b-tagging in DELPHI at LEP

Abstract

The standard method used for tagging b-hadrons in the DELPHI experiment at the CERN LEP Collider is discussed in detail. The main ingredient of b-tagging is the impact parameters of tracks, which relies mostly on the vertex detector. Additional information, such as the mass of particles associated to a secondary vertex, significantly improves the selection efficiency and the background suppression. The paper describes various discriminating variables used for the tagging and the procedure of their combination. In addition, applications of b-tagging to some physics analyses, which depend crucially on the performance and reliability of b-tagging, are described briefly.

Full text

arXiv:hep-ex/0311003v1 1 Nov 2003
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN–EP/2002-088
2 October 2002
b-tagging in DELPHI at LEP
DELPHI Collaboration
Abstract
The standard method used for tagging b-hadrons in the DELPHI experiment at
the CERN LEP Collider is discussed in detail. The main ingredient of b-tagging
is the impact parameters of tracks, which relies mostly on the vertex detector.
Additional information, such as the mass of particles associated to a secondary
vertex, significantly improves the selection efficiency and the background sup-
pression. The paper describes various discriminating variables used for the
tagging and the procedure of their combination. In addition, applications of
b-tagging to some physics analyses, which depend crucially on the performance
and reliability of b-tagging, are described briefly.
(Accepted by Eur. Phys. J. C)

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J.Abdallah26, P.Abreu24, W.Adam54 , T.Adye38, P.Adzic12, T.Albrecht19, T.Alderweireld2, R.Alemany-Fernandez8,
T.Allmendinger19, P.P.Allport25, S.Almehed27 , U.Amaldi30, N.Amapane47, S.Amato51 , E.Anashkin37, A.Andreazza29 ,
S.Andringa24, N.Anjos24 , P.Antilogus28, W-D.Apel19, Y.Arnoud16, S.Ask27 , B.Asman46, J.E.Augustin26 ,
A.Augustinus8, P.Baillon8, A.Ballestrero48, P.Bambade22, R.Barbier28, D.Bardin18, G.Barker19 , A.Baroncelli40,
M.Bates38, M.Battaglia8, M.Baubillier26 , K-H.Becks56, M.Begalli6, A.Behrmann56 , N.Benekos33, A.Benvenuti5,
C.Berat16, M.Berggren26 , L.Berntzon46, D.Bertrand2, M.Besancon42 , N.Besson42 , J.Bibby36, P.Biffi29, D.Bloch9,
M.Blom32, M.Bonesini30 , M.Boonekamp42, P.S.L.Booth25 , G.Borisov23, O.Botner52 , B.Bouquet22, T.J.V.Bowcock25,
I.Boyko18, M.Bracko45, P.Branchini40, R.Brenner52 , E.Brodet36 , P.Bruckman20, J.M.Brunet7, L.Bugge34 ,
P.Buschmann56 , M.Caccia29,10 , M.Calvi30 , T.Camporesi8, V.Canale39 , F.Carena8, N.Castro24, F.Cavallo5, V.Chabaud8,
M.Chapkin44, Ph.Charpentier8, P.Checchia37 , R.Chierici8, P.Chliapnikov44, J.Chudoba8, S.U.Chung8, K.Cieslik20,
P.Collins8, R.Contri15, G.Cosme22 , F.Cossutti50 , M.J.Costa53, F.Couchot22 , B.Crawley1, D.Crennell38, J.Cuevas35,
B.D’Almagne22, J.D’Hondt2, J.Dalmau46 , T.da Silva51 , W.Da Silva26 , G.Della Ricca50, A.De Angelis50, W.De Boer19 ,
C.De Clercq2, B.De Lotto50, N.De Maria47, A.De Min37 , L.de Paula51, L.Di Ciaccio39 , H.Dijkstra8, A.Di Simone40,
K.Doroba55, J.Drees56,8, M.Dris33 , G.Eigen4, T.Ekelof52, M.Ellert52, M.Elsing8, M.C.Espirito Santo8, G.Fanourakis12 ,
D.Fassouliotis12, M.Feindt19, J.Fernandez43, A.Ferrer53, F.Ferro15, U.Flagmeyer56 , H.Foeth8, E.Fokitis33 ,
F.Fulda-Quenzer22, J.Fuster53, M.Gandelman51 , C.Garcia53 , Ph.Gavillet8, E.Gazis33, T.Geralis12 , R.Gokieli8,55,
B.Golob45, J.J.Gomez Cadenas53,8, G.Gomez-Ceballos43 , P.Goncalves24, E.Graziani40, G.Grosdidier22, K.Grzelak55 ,
J.Guy38, C.Haag19 , A.Hallgren52 , K.Hamacher56, K.Hamilton36 , J.Hansen34, S.Haug34 , F.Hauler19 , V.Hedberg27 ,
M.Hennecke19, J.A. Hernando53 , H.Herr8, J.Heuser56,41 , S-O.Holmgren46, P.J.Holt8, M.A.Houlden25, K.Hultqvist46 ,
J.N.Jackson25, P.Jalocha20, Ch.Jarlskog27, G.Jarlskog27, P.Jarry42, D.Jeans36 , E.K.Johansson46, P.D.Johansson46,
P.Jonsson28, C.Joram8, L.Jungermann19 , F.Kapusta26 , M.Karlsson46, S.Katsanevas28, E.Katsoufis33 , R.Keranen19 ,
G.Kernel45, B.P.Kersevan8,45, A.Kiiskinen17, B.T.King25 , N.J.Kjaer8, P.Kluit32, P.Kokkinias12, C.Kourkoumelis3,
O.Kouznetsov18, Z.Krumstein18 , M.Kucharczyk20, W.Kucewicz20 , J.Kurowska55, J.Lamsa1, G.Leder54, F.Ledroit16 ,
L.Leinonen46, R.Leitner31 , J.Lemonne2, V.Lepeltier22 , T.Lesiak20, W.Liebig56 , D.Liko54, A.Lipniacka46, J.H.Lopes51 ,
J.M.Lopez35, D.Loukas12, P.Lutz42, L.Lyons36 , J.MacNaughton54, A.Malek56 , S.Maltezos33, F.Mandl54 , J.Marco43 ,
R.Marco43, B.Marechal51 , M.Margoni37, J-C.Marin8, C.Mariotti8, A.Markou12, C.Martinez-Rivero43,
F.Martinez-Vidal53, J.Masik14 , N.Mastroyiannopoulos12 , F.Matorras43, C.Matteuzzi30, F.Mazzucato37 , M.Mazzucato37,
R.Mc Nulty25, C.Meroni29 , W.T.Meyer1, E.Migliore47, W.Mitaroff54 , U.Mjoernmark27 , T.Moa46, M.Moch19,
K.Moenig8,11, R.Monge15, J.Montenegro32 , D.Moraes51, S.Moreno24 , P.Morettini15, U.Mueller56, K.Muenich56 ,
M.Mulders32, L.Mundim6, W.Murray38, B.Muryn21 , G.Myatt36, T.Myklebust34 , M.Nassiakou12, F.Navarria5,
K.Nawrocki55, R.Nicolaidou42 , P.Niezurawski55, M.Nikolenko18,9, A.Nomerotski37,13, A.Norman36, A.Nygren27,
A.Oblakowska-Mucha21, V.Obraztsov44, A.Olshevski18 , A.Onofre24, R.Orava17, K.Osterberg17, A.Ouraou42 ,
A.Oyanguren53, M.Paganoni30, S.Paiano5, J.P.Palacios25, H.Palka20, Th.D.Papadopoulou33 , L.Pape8, C.Parkes25,
F.Parodi15, U.Parzefall8, A.Passeri40, O.Passon56, L.Peralta24, V.Perepelitsa53 , A.Perrotta5, A.Petrolini15, J.Piedra43 ,
L.Pieri40, F.Pierre42 , M.Pimenta24, E.Piotto8, T.Podobnik45 , V.Poireau42, M.E.Pol6, G.Polok20, P.Poropat†50,
V.Pozdniakov18, N.Pukhaeva2,18, A.Pullia30 , J.Rames14, L.Ramler19 , A.Read34 , P.Rebecchi8, J.Rehn19, D.Reid32,
R.Reinhardt56, P.Renton36, F.Richard22, J.Ridky14 , M.Rivero43, D.Rodriguez43 , A.Romero47, P.Ronchese37,
E.Rosenberg1, P.Roudeau22, T.Rovelli5, V.Ruhlmann-Kleider42, D.Ryabtchikov44, A.Sadovsky18, L.Salmi17 , J.Salt53,
A.Savoy-Navarro26, U.Schwickerath8, A.Segar36, R.Sekulin38, M.Siebel56, A.Sisakian18 , G.Smadja28 , O.Smirnova27,
A.Sokolov44, A.Sopczak23 , R.Sosnowski55, T.Spassov8, M.Stanitzki19, I.Stavitski37,25, A.Stocchi22, J.Strauss54 ,
B.Stugu4, M.Szczekowski55, M.Szeptycka55 , T.Szumlak21 , T.Tabarelli30, A.C.Taffard25, F.Tegenfeldt52,
J.Timmermans32, N.Tinti5, L.Tkatchev18, M.Tobin25, S.Todorovova14, A.Tomaradze8, B.Tome24, A.Tonazzo30,
P.Tortosa53, P.Travnicek14 , D.Treille8, W.Trischuk49, G.Tristram7, M.Trochimczuk55, C.Troncon29, M-L.Turluer42,
I.A.Tyapkin18, P.Tyapkin18 , M.Tyndel38, S.Tzamarias12 , V.Uvarov44, G.Valenti5, P.Van Dam32, J.Van Eldik8,
A.Van Lysebetten2, N.van Remortel2, I.Van Vulpen32, G.Vegni29, F.Veloso24, W.Venus38, F.Verbeure†2, P.Verdier28 ,
V.Verzi39, D.Vilanova42 , L.Vitale50 , V.Vrba14, H.Wahlen56, A.J.Washbrook25, P.Weilhammer8, C.Weiser19, D.Wicke8,

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J.Wickens2, G.Wilkinson36, M.Winter9, M.Witek20, O.Yushchenko44, A.Zalewska20, P.Zalewski55, D.Zavrtanik45,
N.I.Zimin18, A.Zintchenko18, M.Zupan12
1Department of Physics and Astronomy, Iowa State University, Ames IA 50011-3160, USA
2Physics Department, Universiteit Antwerpen, Universiteitsplein 1, B-2610 Antwerpen, Belgium
and IIHE, ULB-VUB, Pleinlaan 2, B-1050 Brussels, Belgium
and Facult´e des Sciences, Univ. de l’Etat Mons, Av. Maistriau 19, B-7000 Mons, Belgium
3Physics Laboratory, University of Athens, Solonos Str. 104, GR-10680 Athens, Greece
4Department of Physics, University of Bergen, All´egaten 55, NO-5007 Bergen, Norway
5Dipartimento di Fisica, Universit`a di Bologna and INFN, Via Irnerio 46, IT-40126 Bologna, Italy
6Centro Brasileiro de Pesquisas F´ısicas, rua Xavier Sigaud 150, BR-22290 Rio de Janeiro, Brazil
and Depto. de F´ısica, Pont. Univ. Cat´olica, C.P. 38071 BR-22453 Rio de Janeiro, Brazil
and Inst. de F´ısica, Univ. Estadual do Rio de Janeiro, rua S˜ao Francisco Xavier 524, Rio de Janeiro, Brazil
7Coll`ege de France, Lab. de Physique Corpusculaire, IN2P3-CNRS, FR-75231 Paris Cedex 05, France
8CERN, CH-1211 Geneva 23, Switzerland
9Institut de Recherches Subatomiques, IN2P3 - CNRS/ULP - BP20, FR-67037 Strasbourg Cedex, France
10Now at Universita dell’Insubria in Como, Dip.to di Scienze CC.FF.MM‘ via Vallegio 11, 1-22100 Como, Italy
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
13Now at Fermilab (FNAL), Kirk and Pine Streets, P.O. Box 500, Batavia, IL 60510
14FZU, Inst. of Phys. of the C.A.S. High Energy Physics Division, Na Slovance 2, CZ-180 40, Praha 8, Czech Republic
15Dipartimento di Fisica, Universit`a di Genova and INFN, Via Dodecaneso 33, IT-16146 Genova, Italy
16Institut des Sciences Nucl´eaires, IN2P3-CNRS, Universit´e de Grenoble 1, FR-38026 Grenoble Cedex, France
17Helsinki Institute of Physics, HIP, P.O. Box 9, FI-00014 Helsinki, Finland
18Joint Institute for Nuclear Research, Dubna, Head Post Office, P.O. Box 79, RU-101 000 Moscow, Russian Federation
19Institut f¨ur Experimentelle Kernphysik, Universit¨at Karlsruhe, Postfach 6980, DE-76128 Karlsruhe, Germany
20Institute of Nuclear Physics,Ul. Kawiory 26a, PL-30055 Krakow, Poland
21Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, PL-30055 Krakow, Poland
22Universit´e de Paris-Sud, Lab. de l’Acc´el´erateur Lin´eaire, IN2P3-CNRS, Bˆat. 200, FR-91405 Orsay Cedex, France
23School of Physics and Chemistry, University of Landcaster, Lancaster LA1 4YB, UK
24LIP, IST, FCUL - Av. Elias Garcia, 14-1o, PT-1000 Lisboa Codex, Portugal
25Department of Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, UK
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, S¨olvegatan 14, SE-223 63 Lund, Sweden
28Universit´e Claude Bernard de Lyon, IPNL, IN2P3-CNRS, FR-69622 Villeurbanne Cedex, France
29Dipartimento di Fisica, Universit`a 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 2, 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, Universit`a di Padova and INFN, Via Marzolo 8, IT-35131 Padua, Italy
38Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, UK
39Dipartimento di Fisica, Universit`a di Roma II and INFN, Tor Vergata, IT-00173 Rome, Italy
40Dipartimento di Fisica, Universit`a di Roma III and INFN, Via della Vasca Navale 84, IT-00146 Rome, Italy
41Now at Inst. of Physical and Chemical Research RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
42DAPNIA/Service de Physique des Particules, CEA-Saclay, FR-91191 Gif-sur-Yvette Cedex, France
43Instituto de Fisica de Cantabria (CSIC-UC), Avda. los Castros s/n, ES-39006 Santander, Spain
44Inst. for High Energy Physics, Serpukov P.O. Box 35, Protvino, (Moscow Region), Russian Federation
45J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia and Laboratory for Astroparticle Physics,
Nova Gorica Polytechnic, Kostanjeviska 16a, SI-5000 Nova Gorica, Slovenia,
and Department of Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
46Fysikum, Stockholm University, Box 6730, SE-113 85 Stockholm, Sweden
47Dipartimento di Fisica Sperimentale, Universit`a di Torino and INFN, Via P. Giuria 1, IT-10125 Turin, Italy
48INFN,Sezione di Torino, and Dipartimento di Fisica Teorica, Universit`a di Torino, Via P. Giuria 1,
IT-10125 Turin, Italy
49Now at Institute of Particule Physics of Canada, Univ. of Toronto, Toronto, Ontario, Canada M5S1A7
50Dipartimento di Fisica, Universit`a di Trieste and INFN, Via A. Valerio 2, IT-34127 Trieste, Italy
and Istituto di Fisica, Universit`a di Udine, IT-33100 Udine, Italy
51Univ. Federal do Rio de Janeiro, C.P. 68528 Cidade Univ., Ilha do Fund˜ao BR-21945-970 Rio de Janeiro, Brazil
52Department of Radiation Sciences, University of Uppsala, P.O. Box 535, SE-751 21 Uppsala, Sweden
53IFIC, Valencia-CSIC, and D.F.A.M.N., U. de Valencia, Avda. Dr. Moliner 50, ES-46100 Burjassot (Valencia), Spain

