arXiv:0704.0594v1  [hep-ex]  4 Apr 2007
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN–PH-EP/2006-023
20 June 2006
Search for a fourth generation
b′-quark at LEP-II at√
s = 196 − 209 GeV
DELPHI Collaboration
Abstract
A search for the pair production of fourth generation b′-quarks was performed
using data taken by the DELPHI detector at LEP-II. The analysed data were
collected at centre-of-mass energies ranging from 196 to 209 GeV, corresponding
to an integrated luminosity of 420 pb−1. No evidence for a signal was found.
Upper limits on BR(b′ → bZ) and BR(b′ → cW) were obtained for b′ masses
ranging from 96 to 103 GeV/c2. These limits, together with the theoretical
branching ratios predicted by a sequential four generations model, were used to
constrain the value of RCKM = | Vcb′V
tb′Vtb
|, where Vcb′ , Vtb′ and Vtb are elements
of the extended CKM matrix.
(Accepted by Eur. Phys. J. C)
http://arxiv.org/abs/0704.0594v1
J.Abdallah26, P.Abreu23, W.Adam55, P.Adzic12, T.Albrecht18, R.Alemany-Fernandez9, T.Allmendinger18, P.P.Allport24,
U.Amaldi30, N.Amapane48, S.Amato52, E.Anashkin37, A.Andreazza29, S.Andringa23, N.Anjos23, P.Antilogus26,
W-D.Apel18, Y.Arnoud15, S.Ask27, B.Asman47, J.E.Augustin26, A.Augustinus9, P.Baillon9, A.Ballestrero49,
P.Bambade21, R.Barbier28, D.Bardin17, G.J.Barker57, A.Baroncelli40, M.Battaglia9, M.Baubillier26, K-H.Becks58,
M.Begalli7, A.Behrmann58, E.Ben-Haim21, N.Benekos33, A.Benvenuti5, C.Berat15, M.Berggren26, L.Berntzon47,
D.Bertrand2, M.Besancon41, N.Besson41, D.Bloch10, M.Blom32, M.Bluj56, M.Bonesini30, M.Boonekamp41,
P.S.L.Booth†24, G.Borisov22, O.Botner53, B.Bouquet21, T.J.V.Bowcock24, I.Boyko17, M.Bracko44, R.Brenner53,
E.Brodet36, P.Bruckman19, J.M.Brunet8, B.Buschbeck55, P.Buschmann58, M.Calvi30, T.Camporesi9, V.Canale39,
F.Carena9, N.Castro23, F.Cavallo5, M.Chapkin43, Ph.Charpentier9, P.Checchia37, R.Chierici9, P.Chliapnikov43,
J.Chudoba9, S.U.Chung9, K.Cieslik19, P.Collins9, R.Contri14, G.Cosme21, F.Cossutti50, M.J.Costa54, D.Crennell38,
J.Cuevas35, J.D’Hondt2, J.Dalmau47, T.da Silva52, W.Da Silva26, G.Della Ricca50, A.De Angelis51, W.De Boer18,
C.De Clercq2, B.De Lotto51 , N.De Maria48, A.De Min37, L.de Paula52, L.Di Ciaccio39, A.Di Simone40, K.Doroba56,
J.Drees58,9, G.Eigen4, T.Ekelof53, M.Ellert53, M.Elsing9, M.C.Espirito Santo23, G.Fanourakis12, D.Fassouliotis12,3,
M.Feindt18, J.Fernandez42 , A.Ferrer54, F.Ferro14, U.Flagmeyer58, H.Foeth9, E.Fokitis33, F.Fulda-Quenzer21, J.Fuster54,
M.Gandelman52, C.Garcia54, Ph.Gavillet9, E.Gazis33, R.Gokieli9,56, B.Golob44,46, G.Gomez-Ceballos42, P.Goncalves23,
E.Graziani40, G.Grosdidier21, K.Grzelak56, J.Guy38, C.Haag18, A.Hallgren53, K.Hamacher58, K.Hamilton36, S.Haug34,
F.Hauler18, V.Hedberg27, M.Hennecke18, H.Herr†9, J.Hoffman56, S-O.Holmgren47, P.J.Holt9, M.A.Houlden24,
J.N.Jackson24, G.Jarlskog27, P.Jarry41, D.Jeans36, E.K.Johansson47, P.D.Johansson47, P.Jonsson28, C.Joram9,
L.Jungermann18, F.Kapusta26, S.Katsanevas28 , E.Katsoufis33, G.Kernel44, B.P.Kersevan44,46, U.Kerzel18, B.T.King24,
N.J.Kjaer9, P.Kluit32, P.Kokkinias12, C.Kourkoumelis3, O.Kouznetsov17, Z.Krumstein17, M.Kucharczyk19, J.Lamsa1,
G.Leder55, F.Ledroit15, L.Leinonen47, R.Leitner31, J.Lemonne2, V.Lepeltier21, T.Lesiak19, W.Liebig58, D.Liko55,
A.Lipniacka47, J.H.Lopes52, J.M.Lopez35, D.Loukas12, P.Lutz41, L.Lyons36, J.MacNaughton55 , A.Malek58, S.Maltezos33,
F.Mandl55, J.Marco42, R.Marco42, B.Marechal52, M.Margoni37, J-C.Marin9, C.Mariotti9, A.Markou12,
C.Martinez-Rivero42, J.Masik13, N.Mastroyiannopoulos12, F.Matorras42, C.Matteuzzi30, F.Mazzucato37 ,
M.Mazzucato37, R.Mc Nulty24, C.Meroni29, E.Migliore48, W.Mitaroff55, U.Mjoernmark27, T.Moa47, M.Moch18,
K.Moenig9,11, R.Monge14, J.Montenegro32 , D.Moraes52, S.Moreno23, P.Morettini14, U.Mueller58, K.Muenich58,
M.Mulders32, L.Mundim7, W.Murray38, B.Muryn20, G.Myatt36, T.Myklebust34, M.Nassiakou12, F.Navarria5,
K.Nawrocki56, R.Nicolaidou41, M.Nikolenko17,10, A.Oblakowska-Mucha20, V.Obraztsov43, O.Oliveira23, S.M.Oliveira23,
A.Olshevski17, A.Onofre23, R.Orava16, K.Osterberg16, A.Ouraou41, A.Oyanguren54, M.Paganoni30, S.Paiano5,
J.P.Palacios24, H.Palka19, Th.D.Papadopoulou33, L.Pape9, C.Parkes25, F.Parodi14, U.Parzefall9, A.Passeri40,
O.Passon58, L.Peralta23, V.Perepelitsa54, A.Perrotta5, A.Petrolini14, J.Piedra42, L.Pieri40, F.Pierre41, M.Pimenta23,
E.Piotto9, T.Podobnik44,46 , V.Poireau9, M.E.Pol6, G.Polok19, V.Pozdniakov17 , N.Pukhaeva17, A.Pullia30, J.Rames13,
A.Read34, P.Rebecchi9, J.Rehn18, D.Reid32, R.Reinhardt58, P.Renton36, F.Richard21, J.Ridky13, M.Rivero42,
D.Rodriguez42, A.Romero48, P.Ronchese37, P.Roudeau21, T.Rovelli5, V.Ruhlmann-Kleider41, D.Ryabtchikov43 ,
A.Sadovsky17, L.Salmi16, J.Salt54, C.Sander18, R.Santos23, A.Savoy-Navarro26, U.Schwickerath9, R.Sekulin38,
M.Siebel58, A.Sisakian17, G.Smadja28, O.Smirnova27, A.Sokolov43, A.Sopczak22, R.Sosnowski56, T.Spassov9,
M.Stanitzki18, A.Stocchi21, J.Strauss55, B.Stugu4, M.Szczekowski56, M.Szeptycka56 , T.Szumlak20, T.Tabarelli30,
A.C.Taffard24, F.Tegenfeldt53, J.Timmermans32, L.Tkatchev17 , M.Tobin24, S.Todorovova13, B.Tome23, A.Tonazzo30,
P.Tortosa54, P.Travnicek13, D.Treille9, G.Tristram8, M.Trochimczuk56, C.Troncon29, M-L.Turluer41, I.A.Tyapkin17,
P.Tyapkin17, S.Tzamarias12, V.Uvarov43, G.Valenti5, P.Van Dam32, J.Van Eldik9, N.van Remortel16, I.Van Vulpen9,
G.Vegni29, F.Veloso23, W.Venus38, P.Verdier28, V.Verzi39, D.Vilanova41, L.Vitale50, V.Vrba13, H.Wahlen58,
A.J.Washbrook24, C.Weiser18, D.Wicke9, J.Wickens2, G.Wilkinson36, M.Winter10, M.Witek19, O.Yushchenko43,
A.Zalewska19, P.Zalewski56, D.Zavrtanik45, V.Zhuravlov17, N.I.Zimin17, A.Zintchenko17 , M.Zupan12
1Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA
2IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium
3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece
4Department of Physics, University of Bergen, Allégaten 55, NO-5007 Bergen, Norway
5Dipartimento di Fisica, Università di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy
6Centro Brasileiro de Pesquisas F́ısicas, rua Xavier Sigaud 150, BR-22290 Rio de Janeiro, Brazil
7Inst. de F́ısica, Univ. Estadual do Rio de Janeiro, rua São Francisco Xavier 524, Rio de Janeiro, Brazil
8Collège de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France
9CERN, CH-1211 Geneva 23, Switzerland
10Institut de Recherches Subatomiques, IN2P3 - CNRS/ULP - BP20, FR-67037 Strasbourg Cedex, France
11Now at DESY-Zeuthen, Platanenallee 6, D-15735 Zeuthen, Germany
12Institute of Nuclear Physics, N.C.S.R. Demokritos, P.O. Box 60228, GR-15310 Athens, Greece
13FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, CZ-180 40, Praha 8, Czech Republic
14Dipartimento di Fisica, Università di Genova and INFN, Via Dodecaneso 33, IT-16146 Genova, Italy
15Institut des Sciences Nucléaires, IN2P3-CNRS, Université de Grenoble 1, FR-38026 Grenoble Cedex, France
16Helsinki Institute of Physics and Department of Physical Sciences, P.O. Box 64, FIN-00014 University of Helsinki,
Finland
17Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federation
18Institut für Experimentelle Kernphysik, Universität Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany
19Institute of Nuclear Physics PAN,Ul. Radzikowskiego 152, PL-31142 Krakow, Poland
20Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, PL-30055 Krakow, Poland
21Université de Paris-Sud, Lab. de l’Accélérateur Linéaire, IN2P3-CNRS, Bât. 200, FR-91405 Orsay Cedex, France
22School of Physics and Chemistry, University of Lancaster, Lancaster LA1 4YB, UK
23LIP, FCUL, IST, CFCUC - Av. Elias Garcia, 14-1o, PT-1000 Lisboa Codex, Portugal
24Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK
25Dept. of Physics and Astronomy, Kelvin Building, University of Glasgow, Glasgow G12 8QQ
26LPNHE, IN2P3-CNRS, Univ. Paris VI et VII, Tour 33 (RdC), 4 place Jussieu, FR-75252 Paris Cedex 05, France
27Department of Physics, University of Lund, Sölvegatan 14, SE-223 63 Lund, Sweden
28Université Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France
29Dipartimento di Fisica, Università di Milano and INFN-MILANO, Via Celoria 16, IT-20133 Milan, Italy
30Dipartimento di Fisica, Univ. di Milano-Bicocca and INFN-MILANO, Piazza della Scienza 3, IT-20126 Milan, Italy
31IPNP of MFF, Charles Univ., Areal MFF, V Holesovickach 2, CZ-180 00, Praha 8, Czech Republic
32NIKHEF, Postbus 41882, NL-1009 DB Amsterdam, The Netherlands
33National Technical University, Physics Department, Zografou Campus, GR-15773 Athens, Greece
34Physics Department, University of Oslo, Blindern, NO-0316 Oslo, Norway
35Dpto. Fisica, Univ. Oviedo, Avda. Calvo Sotelo s/n, ES-33007 Oviedo, Spain
36Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
37Dipartimento di Fisica, Università di Padova and INFN, Via Marzolo 8, IT-35131 Padua, Italy
38Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK
39Dipartimento di Fisica, Università di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy
40Dipartimento di Fisica, Università di Roma III and INFN, Via della Vasca Navale 84, IT-00146 Rome, Italy
41DAPNIA/Service de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-Yvette Cedex, France
42Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, ES-39006 Santander, Spain
43Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation
44J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
45Laboratory for Astroparticle Physics, University of Nova Gorica, Kostanjeviska 16a, SI-5000 Nova Gorica, Slovenia
46Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
47Fysikum, Stockholm University, Box 6730, SE-113 85 Stockholm, Sweden
48Dipartimento di Fisica Sperimentale, Università di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy
49INFN,Sezione di Torino and Dipartimento di Fisica Teorica, Università di Torino, Via Giuria 1, IT-10125 Turin, Italy
50Dipartimento di Fisica, Università di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy
51Istituto di Fisica, Università di Udine and INFN, IT-33100 Udine, Italy
52Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fundão BR-21945-970 Rio de Janeiro, Brazil
53Department of Radiation Sciences, University of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden
54IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain
55Institut für Hochenergiephysik, Österr. Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria
56Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland
57Now at University of Warwick, Coventry CV4 7AL, UK
58Fachbereich Physik, University of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany
† deceased
1 Introduction
The Standard Model (SM), although in agreement with the available experimental
data [1], leaves several open questions. In particular, the number of fermion generations
and their mass spectrum are not predicted. The measurement of the Z decay widths [1]
established that the number of light neutrino species (m < mZ/2, where mZ is the Z boson
mass) is equal to three. However, if a heavy neutrino or a neutrinoless extra generation
exists, this bound does not exclude the possibility of extra generations of heavy quarks.
