mixtures of CP-even and CP-odd components. They are usually denoted H, H and H, in increasing mass. The main production mechanisms are the same as in the CP conserving case, except that, a priori, any scalar can be produced in association with a Z boson or through  and  fusions, and any couple of different Higgs bosons can be pair-produced. The main phenomenological difference with respect to the CP-conserving case lies in the strength of the couplings of the Z boson to the Higgs scalars. In significant regions of the parameter space, CP violation turns off the otherwise dominant coupling between the Z boson and the lightest Higgs boson. In that case, if none of the other processes of Fig. 1 are possible (due e.g. to kinematics), the dominant Higgs boson production mechanism at LEP becomes the Yukawa process of Fig. 2. Of the two phases of LEP, only LEP1 has a significant sensitivity to this process. In the Standard Model, the corresponding cross-sections are negligible, e.g. a fraction of a pb for a few  Higgs boson. In the MSSM, these can be enhanced by up to three orders of magnitude with respect to their Standard Model values, leading to detectable signals which become valuable in the case of CP violation.

Figure 2: Additional production process of MSSM neutral Higgs bosons at LEP. The radiation of a Higgs boson off a Z boson decay fermion gives a detectable signal only at LEP1. This signal is exploited in the case of CP violation.

The decay properties of the Higgs bosons are moderately affected by CP violation, at least in the range of masses accessible at LEP, that is up to masses around 100  [2]. In most of the MSSM parameter space of the scenarios studied hereafter, the three neutral Higgs bosons decay mainly into the pair of heaviest fermions kinematically permitted, even if CP is not conserved. Below the  threshold, a Higgs boson would decay into  or  pairs with a significant lifetime. Above the  threshold, the lifetime is negligible and Higgs bosons decay at the primary vertex. Up to a mass of 3   the main decays are into  pairs and also into hadronic channels with a large proportion of two-prong final states. Above 3   the dominant decays are successively into ,  and finally  pairs for Higgs boson masses above 12 . Besides these decays into fermions, there are also regions of the parameter space where one neutral Higgs boson can undergo cascade decays to a pair of Higgs bosons, as for example  if CP is conserved or  in the contrary case. In some cases, especially if CP is not conserved, this mode dominates over the decays into SM particles. In the scenarios considered in this paper, charged Higgs bosons have a mass above 60  and decay either into the pair of heaviest fermions allowed by kinematics, that is into cs or pairs, or into a W and a light Higgs boson, e.g. into a WA pair if CP is conserved. Finally, these scenarios do not allow neutral or charged Higgs boson decays into supersymmetric particles such as sfermions, charginos or invisible neutralinos. Note that searches for neutral Higgs bosons decaying into invisible products were performed at LEP, as reported in Ref. [3].

The different decay channels define the topologies that were searched for to cover the MSSM parameter region kinematically accessible at LEP energies. These topologies are described in Section 2. Section 3 summarizes the definition and techniques related to confidence levels used in the statistical interpretation of the searches. The eight CP-conserving MSSM benchmark scenarios studied in this analysis are presented in Section 4 and the results obtained in these scenarios when combining all searches are given in Section 5. Similarily, the CP-violating scenarios and the corresponding results are covered in Sections 6 and  7. The top quark mass has a significant impact on the properties of the Higgs bosons (e.g. mass spectrum of the neutral Higgs bosons, CP-violating effects). Results are thus derived for several values of this mass, namely:  = 169.2, 174.3, 179.4 and 183.0 , which were defined after the measurement of the top quark mass at the Tevatron, run I [4]. Of the two values close to the present experimental measurement of  = 170.9  1.1  1.5  [5], 174.3  gives the most conservative results and thus was chosen as a reference in most of the exclusion plots and to quote absolute mass and  limits. Readers interested in similar analyses at LEP are referred to Ref. [6, 7].