iv
54Institut f¨ur Hochenergiephysik, ¨
Osterr. Akad. d. Wissensch., Nikolsdorfergasse 18, AT-1050 Vienna, Austria
55Inst. Nuclear Studies and University of Warsaw, Ul. Hoza 69, PL-00681 Warsaw, Poland
56Fachbereich Physik, University of Wuppertal, Postfach 100 127, DE-42097 Wuppertal, Germany
†deceased

1
1 Introduction
The study of heavy b- and c- quarks is one of the most interesting subjects in exper-
imental High Energy Physics, directly related to the verification of the Standard Model
(SM) and the search for its possible violations. Where these may occur is very model-
dependent, but it may well be that the third generation particles will provide some impor-
tant clues to new effects. This is a large part of the motivation for studying b-quarks at
LEP, where top-quark pair production is kinematically inaccessible. It is thus important
to have algorithms for selecting events with b-quarks while keeping backgrounds small. Ef-
ficiency and purity or background rejection are important parameters of these techniques.
Because searches for such deviations from the SM often involve precision measurements,
it is crucial to have a very well understood and monitored b-tagging algorithm.
A further reason for selecting b-quarks is the search for the Higgs boson. For the SM
Higgs with mass of relevance for LEP and the Tevatron, the predominant decay mode is
to b¯
bpairs. Thus tagging b-jets provides a valuable means of selecting candidates while
reducing backgrounds to low levels, thereby enabling searches to achieve high sensitivity.
In this paper the b-tagging technique developed for the DELPHI experiment at the
LEP electron-positron collider is described. LEP ran at centre-of-mass energies around
the Z(91 GeV) over the period 1989 to 1995, and then at higher energies up to 208 GeV,
before being turned off in 2000. Much of the technique used here would be applicable,
with suitable modifications, in other experimental situations.
The lifetimes of b-hadrons are around 1.6 ps. This means that flight distances are of
order 3 mm for a 35 GeV b-hadron, this being a typical energy in a 2-jet event at the Z,
or in a 4-jet event at LEP2 energies. Correspondingly the decay tracks from a b-hadron
have non-zero impact parameters1, i.e. when extrapolated backward in space they do not
pass exactly through the beam interaction region. The scale of these impact parameters
is cτ ≈400 µm. This is to be compared with the DELPHI experimental resolution σof
about
σ= 27 ⊕63/(psin3/2θ)µm (1)
where pand θare the momentum (in GeV/c) and the polar angle of the track. The
symbol ⊕denotes the quadratic sum of terms. Eqn. (1) is for the impact parameter
(IP) in the plane perpendicular to the beam; along the beam direction, the resolution is
slightly worse. Because the micro-vertex detector is crucial for achieving this accuracy in
IP measurements, it is described in Section 2.
The impact parameters provide the main variable for b-tagging. For all the tracks in a
jet, the observed impact parameters and resolutions are combined into a single variable,
the lifetime probability, which measures the consistency with the hypothesis that all
tracks come directly from the primary vertex. For events without long-lived particles,
this variable should be uniformly distributed between zero and unity. In contrast, for
b-jets it has predominantly small values. Details of how this variable is constructed are
elaborated in Section 3.
Other features of the event are also sensitive to b-quarks, and some of them are also
used together with the IP information to construct a ‘combined tag’. For example, b-
hadrons have a 10% probability of decaying to electrons or muons, and these often have a
transverse momentum with respect to the b-jet axis of around 1 GeV/c or larger. On its
own, the high-pTlepton tag would have too low an efficiency for many b-quark studies, but
the presence of such a lepton is useful information to combine with the IP measurements.
The combined tag also makes use of other variables which have significantly different
1See Section 3.1 for more detailed definitions and discussion of impact parameters.

2
distributions for b-quark and for other events, e.g. the charged particle rapidities with
respect to the jet axis. Further details on these variables and the way in which they
are combined are given in Section 4. The combined tag including the lifetime probability
and secondary vertex mass, rapidities and fractional energy (described in Section 4.3) was
used for the measurements at the Z(see Sections 6.1 – 6.4). For most LEP2 b-tagging
analyses, the transverse momentum missing at the secondary vertex and the transverse
momentum with respect to the jet axis of any electron or muon were also used in the
combination.
The combination method used is optimal for uncorrelated variables. The extent to
which it is possible to improve on the ‘combined tag’, for example by using extra infor-
mation such as the jet energy, is investigated in Section 4.6. The resulting ‘equalised tag’
was used in the Higgs search at LEP2 (see Section 6.5).
Section 5 contains some technical aspects of the b-tagging. In particular it describes
some modifications that were required to the physics generators of the Monte Carlo
simulation.
Finally, some physics studies for which b-tagging plays a crucial role are outlined in
Section 6. First there is the measurement of the fraction of hadronic Zdecays which
contain b-quarks (see Section 6.1). A precise measurement of this quantity requires high
efficiency tagging, while keeping down the backgrounds from other quarks in order to
reduce the systematic errors. This is followed by applications of b-tagging to the mea-
surement of the production rate of events with 4 b-jets, and of the b-hadron charged decay
multiplicity. Section 6.4 describes a measurement of the b-fraction in 3-jet events, which
is sensitive to the mass of the b-quark. This uses anti b-tagging to select light quark
events. Finally the crucial reliance on b-tagging of the search for the Higgs is described
in Section 6.5.
2 The DELPHI Vertex Detector
2.1 Overview
The silicon vertex detectors of the DELPHI experiment have undergone various up-
grades throughout the lifetime of the experiment. For the statistics collected in 1991-1993
it provided measurements in the transverse (Rφ) plane2only [1].
The DELPHI Double Sided Vertex Detector (DSVD) [2] was installed in the exper-
iment in early 1994 and by the end of the Zrunning at LEP had contributed to the
reconstruction and analysis of approximately 2 million Zdecays. Two of its three layers
were equipped with double-sided orthogonal readouts, thereby upgrading the IP and ver-
texing capabilities by adding information from the longitudinal (Rz) plane. The extra
coordinate helps to associate tracks to vertices where the single Rφ view alone might
have ambiguities. This upgrade led to about a 30% improvement in the b-tagging effi-
ciency at fixed purity. The geometrical layout of the DSVD is shown in figure 1. The
three layers, termed Closer, Inner, and Outer, were at average radii of 6.3, 9.0 and 10.9
cm respectively, with the Outer and Closer layers instrumented with the double-sided
orthogonal readout. The three-layer polar angular coverage was between 44◦and 136◦,
with the Closer Layer providing additional coverage in anticipation of the subsequent SiT
upgrade described below. The transverse view displays the large degree of overlap (up to
2DELPHI uses a cylindrical polar co-ordinate system, with the zaxis along the beam direction (and the magnetic field
axis). Rand φare the radial and azimuthal co-ordinates in the transverse plane, θis the polar angle with respect to the
beam axis. The Cartesian co-ordinates xand yare horizontal and vertical respectively.

3
20% of the sensitive region in the Inner Layer), which was an important ingredient for the
alignment. The average thickness of each silicon module was 0.5% of a radiation length.
The zreadout was routed via an integrated double metal layer, thus adding negligible
extra material in the barrel region, and helping to keep multiple scattering to a minimum.
The DELPHI Silicon Tracker (SiT) [3] was a further upgrade for the physics require-
ments at LEP2, and the barrel part relevant for b-tagging was fully installed in 1996.
Physics objectives of LEP2, such as the measurement of four-fermion processes and the
searches for the Higgs boson or for super-symmetric particles, required a larger polar
angle coverage than at LEP1. The design goal was to achieve an equivalent b-tagging
performance to the DELPHI DSVD, and in addition to extend this to around 25◦in θ,
after which the b-tagging capabilities were limited by multiple scattering in the beam-
pipe. The SiT also incorporated end-caps of mini-strip and pixel detectors for tracking
in the forward region [3,4]. The geometrical layout of the SiT is shown in figure 2. The
radii of the layers were similar to the DSVD, but the Outer and Inner layers were doubled
in length to provide the extra angular coverage. The Closer Layer was double-sided, the
Inner Layer was double-sided for 21◦< θ < 44◦(and the corresponding backward region)
and single-sided in the centre, and the Outer Layer provided Rφ and Rz measurements
from its crossed detector arrangement [3]. The impact of this detector on b-tagging is
shown in figure 3.
2.2 Alignment and Performance
b-tagging quality relies on excellent alignment of the vertex detector. The starting
point of the alignment was the information from an optical and mechanical survey before
installation. This was refined with the information from tracks from Zdecays, using a
stand-alone procedure where the momentum of the track was the only information taken
from the rest of the DELPHI detector. The precision of the vertex detector hits has
allowed a number of important effects to be identified, including some common to all
LEP vertex detectors and certain previously unmeasured properties of silicon detectors.
They include:
•coherent deformations, such as a torsion or shear of the entire structure;
•bowing of the silicon modules due to the different response of the silicon and the
module support to changes in temperature and humidity;
•barycentric shift effects, whereby the centres of gravity of the charge clouds of elec-
trons and holes in the silicon do not correspond to the mid-plane of the detector,
nor to each other;
•acollinearity of the LEP electron and positron beams leading to lepton pairs from Z
decays which cannot be assumed to be back-to-back in the alignment procedure.
More details can be found in [5]. The precise vertex detector alignment has also led to
better understanding of other detectors, such as the TPC, the track distortions of which
were corrected.
The ultimate performance of the vertex detector with respect to b-tagging can be
measured by the IP resolution, which in the Rφ plane can be parametrised by:
σRφ = 27 ⊕63
p sin3
2θµm (2)
with pin GeV/c. The IP resolution in the Rz plane for two typical θregions can be
parametrised by:

4
σRz = 39 ⊕71
pµm (for 80◦< θ < 90◦) (3)
σRz = 96 ⊕151
pµm (for 45◦< θ < 55◦),(4)
These equations are the quadratic sums of a constant and a momentum dependent term,
corresponding to the intrinsic resolution and to the multiple scattering contributions re-
spectively. For tracks coming from b-decays, these contributions are of similar magnitude.
Typical distributions of the IP resolutions as functions of momenta are shown in figure 4.
3 Lifetime Tagging
b-hadrons in many aspects are significantly different from all other particles. They
have a long lifetime, large mass, high decay multiplicity, substantial leptonic branching
rate, etc. The most important property for the selection of b-hadrons is their lifetime.
Among the main features of lifetime tagging are a simple and transparent definition and
ease of control, since it relies on a single measured quantity, the track IP.
In this section the definition of the main elements entering in the lifetime tagging
together with the principles of its construction are given. This tagging itself provides
efficient separation of the b-quark from other flavours, which is further enhanced by
including additional variables (see Section 4). The method of lifetime tagging used by
DELPHI was originally proposed by the ALEPH collaboration [6].
3.1 Impact Parameter
The general 3-dimensional IP is the minimal distance between the estimated primary
interaction point and the track trajectory. The decay of a long-lived particle produces
tracks with large impact parameters, which is not the case for particles from the primary
interaction. Lifetime tagging is based on this difference.
For b-tagging in DELPHI, a slightly different approach is adopted, with a separation
of the 3-dimensional information into Rφ and Rz components. The IP component in
the Rφ plane is defined as the minimal distance between the primary vertex (PV) and
the track trajectory projected onto the plane perpendicular to the beam direction. The
point of the closest approach (PC) of the track trajectory to the primary vertex in the Rφ
plane is also used to define the Rz component of the IP. This is the difference between
the z-coordinates of the primary vertex and of the point PC(see fig. 5).
According to these definitions, there are two ingredients in the IP computation: the
parameters of the track trajectory, provided by the track fit, and the position of the
primary interaction. The parameters of the track trajectory are the track direction given
by its polar and azimuthal angles (θ, φ) at the point P0of the closest approach to the
origin O; and (εRφ,εRz ), the equivalent of the IP components but defined with respect
to the origin O, rather than with respect to the primary vertex. The reconstruction of
the primary vertex is explained in the next section. In the approximation that the tracks
can be regarded as straight lines between P0and PC, the IP components dRφ and dRz
with respect to the primary vertex position −→
Vare calculated as:

5
dRφ =εRφ −(−→
e·−→
V) (5)
dRz =εRz + cot θ(−→
u·−→
V)−Vz
=εRz −(−→
l·−→
V) (6)
Here −→
uis the unit vector along the track direction in the Rφ plane: −→
u={cos φ, sin φ, 0};
−→
eis the unit vector perpendicular to the track direction in Rφ plane: −→
e=
{sin φ, −cos φ, 0}; and −→
l={−cot θcos φ, −cot θsin φ, 1}. Figure 5 illustrates these
definitions of the IP components.
The main reason for the separation of the 3-dimensional IP into Rφ and Rz components
is that the measurement of the particle trajectory in DELPHI is performed independently
in these two planes with somewhat different precision (see eqns. (2) – (4)). Also the beam-
spot is smaller in the transverse directions. In addition, there are 3 sensitive layers of
vertex detector in the Rφ plane and only 2 layers in the Rz plane; the fraction of tracks
with wrong hit association in the Rz plane is thus higher. The separate treatment of
the IP components provides the freedom to reject bad measurements in the Rz plane,
while keeping useful Rφ information. Finally, the data before 1994 were taken with the
2-dimensional vertex detector providing track measurements in the Rφ plane only. The
separate use of the Rφ and Rz information is one of the crucial points of our tagging
algorithm, significantly influencing its structure.
3.2 Primary Vertex
The primary vertex is reconstructed for each event using a set of selected tracks and
the beam-spot position. The beam-spot is the zone of intersection of the two colliding
beams of LEP. It has a small size in the Rφ plane (σx≃150µm, σyless than 10µm),
while it is several millimetres long along the beam direction. It is relatively stable within
a fill, and so can be used as a constraint for the primary vertex fit.
The beam-spot is measured using events which have a vertex formed by at least 3
tracks with hits in the silicon strip detectors. These vertices are used to fit the position
in 3 dimensions and also the xand zsize of the interaction region in time periods of
around 20 minutes. The size of the interaction region in yis not fitted, because it is
smaller than the corresponding position error, and the value σy= 10 µm is used.
The PV position is obtained by minimising the χ2function:
χ2(−→
V) = X
aX
α,β=1,2
da
α(S−1
a)αβ da
β+X
i
(Vsp
i−Vi)2
(σsp
i)2(7)
Here {da
1, da
2}={da
Rφ, da
Rz}is the 2-dimensional vector of IP components for each track
aentering in the PV fit and Sais the covariance matrix of the measured quantities
{εa
Rφ, εa
Rz}; since measurements in the Rφ and Rz planes are made independently, the
matrix Sais almost diagonal. Vsp
iand σsp
iare the beam-spot position and size for the
xand ycoordinates. The first summation in equation (7) runs over all tracks selected
for the PV fit. Because of our definitions (5-6) of the IP components, the dependence
of χ2on the vertex position −→
Vis quadratic and hence the minimisation of (7) can be
performed analytically.
An important part of the PV reconstruction is the selection of tracks and the rejection
of bad measurements. Tracks with wrong hit associations in the vertex detector, as well

6
as those coming from decays of long-lived particles or from interactions in the detector
material, bias the fitted PV position and a special rejection procedure attempts to reduce
this bias.
For the PV computation, tracks with at least two Rφ measurements and at least
one Rz measurement are selected. First the fit using all these tracks (Ntr) is performed
and χ2(Ntr) is computed. After that each track iis consecutively removed and the
corresponding χ2
i(Ntr −1) is obtained. The track igiving the maximal difference χ2(Ntr)−
χ2
i(Ntr −1) is excluded from the fit if this difference exceeds a threshold value ∆, which
was set to 6. This procedure is repeated while there are tracks with a χ2difference
exceeding ∆. Since the beam-spot position constraint is used for the PV computation,
all tracks may be rejected for some events. In this case the PV coincides with the beam-
spot and its covariance matrix corresponds to the beam-spot size. The fraction of such
events is about 1% for Zhadronic events.
This fitting procedure gives an average precision of the PV position for q¯q(where
q=uds), c¯c,b¯
bsimulated Zhadronic decays of σx= 36,44,60 µm and σz= 43,50,70 µm
respectively, although the actual precision depends strongly on the number of tracks.
The somewhat degraded precision for b¯
bevents is explained by the smaller multiplicity of
primary tracks and by tracks from b-hadron decay occasionally included in the primary
vertex.
3.3 Error and Sign of Impact Parameter
Since the PV position is used in the definition of an IP, the impact parameters of all
tracks included in the PV fit are correlated with each other; their correlation coefficient
is about 0.2. From equations (5-7) and the standard error propagation formalism, the
error on the Rφ IP is given by:
σ2
Rφ =(σtr
Rφ)2−(σpv
Rφ)2if the track is included in the PV fit
(σtr
Rφ)2+ (σpv
Rφ)2otherwise (8)
with similar equations for σ2
Rz. Here σtr
Rφ (σtr
Rz) is the error on εRφ (εRz) coming from the
track fit and σpv is the error from the PV fit, and includes implicitly the influence of all
other impact parameters. More explicitly:
(σpv
Rφ)2=X
i,j
eiSV
ij ej(9)
(σpv
Rz)2=X
i,j
liSV
ij lj(10)
where SV
ij is the covariance matrix of the primary vertex fit, −→
eand −→
lare defined in
Section 3.1, and repeated indices imply summation. The simplicity of the final equations
is a consequence of our choice of IP components.
Using equations (5, 6 and 8) the track significances SRφ and SRz are defined simply
as:
SRφ =dRφ/σRφ (11)
SRz =dRz/σRz (12)
The track significance thus compares the measured value of the IP with its expected
precision. This quantity is used as an input variable for the lifetime tagging. Tracks from

7
decays of long-lived particles (τ’s, b-, c- and s-hadrons) often have large IPs, significantly
exceeding σRφ and σRz.
Equations (5-6) define the magnitude of IP components and their geometrical sign,
while in the b-tagging method and throughout this paper the lifetime sign for IP is used.
It requires knowledge of the flight path of the long-lived particle. In the simplest case
the flight path is approximated by the direction of the jet3to which the given particle
belongs. Often the decay point of the long-lived particle can be reconstructed (see Section
4.2); in this case the flight direction is defined as the direction from the primary to the
secondary vertex. As can be seen in fig. 6, this improves the measurement of the flight
direction. The azimuthal angle precision becomes slightly better than that for the polar
angle because the vertex detector is more precise in the Rφ plane. To obtain the lifetime
sign of the Rφ and Rz IPs, the point of closest approach in space of the track to the
estimated B-flight path is computed and the sign is set negative (positive) if this point
is upstream (downstream) of the PV position. The significance is assigned the same sign
as the IP.
With this definition, tracks from decays of long-lived particles have predominantly
positive signs while tracks coming directly from the PV are equally likely to be positive
or negative. For b-tagging, tracks with positive IP are used, thus reducing by half the
number of background tracks.
The distributions of positive and negative Rφ significance are shown in fig. 7. The
excess of positively signed tracks with large significance is clearly seen.
3.4 Track Probability
The distribution of the negative track significance is determined mainly by tracks
coming from the PV, including scatters in the detector material, tracks with wrong hit
association etc, while the contribution of tracks coming from decays of long-lived particles
is about 1%. This distribution can thus be used to define the probability P(S0) for a
track from the PV to have the measured value of the modulus of its significance exceeding
the value S0. This function is obtained by integration of the probability density function
of the negative significance f(S) from S0to infinity and assuming that P(S0) is the same
for primary tracks with either positive or negative significance:
P(S0) = Z∞
S0
f(S)dS (13)
By definition, tracks from the PV should have a flat distribution of P(S0) between 0
and 1, while tracks from decays of long-lived particles and with large positive values of S0
have small values of P(S0), reflecting the small probability for tracks from the primary
vertex to have such large values of the IP and hence of S0. As an example, fig. 8 shows
the distribution of P(S0
Rφ) for tracks with positive IP. The peak at small values of P(S0
Rφ)
is produced mainly by the long-lived particles. The transformation from significance to
track probability is referred to as the calibration of the detector resolution.
For LEP1 analyses, the above calibration was performed using tracks from Zdecays.
At LEP2, there was the possibility of again using Zdata for calibration; each year, short
runs at the Zwere taken before the start of and also interspersed with the high energy
running. Alternatively, the calibration could be carried out using the same type of data
as used to perform the relevant physics analysis. Thus for the Higgs search of Section
6.5, 4-jet events were also used for calibration in the channel where the Hand Zboth
3The default jet clustering algorithm is JADE, with ycut set at 0.01. However, the user of the b-tagging package has
the option of using any jet algorithm.

8
decay to 2 jets, while in the corresponding channel where the Zdecays to two neutrinos,
calibration was performed using ‘2-jets + missing energy’ events. The use of calibration
samples closely related to the data sample in principle allows for the following possible
effects:
•because of possible movements of the relative positions of the different parts of the
vertex detector with respect to the rest of DELPHI, the calibration could be time-
dependent;
•track confusion and lifetime-signing (and hence calibration) could depend on the
event topology;
•the IP resolution changes with polar angle θ. The jet distribution in θdepends on
the particular physical process considered;
•the IP resolution is also energy dependent. The jet and track energy spectra depend
on the physical process.
The calibration was performed separately for categories of tracks with different life-
time sensitivities. The categories were determined by the number of associated VD hits.
A small number of VD hits associated with a track is often caused by incorrect recon-
struction, and the significance distribution of such tracks has a larger non-Gaussian tail.
By using a different track probability for them, this difference was taken into account.
This approach was also used for the analysis of the data collected in 2000, when one
out of the 12 sectors of the TPC was not operational during the last part of the data
taking; tracks reconstructed without the TPC have worse precision, which requires using
a separate track probability for them.
Another property of the track probability is that it can be defined directly from the
data. This is very important, in that it allows the calibration of the detector resolution
independently of the simulation. Such calibration allows to take into account possible
differences between data and simulation. As a consequence, it also reduces the systematics
due to detector effects in physics measurements.
For the construction of P(S0) it is important to reduce the contribution of tracks
coming from the decay of long-lived particles. Using the negative significance distribu-
tion partially solves this problem. Additional suppression of the lifetime information
is achieved by applying anti-btagging to the event sample used for calibration. This
anti-btagging is based on tracks with positive IPs, and hence does not bias the nega-
tive significance distribution. The anti-btagging reduces the fraction of b¯
bevents in the
selected sample of hadronic Zevents from 21.6% to less than 5% and the contribution
of tracks from decays of b-hadrons is reduced correspondingly. Additional selection cri-
teria for tracks used for calibration decrease the contribution from the decay products
of light long-lived hadrons (K0, hyperons) and hence reduce the tail of the significance
distribution. They are specified in the next section.
3.5 Lifetime Probability
Track probabilities are directly used to construct a lifetime probability [6]. For any
group of N tracks it is defined as:
PN= Π ·
NRφ+NRz −1
X
j=0
(−log Π)j/j!,where Π =
NRφ
Y
i=1
P(Si
Rφ)·
NRz
Y
i=1
P(Si
Rz) (14)
Here P(Si
Rφ), P(Si
Rz) are the track probabilities and NRφ,NRz are the number of Rφ
and Rz IPs used in the tagging. The definition of PNthus ignores the small off-diagonal