Moreover the fit to the electroweak data [2] does not deteriorate with the inclusion of one
extra heavy generation, if the new up and down-type quarks mass difference is not too
large. It should be noticed however that in this fit no mixing of the extra families with
the SM ones is assumed.
The subject of this paper is the search for the pair production of a fourth generation
b′-quark at LEP-II: b′ production and decay are discussed in section 2; in section 3, the
data sets and the Monte Carlo (MC) simulation are described; the analysis is discussed
in section 4; the results and their interpretation within a sequential model are presented
in sections 5 and 6, respectively.
2 b′-quark production and decay
Extra generations of fermions are predicted in several SM extensions [3,4]. In sequen-
tial models [5–7], a fourth generation of fermions carrying the same quantum numbers as
the SM families is considered. In the quark sector, an up-type quark, t′, and a down-type
quark, b′, are included. The corresponding 4× 4 extended Cabibbo-Kobayashi-Maskawa
(CKM) matrix is unitary, approximately symmetric and almost diagonal. As CP-violation
is not considered in the model, all the CKM elements are assumed to be real.
The b′-quark may decay via charged currents (CC) to UW, with U = t′, t, c, u, or via
flavour-changing neutral currents (FCNC) to DX , where D = b, s, d and X = Z,H, γ, g
(Fig. 1). As in the SM, FCNC are absent at tree level, but can appear at one-loop level,
due to CKM mixing. If the b′ is lighter than t′ and t, the decays b′ → t′W and b′ → tW
are kinematically forbidden and the one-loop FCNC decays can be as important as the
CC decays [6].
The analysis of the electroweak data [1] shows that the mass difference |mt′ −mb′ | <
60 GeV/c2 is consistent with the measurement of the ρ parameter [3,5]. In particular,
when mZ + mb < mb′ < mH + mb, either b
′ → cW or b′ → bZ decay tend to be domi-
nant [5–7]. In this case, the partial widths of the CC and FCNC b′ decays depend mainly
on mt′ , mb′ and RCKM = | Vcb′V
tb′Vtb
|, where Vcb′ , Vtb′ and Vtb are elements of the extended
4 × 4 CKM matrix [7].
Limits on the mass of the b′-quark have been set previously at various accelerators.
At LEP-I, all the experiments searched for b′ pair production (e+e− → b′b̄′), yielding a
lower limit on the b′ mass of about mZ/2 [8]. At the Tevatron, both the D0 [9] and
CDF [10] experiments reported limits on σ(pp̄ → b′b̄′) × BR(b′ → bX)2, where BR is
the branching ratio corresponding to the considered FCNC b′ decay mode and X = γ,Z.
Assuming BR(b′ → bZ) = 1, CDF excluded the region 100 < mb′ < 199 GeV/c2.
Although no dedicated analysis was performed for the b′ → cW decay, the D0 limits on
σ(pp̄ → tt̄) × BR(t → cW)2 from Fig. 44 and Table XXXI of reference [11] can give a
hint on the possible values for BR(b′ → cW) [12].
In the present analysis the on-shell FCNC (b′ → bZ) and CC (b′ → cW) decay modes
were studied and consequently the mass range 96 GeV/c2 < mb′ < 103 GeV/c
2 was
considered. This mass range is complementary to the one covered by CDF [10]. The
mass range mW + mc < mb′ < mZ + mb was not considered because in this region
the evaluation of the branching ratios for the different b′ decays is particularly difficult
from the theoretical point of view [7]. In the present analysis no assumptions on the
BR(b′ → bZ) and BR(b′ → cW) in order to derive mass limits were made. Different
final states, corresponding to the different b′ decay modes and subsequent decays of the
Z and W bosons, were analysed.
3 Data samples and Monte Carlo simulation
The analysed data were collected with the DELPHI detector [13] during the years
1999 and 2000 in LEP-II runs at
s = 196 − 209 GeV and correspond to an integrated
luminosity of about 420 pb−1. The luminosity collected at each centre-of-mass energy is
shown in Table 1. During the year 2000, an unrecoverable failure affected one sector of
the central tracking detector (TPC), corresponding to 1/12 of its acceptance. The data
collected during the year 2000 with the TPC fully operational were split into two energy
bins, below and above
s = 206 GeV, with 〈
s〉 = 204.8 GeV and 〈
s〉 = 206.6 GeV,
respectively. The data collected with one sector of the TPC turned off were analysed
separately and have 〈
s〉 = 206.3 GeV.
s (GeV) 196 200 202 205 207 206∗
luminosity (pb−1) 76.0 82.7 40.2 80.0 81.9 59.2
Table 1: The luminosity collected with the DELPHI detector at each centre-of-mass
energy is shown. The energy bin labelled 206∗ corresponds to the data collected with one
sector of the TPC turned off.
Signal samples were generated using a modified version of PYTHIA 6.200 [14]. Al-
though PYTHIA does not provide FCNC decay channels for quarks, it was possible to
activate them by modifying the decay products of an available channel. The angular
distributions assumed for b′ pair production and decay were those predicted by the SM
for any heavy down-type quark. Different samples, corresponding to b′ masses in the
range between 96 and 103 GeV/c2 and with a spacing of 1 GeV/c2 were generated at
each centre-of-mass energy. Specific Monte Carlo simulations (for both SM and signal
processes) were produced for the period when one sector of the TPC was turned off.
The most relevant background processes for the present analyses are those leading
to WW or ZZ bosons in the final state, i.e. four-fermion backgrounds. Radiation in
these events can mimic the six-fermion final states for the signal. Additionally qq̄(γ) and
Bhabha events can not be neglected since for signal final states with missing energy these
backgrounds can become important. SM background processes were simulated at each
centre-of-mass energy using several Monte Carlo generators. All the four-fermion final
states (both neutral and charged currents) were generated with WPHACT [15], while
the particular phase space regions of e+e− → e+e−f f̄ referred to as γγ interactions were
generated using PYTHIA [14]. The qq(γ) final state was generated with KK2F [16].
Bhabha events were generated with BHWIDE [17].
The generated signal and background events were passed through the detailed simu-
lation of the DELPHI detector [13] and then processed with the same reconstruction and
analysis programs as the data.
4 Description of the analyses
Pair production of b′-quarks was searched for in both the FCNC (b′ → bZ) and CC
(b′ → cW) decay modes. The b′ decay modes and the subsequent decays of the gauge
bosons (Z or W) lead to several different final states (Fig. 2). The final states considered
and their branching ratios are shown in Table 2. The choice of the considered final
states was done taking into account their signatures and BR. About 81% and 90% of the
branching ratio to the FCNC and CC channels were covered, respectively. All final states
include two jets originating from the low energy b (c) quarks present in the FCNC (CC)
b′ decay modes. A common preselection was adopted, followed by a specific analysis for
each of the final states (Table 2).
b′ decay boson decays BR (%) final states
b′ → bZ (FCNC) ZZ → l+l−νν̄ 4.0 bb̄l+l−νν̄
ZZ → qq̄νν̄ 28.0 bb̄qq̄νν̄
ZZ → qq̄qq̄ 48.6 bb̄qq̄qq̄
b′ → cW (CC) WW → qq̄l+ν 43.7 cc̄qq̄l+ν
WW → qq̄qq̄ 45.8 cc̄qq̄qq̄
Table 2: The final states considered in this analysis are shown. About 81% and 90% of
the branching ratio to the FCNC and CC channels were covered, respectively.
Events were preselected by requiring at least eight good charged-particle tracks and
the visible energy measured at polar angles1 above 20◦, to be greater than 0.2
s. Good
charged-particle tracks were defined as those with a momentum above 0.2 GeV/c and
impact parameters in the transverse plane and along the beam direction below 4 cm and
below 4 cm/ sin θ, respectively.
The identification of muons relied on the association of charged particles to signals
in the muon chambers and in the hadronic calorimeters and was provided by standard
DELPHI algorithms [13]. The identification of electrons and photons was performed
by combining information from the electromagnetic calorimeters and the tracking sys-
tem. Radiation and interaction effects were taken into account by an angular clustering
procedure around the main shower [18].
The search for isolated particles (charged leptons and photons) was done by construct-
ing double cones oriented in the direction of charged-particle tracks or neutral energy
deposits. The latter ones were defined as calorimetric energy deposits above 0.5 GeV,
not matched to charged-particle tracks and identified as photon candidates by the stan-
dard DELPHI algorithms [13,18]. For charged leptons (photons), the energy in the region
between the two cones, which had half-opening angles of 5◦ and 25◦ (5◦ and 15◦), was
required to be below 3 GeV (1 GeV), to ensure isolation. All the charged-particle tracks
1In the standard DELPHI coordinate system, the positive z axis is along the electron beam direction. The polar angle
(θ) is defined with respect to the z axis. In this paper, polar angle ranges are always assumed to be symmetric with respect
to the θ = 90◦ plane.
final state assignment criteria
bb̄l+l−νν̄ at least 1 isolated lepton
bb̄qq̄νν̄ no isolated leptons
Emissing > 50 GeV
bb̄qq̄qq̄ no isolated leptons
Emissing < 50 GeV
cc̄qq̄l+ν only 1 isolated lepton
cc̄qq̄qq̄ no isolated leptons
Emissing < 50 GeV
Table 3: Summary of the final state assignment criteria.
and neutral energy deposits inside the inner cone were associated to the isolated particle.
Its energy was then re-evaluated as the sum of the energies inside the inner cone and
was required to be above 5 GeV. For well identified leptons or photons [13,18] the above
requirements were weakened. In this case only the external cone was used (to ensure
isolation) and its angle α was varied according to the energy of the lepton (photon) can-
didate, down to 2◦ for Pℓ ≥ 70 GeV/c (3◦ for Pγ ≥ 90 GeV/c), with the allowed energy
inside the cone reduced by sinα/ sin 25◦ (sinα/ sin 15◦). Isolated leptons were required
to have a momentum greater than 10 GeV/c and a polar angle above 25◦. Events with
isolated photons were rejected.