2 Search channels

final state range disc. ref.
(GeV) () (pb) info.
 with direct decays
91 , 2.5 no [8]
91 (h ) (Z any) 2.5 no [8]
91 (h 2 prongs) ( ) 0.5 no [9]
91 (h jet) ( , ) 0.5 no [9]
91 (h jet jet) ( , ) 3.6 no [10]
91 (h jet jet) ( , , ) 33.4 no [11]
161,172 (h )(Z any), (h )( ) 19.9 1d [17]
183 (h )(Z any), (h )( ) 52.0 1d [18]
189 (h )(Z any), (h )( ) 158.0 2d [19]
192-208 (h )(Z any) 452.4 2d [20, 1]
192-208 (h )( ) 452.4 2d [20, 1]
189-208 (h hadrons)(Z any but ) 610.4 mix [22]
 with direct decays
91 4 prongs 5.3 no [12]
91  hadrons 0.5 no [13]
91  jet jet 3.6 no [10]
91 , 33.4 no [14]
91 79.4 no A.1
91 79.4 no [21]
133 6.0 no [16]
161,172 , 20.0 1d [17]
183 , 54.0 1d [18]
189 , 158.0 2d [19]
192-208 452.4 2d [20, 1]
192-208 452.4 2d [20, 1]
189-208 570.9 1d [21]
189-208 610.2 no [21]
189-208 hadrons 610.4 mix [22]
 or  with  cascade
91 16.2 no [15]
91 () (Z any but ) 9.7 no [15]
91 () (Z any or A ) 12.5 no [15]
91 ( 4 prongs) (Z any or A 2 prongs) 12.9 no [15]
91 ( hadrons) (  or A hadrons) 15.1 no [15]
91 ( ) (  or A ) 15.1 no [15]
161,172 ( any) ( , or A any) 20.0 1d [17]
183 ( ) ( ) 54.0 1d [18]
192-208 ( , , ) ( ) 452.4 2d [20, 1]
192-208 ( ) ( ) 452.4 2d A.2
189-208 ( ) (  or A ) 610.2 no [21]
ffh or ffA Yukawa production
91 (h ), (A ) 79.4 no [21]
91 (h ), (A ) 79.4 no [21]
91 (h ), (A ) 79.4 no [21]

189-208 , , , 610.4 2d [23]
189-208 570.8 1d [23]
Table 1: List of signals expected from MSSM Higgs bosons that were searched for in the DELPHI data sample. Indicated for each signal are the centre-of-mass energy, final state, analysed mass range, integrated luminosity, level of discriminant information included in the confidence level estimates (none, one- or two-dimensional) and the reference where details of the analysis are published. Here h and A denote any neutral Higgs boson allowed to be produced in each of the indicated production processes. The mass range applies to  for  production, to + for  production, to  for  processes, to the Higgs boson mass for either Yukawa process and to  for  production. When no upper bound is given, the limit imposed by kinematics or vanishing branching fractions must be understood.

The different analyses performed to search for neutral and charged Higgs bosons in the whole LEP1 and LEP2 DELPHI data samples are summarized in Table 1 which lists the final states, mass ranges, integrated luminosities and the references for more details about the selections and their performance. Two channels, the  signal at LEP1 and the (h   ) ( ) signal at A masses below the  threshold, were analysed for this paper, using selections already published. The efficiencies and the references for the selections can be found in the Appendices 1 and 2 of this paper. In the Table, the notations h and A which label the different analysis channels must be understood as generic notations for any pair of neutral Higgs bosons that could be produced in each of the production processes listed in the Table. As an example, the hZ analyses, originally designed to search for the CP-even h boson in CP-conserving scenarios, can be applied to search for the second CP-even Higgs boson, H, as well as for any of the three Higgs scalars in CP-violating scenarios. It must be noted that the kinematic properties of the signal processes are only slightly affected by CP-violation, since, when CP is not conserved, the production processes still proceed through the CP-even and CP-odd components of the neutral Higgs bosons, as explained in Ref. [7]. The same topological searches can thus be applied whether CP is conserved or not.

As compared with our previous publication [1], the following changes were introduced in the experimental results used. The MSSM interpretation in Ref. [1] relied only on searches performed at LEP2 at masses above 12  in  in the  process, with either direct or cascade decays, and above 40  in ,  in the  channels, with only direct decays of the Higgs bosons. The corresponding channels have their  values in bold characters in Table 1. Scans of the MSSM parameter space were thus restricted to  above 12  and assumed the published LEP1 limits11144 (46)  when  is above (below) the threshold [14] to be valid. Including all LEP1 results, which have a sensitivity starting from vanishing h and A masses, and the additional LEP2 searches of Ref. [21], whose sensitivity in the  mode complements that of the two other sets of results, allows scans of the MSSM parameter space to be performed with no restriction on masses. Moreover, some of the analyses of Ref. [21] cover production processes which are negligible if CP is conserved but are enhanced by CP violation, such as Yukawa processes or the production of  final states. Adding the searches for neutral Higgs bosons decaying into hadrons of any flavour [22] is expected to provide sensitivity in scenarios where the Higgs boson decays into  would vanish. As their mass coverage starts at low mass, these analyses also increase the experimental sensitivity to Higgs bosons below the  threshold, a region otherwise covered only by analyses of subsets of the LEP1 data. Finally, the charged Higgs boson searches [23] help in a few CP-conserving scenarios in the low  region where the charged bosons are kinematically accessible at LEP2.