9
elements of the IP error matrix and the correlation between different IPs coming from
the use of the common PV.
The variable PNhas a simple and straightforward definition and can be computed
for any group of tracks (e.g. a jet, hemisphere or whole event) which makes it flexi-
ble and easily adjustable to different physics applications. No other combination of IP
measurements was found to give a better selection of b-quarks.
An attractive feature of lifetime tagging is that it is constructed using only the track
IPs. This provides the possibility of achieving a good description of the b-tagging effi-
ciency by the accurate tuning of the track resolution in simulation, as described in Section
3.6. It allows a significant decrease in the systematic uncertainties due to detector effects
in physics measurements.
The meaning of the variable PNis very similar to that of track probability P(S):
it is the probability for Ntracks coming from the PV to have the product of their
track probabilities exceeding the observed value. It varies between 0 and 1 and has a flat
distribution for any group of Nuncorrelated tracks coming from the PV. The contribution
of tracks from secondary decays shifts PNto lower values, producing a peak near 0.
The flat distribution of PNfor primary tracks can be verified by computing P−
Nfor
the sample of all tracks with negative impact parameters in anti-btagged events. As
explained in Section 3.4, the contribution of tracks from decays of long-lived particles in
such a sample is small. The distribution of P−
Nis shown as the dotted curve in fig. 9. It is
relatively flat, although there is a small peak near zero. This peak is produced by tracks
from decays of long-lived particles, which are occasionally assigned to have negative IPs
because of the error in their flight direction estimate. However, the value of this excess
is significantly less than the peak in the distribution of P+
N, computed using positive IPs.
This distribution is shown as the solid curve in fig. 9. The latter peak is mainly produced
by the b¯
bevents, as can be seen from fig. 9.
The separation of tracks into two samples depending on the sign of their IP is very
important. The sample of negative IP tracks is used for the calibration of the detector
resolution and the quality of this calibration is verified by the P−
Ndistribution. In contrast,
positive IP tracks are used for b-tagging. Thus the samples of tracks used in the calibration
and in the analysis do not overlap. The P−
Ndistribution also gives a good estimate of the
background level from light quarks at the corresponding value of P+
N.
The Rφ and Rz components enter in eqn. (14) separately. As explained in Section 3.1,
the fraction of wrong measurements in Rz is higher. Therefore, tighter selection criteria
are applied to tracks for the Rz IP, and for some tracks only the Rφ measurement is
used. Thus, the separate treatment of IP components also allows the use of information
which would otherwise be lost.
More specifically, the conditions applied to the tracks are as follows. All tracks with
positive IP and at least one measurement in the VD are candidates for lifetime tagging.
Tracks coming from reconstructed K0or Λ decays4are rejected. Both Rφ and Rz IP
components are required to be less than 0.2 cm, although this condition is removed if the
track comes from a reconstructed secondary vertex (see Section 4.2).
One more parameter is used to provide additional suppression of bad Rz measure-
ments. It is the distance Dof closest approach in 3-dimensions between the track and
the expected flight path of the long-lived particle, defined in the section 3.3. All tracks,
both from the primary and secondary vertices, should have a small value of Dprovided
the secondary vertex is close to the estimated flight direction. Therefore a large value of
Dwith respect to its expected precision σDis used to identify wrong IP measurements.
4For V0reconstruction procedure see [7].

10
Rz IP measurements are rejected if D/σDexceeds 2.5. Both Rφ and Rz measurements
are excluded from lifetime tagging if D/σDexceeds 10.
Figure 10 shows the performance of the lifetime probability applied to simulated
hadronic decays of the Z. The figure shows the efficiency of the b-quark selection versus
the contamination of the selected sample by (u, d, s, c) flavours (Nudsc /(Nudsc +Nb)). The
suppression of background flavours is shown for tagging of one jet (i.e. using only tracks
from the given jet), and for the whole event. Event tagging is more efficient because
b-quarks are produced in pairs.
b-tagging using only lifetime information is rather efficient and is sufficient for the
needs of many physics applications. An important feature is its simple control of the
tagging efficiency in simulation. Its performance is however substantially enhanced by
including additional discriminating variables, such as the mass at the secondary vertex
or the presence of energetic leptons. This method of ‘combined b-tagging’ is described in
Section 4.
3.6 Tuning
Almost all precision measurements and searches for rare processes rely on a comparison
of the observed data distributions with those predicted by a detailed simulation. For this
comparison both the generation of the intrinsic physical processes and the simulation of
detector response must be as realistic as possible. For the selection of events containing
b-hadrons, the most important variables are the track IPs, therefore the description of the
IP resolution can significantly influence the physics result and the value of the systematic
uncertainty.
The generated events in the DELPHI experiment are processed by the detector sim-
ulation package [8] and the same reconstruction program [9] as for the data. For the
simulation, the reconstruction program first applies some additional smearing to the re-
construction inputs to improve agreement with the particular data set being represented.
For the vertex detector, this includes applying corrections for inefficient regions, adding
noise hits, and randomly modifying the positions of the modules to simulate the effects
of residual misalignments in the real data.
However, even after this procedure some disagreement between data and simulation in
the track resolution description remains. This difference can be clearly seen, for example,
in the distribution of the track significance (see fig. 11). Any disagreement in this
quantity can result in a large discrepancy in the b-tagging description.
A detailed description of the method including the correction of the detector resolution
in the Rφ plane for the initial micro-vertex detector [1] is given in [10]. The application
of this method for the tuning in the Rz plane for the DSVD at LEP1 and the SiT at
LEP2 is similar and consists of the following steps:
•the appropriate parameterisations of the negative lifetime-signed IP (dRφ and dRz)
distributions are determined;
•the numerical coefficients for these parameterisations are extracted from the data;
•the errors of dRφ and dRz given by the track fit are corrected both in data and in the
simulation according to the parametrisation obtained while the correlation between
dRφ and dRz is not changed;
•additional smearing of Rφ and Rz IPs in simulation is performed in order to repro-
duce the observed real data distributions.
The improvements in the significance description after applying this method can be
seen in fig. 12. Fig. 13 shows the data to simulation ratio of the selection efficiency as

11
a function of the cut on the b-tagging variables. For the non-tuned version of b-tagging
(dashed line) the difference between data and simulation is very significant for strong
b-tagging cuts, corresponding to purer samples of Bevents. The tuning results in better
agreement for both the lifetime and the combined b-tagging variables, the latter being
described in the next section. The remaining differences between data and simulation
can be explained by the uncertainties of the modelling of Bdecay and to a lesser extent
its hadronic production.
This tuning procedure is incorporated in the b-tagging package and is used in all
DELPHI measurements involving b-quark selection.
4 Combined Tagging
Efficient utilisation of different properties of b-hadrons requires the development of
a technique for their combination into a single tagging variable. The simplest solution
of applying some system of cuts on different discriminating variables, which was tried
in other collaborations [11, 12], is not optimal due to a significant overlap between the
signal and background for some of them. Instead, DELPHI uses a likelihood ratio method
of variable combination [13, 14]. This approach has the important advantage of being
technically very simple while at the same time providing powerful separation of signal
and background. For independent variables, it gives optimal tagging, i.e. the best possible
background suppression for a given signal efficiency [15]. It can easily be extended to
any number of discriminating variables, and can deal with different numbers of variables
in different events. However, its practical application requires the careful selection of
variables with reduced correlations among them. The description of this likelihood ratio
method, the set of variables used and the performance of the DELPHI combined b-tagging
is given below.
4.1 Description of Method
The combined tagging variable yin the likelihood ratio method is defined as:
y=fbgd(x1, ..., xn)
fsig(x1, ..., xn)(15)
where fbgd(x1, ..., xn), fsig (x1, ..., xn) are the probability density functions of the discrim-
inating variables x1, ..., xnfor the background and the signal respectively. The selection
of all events with y < y0gives the optimal tagging of the signal. It should be stressed
that such tagging is absolutely the best for a given set x1, ..., xnof variables.
In practical applications the determination and utilisation of multi-dimensional prob-
ability density functions is quite difficult for n > 2. The solution consists in a special
selection of discriminating variables having reduced correlations among them. In the
limit of independent variables5, expression (15) becomes:
y=
n
Y
i=1
fbgd
i(xi)
fsig
i(xi)=
n
Y
i=1
yi; (16)
yi=fbgd
i(xi)/fsig
i(xi) (17)
5Two variables are independent if, for the signal and for each separately treated background component (e.g. cand
uds), the distribution of one is independent of any selection on the other.

12
where fbgd
i(xi), fsig
i(xi) are probability density functions of each individual variable xifor
the background and signal, and are determined from simulation.
This scheme is used in DELPHI to construct the combined b-tagging. For each indi-
vidual variable xithe value yiis computed from (17); the combined tag yis defined as the
product of the yi. It is not exactly optimal any more, because the discriminating variables
are not independent, but the variables are chosen such that the correlations between them
are small enough that the resulting tagging is very close to optimal. Furthermore, the
efficiencies and mis-tag rates are determined from simulation (and sometimes from the
actual data), thereby taking into account any small correlations.
In DELPHI all discriminating variables and the b-tagging itself are computed indepen-
dently for each jet in an event, where ideally all tracks coming from the fragmentation of
the b-quark and from the decay of the b-hadron are combined in one jet by a jet clustering
algorithm. In this case the background for the bquark selection can be separated into
two different parts – jets generated by c-quarks and by light (q=u, d, s) quarks. These
two components are independent and have very different distributions of discriminating
variables.
To define the extra discriminating variables for the b-tagging, tracks are selected so
as to come preferentially from b-hadron decay. For this purpose all jets in an event are
classified into 3 categories. In the first category all jets with one or more reconstructed
secondary vertices are included. A reconstructed secondary vertex provides a clean se-
lection of b-hadron decay products and a large number of discriminating variables can
be defined in this case. If the secondary vertex is not reconstructed, tracks from the B
decay are selected by requiring the track significance probability to be less than 0.05, and
the second category includes all jets with at least 2 such offsets. This criterion is less
strong, allowing more background jets to pass the cut. Finally, if the number of offsets
is less than 2, the jet is included in the third category and in this case only a reduced
set of inclusive discriminating variables, like the lifetime probability (see Section 3.5),
is used. In Zhadronic events the fractions of jets classified into categories 1, 2, 3 are
44%, 14%, 42% respectively for b-quark, 8%, 8%, 84% for c-quark and 0.6%, 2.8%, 96.6%
for light quark jets.
The tagging variable yαfor a jet of category αis defined as:
yα=nc
α/nb
αY
i
yc
i,α +nq
α/nb
αY
i
yq
i,α; (18)
y(c,q)
i,α =f(c,q)
i,α (xi)/fb
i,α(xi)
where fq
i,α(xi), fc
i,α(xi), fb
i,α(xi) are the probability density functions of xiin jet category
αgenerated by uds,cand bquarks respectively and nq
α,nc
αand nb
αare their normalised
rates, such that Pnq
α=Rq,Pnc
α=Rc, and Pnb
α=Rb.Rq,Rcand Rbare the
normalised production rates of different flavours and Rq+Rc+Rb= 1.
As can be seen from eqn. (18), the classification into different categories effectively
works as an additional discriminating variable with the discrete probabilities given by
n(q,c,b)
α. For example, the b-purity of a sample of jets with reconstructed secondary vertices
is about 85%. However, the primary purpose of this separation is to allow the use of a
larger number of discriminating variables when a secondary vertex is found. The search
for the secondary Bdecay vertex is thus an important ingredient of DELPHI b-tagging.
It is often convenient to define Xj et =−log10 yαas the jet tagging variable, and this
variable is used in all applications described in Section 6. The event variable Xev is
defined as the sum of the largest two Xjet values for the individual jets in the event.

13
4.2 Secondary Vertex Reconstruction
A secondary vertex (SV) is searched for in each jet of the event. In the first stage
all possible combinations of pairs of tracks are selected as SV candidates if they have a
common vertex with the χ2of the fit less than 4. After that all tracks from the same
jet are tested one by one for inclusion in a given SV candidate. The track producing
the smallest change ∆ of the vertex fit χ2is included in the SV candidate if this change
does not exceed the threshold ∆ = 5. This value and all other numerical parameters
of the algorithm were selected by optimising the efficiency of the SV reconstruction and
background suppression. This procedure is repeated until all tracks satisfying the above
condition are included in the SV candidate. The SV candidate is rejected if the distance
to the primary vertex divided by its error is less than 4. Additionally, at least two tracks
in the SV candidate are required to have VD measurements in both Rφ and Rz planes.
The decay of the b-hadron is usually followed by decays of one or two Dmesons, thereby
producing several secondary vertices. It thus often happens that some secondary tracks
cannot be fitted to a single secondary vertex. However, the spatial distance between
any secondary track and the flight trajectory of the b-hadron should be small since the
D-mesons tend to travel in the direction of the initial b-hadron. Using this property
some tracks of far-decaying Dmesons can be recuperated, which is important for the
computation of such quantities as the b-hadron mass. The flight trajectory of the b-
hadron is defined as the vector from the primary to the secondary vertex. Any track
from the same jet having an Rφ or Rz component track probability less than 0.03 and
not included in the SV fit is attached to the SV candidate if its distance in space to the
flight trajectory divided by its error is less than 3. Although not included in the SV fit,
such tracks are used in the computation of all discriminating variables.
Sometimes the decay vertex of a D-meson can be reconstructed separately from the
b-hadron decay vertex, which then results in two or more secondary vertices in the same
jet. In that case, all tracks included in these vertices are combined for the computation
of the b-tagging discriminating variables.
Three additional criteria are used to suppress the background of light quarks in the
sample of jets with secondary vertices. The first one makes use of the momentum vector
of the b-hadron. This is defined as the sum of the momenta of all tracks included in
the SV candidate. Additionally, the momenta of all other neutral and charged particles
with pseudo-rapidity exceeding 2 are also included; the pseudo-rapidity is computed with
respect to the flight direction of the b-hadron. Then, the trajectory directed along the B-
momentum and passing through the SV position is constructed and the impact parameter
δSV of this trajectory with respect to the primary vertex is computed. For a real b-hadron
the momentum direction should be close to the flight direction and δSV should be small
compared to its error6σδSV , while for a false secondary vertex the flight and momentum
directions are much less correlated. Therefore SV candidates with (δSV /σδS V )2>12 are
rejected. For the second criterion the lifetime probability using all tracks included in the
SV candidate is computed and the candidate is rejected if this probability exceeds 0.01.
The third criterion requires the distance between the primary and secondary vertex to
be less than 2.5 cm, because the contribution of false secondary vertices and of strange
particle decays becomes rather high at large distances. Any background jet with a very
distant SV would give an extremely strong b-tagging value and this cut effectively rejects
such cases.
6σδSV is computed using the uncertainties in the positions of primary and secondary vertices and the uncertainty in
the B-hadron flight direction estimate, obtained from the simulation.