All the events were clustered into two, four or six jets using the Durham jet algo-
rithm [19], according to the number of jets expected in the signal in each of the final
states, unless explicitly stated otherwise. Although two b jets are always present in the
FCNC final states, they have a relatively low energy and b-tagging techniques [20] were
not used.
Events were assigned to the different final states according to the number of isolated
leptons and to the missing energy in the event, as detailed in Table 3. Within the same
b′ decay channel, the different selections were designed to be mutually exclusive. For the
final states involving charged leptons (bb̄l+l−νν̄ and cc̄qq̄l+ν), events were divided into
different samples according to the lepton flavour identification: e sample (well identified
electrons), µ sample (well identified muons) and no-id sample (leptons with unidentified
flavour or two leptons identified with different flavours).
Specific analyses were then performed for each of the final states. The selection criteria
for the bb̄qq̄qq̄ and cc̄qq̄qq̄ final states were the same. The bb̄l+l−νν̄ final state has a very
clean signature (two leptons with ml+l− ∼ mZ, two low energy jets and missing mass close
to mZ) and consequently a sequential cut analysis was adopted. For all the other final
states, a sequential selection step was followed by a discriminant analysis. In this case,
a signal likelihood (LS) and a background likelihood (LB) were assigned to each event,
based on Probability Density Functions (PDF), built from the distributions of relevant
physical variables. The discriminant variable was defined as ln(LS/LB).
4.1 The bb̄l+l−νν̄ final state
The FCNC bb̄l+l−νν̄ final state events were preselected as described above, by re-
quiring at least eight good charged-particle tracks, the visible energy measured at polar
angles above 20◦, to be greater than 0.2
s and at least one isolated lepton. Distribu-
tions of the relevant variables are shown in Fig. 3 for all the events assigned to this final
state after the preselection. The event selection was performed in two levels. In the first
one, events were required to have at least two leptons and an effective centre-of-mass
energy [21],
s′, below 0.95
s. The particles other than the two leptons in the events
were clustered into two jets and the Durham resolution variable in the transition from
two jets to one jet2 was required to be greater than 0.002. The number of data events and
the SM expectation after the first selection level is shown in Table 4. The background
composition and the signal efficiencies at this level of selection for mb′ = 100 GeV/c
2 and√
s = 205 GeV are given in Table 8. The efficiencies for the other relevant b′ masses and√
s values were found to be the same within errors. Data, SM expectation and signal
distributions at this selection level are shown in Fig. 4.
s (GeV) data (SM expectation ± statistical error)
e sample µ sample no-id sample
196 2 (2.6±0.3) 1 (2.9±0.3) 47 (35.9±1.4)
200 3 (2.5±0.4) 4 (3.4±0.4) 30 (37.4±1.4)
202 2 (1.3±0.2) 1 (1.7±0.2) 20 (18.7±0.7)
205 5 (2.5±0.4) 3 (3.0±0.4) 35 (36.2±1.4)
207 3 (2.3±0.4) 3 (3.1±0.4) 45 (35.1±1.3)
206∗ 1 (1.9±0.3) 2 (2.6±0.2) 31 (27.6±1.0)
total 16 (13.2±0.8) 14 (16.7±0.8) 208 (191.0±3.0)
Table 4: First selection level of the bb̄l+l−νν̄ final state: the number of events selected
in data and the SM expectations after the first selection level for each sample and cen-
tre-of-mass energy are shown.
In the final selection level the momentum of the more energetic (less energetic) jet
was required to be below 30 GeV/c (12.5 GeV/c). Events in the e and no-id samples
had to have a missing energy greater than 0.4
s. In the µ sample events were required
to have an angle between the two muons greater than 125◦. In the no-id sample, the
angle between the two charged leptons had to be greater than 140◦ and pmis/Emis < 0.4,
where pmis and Emis are the missing momentum and energy, respectively. After the final
selection, one data event was selected for an expected background of 1.5±0.7. This event
belonged to the no-id sample and was collected at
s = 200 GeV. The signal efficiencies
for mb′ = 100 GeV/c
2 and
s = 205 GeV are 30.6 ± 2.5% (e sample), 48.6 ± 2.7% (µ
sample) and 7.2 ± 0.8% (no-id sample) and their variation with mb′ and
s was found
to be negligible in the relevant range.
4.2 The bb̄qq̄νν̄ final state
The FCNC bb̄qq̄νν̄ final state is characterised by the presence of four jets and a
missing mass close to mZ. At least 20 good charged-particle tracks and
s′ > 0.5
were required. Events were clustered into four jets. Monojet-like events were rejected by
requiring − log10(y2→1) < 0.7 (y2→1 is the Durham resolution variable in the two to one
jet transition). Furthermore, − log10(y4→3) was required to be below 2.8 and the energy
of the leading charged particle of the most energetic jet was required to be below 0.1
2The Durham resolution variable is the minimum value of the scaled transverse momentum obtained in the transition
from n to n− 1 jets [19] and will be represented by yn→n−1.
A kinematic fit imposing energy-momentum conservation and no missing energy was
applied and the background-like events with χ2/n.d.f. < 6 were rejected. The data,
SM expectation and signal distributions of this variable are shown in Fig. 5. Table 5
summarizes the number of selected data events and the SM expectation. The background
composition and the signal efficiency at this level of selection for mb′ = 100 GeV/c
2 and√
s = 205 GeV are given in Table 8. The efficiencies for the other relevant b′ masses and√
s values were found to be the same within errors.
s (GeV) data (SM expectation ± statistical error)
196 123 (106.3±4.0)
200 111 (104.8±4.0)
202 50 (49.8±1.9)
205 88 (94.2±3.7)
207 99 (91.2±3.6)
206∗ 62 (65.7±2.6)
total 533 (511.7±8.3)
Table 5: First selection level of the bb̄qq̄νν̄ final state: the number of events selected in
data and the SM expectation for each centre-of-mass energy are shown.
A discriminant selection was then performed using the following variables to build the
PDFs:
• the missing mass;
• Aj1j2cop × min(sin θj1 , sin θj2), where Aj1j2cop is the acoplanarity3 and θj1,j2 are the polar
angles of the jets when forcing the events into two jets4;
• the acollinearity between the two most energetic jets5 with the event particles clus-
tered into four jets;
• the sum of the first and third Fox-Wolfram moments (h1 + h3) [22];
• the polar angle of the missing momentum.
The data, SM expectation and signal distributions of these variables are shown in Fig. 6.
4.3 The bb̄qq̄qq̄ final state
The FCNC bb̄qq̄qq̄ final state is characterised by the presence of six jets and a small
missing energy. All the events were clustered into six jets and only those with at least
30 good charged-particle tracks were accepted. Moreover, events were required to have√
s′ > 0.6
s, − log10(y2→1) < 0.7 and − log10(y6→5) < 3.6. The number of selected data
events and the expected background at this level are shown in Table 6. The background
composition and the signal efficiency at this level of selection for mb′ = 100 GeV/c
2 and√
s = 205 GeV are given in Table 8. The efficiencies for the other relevant b′ masses and√
s values were found to be the same within errors.
A discriminant selection was performed using the following variables to build the PDFs:
3The acoplanarity between two particles is defined as |180◦ − |φ1 −φ2||, where φ1,2 are the azimuthal angles of the two
particles (in degrees).
4While the signal is characterised by the presence of four jets in the final state, the two jets configuration is used mainly
for background rejection.
5The acollinearity between two particles is defined as 180◦ − α1,2, where α1,2 is the angle (in degrees) between those
two particles.
s (GeV) data (SM expectation ± statistical error)
196 349 (326.7±5.3)
200 347 (342.1±5.5)
202 165 (162.1±2.6)
205 322 (319.0±5.2)
207 287 (307.6±5.0)
206∗ 192 (215.8±3.6)
total 1662 (1673.9±11.4)
Table 6: First selection level of the bb̄qq̄qq̄ and cc̄qq̄qq̄ final states: the number of events
selected in data and the SM expectations for each centre-of-mass energy are shown.
• the Durham resolution variable, − log10(y4→3);
• the Durham resolution variable, − log10(y5→4);
• the acollinearity between the two most energetic jets, with the event forced into four
jets;
• the sum of the first and third Fox-Wolfram moments;
• the momentum of the most energetic jet;
• the angle between the two most energetic jets (with the events clustered into six
jets).
The distributions of these variables are shown in Fig. 7 for data, SM expectation and
signal.
4.4 The cc̄qq̄l+ν final state
The signature of this CC final state is the presence of four jets (two of them having
low energy), one isolated lepton and missing energy (originating from the W → lν̄ decay).
The events were accepted if they had at least 15 good charged-particle tracks. The event
particles other than the identified lepton were clustered into four jets. Part of the qq̄
and γγ background was rejected by requiring − log10(y2→1) < 0.7. Furthermore, there
should be only one charged-particle track associated to the isolated lepton, and the leading
charged particle of the most energetic jet was required to have a momentum below 0.1
The number of selected data events and SM expectations at this level are summarized in
Table 7. The background composition and the signal efficiencies at this level of selection
for mb′ = 100 GeV/c
2 and
s = 205 GeV are given in Table 8. The efficiencies for the
other relevant b′ masses and
s values were found to be the same within errors.
The PDFs used to calculate the background and signal likelihoods were based on the
following variables:
• the sum of the first and third Fox-Wolfram moments;
• the invariant mass of the two jets, with the event particles other than the identified
lepton clustered into two jets;
• the Durham resolution variable, − log10(y4→3);
|~pi|/
s, where ~pi are the momenta of the charged particles (excluding the lepton)
in the same hemisphere as the lepton (the hemisphere is defined with respect to the
lepton);
• the acollinearity between the two most energetic jets;
s (GeV) data (SM expectation ± statistical error)
e µ no-id
196 65 (51.1±1.4) 53 (56.1±1.5) 38 (34.4±1.4)
200 54 (58.1±1.7) 63 (59.9±1.6) 40 (35.0±1.4)
202 30 (27.8±0.8) 21 (28.4±0.8) 13 (16.9±0.7)
205 56 (50.8±1.5) 66 (53.6±1.5) 32 (33.3±1.4)
207 53 (53.8±1.6) 48 (57.2±1.6) 35 (33.8±1.4)
206∗ 31 (37.2±1.4) 42 (39.3±1.1) 21 (23.4±1.0)
total 289 (278.8±3.5) 293 (294.5±3.4) 179 (176.8 ± 2.8)
Table 7: First selection level of the cc̄qq̄l+ν final state: the number of events selected in
data and the SM expectations for each sample and centre-of-mass energy are shown.
• the angle between the lepton and the missing momentum.
The data, SM expectation and signal distributions of these variables are shown in Fig. 8.
In order to improve the efficiency, events with no leptons seen in the detector were
kept in a fourth sample. For this sample, the selection criteria of the bb̄qq̄νν̄ final state
were applied and the same variables as in section 4.2 were used to build the PDFs. The
signal efficiency after the first selection level for mb′ = 100 GeV/c
2 and
s = 205 GeV
was 8.9±0.9%. The efficiencies for the other relevant b′ masses and
s values were found
to be the same within errors.
4.5 The cc̄qq̄qq̄ final state
This final state is very similar to bb̄qq̄qq̄ (with slightly different kinematics due to the
mass difference between the Z and the W). The analysis described in section 4.3 was
thus adopted. The number of selected events and the SM expectations can be found in
Table 6. At this level, the signal efficiency for mb′ = 100 GeV/c
2 and
s = 205 GeV was
67.3±1.5%. The efficiencies for the other b′ masses and centre-of-mass energies were the
same within errors. The PDFs were built using the same set of variables as in section 4.3.