Moreover, our previous interpretation was dealing only with the production of the two lightest Higgs bosons, the h and A scalars in CP-conserving scenarios. In this analysis, the production of the third boson, if kinematically accessible, is also accounted for, which can lead to a significant gain in sensitivity in restricted areas of the parameter space. In CP-conserving scenarios, this leads to including the  and  signals besides the usual  and  processes, while in CP-violating models, the HZ and HH signals are taken into account in addition to the dominant HZ and HH channels (the two other processes, HZ and HH being out of reach).

3 Tools for the statistical analysis

When scanning over the parameter space of a model, confidence levels are computed at each point to test the compatibility of data with the hypothesis of background only and with that of background plus signal as expected from the model. Throughout this section, the notations h, H and A must be understood as generic notations for the three neutral Higgs bosons of any type of MSSM scenario.

3.1 Confidence level definitions and calculations

The confidence levels are calculated using a modified frequentist technique based on the extended maximum likelihood ratio [24] which has also been adopted by the LEP Higgs working group. The basis of the calculation is the likelihood ratio test-statistic, :

where is the total signal expected and and are the signal and background densities for event . These densities are constructed using either expected rates only or also additional discriminant information, which can be one- or two-dimensional. Table 1 presents the level of discriminant information for each channel: LEP1 results rely on rates only, while LEP2 results mix channels without or with discriminant information. As an example, in neutral Higgs boson channels with discriminant information, the first variable is the reconstructed Higgs boson mass in the  analyses and the sum of the reconstructed h and A masses in the  analyses, while the second variable, if any, is channel-dependent, as specified in the references listed in the Table. Charged Higgs analyses use discriminant information in a similar way [23]. The searches for Higgs bosons decaying hadronically encompass analyses without or with 1d discriminant information together with analyses whose selections vary with the mass hypothesis [22].

The observed value of  is compared with the expected Probability Density Functions (PDFs) for , which are built using Monte Carlo sampling under the assumptions that background processes only or that both signal and background are present. The confidence levels  and  are their integrals from to the observed value of . Systematic uncertainties in the rates of signal or background events are taken into account in the calculation of the PDFs for  by randomly varying the expected rates while generating the distribution [25], which has the effect of broadening the expected  distribution and therefore making extreme events seem more probable.

 is the probability of obtaining a result as background-like or more so than the one observed if the background hypothesis is correct. Similarly, the confidence level for the hypothesis that both signal and background are present, , is the probability, in this hypothesis, to obtain more background-like results than those observed. The quantity  is defined as the ratio of these two probabilities, /. It is not a true confidence level, but a conservative pseudo-confidence level for the signal hypothesis. All exclusions discussed hereafter use  and require it to be 5% for an exclusion confidence of 95%. As using  instead of  is conservative, the rate of fake exclusions is ensured to be below 5% when  is equal to 5%.

3.2 Estimation of expected signal and background densities

The expected signal and background densities, which are required to check the consistency of the data with the background and signal processes have two components: the overall normalization which sets the expected rates and the Probability Density Functions (PDF) of the additional discriminant information, if any.

The expected background and signal rates were calculated from the number of simulated events passing the cuts. For the signal the efficiencies derived from simulations at given mass points had to be interpolated to estimate efficiencies at Higgs boson masses which were not simulated. In most cases this was done using one polynomial or if necessary two polynomials, one to describe the slow rise, and a second to handle the kinematic cut-off, which can be much more abrupt. For the cases where two signal masses must be allowed, a two-dimensional parameterization was used.