14
Candidates remaining after these selections are considered as reconstructed secondary
vertices. With this procedure a SV is reconstructed for about 44% of jets with b-hadrons
(50% for jets inside the VD acceptance). The b-purity of the sample of jets with a recon-
structed SV is about 85% for hadronic decays of the Z, which should be compared with
the initial b-purity of about 22%. More than one SV in a single jet is allowed, reflecting
the possibility of cascade (B→D) decays giving rise to distinguishable secondary ver-
tices. In this case the tracks from all secondary vertices are combined for the computation
of the SV discriminating variables.
4.3 Discriminating Variables
In this section the discriminating variables used in b-tagging are described. All defini-
tions are given first for jets with reconstructed secondary vertices. Then the modifications
for other jet categories are described. All discriminating variables, except the transverse
momentum of a lepton, are computed using the charged particles included in the sec-
ondary vertex.
The jet lifetime probability,P+
j, is constructed using equation (14) from the positive
IPs of all tracks included in the jet.
The mass of particles7combined at the secondary vertex,Ms, is very sensitive to the
quark flavour. The mass at the secondary vertex in a jet generated by a c-quark is limited
by the mass of the D-meson, which is about 1.8 GeV/c2, while the mass in a b-jet can go
up to 5 GeV/c2. The limit of 1.8 GeV/c2for the c-jets can be clearly seen in fig. 14(a).
Some c-jets do have a higher value of Msdue to tracks incorrectly attached to the SV.
The fraction of the charged jet energy included in the secondary vertex,Xch
s, reflects
the differences in the fragmentation properties of different flavours. The fragmentation
function for the c-quark is softer than for the b-quark, as seen in the distribution of Xch
s
in fig. 14(b).
The transverse momentum at the secondary vertex,Pt
s, first introduced by the SLD
collaboration [12], takes into account missing particles not included in the SV definition.
Pt
sis defined as the resultant transverse momentum (with respect to the b-hadron’s es-
timated flight direction) of all charged particles attached to the SV. Missing particles
can be neutrinos from semileptonic decay, other neutral particles or non-reconstructed
charged particles. In all cases, due to the high mass of the b-hadron, the value of Pt
sfor
b-quark jets is higher, as can be seen from fig. 14(c).
The rapidity of each track included in the secondary vertex,Rtr
s, is quite a strong dis-
criminating variable, significantly improving the b-quark selection. Although a b-hadron
on average is produced with a higher energy, the rapidities of particles from B-decays
are less than those from D-meson decay, as can be seen from fig. 14(d). This is mainly
explained by the higher b-hadron mass. The variable Rtr
sis defined for each track in the
SV and the corresponding variable yRfor each track is used in (18) for the computation of
the b-tag. Although there is overlap between the signal and background for an individual
track rapidity, because of the large number of secondary tracks the inclusion of all the
rapidities in the b-tag results in a significant gain.
The transverse momentum of an identified energetic lepton,pt
l. It is independent of
the track IP and can be defined for any category of jet containing a muon or electron. A
more detailed description of this variable and of some specific features of its inclusion in
the combined b-tagging scheme are given in the next section.
7For computation of discriminating variables, such as mass or track rapidity, elsewhere in this paper, charged particles
are given the pion mass, whereas neutrals (except for K0
sand Λ) are assumed to be massless.

15
All these variables are defined for the first category of jets (with reconstructed SV).
For the two other categories, a reduced set of variables is used. For jets with at least
two offsets, the jet lifetime probability, the effective mass of all tracks with offsets, their
rapidities and any lepton transverse momentum are computed. For jets with less than
two offsets the effective mass is not used, as there is no reliable criterion for selecting the
particles from B-decay; however the track rapidities for all tracks with positive IP are
still included in the tagging. The ratios of probability density functions are computed
separately for each jet category. The possibility of treating in the same way different
categories of events with different sets of discriminating variables is a very important
feature of the likelihood ratio method of b-tagging.
The distributions of Ms,Xch
s,Pt
sand Rtr
sare shown in figure 14. These distributions
are shown for b-quark jets and also for c-quark jets, the latter constituting the main
background for b-tagging.
Combined b-tagging using the complete set of discriminating variables performs much
better than the simple lifetime tagging. This is illustrated in fig. 15. The performance
is tested using jets of Zhadronic decays. The figure shows the contamination of the
selected sample by other flavours (Nudsc /(Nudsc +Nb)) versus the efficiency of b-jet selec-
tion. Compared with the tagging using only P+
j, combined tagging provides much better
suppression of background, especially in the region of high purity. A very pure sample
with contamination below 0.5% can be obtained for a sizable befficiency, which opens
new possibilities for measurements with b-hadrons.
4.4 Lepton Tagging
Leptons with high transverse momentum have long been used in a variety of ways to
identify the quark flavour of the jet from which they originate. This section describes the
inclusion of this information within the standard DELPHI b-tagging algorithm.
Knowing the probabilities Pq,c,b of finding a lepton in a light quark-jet, a c-jet or a
b-jet respectively, and the transverse momentum distributions fq,c,b(pt
l) of these leptons,
the contribution of identified leptons to the global discriminating variable (18) is:
y(c,q)
pt
l=




f(c,q)(pt
l)
fb(pt
l)
P(c,q)
Pbif a lepton is found,
1−P(c,q)
1−Pbotherwise,
(19)
The quantities appearing in this expression are extracted from a sample of simulated
hadronic Zdecays, where all reconstructed particles are clustered into jets.
Reconstructed particles are identified as leptons if they satisfy a tight electron tag
(from energy loss by ionisation in the TPC, or from associated energy deposits in the
electro-magnetic calorimeters), a tight muon tag (from the muon chambers only), or a
standard muon tag confirmed by a minimum ionisation energy deposit in the hadron
calorimeters. Detailed descriptions of these different categories of tags and of their per-
formance are given in ref. [7]. The quantities Pq,c,b are simply defined as the fractions
of jets of the corresponding flavour inside which a lepton is identified, and are 3%, 9.8%
and 18.7% for light quarks, c-quarks and b-quarks respectively.
The transverse momentum of the lepton is evaluated with respect to the jet to which
it belongs, when the lepton momentum is subtracted from the total jet momentum. The
tagging contribution y(c,q)
pt
lof the leptons is then obtained from the ratio of the transverse
momentum distributions f(c,q)(pt
l) and fb(pt
l).

16
Figure 16 shows the superimposed distributions of transverse momenta for leptons
found in b-jets, c-jets, and light quark-jets. The agreement of these with the data ob-
tained from real hadronic Zdecays (recorded in 1994) is excellent. Because of the small
branching ratio of b-hadrons to high pt
lleptons, the intrinsic discriminating power of lep-
ton tagging is weaker than that of lifetime and secondary vertex information. However,
it does provide useful information since it is fully independent of the above, and supple-
ments the b-tagging in particular when no other hints of Bdecays are found (for example
in case of fast decay, or decay outside the vertex-detector acceptance).
In principle, the distribution in transverse momentum at the secondary vertex Pt
s
depends on whether or not there is a lepton present, because it is accompanied by an
unseen neutrino. However, because semi-leptonic decays are multi-body, there is not
a strong correlation between the lepton and the neutrino transverse momenta, and the
difference in the Pt
sspectra (i.e. with and without charged leptons) is small, as can be
seen from fig. 17.
The use of the algorithm at LEP2 requires some additional care. In this case, data
available for detector calibration are less abundant, and some experimental aspects are
less well understood. In particular, lepton identification or misidentification probabilities
are not perfectly reproduced, and this leads in general to an excess of simulated events
with respect to real data, mainly in the low transverse momentum region. To correct
for this, rejection factors are computed for each category of identified leptons in the
simulation, and applied randomly.
Finally, it is not obvious that lepton tagging calibrated on Zdata will produce efficient
discrimination in the context of Higgs searches at LEP2, especially in 4-jet events. This
is because in the Higgs search events are reconstructed by constraining the number of jets
rather than fixing the jet algorithm resolution parameter as was done for the calibration;
as a result the measured transverse momentum distributions are different. Figure 18
shows the distributions of the flavour ratios (i.e. the discriminating power) after the
applied corrections. The data at the Zand at high energy are in fact in approximate
agreement.
4.5 Event b-tagging
b-hadrons are almost always produced in pairs and the presence of the second b-hadron
significantly improves the b-tagging of an event as a whole. The likelihood ratio method
provides a simple way for combining the information from the two b-hadrons. Keeping in
mind that each flavour is produced independently from all other flavours, one can write
the equation for the event tagging variable, where the two jets8are of categories αand
β, as:
yev
αβ =Rb
Rc
nc
αnc
β
nb
αnb
βY
i
yc
i,α Y
i
yc
iβ +Rb
Rq
nq
αnq
β
nb
αnb
βY
i
yq
i,α Y
i
yq
iβ (20)
It was found, however, that a simpler way of combining the information from two jets
into a single tagging variable:
yev
αβ =yα·yβ(21)
works equally well. Here yα,yβare given by eqn. (18). The difference between these two
equations is that (21) neglects the correlated production of the same background flavours
in an event. The b-tagging variable computed from (21) was used in the Higgs search
(see Section 6.5).
8In events with more than 2 jets, the smallest two values of ywere used.

17
Figure 15 compares the performance of event tagging and of jet tagging for Zevents.
As can be seen, very strong suppression of background (down to 10−3level) can be
achieved with event tagging.
4.6 Equalised Tagging
Physics analyses at the edge of detector capabilities, like the search for a Higgs boson,
demand extremely high performance of the b-tagging. The only way to achieve this
objective is to expand the set of discriminating variables. But adding a new variable in
the combining relation (16) becomes more and more difficult with the growth of their
number due to the increasing influence of correlations among them.
However, the combined method can be modified to include correlated variables. The
main idea of the combined method which guarantees optimal tagging for non-correlated
variables consists in assigning the same value of the tagging variable to different events
having the same likelihood ratio for background to signal. As described below, the con-
sistent application of this principle while extending the set of discriminating variables
gives a desirable improvement of the tagging performance. The simplest way to explain
this approach is to consider a particular example, obtained from simulation samples and
presented in figure 19.
The upper plot in fig. 19 shows the simulated distributions of charged multiplicity Nch
in b-jets from the process e+e−→HZ and in light quark jets from e+e−→W+W−. The
latter process presents the main background for the SM Higgs search, and is suppressed
mainly by the b-tagging. The fact that these two distributions are different implies that
it is useful to include this variable in the tagging. The lower plot in fig. 19 shows the
ratio R(W+W−/HZ) of the number of light quark jets from the e+e−→W+W−process
to that of b-jets from e+e−→HZ in the simulation, as a function of the tagging variable
Xjet:
Xjet =−log10 yj et,(22)
where yjet is defined by equations (16-17). Two subsamples of events with Nch <7
and Nch >19 are considered separately. As can be clearly seen, for the same value of
Xjet the ratio R(W+W−/H Z) in the two subsamples is different. Events with the same
value Xjet are thus not equivalent; in one subsample they will contain more background
contamination than in the other. To restore their equivalence, the variable Xjet should be
modified in such a way that all events with the same value of X′
jet in different subsamples
will have the same ratio R(W+W−/HZ). Due to the equivalence principle formulated
above, such a modification should give better tagging. Technically, equalising of Xjet is
achieved by a linear transformation:
X′
jet =A·Xj et +B, (23)
assuming that the dependence of R(W+W−/H Z) on Xj et in each case can be approx-
imated by an exponential, as shown in fig. 19. The coefficients Aand Bare different
for each subsample; their calculation using the parameters of the exponential functions
is straightforward.
Including a new independent variable xnew in the tagging using (16) is equivalent to
the transformation X′
jet =Xj et −log10 ynew , where ynew =fbgd (xnew )/f sig(xnew ), i.e. it is
a particular case of (23). Such a simple transformation cannot be used for Nch because
of its strong correlation with other discriminating variables, which is reflected in the