5 Results
For all final states, a good agreement between data and SM expectation was found. The
summary of the total number of selected data events, SM expectations, the corresponding
background composition and the signal efficiencies for the studied final states are shown
in Table 8. In the bb̄l+l−νν̄ final state, one data event was retained after the final
selection level, for a SM expectation of 1.5 ± 0.7 events. This event belonged to the no-id
sample and was collected at
s = 200 GeV. For all the other final states, discriminant
analyses were used. In these cases, a discriminant variable, ln(LS/LB), was defined. The
distributions of ln(LS/LB), for the different analysis channels are shown in Fig. 9. No
evidence for a signal was found in any of the channels and the full information, i.e. event
numbers and the shapes of the distributions of the discriminant variables were used to
derive limits on BR(b′ → bZ) and BR(b′ → cW).
data background signal
final state (SM ± stat. error) composition (%) efficiency (%)
qq̄ WW ZZ γγ
bb̄l+l−νν̄ e sample 16 (13.2±0.8) 16 16 68 0 35.1±2.6
(first selection µ sample 14 (16.7±0.8) 0 10 90 0 53.4±2.7
level) no-id sample 208 (191.0±3.0) 8 80 12 0 12.3±1.0
bb̄qq̄νν̄ 533 (511.7±8.3) 76 17 2 5 57.6±1.7
bb̄qq̄qq̄ 1662 (1673.9±11.4) 35 65 0 0 66.0±1.5
e sample 289 (278.8±3.5) 7 82 11 0 45.3±2.7
cc̄qq̄l+ν µ sample 293 (294.5±3.4) 2 97 1 0 56.4±2.7
no-id sample 179 (176.8±2.8) 9 84 7 0 5.3±0.7
no lepton sample 533 (511.7±8.3) 76 17 2 5 8.9±0.9
cc̄qq̄qq̄ 1662 (1673.9±11.4) 35 65 0 0 67.3±1.5
Table 8: Summary of the total number of selected data events and SM expectations for
the studied final states after the final selection (first selection level for bb̄l+l−νν̄). The
corresponding background composition and signal efficiencies for mb′ = 100 GeV/c
2 and√
s = 205 GeV are also shown.
5.1 Limits on BR(b′ → bZ) and BR(b′ → cW)
Upper limits on the product of the e+e− → b′b̄′ cross-section and the branching ratio
as a function of the b′ mass were derived at 95% confidence level (CL) in each of the
considered b′ decay modes (FCNC and CC), taking into account the values of the dis-
criminant variables and their expected distributions for signal and background, the signal
efficiencies and the data luminosities at the various centre-of-mass energies.
Assuming the SM cross-section for the pair production of heavy quarks at LEP [7,14],
these limits were converted into limits on the branching ratios corresponding to the
b′ → bZ and b′ → cW decay modes. The modified frequentist likelihood ratio method [23]
was used. The different final states and centre-of-mass energy bins were treated as inde-
pendent channels. For each b′ mass only the channels with
s > 2mb′ were considered.
In order to avoid some non-physical fluctuations of the distributions of the discriminant
variables due to the limited statistics of the generated events, a smoothing algorithm was
used. The median expected limit, i.e. the limit obtained if the SM background was the
only contribution in data, was also computed. In Fig. 10 the observed and expected limits
on BR(b′ → bZ) and BR(b′ → cW) are shown as a function of the b′ mass. The 1σ and
2σ bands around the expected limit are also shown. The observed and expected limits
are statistically compatible. At 95% CL and for mb′ = 96 GeV/c
2, the BR(b′ → bZ) and
BR(b′ → cW) have to be below 51% and 43%, respectively. These limits were evaluated
taking into account the systematic uncertainties, as explained in the next subsection.
The limits obtained for BR(b′ → bZ) are compatible with those presented by CDF [10]
for a b′ mass of 100 GeV/c2. Below this mass, the DELPHI result is more sensitive and
the CDF limit degrades rapidly. For higher b′ masses, the LEP-II kinematical limit is
reached and the present analysis looses sensitivity.
5.2 Systematic uncertainties
The evaluation of the limits was performed taking into account systematic uncertain-
ties, which affect the background estimation, the signal efficiency and the shape of the
distributions used. The following systematic uncertainties were considered:
• SM cross-sections: uncertainties on the SM cross-sections translate into uncertainties
on the expected number of background events. The overall uncertainty on the most
relevant SM background processes for the present analyses is typically less than
2% [24], which leads to relative changes on the branching ratio limits below 6%;
• Signal generation: uncertainties on the final state quark hadronisation and fragmen-
tation modelling were studied. The Lund symmetric fragmentation function was
tested and compared with schemes where the b and c quark masses are taken into
account [14]. This systematic error source was estimated to be of the order of 20%
in the signal efficiency, by conservatively taking the maximum observed variation.
The relative effect on the branching ratio limits is below 16%;
• Smoothing: the uncertainty associated to the discriminant variables smoothing was
estimated by applying different smoothing algorithms. The smoothing procedure
does not change the number of SM expected events or the signal efficiency, but may
lead to differences in the shape of the discriminant variables. The relative effect of
this uncertainty on the limits evaluation was found to be below 9%.
Further details on the evaluation of the systematic errors and the derivation of limits can
be found in [25].
6 Constraints on RCKM
The branching ratios for the b′ decays can be computed within a four generations
sequential model [5–7]. As discussed before, if the b′ is lighter than both the t and the t′
quarks and mZ < mb′ < mH, the main contributions to the b
′ width are BR(b′ → bZ) and
BR(b′ → cW) [7]. Using the unitarity of the CKM matrix, its approximate diagonality
(Vub′ Vub ≈ 0) and taking Vcb ≈ 10−2 [12], the branching fractions can be written as a
function of three variables: RCKM = | Vcb′V
tb′ Vtb
|, mt′ and mb′ [5–7].
Fixing mt′ − mb′ , the limits on BR(b′ → bZ) and BR(b′ → cW) (Fig. 10) can be
translated into 95% CL bounds on RCKM as a function of mb′ . Two extreme cases were
considered: the almost degenerate case, with mt′−mb′ = 1 GeV/c2, and the case in which
the mass difference is close to the largest possible value, mt′ − mb′ = 50 GeV/c2 [3,5].
The results are shown in Fig. 11 and Fig. 12. In the figures, the upper curve was obtained
from the limit on BR(b′ → cW), while the lower curve was obtained from the limit on
BR(b′ → bZ), which decreases with growing mt′ . This suppression is due to the GIM
mechanism [26] as mt′ approaches mt. On the other hand, as the b
′ mass approaches
the bZ threshold, the b′ → bg decay dominates over b′ → bZ [7] and the lower limit on
RCKM becomes less stringent. The expected limits on BR(b
′ → bZ) did not allow to set
exclusions for low values of RCKM and mt′ −mb′ = 1 GeV/c2 (see Fig. 11).
7 Conclusions
The data collected with the DELPHI detector at
s = 196−209 GeV show no evidence
for the pair production of b′-quarks with masses ranging from 96 to 103 GeV/c2.
Assuming the SM cross-section for the pair production of heavy quarks at LEP, 95%
CL upper limits on BR(b′ → bZ) and BR(b′ → cW) were obtained. It was shown that, at
95% CL and for mb′ = 96 GeV/c
2, the BR(b′ → bZ) and BR(b′ → cW) have to be below
51% and 43%, respectively. The 95% CL upper limits on the branching ratios, combined
with the predictions of the sequential fourth generation model, were used to exclude
regions of the (RCKM , mb′) plane for two hypotheses of the mt′ − mb′ mass difference.
It was shown that, for mt′ −mb′ = 1 (50) GeV/c2 and 96 GeV/c2 < mb′ < 102 GeV/c2,
RCKM is bounded by an upper limit of 3.8×10−3 (1.2×10−3). For mb′ = 100 GeV/c2 and
mt′ −mb′ = 50 GeV/c2, the CKM ratio was constrained to be in the range 4.6 × 10−4 <
RCKM < 7.8 × 10−4.
Acknowledgements
We are greatly indebted to our technical collaborators, to the members of the CERN-
SL Division for the excellent performance of the LEP collider, and to the funding agencies
for their support in building and operating the DELPHI detector.
We acknowledge in particular the support of
Austrian Federal Ministry of Education, Science and Culture, GZ 616.364/2-III/2a/98,
FNRS–FWO, Flanders Institute to encourage scientific and technological research in the
industry (IWT) and Belgian Federal Office for Scientific, Technical and Cultural affairs
(OSTC), Belgium,
FINEP, CNPq, CAPES, FUJB and FAPERJ, Brazil,
Czech Ministry of Industry and Trade, GA CR 202/99/1362,
Commission of the European Communities (DG XII),
Direction des Sciences de la Matière, CEA, France,
Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, Germany,
General Secretariat for Research and Technology, Greece,
National Science Foundation (NWO) and Foundation for Research on Matter (FOM),
The Netherlands,
Norwegian Research Council,
State Committee for Scientific Research, Poland, SPUB-M/CERN/PO3/DZ296/2000,
SPUB-M/CERN/PO3/DZ297/2000, 2P03B 104 19 and 2P03B 69 23(2002-2004)
FCT - Fundação para a Ciência e Tecnologia, Portugal,
Vedecka grantova agentura MS SR, Slovakia, Nr. 95/5195/134,
Ministry of Science and Technology of the Republic of Slovenia,
CICYT, Spain, AEN99-0950 and AEN99-0761,
The Swedish Research Council,
Particle Physics and Astronomy Research Council, UK,
Department of Energy, USA, DE-FG02-01ER41155,
EEC RTN contract HPRN-CT-00292-2002.
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Z / H / g / γ
b / s / d
t′ / t / c / u
a) b)
Figure 1: The Feynman diagrams corresponding to the b′ (a) FCNC and (b) CC decay
modes are shown.
Z/γ Z
l−/ q̄ / q̄
l+/ q / q
ν̄ / ν̄ / q̄
ν / ν / q
Z/γ W
q̄ / q̄
q / q
ν / q̄
l+/ q
a) b)
Figure 2: The final states associated to the b′ (a) FCNC and (b) CC decay modes are
shown. Only those states analysed here are indicated.
DELPHI
0 50 100 150
αl1,tr (˚)
a)       (e sample)
0 20 40 60 80 100
pmis (GeV/c)
b)      (µ sample)
0 20 40 60 80
pjet 1 (GeV/c)
c)      (no-id sample)
SM expectation
signal (mb’=100 GeV/c
Figure 3: Data and SM expectation after the preselection level for the bb̄l+l−νν̄ final state
and centre-of-mass energies above 200 GeV. (a) The angle between the most energetic
lepton and the closest charged-particle track (e sample), (b) the missing momentum (µ
sample) and (c) the momentum of the most energetic jet (no-id sample) are shown. The
signal distributions for mb′ = 100 GeV/c
2 and
s = 205 GeV are also shown with
arbitrary normalisation. The background composition is 11% of qq̄, 69% of WW, 15% of
ZZ and 5% of γγ for the e sample, 6% of qq̄, 90% of WW and 4% of ZZ for the µ sample
and 45% of qq̄, 48% of WW, 5% of ZZ and 2% of γγ for the no-id sample.
DELPHI
0 20 40 60 80
pjet 1 (GeV/c)
a)       (e sample)
0 50 100 150
αll (˚)
b)      (µ sample)
0 0.25 0.5 0.75 1
pmis / Emis
c)      (no-id sample)
SM expectation
signal (mb’=100 GeV/c
Figure 4: Data and SM expectation after the first selection level for the bb̄l+l−νν̄ final
state and for centre-of-mass energies above 200 GeV. (a) The momentum of the most
energetic jet (e sample), (b) the angle between the two leptons (µ sample) and (c) the
ratio between the missing momentum and missing energy (no-id sample) are shown. The
signal distributions for mb′ = 100 GeV/c
2 and
s = 205 GeV are also shown with
arbitrary normalisation. The arrows represent the cuts applied in the second selection
level.