The shapes of the PDFs were derived using histograms which are taken from the simulated events. In the case of two-dimensional PDFs these distributions were smoothed using a two-dimensional kernel, which consists of a Gaussian distribution with a small component of a longer tail [26]. The global covariance of the distribution was used to determine the relative scale factors of the two axes. The width of the kernel varied from point to point, such that the statistical error on the estimated background processes was constant at 20%. Finally multiplicative correction factors (each a one-dimensional distribution for one of the two dimensions of the PDF) were derived such that when projected onto either axis the PDF has the same distribution as would have been observed if it had been projected onto the axis first and then smoothed. This makes better use of the simulation statistics if there are features which are essentially one-dimensional, such as mass peaks. The error parameter fixed to 20% was an important choice. It was set by dividing the background simulation into two subsamples, generating a PDF with one and using the other to test for over-training by calculating the  obtained from simulation of background events. This should be 0.5 if the results are not to be biased, and a value of 20% for the error gave the closest approximation to 0.5 in all channels. Examples of smoothed two-dimensional PDFs are given in Fig. 3.

The signal simulations were made at fixed Higgs boson masses, but in order to test a continuous range of masses, interpolation software [27] was used to create signal PDFs at arbitrary masses. In the last year of operation, LEP energy was varied continuously while simulations were made at fixed beam energies. The same interpolation software was used to create signal and background PDFs at the correct centre-of-mass energies [1]. The interpolation was done by linearly interpolating the cumulative distributions taking as a parameter the signal mass or the centre-of-mass energy. The procedure has been tested over ranges up to 40  in mass while the actual shifts in the simulations were up to 0.3  in , and 5  in mass for the  signals overall, but less than 0.5  for Higgs boson masses between 113.5 and 116.5 . For the  channels, the actual shifts were 5  in either mass for Higgs boson masses between 80 and 95  and up to 20  elsewhere. Comparisons of simulated and interpolated distributions for a given mass were made in all channels and showed good agreement.

3.3 The case of non-independent channels

When combining the results in all channels to derive confidence levels, only independent channels must be included, which requires some special treatment for a few non-independent cases.

a) different signals - one analysis with mass hypothesis-independent selections
analysis  (GeV) signals added ref.
ffh four-b 91 (h  ), (A  ), (hA  ) [21]
ffh 91 (h  ), (A  ), (hA  ) [21]
ffh four- 91 (h  ), (A  ) [21]
161-172 (h ) ( ), () ( ) [17]
189-208 (h ) ( ), (h ) ( ), (hA  ) [19, 20, 1]
 four-jet 161-183 (h ) ( ), () ( ) [17, 18]
 four-jet 192-208 (h ) ( ), () ( ), (hA  ) [20, 1]
 four-jet 161-172 (hA  ), () A [17]
 four-jet 192-208 (hA  ), (h ) ( ) [20, 1]
four-b 189-208 ()A, ()Z, (hA  ) [21]
b) different analyses - one final state
final state  (GeV) competing analyses ref.
four-jet 91 , [14]
multi-jet 91 three and four-jet analyses [21]
192-208 low mass and high mass hZ analyses [1]
189-208 low mass and high mass flavour-blind analyses [22]
189-208 hZ and flavour-blind analyses [19, 20, 1, 22]
ll,l=e, 189-208 hZ and flavour-blind analyses [19, 20, 1, 22]
four-jet 192-208 low mass and high mass hZ analyses [1]
189-208 low mass and high mass hZ flavour-blind analyses [22]
189-208 three and four-jet hA flavour-blind analyses [22]
189-208 cscs and WAWA analyses [23]
189-208 , , four-b, flavour-blind,  and  analyses [19, 20, 1, 21, 22, 23]
jet jet 189-208  and  analyses [23]
Table 2: a) list of signals from the two lightest Higgs bosons h and A treated by a single analysis: the signal expectations are combined (rates added, PDFs summed with weights according to the rates) prior to the confidence level calculations. b) list of different analyses of the same final state: only one analysis is selected at each point in the scans, based on the best expected performance for exclusion. In this Table, h and A denote any neutral Higgs boson allowed to be produced in the indicated production processes.

The first case is that of different signals covered by the same analysis. The treatment of this depended upon whether the analyses were themselves independent of the mass hypothesis for the Higgs bosons. The set of search channels (see Table 1) contains mostly analyses of this kind. In that case, all signals selected by one analysis were combined into one global channel prior to the confidence level computation. Expected rates were added together and PDFs were summed with weights given by the expected rates of the individual signals. As an illustration, Table 2-a gives the list of these signals and analyses on the example of the production of the lightest Higgs bosons, h and A, through the  and  processes. When extending the combination to the third Higgs boson, H, the same procedure was followed, first for the various signals from that boson in the  and  processes, and then to combine  and  signals or  and  signals. The PDF combination in such a case is illustrated in Fig. 3.