18
significantly different slopes of the lines in fig. 19. Instead, the transformation (23)
works reasonably well.
A practical application of the equalising method is to the Standard Model Higgs boson
search. A set of additional discriminating variables is defined for each jet of the event.
For each new variable, jets are classified in 3 to 5 subsamples. For example, for Nch
these subsamples are: Nch <7; 7 ≤Nch <12; 12 ≤Nch <20; Nch ≥20. For
each subsample the transformation (23) is applied independently and the new tagging
variable X′
jet is computed. The parameters of the transformation are determined from
the condition that the dependence of R(W+W−/HZ) on the modified X′
jet becomes the
same for all subsamples. The variables are included in the tagging sequentially. For each
new variable, the X′
jet obtained at the previous step is used. As before, the global event
b-tagging variable Xevt is defined as the sum of the two highest X′
jet values among all jets
in the event.
The additional variables included in the b-tagging using this equalising method reflect
mainly kinematic properties of b-quarks. They are: the polar angle of the jet direction;
the jet energy and invariant mass; the charged multiplicity of the jet; the angle to the
nearest jet direction; and the number of particles with negative IP.
Returning to the example of Nch, fig. 20 shows that equalising over this variable
improves the suppression of the e+e−→W+W−background. As can be seen from
fig. 19, the largest difference between subsamples with different Nch is observed at low
Xjet values, while the background suppression at high Xjet is almost the same. The main
improvement from the equalising procedure can thus be expected for the low purity / high
efficiency tagging, corresponding to low Xjet values. Exactly such behaviour is observed in
fig. 20: including Nch gives almost no improvement for the region of strong background
suppression. However, equalising the b-tagging for the complete set of variables given
above suppresses the e+e−→W+W−background by an extra factor of more than 2 over
a wide range of e+e−→HZ efficiency. This additional suppression is important for the
Higgs boson search since it results in a sizable increase of its detection sensitivity.
The same equalisation procedure was applied for the e+e−→hA channel when both
Higgs bosons decay into b¯
b, which is the dominant channel with BR larger than 90% at
LEP2 energies. A new XhA
jet was constructed with the condition that all events with the
same value of XhA
jet in different subsamples will have the same ratio R(W+W−/hA). The
XhA
jet variable was used in the search of the hA 4b channel as described in section 6.5.
4.7 Different Ways of Combining Variables
As can thus be seen, for combining the separate variables that are relevant for b-
tagging, three different methods have been used :
•The IPs of the different tracks are combined by constructing the lifetime probability
P+from the probabilities for the significance values of the various tracks (see Section
3.5);
•For the different variables contributing to the ‘combined tag’, a likelihood ratio
method is used, as described in Section 4.1;
•For extra variables, the ‘equalisation’ method of Section 4.6 is used.
To some extent these differences are a result of the historical evolution of our b-
tagging algorithms, but there is some underlying logic to these differences. Thus the
likelihood ratio method is guaranteed to give the optimal signal/background ratio even for
correlated variables (assuming of course that the simulation accurately describes the data,

19
including the correlations). However, the method is much simpler when the variables are
uncorrelated, and this is how the likelihood ratio method was used in ‘combined tagging’.
This could have been used for combining the individual IPs, since the error corre-
lations between tracks are small. However, it would have been necessary to produce
signal/background probability ratios separately for each class of track (i.e. for each pat-
tern of hits in the VD). We preferred to use the lifetime probability, where instead the
tuning was performed separately for the different track classes.
Finally, for the Higgs search, extra variables were included to improve the b-tagging
performance. Some of these had significant correlations with those already used, so they
could not simply be added as extra variables in an extended combined tagging approach.
This led instead to the ‘equalised tagging’.
5 Modelling and Tuning of Mass-related Parameters
The agreement between data and simulation is sensitive to the modelling of the physics
in the event generator, and to the tuning of its parameters. A detailed description of the
physics model in the main generator used by DELPHI at LEP can be found in [16]. The
strategy adopted for the parameter tuning and its corresponding results can be found
in [17]. In this section, two aspects of the modelling are mentioned, which are specially
relevant in the context of b-tagging, and which have been investigated recently [18, 19]:
the modelling of the rate of gluons radiated off b-quarks relative to light quarks, and
the probability of secondary b-quark production through gluon splitting. Both quantities
affect the description of the dependence of Rbon the jet multiplicity (and on event shape
variables), and depend critically on the way quark mass parameters are introduced in the
treatment of the quark fragmentation and subsequent hadronization used in the generator.
They are important for several of the measurements in Section 6, particularly those
involving the analysis of multi-jet b-tagged events, such as the measurement performed
at LEP1 of the running bquark mass at the MZenergy scale (see Section 6.4), and the
LEP2 Higgs boson search (see Section 6.5).
5.1 Treatment of Gluon Radiation off b-quarks
Discrepancies between simulation and data were observed, which could be attributed,
entirely or at least partly, to imperfect modelling of mass effects in the generator. As
an example, the Rbfraction evaluated separately for two and three jet events, using the
method described in Section 6.1, is illustrated in figs. 21, where JETSET version 7.4 [16]
was used for the simulation. Similar behaviour is observed in the comparison of two and
four jet events.
Because of their higher mass, b-quarks radiate fewer gluons than lighter flavours. This
results in fewer multi-jet events in the case of b-quarks. From kinematic arguments, the
suppression scales approximately as m2
b/(s·y), where mb,sand yare the bmass, the
square of the collision energy and the jet resolution parameter, respectively [20]. It is
observed explicitly in the value of Rbq
3, the double ratio of the 3-jet rate for band light
quarks,9used in the measurement of the running b-quark mass at the MZenergy scale
(see Section 6.4). Quantitatively the suppression is of order 5%.
In the original JETSET prescription, used up to version 7.3, mass effects were ignored al-
together, both in the parton shower evolution describing the fragmentation of the quarks,
9Rbq
3is defined as the ratio of the b-quark and light quark rates in 3-jet events, divided by the corresponding flavour
ratio for events with any number of jets

20
and in the 3-parton matrix element used to correct the first emissions of quarks and anti-
quarks in the shower. The phase space treatment did include masses, however, and
induced a large suppression of radiation from the bquark. In version 7.4, and later in
PYTHIA versions up to 6.130, an intermediate “improvement” was introduced, in that
matrix element expressions incorporating quark masses were now used in the matching
procedure. The suppression of the radiation resulting from this intermediate treatment,
which was in place during much of the LEP period, was however exaggerated by as much
as a factor of 2, and resulted in the largest discrepancy with the data [18, 19]. Starting
with PYTHIA version 6.130, and up to version 6.152, mass effects were also introduced in
the shower evolution through a correction to the expressions of the probabilities of the
first branchings of each quark. From PYTHIA version 6.153, a fully consistent treatment
is available, including a massive treatment of all branchings in the shower, now taking
into account in the specification of the matrix element the nature of the couplings of the
source (vector, axial,...) decaying into quarks, as well as the possibility of unequal quark
masses (as in the case of W→c¯s). Considerable overall improvement was achieved in
the description of both b-tagged 3– and 4–jet rates, thanks to these developments [18,19].
5.2 Treatment of Gluon Splitting to b-quark Pairs
Secondary b-quark pair production from gluon splitting can also result in b-tagged
multi-jet events. The corresponding rate is small but is poorly known both theoretically
and experimentally. This implies an uncertainty in the predictions, particularly of the
b-tagged 4-jet rate at LEP2 energies.
Measurements by LEP and SLD collaborations at √s=MZgive gb¯
b= (0.254 ±
0.051)% [21], where gb¯
bis defined as the fraction of hadronic events containing a gluon
splitting to a b¯
bpair. This is consistent with the best theoretical estimates, which are
around 0.2% [18], with relative uncertainties due to unknown sub-leading logarithmic
corrections, which may be as large as 30%.
The rate predicted by Monte Carlo generators based on parton shower methods is also
sensitive to the treatment of sub-leading and kinematic effects in the shower evolution.
While the original JETSET and PYTHIA prescription resulted in only 0.15%, since version
6.131 a set of new options has been introduced which bring this rate closer to the measured
values [18]. Two of these options, which almost exactly double the original rate, have been
recommended [18] and are used in the latest simulations at LEP2 energies10 . The first
of these options (MSTJ(44)=3) uses the mass of the virtual gluon involved in a splitting
to define the scale m2
g/4 relevant for αs, the strong coupling constant, rather than the
default p2
Tprescription used for other types of branchings in the shower evolution. The
second option (MSTJ(42)=3) reduces the conditions on coherence in the emissions, in the
case of gluon splittings into heavy quark pairs, by introducing a mass correction into the
angular criterion used to restrict the successive branchings in the shower.
The impact on the b-tagged 4-jet rate at LEP2 is best illustrated in the context of the
Higgs search or of the measurement of Zboson pair production. At LEP2 energies the
rate of gluons which can split into bquark pairs is less suppressed by kinematics than
at LEP1. For instance at 189 GeV it is as large as 0.4% using the original JETSET and
PYTHIA prescription. In a subsample of events enriched with 4-jet events, it can reach
levels near 1% depending on the criterion used on the jet resolution parameter. With
the new options described above, these values are roughly doubled. The effect of this
doubling on the Higgs search was studied by comparing the numbers of events predicted
10For simulations performed with versions of PYTHIA prior to 6.131, a re-weighting procedure was used to increase the
g→b¯
brate by a factor of about 2.

21
to be selected, when assuming the default value for the rate of gluon splittings into b
quark pairs or the doubled one. The relative difference between these two numbers is
about 2.5%; it varies slightly with the b-tagging cut but does not exceed 5%. It was
taken into account in the final evaluation in this channel (see Section 6.5 and references
therein).
6 Physics Applications
In this section, some analyses involving b-tagging are described. The aim is not to
present the physics results, which have already been published, but rather to illustrate
how b-tagging works in practice. The extent to which uncertainties in tagging influ-
ence the final results is also mentioned. Much more detail, including the estimation of
systematics, can be found in the published papers.
6.1 Measurement of Rbat the Z
One of the most challenging measurements at LEP1 is the determination of Rb, the
branching ratio for Zhadronic decays into b-quarks. All accurate measurements of Rb
use the so-called double tag method. This compares the fractions of events in which
there is a b-tag in a single hemisphere with those in which both hemispheres are tagged.
It allows the extraction from the data of both Rband the efficiency ǫbfor tagging a
hemisphere as coming from a b-quark. We thus do not have to rely on the simulation for
the calculation of this important quantity. The small background mis-tag rates, ǫcand
ǫuds, and the correlation between hemispheres, ρb, are taken from the simulation. The
tracks are separated into two hemispheres by the plane perpendicular to the thrust axis.
The highest b-tagging value Xjet =−log10 yjet (see eqn. (18)) of any jet in the given
hemisphere is taken as the hemisphere tag.
The correlation ρballows for the fact that there are small differences between the
overall hemisphere b-tagging efficiency, and the efficiency for tagging a hemisphere if the
other one has already been tagged. These correlations arise, for example, from the fact
that at the Z, hadronic events tend to consist of back-to-back jets; if one jet is at large
positive cosθwhere the tagging efficiency is lower (see fig. 3), then the other jet is likely to
be at large negative cosθ, again with lower efficiency; thus the efficiencies are correlated.
The systematic uncertainty on ρbwas estimated by comparing data and simulation for
various kinematic variables that were sensitive to the separate contributions to ρb.
In particular, it was found that a large correlation arose from the use of a common
PV for the whole event; if the PV was badly measured as being closer to the SV in one
hemisphere, then the IP values in that hemisphere would all be systematically reduced
in magnitude, while those in the opposite hemisphere would be increased. This was over-
come by determining a separate PV for each hemisphere of the event. This modification
slightly reduced the flavour discrimination power of the algorithm, and hence increased
the statistical error, in exchange for a large decrease in the correlation and a smaller
systematic error.
Achieving high accuracy for Rbrequires the following:
•the b-tag must reach very high efficiency to reduce the statistical error: δRb∼1/ǫb;
•at the same time the b-tag must have high purity to reduce the systematic errors
coming from our knowledge of the background: δRb∼ǫxRx/ǫb, where x=qor c;