DELPHI
0 5 10 15 20 25 30 35 40
0 5 10 15 20 25 30 35 40
0 5 10 15 20 25 30 35 40
χ2/n.d.f.
SM expectation
signal (mb’=100 GeV/c
Figure 5: Comparison of data and SM expectation distributions of the χ2/n.d.f. of the fit
imposing energy-momentum conservation and no missing energy for the bb̄qq̄νν̄ final state
at centre-of-mass energies above 200 GeV. The arrow shows the applied cut. The signal
for mb′ = 100 GeV/c
2 and
s = 205 GeV is also shown with arbitrary normalisation.
DELPHI
0 50 100 150 200
missing mass (GeV/c
0 10 20 30 40
scaled acoplanarity (˚)
0 50 100 150
acolj1j2 (˚)
0 0.5 1 1.5
h1+h3
0 50 100 150
θmis (˚)
SM expectation
signal (mb’=100 GeV/c
Figure 6: Variables used in the discriminant analysis (bb̄qq̄νν̄ final state). The data and
SM expectation distributions for centre-of-mass energies above 200 GeV are shown for (a)
the missing mass, (b) Aj1j2cop ×min(sin θj1 , sin θj2), where Aj1j2cop is the acoplanarity and θj1,j2
are the polar angles of the jets when forcing the events into two jets, (c) the acollinearity
between the two most energetic jets (with the event particles clustered into four jets),
(d) the sum of the first and third Fox-Wolfram moments and (e) the polar angle of the
missing momentum. The signal distributions for mb′ = 100 GeV/c
2 and
s = 205 GeV
are also shown with arbitrary normalisation.
DELPHI
1 1.5 2 2.5 3
-log10(y4→3)
1 2 3 4
-log10(y5→4)
0 50 100 150
acolj1j2 (4 jets) (˚)
0 0.2 0.4 0.6 0.8 1
h1+h3
0 20 40 60 80 100
pj1 (GeV/c)
/c e)
0 50 100 150
αj1j2 (˚)
data SM expectation signal (mb’=100 GeV/c
Figure 7: Variables used in the discriminant analysis (bb̄qq̄qq̄ final state). The data
and SM expectation for centre-of-mass energies above 200 GeV are shown for (a)
− log10(y4→3), (b) − log10(y5→4), (c) the acollinearity between the two most energetic
jets, with the events clustered into four jets (see text for explanation), (d) the h1 + h3
Fox-Wolfram moments sum, (e) the momentum of the most energetic jet and (f) the angle
between the two most energetic jets. The signal distributions for mb′ = 100 GeV/c
2 and√
s = 205 GeV are also shown with arbitrary normalisation.
DELPHI
0 0.25 0.5 0.75 1
h1+h3
a)       (e sample)
0 50 100 150
mj1j2 (2 jets) (GeV/c
b)       (e sample)
1 2 3 4
-log10(y4→3)
c)      (µ sample)
0 0.1 0.2 0.3 0.4
Σptracks lepton hem. / √s
d)      (µ sample)
0 50 100 150
acolj1j2 (˚)
e)      (no-id sample)
0 50 100 150
αlν (˚)
f)       (no-id sample)
data SM expectation signal (mb’=100 GeV/c
Figure 8: Variables used in the discriminant analysis (cc̄qq̄l+ν final state). The data
events and background expectation for centre-of-mass energies above 200 GeV are shown
for (a) the h1 + h3 Fox-Wolfram moments sum (e sample), (b) the invariant mass of
the two jets with the events clustered into two jets (e sample), (c) − log10(y4→3) (µ
sample), (d)
|~pi|/
s, where ~pi are the momenta of the charged particles (excluding
the lepton) in the same hemisphere as the lepton (µ sample), (e) the acollinearity between
the two most energetic jets (no-id sample) and (f) the angle between the lepton and the
missing momentum (no-id sample). The signal distributions for mb′ = 100 GeV/c
2 and√
s = 205 GeV are also shown with arbitrary normalisation.
DELPHI
-10 0 10
ln(LS/LB)
-10 -5 0 5
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
-10 0 10
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
SM expectation
Signal (mb’=100 GeV/c
Figure 9: Discriminant variables ln(LS/LB) for data and SM simulation (centre-of–
mass energies above 200 GeV). FCNC b′ decay mode: (a) bb̄qq̄νν̄ and (b) bb̄qq̄qq̄.
CC b′ decay mode: (c) cc̄qq̄l+ν (e sample), (d) cc̄qq̄l+ν (µ sample), (e) cc̄qq̄l+ν (no-id
sample) (f) cc̄qq̄l+ν (no lepton sample) and (g) cc̄qq̄qq̄. The signal distributions for
mb′ = 100 GeV/c
2 and
s = 205 GeV are also shown with arbitrary normalisation.
DELPHI
96 97 98 99 100 101 102 103
mb’ (GeV/c
a) b’→ bZ decay
observed limit
expected limit
expected ± 1σ
expected ± 2σ
96 97 98 99 100 101 102 103
96 97 98 99 100 101 102 103
mb’ (GeV/c
96 97 98 99 100 101 102 103
b) b’→ cW decay
observed limit
expected limit
expected ± 1σ
expected ± 2σ
Figure 10: The observed and expected upper limits at 95% CL on (a) BR(b′ → bZ) and
(b) BR(b′ → cW) are shown. The 1σ and 2σ bands around the expected limit are also
presented. Systematic errors were taken into account in the limit evaluation.
DELPHI
Figure 11: The excluded region in the plane (RCKM , mb′) with mt′ −mb′ = 1 GeV/c2,
obtained from the 95% CL upper limits on BR(b′ → bZ) (bottom) and BR(b′ → cW)
(top) is shown. The light and dark shadings correspond to the observed and expected
limits, respectively. The expected limits on BR(b′ → bZ) did not allow exclusions to be
set for low values of RCKM .
DELPHI
Figure 12: The excluded region in the plane (RCKM , mb′) with mt′ −mb′ = 50 GeV/c2,
obtained from the 95% CL upper limits on BR(b′ → bZ) (bottom) and BR(b′ → cW)
(top) is shown. The light and dark shadings correspond to the observed and expected
limits, respectively.

  A search for the pair production of fourth generation b'-quarks was performed
using data taken by the DELPHI detector at LEP-II. The analysed data were
collected at centre-of-mass energies ranging from 196 to 209 GeV, corresponding
to an integrated luminosity of 420 pb^{-1}. No evidence for a signal was found.
Upper limits on BR(b' -> bZ) and BR(b' -> cW) were obtained for b' masses
ranging from 96 to 103 GeV/c^2. These limits, together with the theoretical
branching ratios predicted by a sequential four generations model, were used to
constrain the value of R_{CKM}=|V_{cb'}/V_{tb'}V_{tb}|, where V_{cb'}, V_{tb'}
and V_{tb} are elements of the extended CKM matrix.

Introduction
The Standard Model (SM), although in agreement with the available experimental
data [1], leaves several open questions. In particular, the number of fermion generations
and their mass spectrum are not predicted. The measurement of the Z decay widths [1]
established that the number of light neutrino species (m < mZ/2, where mZ is the Z boson
mass) is equal to three. However, if a heavy neutrino or a neutrinoless extra generation
exists, this bound does not exclude the possibility of extra generations of heavy quarks.
Moreover the fit to the electroweak data [2] does not deteriorate with the inclusion of one
extra heavy generation, if the new up and down-type quarks mass difference is not too
large. It should be noticed however that in this fit no mixing of the extra families with
the SM ones is assumed.
The subject of this paper is the search for the pair production of a fourth generation
b′-quark at LEP-II: b′ production and decay are discussed in section 2; in section 3, the
data sets and the Monte Carlo (MC) simulation are described; the analysis is discussed
in section 4; the results and their interpretation within a sequential model are presented
in sections 5 and 6, respectively.
2 b′-quark production and decay
Extra generations of fermions are predicted in several SM extensions [3,4]. In sequen-
tial models [5–7], a fourth generation of fermions carrying the same quantum numbers as
the SM families is considered. In the quark sector, an up-type quark, t′, and a down-type
quark, b′, are included. The corresponding 4× 4 extended Cabibbo-Kobayashi-Maskawa
(CKM) matrix is unitary, approximately symmetric and almost diagonal. As CP-violation
is not considered in the model, all the CKM elements are assumed to be real.
The b′-quark may decay via charged currents (CC) to UW, with U = t′, t, c, u, or via
flavour-changing neutral currents (FCNC) to DX , where D = b, s, d and X = Z,H, γ, g
(Fig. 1). As in the SM, FCNC are absent at tree level, but can appear at one-loop level,
due to CKM mixing. If the b′ is lighter than t′ and t, the decays b′ → t′W and b′ → tW
are kinematically forbidden and the one-loop FCNC decays can be as important as the
CC decays [6].
The analysis of the electroweak data [1] shows that the mass difference |mt′ −mb′ | <
60 GeV/c2 is consistent with the measurement of the ρ parameter [3,5]. In particular,
when mZ + mb < mb′ < mH + mb, either b
′ → cW or b′ → bZ decay tend to be domi-
nant [5–7]. In this case, the partial widths of the CC and FCNC b′ decays depend mainly
on mt′ , mb′ and RCKM = | Vcb′V
tb′Vtb
|, where Vcb′ , Vtb′ and Vtb are elements of the extended
4 × 4 CKM matrix [7].
Limits on the mass of the b′-quark have been set previously at various accelerators.
At LEP-I, all the experiments searched for b′ pair production (e+e− → b′b̄′), yielding a
lower limit on the b′ mass of about mZ/2 [8]. At the Tevatron, both the D0 [9] and
CDF [10] experiments reported limits on σ(pp̄ → b′b̄′) × BR(b′ → bX)2, where BR is
the branching ratio corresponding to the considered FCNC b′ decay mode and X = γ,Z.
Assuming BR(b′ → bZ) = 1, CDF excluded the region 100 < mb′ < 199 GeV/c2.
Although no dedicated analysis was performed for the b′ → cW decay, the D0 limits on
σ(pp̄ → tt̄) × BR(t → cW)2 from Fig. 44 and Table XXXI of reference [11] can give a
hint on the possible values for BR(b′ → cW) [12].
In the present analysis the on-shell FCNC (b′ → bZ) and CC (b′ → cW) decay modes
were studied and consequently the mass range 96 GeV/c2 < mb′ < 103 GeV/c
2 was
considered. This mass range is complementary to the one covered by CDF [10]. The
mass range mW + mc < mb′ < mZ + mb was not considered because in this region
the evaluation of the branching ratios for the different b′ decays is particularly difficult
from the theoretical point of view [7]. In the present analysis no assumptions on the
BR(b′ → bZ) and BR(b′ → cW) in order to derive mass limits were made. Different
final states, corresponding to the different b′ decay modes and subsequent decays of the
Z and W bosons, were analysed.
3 Data samples and Monte Carlo simulation
The analysed data were collected with the DELPHI detector [13] during the years
1999 and 2000 in LEP-II runs at
s = 196 − 209 GeV and correspond to an integrated
luminosity of about 420 pb−1. The luminosity collected at each centre-of-mass energy is
shown in Table 1. During the year 2000, an unrecoverable failure affected one sector of
the central tracking detector (TPC), corresponding to 1/12 of its acceptance. The data
collected during the year 2000 with the TPC fully operational were split into two energy
bins, below and above
s = 206 GeV, with 〈
s〉 = 204.8 GeV and 〈
s〉 = 206.6 GeV,
respectively. The data collected with one sector of the TPC turned off were analysed
separately and have 〈
s〉 = 206.3 GeV.
s (GeV) 196 200 202 205 207 206∗
luminosity (pb−1) 76.0 82.7 40.2 80.0 81.9 59.2
Table 1: The luminosity collected with the DELPHI detector at each centre-of-mass
energy is shown. The energy bin labelled 206∗ corresponds to the data collected with one
sector of the TPC turned off.