A different procedure was applied in the case of different signals covered by the same analysis whose selections do depend on the mass hypothesis, as most searches of Ref. [22] do. Different signals are covered by these analyses only when including signals from the third Higgs boson, H. In that case, in each analysis only one signal (from either h or H) was selected at each point in the scanned parameter space and at each centre-of-mass energy, on the basis of the smallest expected  from experiments with no signal (that is, on the basis of the strongest average exclusion if no signal is present).

The second case of non-independent channels is that of a large overlap in the events selected by different analyses sensitive to the same final state. The list of such analyses and final states is detailed in Table 2-b. Again, for each final state, only that analysis with the strongest expected exclusion power was retained at each test point. This is not optimal but ensures that the channels which are then combined in the global confidence level computations are independent.

When the two cases just described (different signals covered by one analysis, different analyses sensitive to the same final state) were present simultaneously, the signal addition was performed before the final analysis selection. Then if that step involved more than two analyses, the final selection was made in successive iterations. To quote the four-jet final state as an example, at energies above 190 GeV, the total  and  signals were first computed in each of the three four-jet analyses of Ref. [1] and in the four-b analysis of Ref. [21]. This summed three signals in the low and high mass  dedicated four-jet analyses ((h ) ( ), () ( ) and hA  ), two signals in the  dedicated four-jet analysis (hA   and (h ) ( )) and three signals in the four-b analysis (()A, ()( ) and hA  ). The signals due the third Higgs boson, H, were computed in the same way and added to those from the h boson. Then, a choice was made between the low and high mass  dedicated four-jet analyses. The result of this selection was compared with the  dedicated four-jet analysis, and the best of these was confronted with the four-b analysis. A choice was made between the remaining analysis and the best between the various flavour-blind multi-jet analyses, that is the low mass and high mass hZ dedicated flavour-blind analyses, and the three and four-jet hA dedicated flavour-blind analyses [22]. As multi-jet flavour-blind analyses use mass-hypothesis dependent criteria, selecting the best one implied also a choice between the h and H signals for each of them. The analysis retained was finally compared with the result of the selection between the two charged Higgs multi-jet analyses, the cscs and WAWA dedicated analyses [23].

Figure 3: An example of two-dimensional PDFs from the analysis of the     channel at  = 206.6 GeV [1]. The first discriminant variable is built from the reconstructed Higgs boson mass while the second is the event b-tagging variable. Top, left: PDF for a  signal with  = 102 . Top, right: PDF for a  signal with  = 115 . Bottom: PDF expected from the occurrence of both signals in a scenario where the expectations for the two signals are similar (cross-sections 32 and 42 fb, branching fractions into  92% and 91%, selection efficiencies 69% and 66% for  and , respectively) leading to a double peak in the combined PDF.

4 The Cp-conserving Mssm scenarios

In most of the parameter space of the CP-conserving MSSM scenarios, only  and  productions are kinematically possible at LEP energies. These processes have complementary cross-sections since the hZZ and hAZ couplings are proportional to  and , respectively, where  is the ratio of the doublet vacuum expectation values and  is the Higgs doublet mixing angle which enters the definition of the two CP-even Higgs eigenstates as a mixture of the real, neutral components of the initial Higgs field doublets [2, 28]. If kinematically allowed,  production dominates at low  or at large , while in the rest of the parameter space, it is suppressed with respect to  pair-production. The third neutral Higgs boson, H, in some scenarios and in limited regions of the parameter space, is light enough and can be produced with a large  or  cross-section. As the HZZ coupling is proportional to , and the HAZ one is proportional to ,  production, when allowed by kinematics, plays a role at large , and  production at low . Similarily, charged Higgs bosons kinematically accessible at LEP2 energies are predicted in limited regions of the parameter space, typically when A is light, whatever . The minimal value of the mass of such charged Higgs bosons is 60  in the scenarios under study. The coverage of the region of the MSSM parameter space kinematically accessible at LEP is then assured primarily by the  and  searches, with the help of the ,  and to a lesser extent  channels.