22
•there must be excellent agreement between data and simulation to reduce the sys-
tematic errors due to the modelling of the detector resolution, and because there are
quantities taken from the simulation and not measured directly in the data.
In the DELPHI Rbmeasurement, both the crucial high-purity b-tag in the “multivari-
ate” analysis [14], which finally gave the best precision, and the “combined b-tag” analysis
used the combined hemisphere tag described earlier (see Section 4). This required the
presence of a SV and included the hemisphere lifetime probability Pj, the SV mass Ms,
the charged energy fraction Xch
s, and the rapidities of the tracks at the SV. The missing
transverse momentum Pt
sand the lepton transverse momentum Pt
lwere not used.
The sources of the systematic error are our knowledge of b-hadron, charm- and light-
quark physics (such as lifetimes, decay modes and multiplicities) and our understanding of
the detector resolution. The first contribution is minimised by measuring the b-efficiency
from the data itself and by reducing the charm- and light-quark mis-tag rates to the
minimum possible so as to give a very pure b-tag. The second contribution is minimised
by having good agreement between data and simulation for the detector resolution.
The high statistical precision of the result is mainly due to the high performance of
the DELPHI b-tag: at 98.5% hemisphere b-purity, the hemisphere b-efficiency is 29.6%,
while the mis-tag efficiencies ǫc= 0.4% and ǫuds = 0.05%.
The smallness of the systematic error comes specifically from the fact that the con-
tribution from the detector resolution understanding is very small. First, the DELPHI
vertex detector has three layers of silicon detectors allowing better pattern recognition
than for a detector with only two layers. The design of the detector is such that the
intrinsic IP resolutions in both the Rφ and Rz components are good – 27 and 39 µm
respectively – and consequently also the precision of the primary and secondary vertex
positions (see Sections 3.2 and 4.2). Secondly, the detector IP resolution is tuned with
high accuracy, as described in section 3.6, resulting in a good agreement between data and
simulation (see fig. 13(b)). As a consequence the error coming from our understanding
of the detector resolution amounts to only 20% of the total error.
In summary the performance of the b-tag and the understanding of the detector resolu-
tion result in very good stability of the Rbmeasurement as a function of the b-efficiency as
shown in fig. 22; the highest and lowest efficiencies shown of 44.0% and 21.0% correspond
to b-purities of 91.6% and 99.4% respectively. Thus, a stable Rbresult was obtained while
the background contribution varied by more than a factor of 10. The total relative error
was only 0.4%.
6.2 R4b, the Rate of Events with 4 b-quarks at the Z
Four bjets are produced predominantly when, in an event with a bpair, a gluon is
radiated from one of the quarks and itself produces another bpair. This analysis thus
gives information on the gb¯
bcoupling.
The high purity and efficiency of the tagging method, together with the good agree-
ment between data and simulation, allowed DELPHI to measure for the first time the
rate of Zevents with 4 b-quarks in the final state [22]. R4bhas been measured to be (6.0
±1.9 (stat)±1.4 (syst)) ×10−4at a signal efficiency ǫ4b=(3.16±0.11)%. The analysis
required 3 jets identified as coming from b-quarks. This means that the b-efficiency enters
to the third power, demanding a very high efficiency of a tight b-tag. The high purity of
the tag is required in order to suppress the background from gluon splitting into c-quarks,
that is a factor of 10 higher than the splitting into b-quarks. Thus, the measurement re-
lies on the b-tagging performance and data/MC agreement in the b-tagging of the third

23
jet, sorted by decreasing b-tag value, see fig. 23. The uncertainty coming from the b-tag
amounts to only 6% of the total systematic error and is determined mainly by the IP
resolution description.
This analysis used the b-tag algorithm of Section 6.1, except that if no SV was found,
the jet lifetime probability Pjwas used by itself.
6.3 Measurement of the b-hadron Charged Multiplicity
The good agreement between data and simulation achieved by the tuning of the track
resolution allowed DELPHI to measure with very high precision the charged multiplicity
nBof weakly decaying b-hadrons [23]. The basis for the measurement is the determination
of the number of tracks in a b-jet which come from the SV rather than from the PV. In
the hemisphere opposite to the b-tagged one, the difference
N+−=n+−n−(24)
is computed, in which n+and n−are the numbers of tracks with positive and with
negative IP respectively. The quantity N+−is obtained as a function of the b-tagging
purity and the value of nBis extracted by comparing N+−from data and simulation,
extrapolated to the limit of 100% b-purity.
The result was nB= 4.97 ±0.03 ±0.06. The measurement reaches 1.3% precision, due
to the good understanding of the IP resolution, to the efficient method for determining
the sign of the IP (see Section 3.3) and to the precision of the VD alignment (see section
2.2). The tracking efficiency is 99±1%(syst), its uncertainty dominates the systematic
error on nB.
This analysis used the same b-tag algorithm as the previous analysis.
6.4 Measurement of the Running b-quark Mass at MZ
The bquark mass determination at the MZscale has been performed by DELPHI
by measuring the Rbq
3observable, as defined in Section 5.1. Two different jet-finding
algorithms, Durham [24] and Cambridge [25], were used to reconstruct the jets. Special
features of this analysis in connection with the flavour tagging performance of DELPHI
are:
•band qinitiated events are selected using the same technique,
•the efficiency versus purity working points are chosen so as to minimise the total
error on the result (including effects from corrections and biases).
The directly measured observable, Rbq −meas
3, had to be corrected for detector accep-
tance effects, for kinematic biases introduced by the tagging procedure and for the
hadronization process in order to get the observable at the parton level, Rbq−par
3[26].
This quantity was then compared with theoretical predictions based on ‘Next to Leading
Order’ analytic calculations [20] to evaluate the b-quark mass at the MZenergy scale.
In the original analysis [26], q- and b-quark initiated events were selected by the
lifetime-signed IPs of charged particles in the event (see Section 3.5). In more recent
versions of the analysis, the combined tagging technique of Section 4 has also been used.
The flavour composition of the samples tagged as q-quark and as b-quark by the two
methods are shown in Table 1.
The magnitude of the corrections applied in each of the two b-tagging techniques is
illustrated in fig. 24, where the corresponding Rbq−meas
3observables are shown, using

24
Method Tagged Sample Actually q(%) Actually c(%) Actually b(%)
IP q85.8 12.6 1.7
IP b5.0 15.3 79.7
Comb q82.0 15.5 2.5
Comb b4.3 10.4 85.4
Table 1: Flavour compositions of the samples tagged as q-quark and b-quark events for
each tagging method.
simulated DELPHI data and the DURHAM jet finding algorithm, together with the
parton-level one, Rbq−par
3, obtained with PYTHIA 6.131. For yc= 0.02, the corrections are
10% for both techniques, although in opposite directions.
For the simulation the same corrected result is (obviously) obtained, but for real data
this is not the case. This difference between the two techniques arises mainly from the
imperfect modelling of the physics processes affecting the fragmentation and decay of
heavy and light quarks. Half of this difference is taken as the systematic uncertainty
associated with this measurement. The error induced by the tagging uncertainties is
in the range 0.3% to 0.4%, compared with the total error of order 1% on the flavour
independence of the strong coupling constant. In terms of the running b-quark mass,
these errors correspond to 150 and 500 MeV respectively.
6.5 Higgs Searches in 4-jet Topology
One of the main topics at LEP2 energies has been the search for the SM Higgs boson,
both in the Standard Model (SM) and in the Minimal Super-Symmetric Model (MSSM).
Here the approach used in the dominant 4-jet channel is outlined.
Radiative production from a virtual Z e+e−→Z∗→HZ is (in principle!) the main
Higgs process at LEP2 and is referred to as Higgsstrahlung. The mass of the Higgs boson
is at present unknown, but for a given mass its other properties are determined from the
SM. The Higgs boson couples to massive fermions and to the W±and Zbosons.
The predominant decay mode for the SM Higgs in the mass range of interest for LEP2
searches is expected to be to pairs of bquarks with a branching ratio ranging from 87%
to 80% with increasing Higgs mass. The same decay modes are dominant for hand Afor
many choices of values of the parameters in the MSSM, in particular for tanβ > 1. The
identification of bjets and rejection of non-bjets is the most important ingredient in the
majority of analyses designed to search for the neutral Higgs boson.
The four-jet final state includes the Higgs boson decaying to b¯
b, and also in principle
to q¯qor gg. It is characterised by a large amount of visible energy. As the Higgs boson
decays mainly to bquarks, when the Zalso decays to b¯
bthe event will contain 4 bjets.
If instead the Zdecays to other quark pairs, the topology will again be 4 jets, but with
only two of them due to b’s.
The main backgrounds are two-fermion processes e+e−→q¯q(γ), and four fermion
processes involving W+W−and ZZ. Pair production of W±can result in cjets, but
only very rarely in bjets. The Z Z is an irreducible background if the masses of the
Higgs boson and of the Zare close, and the Zdecays to b¯
b. The cross-sections of the

25
background processes are much higher than that for the Higgs production. At the highest
LEP2 energies (around 208 GeV) and for mH= 114 GeV/c2,σHqq = 0.072 pb while
σ4f= 19 pb and σ2f= 78 pb.
In searches for the Higgs bosons at LEP2 in DELPHI, the various differences between
bjets and light quark jets were accumulated in a single variable Xjet defined for each
jet, as described in Section 4. Extra variables which help discriminate between the
signal and background were included in the construction of the equalised tag (see Section
4.6). Including these extra variables in the tagging algorithm significantly improves the
rejection of the light quark background.
The b-tagging value Xev of the event in the search for the SM Higgs boson is defined
as the maximum b-tagging value for any di-jet in the event, computed as the sum of the
corresponding jet b-tagging values. In figure 25 the distribution of this equalised b-tagging
variable is shown after the common four jet preselection [27] where good agreement
between data and background simulation can be observed.
In the top part of figure 26 the performance of combined and equalised methods are
compared for a SM Higgs boson mass of 114 GeV/c2. As an example using only the
b-tagging variable, for a signal efficiency of 40% the q¯q(γ) contribution is reduced to
5.6% using combined b-tagging, wheras it is even more strongly suppressed to 4.3% using
equalised b-tagging. The W W component is reduced twice as much using equalised as
compared with combined b-tagging.
In the bottom part of figure 26, the performance of the hA equalised b-tagging is shown
in the hA →4bchannel and compared with the performance of combined b-tagging. The
presence of four b-jets in the signal makes the analysis of the hA →4bchannel different
from the HZ case, where in most of the cases only two b-jets are present. The event
b-tagging value XhA
ev for the Higgs boson search in the hA →4bchannel is defined as the
minimum b-tagging value for any di-jet in the event and is computed as the sum of the
corresponding jet b-tagging values. As can be seen, the application of the hA equalised
b-tagging improves significantly the performance of the hA →4bchannel selection.
As an example using only the XhA
ev b-tagging variable, for a signal efficiency of 50%
the q¯q(γ) mistag rate is 0.8% using combined b-tagging, while it is reduced to 0.5% using
equalised b-tagging. The W W efficiency is reduced from 0.1% to 0.06% when changing
from combined to equalised tagging. The Z Z efficiency is also reduced from 3.7% to
3.3%.
In the search for the SM Higgs boson in the four jet channel, the b-tagging variable was
combined with another set of discriminant variables [27] using an artificial neural network.
The final confidence level estimation is calculated using two-dimensional information,
where one dimension is the neural network output and the other is the reconstructed
Higgs boson mass.
b-tagging is also used in the selection of the Higgs di-jet [27] from among the 6 possible
Higgs di-jet candidates in a 4-jet event. The proportion of correct matchings for the Higgs
di-jet, estimated in simulated signal events with 114 GeV/c2mass, is around 53% at pre-
selection level, increasing to above 70% after the tight selection cut (see table 1 of [27]),
while keeping a low rate of wrong pairings for ZZ background events.
7 Conclusion
The standard approach used by DELPHI for tagging b-hadrons has been described.
By using not only the track impact parameters, which are sensitive to the longer lifetimes
of hadrons containing b-quarks, but also other kinematic information related to secondary

26
vertices, track rapidities and any leptons, the efficiency/purity has been improved. For
Zevents, a purity of 98.5% for b-jets was achieved for an efficiency of 30%. Such high
purity was required for the accurate measurement of Rbat the Z.
The tagging algorithm can also be applied to complete events, rather than just to
single hemispheres. For the SM Higgs search at LEP2, the sum of the two largest b-tag
variables for jets in the event was used. High efficiency b-tagging was required in order to
extract any possible H→b¯
bdecays from the large backgrounds. For a signal efficiency
of 60%, a rejection factor of 140 for the W+W−background was achieved.
In contrast, the algorithm could be used in an anti-tagging mode, to select jets from
light-quarks. This was used (together with conventional b-tagging), to compare the 3-jet
rates for b- and for light quarks. This is sensitive to the b-quark mass.
For these and for other physics processes, it was crucial to have an efficient, well
understood procedure for tagging bquarks. This resulted in systematic errors being kept
to a minimum, and enabled many significant measurements to be performed.
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), 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 Mati`ere, CEA, France,
Bundesministerium f¨ur 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)
JNICT–Junta Nacional de Investiga¸c˜ao Cient´ıfica e Tecnol´ogica, 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 Natural Science Research Council,
Particle Physics and Astronomy Research Council, UK,
Department of Energy, USA, DE-FG02-01ER41155.
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[27] DELPHI Collaboration, Phys. Lett. B499 (2001) 23.

28
Figure 1: Schematic cross sections of the Double Sided Vertex Detector in (a) the trans-
verse (Rφ) view and (b) a three-dimensional view. Dimensions are in cm.