Signal samples were generated using a modified version of PYTHIA 6.200 [14]. Al-
though PYTHIA does not provide FCNC decay channels for quarks, it was possible to
activate them by modifying the decay products of an available channel. The angular
distributions assumed for b′ pair production and decay were those predicted by the SM
for any heavy down-type quark. Different samples, corresponding to b′ masses in the
range between 96 and 103 GeV/c2 and with a spacing of 1 GeV/c2 were generated at
each centre-of-mass energy. Specific Monte Carlo simulations (for both SM and signal
processes) were produced for the period when one sector of the TPC was turned off.
The most relevant background processes for the present analyses are those leading
to WW or ZZ bosons in the final state, i.e. four-fermion backgrounds. Radiation in
these events can mimic the six-fermion final states for the signal. Additionally qq̄(γ) and
Bhabha events can not be neglected since for signal final states with missing energy these
backgrounds can become important. SM background processes were simulated at each
centre-of-mass energy using several Monte Carlo generators. All the four-fermion final
states (both neutral and charged currents) were generated with WPHACT [15], while
the particular phase space regions of e+e− → e+e−f f̄ referred to as γγ interactions were
generated using PYTHIA [14]. The qq(γ) final state was generated with KK2F [16].
Bhabha events were generated with BHWIDE [17].
The generated signal and background events were passed through the detailed simu-
lation of the DELPHI detector [13] and then processed with the same reconstruction and
analysis programs as the data.
4 Description of the analyses
Pair production of b′-quarks was searched for in both the FCNC (b′ → bZ) and CC
(b′ → cW) decay modes. The b′ decay modes and the subsequent decays of the gauge
bosons (Z or W) lead to several different final states (Fig. 2). The final states considered
and their branching ratios are shown in Table 2. The choice of the considered final
states was done taking into account their signatures and BR. About 81% and 90% of the
branching ratio to the FCNC and CC channels were covered, respectively. All final states
include two jets originating from the low energy b (c) quarks present in the FCNC (CC)
b′ decay modes. A common preselection was adopted, followed by a specific analysis for
each of the final states (Table 2).
b′ decay boson decays BR (%) final states
b′ → bZ (FCNC) ZZ → l+l−νν̄ 4.0 bb̄l+l−νν̄
ZZ → qq̄νν̄ 28.0 bb̄qq̄νν̄
ZZ → qq̄qq̄ 48.6 bb̄qq̄qq̄
b′ → cW (CC) WW → qq̄l+ν 43.7 cc̄qq̄l+ν
WW → qq̄qq̄ 45.8 cc̄qq̄qq̄
Table 2: The final states considered in this analysis are shown. About 81% and 90% of
the branching ratio to the FCNC and CC channels were covered, respectively.
Events were preselected by requiring at least eight good charged-particle tracks and
the visible energy measured at polar angles1 above 20◦, to be greater than 0.2
s. Good
charged-particle tracks were defined as those with a momentum above 0.2 GeV/c and
impact parameters in the transverse plane and along the beam direction below 4 cm and
below 4 cm/ sin θ, respectively.
The identification of muons relied on the association of charged particles to signals
in the muon chambers and in the hadronic calorimeters and was provided by standard
DELPHI algorithms [13]. The identification of electrons and photons was performed
by combining information from the electromagnetic calorimeters and the tracking sys-
tem. Radiation and interaction effects were taken into account by an angular clustering
procedure around the main shower [18].
The search for isolated particles (charged leptons and photons) was done by construct-
ing double cones oriented in the direction of charged-particle tracks or neutral energy
deposits. The latter ones were defined as calorimetric energy deposits above 0.5 GeV,
not matched to charged-particle tracks and identified as photon candidates by the stan-
dard DELPHI algorithms [13,18]. For charged leptons (photons), the energy in the region
between the two cones, which had half-opening angles of 5◦ and 25◦ (5◦ and 15◦), was
required to be below 3 GeV (1 GeV), to ensure isolation. All the charged-particle tracks
1In the standard DELPHI coordinate system, the positive z axis is along the electron beam direction. The polar angle
(θ) is defined with respect to the z axis. In this paper, polar angle ranges are always assumed to be symmetric with respect
to the θ = 90◦ plane.
final state assignment criteria
bb̄l+l−νν̄ at least 1 isolated lepton
bb̄qq̄νν̄ no isolated leptons
Emissing > 50 GeV
bb̄qq̄qq̄ no isolated leptons
Emissing < 50 GeV
cc̄qq̄l+ν only 1 isolated lepton
cc̄qq̄qq̄ no isolated leptons
Emissing < 50 GeV
Table 3: Summary of the final state assignment criteria.
and neutral energy deposits inside the inner cone were associated to the isolated particle.
Its energy was then re-evaluated as the sum of the energies inside the inner cone and
was required to be above 5 GeV. For well identified leptons or photons [13,18] the above
requirements were weakened. In this case only the external cone was used (to ensure
isolation) and its angle α was varied according to the energy of the lepton (photon) can-
didate, down to 2◦ for Pℓ ≥ 70 GeV/c (3◦ for Pγ ≥ 90 GeV/c), with the allowed energy
inside the cone reduced by sinα/ sin 25◦ (sinα/ sin 15◦). Isolated leptons were required
to have a momentum greater than 10 GeV/c and a polar angle above 25◦. Events with
isolated photons were rejected.
All the events were clustered into two, four or six jets using the Durham jet algo-
rithm [19], according to the number of jets expected in the signal in each of the final
states, unless explicitly stated otherwise. Although two b jets are always present in the
FCNC final states, they have a relatively low energy and b-tagging techniques [20] were
not used.
Events were assigned to the different final states according to the number of isolated
leptons and to the missing energy in the event, as detailed in Table 3. Within the same
b′ decay channel, the different selections were designed to be mutually exclusive. For the
final states involving charged leptons (bb̄l+l−νν̄ and cc̄qq̄l+ν), events were divided into
different samples according to the lepton flavour identification: e sample (well identified
electrons), µ sample (well identified muons) and no-id sample (leptons with unidentified
flavour or two leptons identified with different flavours).
Specific analyses were then performed for each of the final states. The selection criteria
for the bb̄qq̄qq̄ and cc̄qq̄qq̄ final states were the same. The bb̄l+l−νν̄ final state has a very
clean signature (two leptons with ml+l− ∼ mZ, two low energy jets and missing mass close
to mZ) and consequently a sequential cut analysis was adopted. For all the other final
states, a sequential selection step was followed by a discriminant analysis. In this case,
a signal likelihood (LS) and a background likelihood (LB) were assigned to each event,
based on Probability Density Functions (PDF), built from the distributions of relevant
physical variables. The discriminant variable was defined as ln(LS/LB).
4.1 The bb̄l+l−νν̄ final state
The FCNC bb̄l+l−νν̄ final state events were preselected as described above, by re-
quiring at least eight good charged-particle tracks, the visible energy measured at polar
angles above 20◦, to be greater than 0.2
s and at least one isolated lepton. Distribu-
tions of the relevant variables are shown in Fig. 3 for all the events assigned to this final
state after the preselection. The event selection was performed in two levels. In the first
one, events were required to have at least two leptons and an effective centre-of-mass
energy [21],
s′, below 0.95
s. The particles other than the two leptons in the events
were clustered into two jets and the Durham resolution variable in the transition from
two jets to one jet2 was required to be greater than 0.002. The number of data events and
the SM expectation after the first selection level is shown in Table 4. The background
composition and the signal efficiencies at this level of selection for mb′ = 100 GeV/c
2 and√
s = 205 GeV are given in Table 8. The efficiencies for the other relevant b′ masses and√
s values were found to be the same within errors. Data, SM expectation and signal
distributions at this selection level are shown in Fig. 4.
s (GeV) data (SM expectation ± statistical error)
e sample µ sample no-id sample
196 2 (2.6±0.3) 1 (2.9±0.3) 47 (35.9±1.4)
200 3 (2.5±0.4) 4 (3.4±0.4) 30 (37.4±1.4)
202 2 (1.3±0.2) 1 (1.7±0.2) 20 (18.7±0.7)
205 5 (2.5±0.4) 3 (3.0±0.4) 35 (36.2±1.4)
207 3 (2.3±0.4) 3 (3.1±0.4) 45 (35.1±1.3)
206∗ 1 (1.9±0.3) 2 (2.6±0.2) 31 (27.6±1.0)
total 16 (13.2±0.8) 14 (16.7±0.8) 208 (191.0±3.0)
Table 4: First selection level of the bb̄l+l−νν̄ final state: the number of events selected
in data and the SM expectations after the first selection level for each sample and cen-
tre-of-mass energy are shown.
In the final selection level the momentum of the more energetic (less energetic) jet
was required to be below 30 GeV/c (12.5 GeV/c). Events in the e and no-id samples
had to have a missing energy greater than 0.4
s. In the µ sample events were required
to have an angle between the two muons greater than 125◦. In the no-id sample, the
angle between the two charged leptons had to be greater than 140◦ and pmis/Emis < 0.4,
where pmis and Emis are the missing momentum and energy, respectively. After the final
selection, one data event was selected for an expected background of 1.5±0.7. This event
belonged to the no-id sample and was collected at
s = 200 GeV. The signal efficiencies
for mb′ = 100 GeV/c
2 and
s = 205 GeV are 30.6 ± 2.5% (e sample), 48.6 ± 2.7% (µ
sample) and 7.2 ± 0.8% (no-id sample) and their variation with mb′ and
s was found
to be negligible in the relevant range.
4.2 The bb̄qq̄νν̄ final state
The FCNC bb̄qq̄νν̄ final state is characterised by the presence of four jets and a
missing mass close to mZ. At least 20 good charged-particle tracks and
s′ > 0.5
were required. Events were clustered into four jets. Monojet-like events were rejected by
requiring − log10(y2→1) < 0.7 (y2→1 is the Durham resolution variable in the two to one
jet transition). Furthermore, − log10(y4→3) was required to be below 2.8 and the energy
of the leading charged particle of the most energetic jet was required to be below 0.1
2The Durham resolution variable is the minimum value of the scaled transverse momentum obtained in the transition
from n to n− 1 jets [19] and will be represented by yn→n−1.
A kinematic fit imposing energy-momentum conservation and no missing energy was
applied and the background-like events with χ2/n.d.f. < 6 were rejected. The data,
SM expectation and signal distributions of this variable are shown in Fig. 5. Table 5
summarizes the number of selected data events and the SM expectation. The background
composition and the signal efficiency at this level of selection for mb′ = 100 GeV/c
2 and√
s = 205 GeV are given in Table 8. The efficiencies for the other relevant b′ masses and√
s values were found to be the same within errors.
s (GeV) data (SM expectation ± statistical error)
196 123 (106.3±4.0)
200 111 (104.8±4.0)
202 50 (49.8±1.9)
205 88 (94.2±3.7)
207 99 (91.2±3.6)
206∗ 62 (65.7±2.6)
total 533 (511.7±8.3)
Table 5: First selection level of the bb̄qq̄νν̄ final state: the number of events selected in
data and the SM expectation for each centre-of-mass energy are shown.
A discriminant selection was then performed using the following variables to build the
PDFs:
• the missing mass;
• Aj1j2cop × min(sin θj1 , sin θj2), where Aj1j2cop is the acoplanarity3 and θj1,j2 are the polar
angles of the jets when forcing the events into two jets4;
• the acollinearity between the two most energetic jets5 with the event particles clus-
tered into four jets;
• the sum of the first and third Fox-Wolfram moments (h1 + h3) [22];
• the polar angle of the missing momentum.