At tree level, the production cross-sections and the Higgs branching fractions in the MSSM depend on two free parameters, usually chosen as  and one Higgs boson mass, or, alternatively, two Higgs boson masses, e.g.  and . Radiative corrections introduce additional parameters related to supersymmetry breaking [2, 28]. Hereafter, the usual assumption that some of them are equal at a given energy scale is made: hence, the SU(2) and U(1) gaugino mass parameters are assumed to be unified at the so-called GUT scale, while the sfermion mass parameters or the squark trilinear couplings are taken to be equal at the EW scale. Within these assumptions, the parameters beyond tree level are: the top quark mass, the Higgs mixing parameter, , which defines the Higgsino mass parameter at the EW scale, the common sfermion mass parameter at the EW scale, , the SU(2) gaugino mass parameter at the EW scale, , the gluino mass, , and the common squark trilinear coupling at the EW scale, . The U(1) gaugino mass term at the EW scale, , is related to through the GUT relation . The radiative corrections affect the Higgs boson masses and couplings, with the largest contributions arising from loops involving the third generation quarks and squarks (top/stop and, at large values of , bottom/sbottom). As an example, the h boson mass, which is below that of the Z boson at tree level, increases by a few tens of  in some regions of the MSSM parameter space due to radiative corrections.

4.1 The benchmark scenarios

In the following, eight benchmark scenarios are considered, as suggested in Ref. [29]. The values of their underlying parameters are quoted in Table 3. The first three scenarios are those usually studied at LEP. They have been proposed to test the sensitivity of LEP to Higgs bosons with either masses close to the kinematic limit or decays difficult to detect. Similarly, the five other scenarios are aimed at testing the sensitivity of the Higgs boson searches at hadron colliders. It is thus interesting to establish the LEP constraints in such models too.

The first two scenarios, called the scenario and the no mixing scenario, differ only by the value of , the parameter which controls the mixing in the stop sector (through the product ). This parameter has the largest impact on the mass of the h boson. The scenario leads to the maximum possible h mass as a function of . The no mixing scenario is its counterpart with vanishing mixing, leading to theoretical upper bounds on  which are at least 15  lower than in the scheme.

scenario
() () () () ()
1000 200 800 -200 2
no mixing 1000 200 800 -200 0
large 400 400 200 1000 -300
, 1000 200 800 200 2
, , 1000 200 800 200 -2
no mixing, , large 2000 200 800 200 0
gluophobic 350 300 500 300 -750
small 800 500 500 2.5 -1100
Table 3: Values of the underlying parameters for the eight representative MSSM scenarios scanned in this paper. Note that . These scenarios have been studied for several values of the top quark mass,  = 169.2, 174.3, 179.4 and 183.0 .

The third scenario is called the large scenario to account for a large, positive value of . As a consequence of the low value of and the moderate mixing in the stop sector, this scenario predicts at least one CP-even Higgs boson with a mass within kinematic reach at LEP2 in each point of the MSSM parameter space. However, there are regions for which detecting such a Higgs boson is difficult because of vanishing branching fractions into b-quarks. The values chosen for and are indeed such that, in these regions, radiative corrections lead to suppressed couplings to b-quarks for one or the other CP-even Higgs boson. The dominant decays in these regions being still into hadrons, the main analysis channels suffer from large backgrounds. This scenario was designed to test the sensitivity of LEP through analyses that could not benefit from the b-tagging capabilities of the experiments.

Among the five other benchmark scenarios, three are variants of the and no mixing scenarios. The sign of and that of the mixing parameter have been reversed in the two scenarios derived from the LEP scenario. The changes in the Higgs boson mass spectrum and properties are small. The sign of has been reversed and the value of has been doubled in the scenario derived from the no mixing scenario of LEP. The higher scale leads to a few  increase of the theoretical upper bound on . The last two scenarios have been proposed to test potentially difficult cases for the searches at hadron colliders. Hence, the gluophobic scenario presents regions where the main production channel at the LHC, gluon fusion, is suppressed due to cancellations between the top quark and stop quark loops in the production process. Finally, in the small scenario, important decay channels at the Tevatron and at the LHC, h  and h , are suppressed at large  and moderate . In these regions, the radiatively corrected mixing angle  is low, resulting in suppressed couplings of the ligthest CP-even Higgs boson to down-type fermions since these couplings are proportional to /.

 ()
scenario 169.2 174.3 179.4 183.0
128.2 132.9 138.6 142.7
no mixing 112.8 115.5 118.2 120.3
large 106.1 108.0 110.1 111.6
, 128.4 134.1 140.1 144.3
, ,