29
θ>21°
Inner Layer
R=92 mm
15°<θ<25°
Pixel I
Pixel II
12°<θ<21°
2 Ministrip Layers
Outer Layer
R=106 mm
θ>23° Closer Layer
R=66 mm
θ>24°
10°<θ<18°
Figure 2: Schematic view of the Silicon Tracker

30
DELPHI
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
SiT
DSVD
cosΘthrust
efficiency
Xev > 0
Figure 3: Selection efficiency of Z→b¯
bevents versus cos Θthrust using the combined event
b-tagging variable Xev >0 for the Silicon Tracker and the Double Sided Vertex Detector.
(Xev is defined in Section 4.1.) The extra coverage provided by the Silicon Tracker in the
forward direction is clearly visible.

31
0
25
50
75
100
125
150
1 10
0
50
100
150
1 10
0
50
100
150
1 10
Figure 4: The Rφ IP uncertainty as a function of p sin 3
2θ(upper plot), the Rz IP uncer-
tainty as a function of p sin5
2θ(middle plot) and the Rz IP uncertainty as a function of
pfor tracks with θ= [80◦: 100◦], i.e. perpendicular to the beam direction (lower plot).
The data are from the Double Sided Vertex Detector at the Z. The curves are parame-
terisations of a constant intrinsic resolution term and a momentum-dependent multiple
scattering contribution. Momenta are in Gev/c.

32
PO
e
P
V
R
R
C
PC
C
C
|P − P | cos
d
ε
u
Particle Trajectory
θ
POθ
Vz
Particle Trajectory
O
ε.
d = − (e V)
O
PV
O
PV
φ
R
Rφ
componentR
φ
φ
φ
φ
z
.
θd = + cot (u V) − V
Rz component
Rz εRz
εRz
dRz
θ
O.
|P − P | = (u V)/sin
Figure 5: Definition of Rφ and Rz IP components. −→
uis a unit vector along the track
direction, and −→
eis another unit vector in the Rφ plane, perpendicular to −→
u.−→
Vis a
vector from the origin Oto the primary vertex PV. P0and PCare the points of closest
approach in the Rφ plane of the track trajectory to Oand to PV respectively. The
diagrams show the projections onto the Rφ and Rz planes. The IP components are dRφ
and dRz, while εRφ and εRz are the corresponding components from P0to the origin.

33
0
0.02
0.04
-0.2 -0.1 0 0.1 0.2
SV direction
Jet direction
θ - θtrue [rad]
0
0.02
0.04
0.06
0.08
-0.2 -0.1 0 0.1 0.2
φ - φtrue [rad]
Figure 6: Distributions of the difference between reconstructed and generated directions
of b-hadrons for events with a reconstructed secondary vertex, for simulated Zevents.
The Bdirection is defined as the direction from the primary to the secondary vertex
(solid line) or as the jet direction (dashed line). Especially in φ, the definition using the
secondary vertex gives a better description of the Bdirection.

34
10
10 2
10 3
10 4
10 5
0 10 20 30 40
Rφ Significance
Negative
Positive
Figure 7: Distributions of positive and negative Rφ significances in data Zhadronic
decays. The excess of tracks with large positive significance is due to long-lived particles.
0
200
400
600
800
1000
1200
x 10 3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Track Probability
Z0 → bb
–
Z0 → cc
–
Z0 → qq
– (q=u,d,s)
Figure 8: Simulated distributions at the Zof the Rφ track IP probabilities for different
quark flavours, for tracks with positive lifetime-sign IPs.

35
10 4
10 5
10 6
0 0.2 0.4 0.6 0.8 1
Positive lifetime (all events)
Positive lifetime Z0 → bb
–
Negative lifetime (anti-b tagged)
Lifetime probability
Figure 9: Distributions of positive and negative lifetime probabilities (P+
Nand P−
Nre-
spectively) for simulated Zhadronic events.
10 -2
10 -1
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
b-tag efficiency
1 - Purity
Event tagging
b-tag efficiency
1 - Purity
Jet tagging
Figure 10: Background suppression in simulated Zhadronic events using lifetime tagging.
The efficiency is the fraction of b-jets that are tagged as coming from b-quarks, while the
purity is the fraction of tagged jets that are really from b-quarks.

36
10 2
10 3
10 4
10 5
0 5 10 15
dRφ/σRφ
entries
a
10
10 2
10 3
10 4
10 5
0 5 10 15
dRz/σRz
entries
b
0
0.5
1
1.5
2
2.5
3
0 5 10 15
dRφ/σRφ
RD/MC
c
0
0.5
1
1.5
2
2.5
3
0 5 10 15
dRz/σRz
RD/MC
d
Figure 11: a) and b) The Rφ and Rz significance distributions for tracks with negative
IP. The points with errors are real data, the histogram is simulation. c) and d) The
ratios of these distributions (data divided by simulation).

37
10 2
10 3
10 4
10 5
0 5 10 15
dRφ/σRφ
entries
a
10
10 2
10 3
10 4
10 5
0 5 10 15
dRz/σRz
entries
b
0
0.5
1
1.5
2
2.5
3
0 5 10 15
dRφ/σRφ
RD/MC
c
0
0.5
1
1.5
2
2.5
3
0 5 10 15
dRz/σRz
RD/MC
d
Figure 12: a) and b) The Rφ and Rz significance distributions for tracks with negative
IP after the tuning procedure. The points with errors are real data, the histogram is
simulation. c) and d) The ratios of these distributions (data divided by simulation).
The improvement resulting from tuning is clearly visible.

38
0.6
0.8
1
1.2
0 2 4 6 8 10
Tuned resolution
Non-tuned resolution
-log10PE
+
Data/Simulation
a
0.6
0.8
1
1.2
-4 -2 0 2 4 6
Xev
Data/Simulation
b
Figure 13: The integrated data to simulation ratio of the fraction of selected hemispheres
as a function of the cut on the b-tagging variable for a) the lifetime tagging variable
P+
E, calculated using all positive lifetime IP tracks in an event (see Section 3.5) and
b) combined tagging variable Xev(see Section 4), with tuned (full line) and non-tuned
(dashed line) track resolution.

39
0
0.02
0.04
0.06
0.08
0.1
0 0.5 1 1.5 2 2.5 3
Ms [GeV/c2]
a
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.2 0.4 0.6 0.8 1
Xs
ch
b
c-quark
b-quark
0
0.01
0.02
0.03
0.04
0.05
0.06
-1.5 -1 -0.5 0 0.5 1
log10(Pt
s[GeV/c])
c
0
0.01
0.02
0.03
0 1 2 3 4 5
Rs
tr
d
Figure 14: Distributions of discriminating variables for b- and c- quark jets for simulated
Zhadronic events. a) Mass of particles in SV. b) Fraction of charged jet energy included
in SV. c) Transverse momentum at SV. d) Rapidity for each SV track.

40
10 -3
10 -2
10 -1
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
b-tag efficiency
1 - Purity
b-tag efficiency
1 - Purity
b-tag efficiency
1 - Purity
Lifetime jet tagging
Combined jet tagging
Combined event tagging
Figure 15: Background suppression in Zhadronic events using combined b-tagging.
0
2000
4000
6000
8000
10000
12000
14000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
uds-quarks
c-quark
b-quark
data
pt
l (GeV/c)
Figure 16: Transverse momentum distribution of identified leptons with respect to the jet
from which they originate, measured in hadronic Zdecays at LEP1. The contributions
from light quarks, c-quarks and b-quarks are added and compared to the data.

41
0
0.02
0.04
0.06
-1 0 1 2
Jets with lepton
Jets without lepton
log10(Pt
s[GeV/c])
Figure 17: Distribution of log10(Pt
s) for jets with (solid line) and without (dashed line)
leptons.

42
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
pt
l (GeV/c)
fq(pt
l)/fb(pt
l)
Z0 1994
fit
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
pt
l (GeV/c)
WW/hA 1998
fit Z0fit Z0
fq(pt
l)/fb(pt
l)
Figure 18: The upper figure shows the ratio of the numbers of light-quark and b-quark
events as a function of the lepton transverse momentum (dots), as extracted from sim-
ulated hadronic Zdecays. The line is the fit to that ratio. The lower figure shows the
same ratio, extracted from a simulated Higgs signal and WW background at LEP2. The
line is the Zfit.

43
DELPHI
0
0.025
0.05
0.075
0.1
0 10 20 30 40
b-jet in e+e- → H Z
u,d,s,c-jet in e+e- → W+W-
√s = 206 GeV
MH= 110 GeV/c2
Number of charged tracks in jet
10 -3
10 -2
10 -1
1
10
-2 0 2 4
Nch < 7
Nch > 19
-log10yjet
R(W+W-/H Z0)
Figure 19: Upper plot: Simulated distributions of the number of tracks in a b-jet from the
e+e−→HZ process and in a light quark jet from the e+e−→W+W−process. Lower
plot: the ratio R(W+W−/HZ) of the number of light quark jets from the e+e−→W+W−
process to that of b-jets from e+e−→H Z process in the simulation (arbitrary normali-
sation) as a function of −log10 yj et, shown separately for jets with less than 7 or greater
than 19 tracks. The lines in each case show the exponential fit of these rates.

44
DELPHI
10 -3
10 -2
10 -1
1
0.4 0.5 0.6 0.7 0.8 0.9 1
Standard b-tag
Standard b-tag and Nch
Equalized b-tag (all variables)
Efficiency e+e- → HZ0
Efficiency e+e- → W+W-
Figure 20: Mis-tagging efficiency for e+e−→W+W−versus e+e−→HZ selection
efficiency, as obtained from standard combined b-tagging, b-tagging equalised with respect
to Nch, and equalised b-tagging with the complete set of variables (see text for details).

45
Xjet
0.18
0.19
0.2
0.21
0.22
0.23
0.24
0.25
0 0.5 1 1.5 2 2.5 3 3.5
(Rb(data)-Rb(MC)+0.2172)3jets
(Rb(data)-Rb(MC)+0.2172)2jets
Xjet
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
0 0.5 1 1.5 2 2.5 3 3.5
(Rb(data)-Rb(MC)+0.2172)3jets
−−−−−−−−−−−−−−−−−−−−−−−−−−
(Rb(data)-Rb(MC)+0.2172)2jets
(Rb(data)-Rb(MC)+0.2172)2jets
(Rb(data)-Rb(MC)+0.2172)3jets
Figure 21: Comparison of the measurements of the Rbratio in 2 and 3 jet events at the
Z, as a function of the cut in the b-tagging variable Xjet . The simulation used JETSET
7.4.

46
0.21
0.215
0.22
Rb
DELPHI 94-95
0
0.001
0.002
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
b-efficiency
∆Rb
Total error
Data statistics
MC statistics
uds background
c background
Correlation
Figure 22: Stability of the Rbresult as a function of the b-tagging efficiency, for data
collected in 1994–5. The arrow shows the b-efficiency chosen for the final result.

47
DELPHI
10 -4
10 -3
10 -2
10 -1
-1 0 1 2 3 4 5 6
Xjet (first jet)
1/N dN/dXjet
10 -4
10 -3
10 -2
10 -1
-1 0 1 2 3 4
Xjet (second jet)
1/N dN/dXjet
10 -5
10 -4
10 -3
10 -2
10 -1
-1.5 -1 -0.5 0 0.5 1
Xjet (third jet)
1/N dN/dXjet
Figure 23: Distribution of the b-tagging variables for the first three jets, ordered according
to their b-tagging variable, for Zdata (dots) and simulation (histogram). The arrows
show the positions of the cuts used to select the bjets. The figure is from reference [22].

48
0.8
0.85
0.9
0.95
1
1.05
1.1
0 0.01 0.02 0.03 0.04 0.05
R3bq-meas IP b-tag
R3bq-meas Comb b-tag
DURHAM 94
Pythia 6.131
yc
R3
bq-meas
Figure 24: The Rbq−meas
3observable from simulated DELPHI data for the two tagging
techniques and the parton level Rbq−part
3obtained with PYTHIA 6.131. The Durham jet
finding algorithm is used.

49
Xev
Number of events
1
10
10 2
10 3
-4 -2 0 2 4 6
Xev
Data/Simulation
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-4 -2 0 2 4 6
Figure 25: Top: distribution of the equalised b-tagging variable for 4-jet events at
√s= 192 −210 GeV, data (dots) and simulation (solid line). Bottom: ratio of the
integrated tagging rates in data and simulation as a function of the cut in the equalised
b-tagging variable. The agreement between data and simulation is satisfactory.

50
10 -4
10 -3
10 -2
10 -1
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
HZ
WW
qq
–(γ)
ZZ
Efficiency for a 114 GeV/c2 Higgs boson
Mistag Rate
DELPHI
√s = 206.7 GeV
10 -4
10 -3
10 -2
10 -1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
hA
WW
qq
–(γ)
ZZ
Efficiency for a 90 GeV/c2 Higgs boson
Mistag Rate
DELPHI
√s = 206.7 GeV
Figure 26: Expected SM background mis-tag rates at √s= 206.7 GeV, as functions
of the signal efficiency for a Standard Model Higgs boson of mass 114 GeV/c2(top) and
MSSM Higgs boson of mass 90 GeV/c2and tan β= 20 (bottom) when varying the cut
on the equalised b-tagging variable (solid lines) and combined b-tagging variable (dotted
lines).