The data, SM expectation and signal distributions of these variables are shown in Fig. 6.
4.3 The bb̄qq̄qq̄ final state
The FCNC bb̄qq̄qq̄ final state is characterised by the presence of six jets and a small
missing energy. All the events were clustered into six jets and only those with at least
30 good charged-particle tracks were accepted. Moreover, events were required to have√
s′ > 0.6
s, − log10(y2→1) < 0.7 and − log10(y6→5) < 3.6. The number of selected data
events and the expected background at this level are shown in Table 6. The background
composition and the signal efficiency at this level of selection for mb′ = 100 GeV/c
2 and√
s = 205 GeV are given in Table 8. The efficiencies for the other relevant b′ masses and√
s values were found to be the same within errors.
A discriminant selection was performed using the following variables to build the PDFs:
3The acoplanarity between two particles is defined as |180◦ − |φ1 −φ2||, where φ1,2 are the azimuthal angles of the two
particles (in degrees).
4While the signal is characterised by the presence of four jets in the final state, the two jets configuration is used mainly
for background rejection.
5The acollinearity between two particles is defined as 180◦ − α1,2, where α1,2 is the angle (in degrees) between those
two particles.
s (GeV) data (SM expectation ± statistical error)
196 349 (326.7±5.3)
200 347 (342.1±5.5)
202 165 (162.1±2.6)
205 322 (319.0±5.2)
207 287 (307.6±5.0)
206∗ 192 (215.8±3.6)
total 1662 (1673.9±11.4)
Table 6: First selection level of the bb̄qq̄qq̄ and cc̄qq̄qq̄ final states: the number of events
selected in data and the SM expectations for each centre-of-mass energy are shown.
• the Durham resolution variable, − log10(y4→3);
• the Durham resolution variable, − log10(y5→4);
• the acollinearity between the two most energetic jets, with the event forced into four
jets;
• the sum of the first and third Fox-Wolfram moments;
• the momentum of the most energetic jet;
• the angle between the two most energetic jets (with the events clustered into six
jets).
The distributions of these variables are shown in Fig. 7 for data, SM expectation and
signal.
4.4 The cc̄qq̄l+ν final state
The signature of this CC final state is the presence of four jets (two of them having
low energy), one isolated lepton and missing energy (originating from the W → lν̄ decay).
The events were accepted if they had at least 15 good charged-particle tracks. The event
particles other than the identified lepton were clustered into four jets. Part of the qq̄
and γγ background was rejected by requiring − log10(y2→1) < 0.7. Furthermore, there
should be only one charged-particle track associated to the isolated lepton, and the leading
charged particle of the most energetic jet was required to have a momentum below 0.1
The number of selected data events and SM expectations at this level are summarized in
Table 7. The background composition and the signal efficiencies at this level of selection
for mb′ = 100 GeV/c
2 and
s = 205 GeV are given in Table 8. The efficiencies for the
other relevant b′ masses and
s values were found to be the same within errors.
The PDFs used to calculate the background and signal likelihoods were based on the
following variables:
• the sum of the first and third Fox-Wolfram moments;
• the invariant mass of the two jets, with the event particles other than the identified
lepton clustered into two jets;
• the Durham resolution variable, − log10(y4→3);
|~pi|/
s, where ~pi are the momenta of the charged particles (excluding the lepton)
in the same hemisphere as the lepton (the hemisphere is defined with respect to the
lepton);
• the acollinearity between the two most energetic jets;
s (GeV) data (SM expectation ± statistical error)
e µ no-id
196 65 (51.1±1.4) 53 (56.1±1.5) 38 (34.4±1.4)
200 54 (58.1±1.7) 63 (59.9±1.6) 40 (35.0±1.4)
202 30 (27.8±0.8) 21 (28.4±0.8) 13 (16.9±0.7)
205 56 (50.8±1.5) 66 (53.6±1.5) 32 (33.3±1.4)
207 53 (53.8±1.6) 48 (57.2±1.6) 35 (33.8±1.4)
206∗ 31 (37.2±1.4) 42 (39.3±1.1) 21 (23.4±1.0)
total 289 (278.8±3.5) 293 (294.5±3.4) 179 (176.8 ± 2.8)
Table 7: First selection level of the cc̄qq̄l+ν final state: the number of events selected in
data and the SM expectations for each sample and centre-of-mass energy are shown.
• the angle between the lepton and the missing momentum.
The data, SM expectation and signal distributions of these variables are shown in Fig. 8.
In order to improve the efficiency, events with no leptons seen in the detector were
kept in a fourth sample. For this sample, the selection criteria of the bb̄qq̄νν̄ final state
were applied and the same variables as in section 4.2 were used to build the PDFs. The
signal efficiency after the first selection level for mb′ = 100 GeV/c
2 and
s = 205 GeV
was 8.9±0.9%. The efficiencies for the other relevant b′ masses and
s values were found
to be the same within errors.
4.5 The cc̄qq̄qq̄ final state
This final state is very similar to bb̄qq̄qq̄ (with slightly different kinematics due to the
mass difference between the Z and the W). The analysis described in section 4.3 was
thus adopted. The number of selected events and the SM expectations can be found in
Table 6. At this level, the signal efficiency for mb′ = 100 GeV/c
2 and
s = 205 GeV was
67.3±1.5%. The efficiencies for the other b′ masses and centre-of-mass energies were the
same within errors. The PDFs were built using the same set of variables as in section 4.3.
5 Results
For all final states, a good agreement between data and SM expectation was found. The
summary of the total number of selected data events, SM expectations, the corresponding
background composition and the signal efficiencies for the studied final states are shown
in Table 8. In the bb̄l+l−νν̄ final state, one data event was retained after the final
selection level, for a SM expectation of 1.5 ± 0.7 events. This event belonged to the no-id
sample and was collected at
s = 200 GeV. For all the other final states, discriminant
analyses were used. In these cases, a discriminant variable, ln(LS/LB), was defined. The
distributions of ln(LS/LB), for the different analysis channels are shown in Fig. 9. No
evidence for a signal was found in any of the channels and the full information, i.e. event
numbers and the shapes of the distributions of the discriminant variables were used to
derive limits on BR(b′ → bZ) and BR(b′ → cW).
data background signal
final state (SM ± stat. error) composition (%) efficiency (%)
qq̄ WW ZZ γγ
bb̄l+l−νν̄ e sample 16 (13.2±0.8) 16 16 68 0 35.1±2.6
(first selection µ sample 14 (16.7±0.8) 0 10 90 0 53.4±2.7
level) no-id sample 208 (191.0±3.0) 8 80 12 0 12.3±1.0
bb̄qq̄νν̄ 533 (511.7±8.3) 76 17 2 5 57.6±1.7
bb̄qq̄qq̄ 1662 (1673.9±11.4) 35 65 0 0 66.0±1.5
e sample 289 (278.8±3.5) 7 82 11 0 45.3±2.7
cc̄qq̄l+ν µ sample 293 (294.5±3.4) 2 97 1 0 56.4±2.7
no-id sample 179 (176.8±2.8) 9 84 7 0 5.3±0.7
no lepton sample 533 (511.7±8.3) 76 17 2 5 8.9±0.9
cc̄qq̄qq̄ 1662 (1673.9±11.4) 35 65 0 0 67.3±1.5
Table 8: Summary of the total number of selected data events and SM expectations for
the studied final states after the final selection (first selection level for bb̄l+l−νν̄). The
corresponding background composition and signal efficiencies for mb′ = 100 GeV/c
2 and√
s = 205 GeV are also shown.
5.1 Limits on BR(b′ → bZ) and BR(b′ → cW)
Upper limits on the product of the e+e− → b′b̄′ cross-section and the branching ratio
as a function of the b′ mass were derived at 95% confidence level (CL) in each of the
considered b′ decay modes (FCNC and CC), taking into account the values of the dis-
criminant variables and their expected distributions for signal and background, the signal
efficiencies and the data luminosities at the various centre-of-mass energies.
Assuming the SM cross-section for the pair production of heavy quarks at LEP [7,14],
these limits were converted into limits on the branching ratios corresponding to the
b′ → bZ and b′ → cW decay modes. The modified frequentist likelihood ratio method [23]
was used. The different final states and centre-of-mass energy bins were treated as inde-
pendent channels. For each b′ mass only the channels with
s > 2mb′ were considered.
In order to avoid some non-physical fluctuations of the distributions of the discriminant
variables due to the limited statistics of the generated events, a smoothing algorithm was
used. The median expected limit, i.e. the limit obtained if the SM background was the
only contribution in data, was also computed. In Fig. 10 the observed and expected limits
on BR(b′ → bZ) and BR(b′ → cW) are shown as a function of the b′ mass. The 1σ and
2σ bands around the expected limit are also shown. The observed and expected limits
are statistically compatible. At 95% CL and for mb′ = 96 GeV/c
2, the BR(b′ → bZ) and
BR(b′ → cW) have to be below 51% and 43%, respectively. These limits were evaluated
taking into account the systematic uncertainties, as explained in the next subsection.
The limits obtained for BR(b′ → bZ) are compatible with those presented by CDF [10]
for a b′ mass of 100 GeV/c2. Below this mass, the DELPHI result is more sensitive and
the CDF limit degrades rapidly. For higher b′ masses, the LEP-II kinematical limit is
reached and the present analysis looses sensitivity.
5.2 Systematic uncertainties
The evaluation of the limits was performed taking into account systematic uncertain-
ties, which affect the background estimation, the signal efficiency and the shape of the
distributions used. The following systematic uncertainties were considered:
• SM cross-sections: uncertainties on the SM cross-sections translate into uncertainties
on the expected number of background events. The overall uncertainty on the most
relevant SM background processes for the present analyses is typically less than
2% [24], which leads to relative changes on the branching ratio limits below 6%;
• Signal generation: uncertainties on the final state quark hadronisation and fragmen-
tation modelling were studied. The Lund symmetric fragmentation function was
tested and compared with schemes where the b and c quark masses are taken into
account [14]. This systematic error source was estimated to be of the order of 20%
in the signal efficiency, by conservatively taking the maximum observed variation.
The relative effect on the branching ratio limits is below 16%;
• Smoothing: the uncertainty associated to the discriminant variables smoothing was
estimated by applying different smoothing algorithms. The smoothing procedure
does not change the number of SM expected events or the signal efficiency, but may
lead to differences in the shape of the discriminant variables. The relative effect of
this uncertainty on the limits evaluation was found to be below 9%.
Further details on the evaluation of the systematic errors and the derivation of limits can
be found in [25].
6 Constraints on RCKM
The branching ratios for the b′ decays can be computed within a four generations
sequential model [5–7]. As discussed before, if the b′ is lighter than both the t and the t′
quarks and mZ < mb′ < mH, the main contributions to the b
′ width are BR(b′ → bZ) and
BR(b′ → cW) [7]. Using the unitarity of the CKM matrix, its approximate diagonality
(Vub′ Vub ≈ 0) and taking Vcb ≈ 10−2 [12], the branching fractions can be written as a
function of three variables: RCKM = | Vcb′V
tb′ Vtb
|, mt′ and mb′ [5–7].
Fixing mt′ − mb′ , the limits on BR(b′ → bZ) and BR(b′ → cW) (Fig. 10) can be
translated into 95% CL bounds on RCKM as a function of mb′ . Two extreme cases were
considered: the almost degenerate case, with mt′−mb′ = 1 GeV/c2, and the case in which
the mass difference is close to the largest possible value, mt′ − mb′ = 50 GeV/c2 [3,5].
The results are shown in Fig. 11 and Fig. 12. In the figures, the upper curve was obtained
from the limit on BR(b′ → cW), while the lower curve was obtained from the limit on
BR(b′ → bZ), which decreases with growing mt′ . This suppression is due to the GIM
mechanism [26] as mt′ approaches mt. On the other hand, as the b
′ mass approaches
the bZ threshold, the b′ → bg decay dominates over b′ → bZ [7] and the lower limit on
RCKM becomes less stringent. The expected limits on BR(b
′ → bZ) did not allow to set
exclusions for low values of RCKM and mt′ −mb′ = 1 GeV/c2 (see Fig. 11).
7 Conclusions
The data collected with the DELPHI detector at
s = 196−209 GeV show no evidence
for the pair production of b′-quarks with masses ranging from 96 to 103 GeV/c2.
Assuming the SM cross-section for the pair production of heavy quarks at LEP, 95%
CL upper limits on BR(b′ → bZ) and BR(b′ → cW) were obtained. It was shown that, at
95% CL and for mb′ = 96 GeV/c
2, the BR(b′ → bZ) and BR(b′ → cW) have to be below
51% and 43%, respectively. The 95% CL upper limits on the branching ratios, combined
with the predictions of the sequential fourth generation model, were used to exclude
regions of the (RCKM , mb′) plane for two hypotheses of the mt′ − mb′ mass difference.
It was shown that, for mt′ −mb′ = 1 (50) GeV/c2 and 96 GeV/c2 < mb′ < 102 GeV/c2,
RCKM is bounded by an upper limit of 3.8×10−3 (1.2×10−3). For mb′ = 100 GeV/c2 and
mt′ −mb′ = 50 GeV/c2, the CKM ratio was constrained to be in the range 4.6 × 10−4 <
RCKM < 7.8 × 10−4.
Acknowledgements
We are greatly indebted to our technical collaborators, to the members of the CERN-
SL Division for the excellent performance of the LEP collider, and to the funding agencies
for their support in building and operating the DELPHI detector.
We acknowledge in particular the support of
Austrian Federal Ministry of Education, Science and Culture, GZ 616.364/2-III/2a/98,
FNRS–FWO, Flanders Institute to encourage scientific and technological research in the
industry (IWT) and Belgian Federal Office for Scientific, Technical and Cultural affairs
(OSTC), Belgium,
FINEP, CNPq, CAPES, FUJB and FAPERJ, Brazil,
Czech Ministry of Industry and Trade, GA CR 202/99/1362,
Commission of the European Communities (DG XII),
Direction des Sciences de la Matière, CEA, France,
Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, Germany,
General Secretariat for Research and Technology, Greece,
National Science Foundation (NWO) and Foundation for Research on Matter (FOM),
The Netherlands,
Norwegian Research Council,
State Committee for Scientific Research, Poland, SPUB-M/CERN/PO3/DZ296/2000,
SPUB-M/CERN/PO3/DZ297/2000, 2P03B 104 19 and 2P03B 69 23(2002-2004)
FCT - Fundação para a Ciência e Tecnologia, Portugal,
Vedecka grantova agentura MS SR, Slovakia, Nr. 95/5195/134,
Ministry of Science and Technology of the Republic of Slovenia,
CICYT, Spain, AEN99-0950 and AEN99-0761,
The Swedish Research Council,
Particle Physics and Astronomy Research Council, UK,
Department of Energy, USA, DE-FG02-01ER41155,
EEC RTN contract HPRN-CT-00292-2002.
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Z / H / g / γ
b / s / d
t′ / t / c / u
a) b)
Figure 1: The Feynman diagrams corresponding to the b′ (a) FCNC and (b) CC decay
modes are shown.
Z/γ Z
l−/ q̄ / q̄
l+/ q / q
ν̄ / ν̄ / q̄
ν / ν / q
Z/γ W
q̄ / q̄
q / q
ν / q̄
l+/ q
a) b)
Figure 2: The final states associated to the b′ (a) FCNC and (b) CC decay modes are
shown. Only those states analysed here are indicated.
DELPHI
0 50 100 150
αl1,tr (˚)
a)       (e sample)
0 20 40 60 80 100
pmis (GeV/c)
b)      (µ sample)
0 20 40 60 80
pjet 1 (GeV/c)
c)      (no-id sample)
SM expectation
signal (mb’=100 GeV/c
Figure 3: Data and SM expectation after the preselection level for the bb̄l+l−νν̄ final state
and centre-of-mass energies above 200 GeV. (a) The angle between the most energetic
lepton and the closest charged-particle track (e sample), (b) the missing momentum (µ
sample) and (c) the momentum of the most energetic jet (no-id sample) are shown. The
signal distributions for mb′ = 100 GeV/c
2 and
s = 205 GeV are also shown with
arbitrary normalisation. The background composition is 11% of qq̄, 69% of WW, 15% of
ZZ and 5% of γγ for the e sample, 6% of qq̄, 90% of WW and 4% of ZZ for the µ sample
and 45% of qq̄, 48% of WW, 5% of ZZ and 2% of γγ for the no-id sample.
DELPHI
0 20 40 60 80
pjet 1 (GeV/c)
a)       (e sample)
0 50 100 150
αll (˚)
b)      (µ sample)
0 0.25 0.5 0.75 1
pmis / Emis
c)      (no-id sample)
SM expectation
signal (mb’=100 GeV/c
Figure 4: Data and SM expectation after the first selection level for the bb̄l+l−νν̄ final
state and for centre-of-mass energies above 200 GeV. (a) The momentum of the most
energetic jet (e sample), (b) the angle between the two leptons (µ sample) and (c) the
ratio between the missing momentum and missing energy (no-id sample) are shown. The
signal distributions for mb′ = 100 GeV/c
2 and
s = 205 GeV are also shown with
arbitrary normalisation. The arrows represent the cuts applied in the second selection
level.
DELPHI
0 5 10 15 20 25 30 35 40
0 5 10 15 20 25 30 35 40
0 5 10 15 20 25 30 35 40
χ2/n.d.f.
SM expectation
signal (mb’=100 GeV/c
Figure 5: Comparison of data and SM expectation distributions of the χ2/n.d.f. of the fit
imposing energy-momentum conservation and no missing energy for the bb̄qq̄νν̄ final state
at centre-of-mass energies above 200 GeV. The arrow shows the applied cut. The signal
for mb′ = 100 GeV/c
2 and
s = 205 GeV is also shown with arbitrary normalisation.
DELPHI
0 50 100 150 200
missing mass (GeV/c
0 10 20 30 40
scaled acoplanarity (˚)
0 50 100 150
acolj1j2 (˚)
0 0.5 1 1.5
h1+h3
0 50 100 150
θmis (˚)
SM expectation
signal (mb’=100 GeV/c
Figure 6: Variables used in the discriminant analysis (bb̄qq̄νν̄ final state). The data and
SM expectation distributions for centre-of-mass energies above 200 GeV are shown for (a)
the missing mass, (b) Aj1j2cop ×min(sin θj1 , sin θj2), where Aj1j2cop is the acoplanarity and θj1,j2
are the polar angles of the jets when forcing the events into two jets, (c) the acollinearity
between the two most energetic jets (with the event particles clustered into four jets),
(d) the sum of the first and third Fox-Wolfram moments and (e) the polar angle of the
missing momentum. The signal distributions for mb′ = 100 GeV/c
2 and
s = 205 GeV
are also shown with arbitrary normalisation.
DELPHI
1 1.5 2 2.5 3
-log10(y4→3)
1 2 3 4
-log10(y5→4)
0 50 100 150
acolj1j2 (4 jets) (˚)
0 0.2 0.4 0.6 0.8 1
h1+h3
0 20 40 60 80 100
pj1 (GeV/c)
/c e)
0 50 100 150
αj1j2 (˚)
data SM expectation signal (mb’=100 GeV/c
Figure 7: Variables used in the discriminant analysis (bb̄qq̄qq̄ final state). The data
and SM expectation for centre-of-mass energies above 200 GeV are shown for (a)
− log10(y4→3), (b) − log10(y5→4), (c) the acollinearity between the two most energetic
jets, with the events clustered into four jets (see text for explanation), (d) the h1 + h3
Fox-Wolfram moments sum, (e) the momentum of the most energetic jet and (f) the angle
between the two most energetic jets. The signal distributions for mb′ = 100 GeV/c
2 and√
s = 205 GeV are also shown with arbitrary normalisation.
DELPHI
0 0.25 0.5 0.75 1
h1+h3
a)       (e sample)
0 50 100 150
mj1j2 (2 jets) (GeV/c
b)       (e sample)
1 2 3 4
-log10(y4→3)
c)      (µ sample)
0 0.1 0.2 0.3 0.4
Σptracks lepton hem. / √s
d)      (µ sample)
0 50 100 150
acolj1j2 (˚)
e)      (no-id sample)
0 50 100 150
αlν (˚)
f)       (no-id sample)
data SM expectation signal (mb’=100 GeV/c
Figure 8: Variables used in the discriminant analysis (cc̄qq̄l+ν final state). The data
events and background expectation for centre-of-mass energies above 200 GeV are shown
for (a) the h1 + h3 Fox-Wolfram moments sum (e sample), (b) the invariant mass of
the two jets with the events clustered into two jets (e sample), (c) − log10(y4→3) (µ
sample), (d)
|~pi|/
s, where ~pi are the momenta of the charged particles (excluding
the lepton) in the same hemisphere as the lepton (µ sample), (e) the acollinearity between
the two most energetic jets (no-id sample) and (f) the angle between the lepton and the
missing momentum (no-id sample). The signal distributions for mb′ = 100 GeV/c
2 and√
s = 205 GeV are also shown with arbitrary normalisation.
DELPHI
-10 0 10
ln(LS/LB)
-10 -5 0 5
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
-10 0 10
ln(LS/LB)
-20 -10 0 10
ln(LS/LB)
SM expectation
Signal (mb’=100 GeV/c
Figure 9: Discriminant variables ln(LS/LB) for data and SM simulation (centre-of–
mass energies above 200 GeV). FCNC b′ decay mode: (a) bb̄qq̄νν̄ and (b) bb̄qq̄qq̄.
CC b′ decay mode: (c) cc̄qq̄l+ν (e sample), (d) cc̄qq̄l+ν (µ sample), (e) cc̄qq̄l+ν (no-id
sample) (f) cc̄qq̄l+ν (no lepton sample) and (g) cc̄qq̄qq̄. The signal distributions for
mb′ = 100 GeV/c
2 and
s = 205 GeV are also shown with arbitrary normalisation.
DELPHI
96 97 98 99 100 101 102 103
mb’ (GeV/c
a) b’→ bZ decay
observed limit
expected limit
expected ± 1σ
expected ± 2σ
96 97 98 99 100 101 102 103
96 97 98 99 100 101 102 103
mb’ (GeV/c
96 97 98 99 100 101 102 103
b) b’→ cW decay
observed limit
expected limit
expected ± 1σ
expected ± 2σ
Figure 10: The observed and expected upper limits at 95% CL on (a) BR(b′ → bZ) and
(b) BR(b′ → cW) are shown. The 1σ and 2σ bands around the expected limit are also
presented. Systematic errors were taken into account in the limit evaluation.
DELPHI
Figure 11: The excluded region in the plane (RCKM , mb′) with mt′ −mb′ = 1 GeV/c2,
obtained from the 95% CL upper limits on BR(b′ → bZ) (bottom) and BR(b′ → cW)
(top) is shown. The light and dark shadings correspond to the observed and expected
limits, respectively. The expected limits on BR(b′ → bZ) did not allow exclusions to be
set for low values of RCKM .
DELPHI
Figure 12: The excluded region in the plane (RCKM , mb′) with mt′ −mb′ = 50 GeV/c2,
obtained from the 95% CL upper limits on BR(b′ → bZ) (bottom) and BR(b′ → cW)
(top) is shown. The light and dark shadings correspond to the observed and expected
limits, respectively.
