A Precise Measurement of the B+, B0 and Mean b-hadron Lifetime with the DELPHI Detector at LEP I

0.84 MB·English

by  The DELPHI Collaboration

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN–EP/2003-065
28 Mai 2003
A Precise Measurement of the
+ 0
B B
, and Mean b-hadron
4
0
0
Lifetime with the DELPHI
2

n
a Detector at LEP I
J

6
1
DELPHI Collaboration

1
v
5
2
0
1
0
4
0 Abstract
/
x
e
p- Final results from the DELPHI Collaboration on the lifetime of B+ and
e B0 mesons and the mean b-hadron lifetime, are presented using the data col-
h
lected at the Z0 peak in 1994 and 1995. Elaborate, inclusive, secondary ver-
:
v
texing methods have been employed to ensure a b-hadron reconstruction with
i
X good efficiency. To separate samples of B+ and B0 mesons, high performance
r neural network techniques are used that achieve very high purity signals. The
a
results obtained are:
τ = 1.624 0.014 (stat) 0.018 (syst) ps
B+
± ±
τ = 1.531 0.021 (stat) 0.031 (syst) ps
B0
τB+ = 1.060±0.021 (stat)±0.024 (syst)
τB0 ± ±
and for the average b-hadron lifetime:
τ = 1.570 0.005 (stat) 0.008 (syst) ps.
b
± ±
(Accepted by Eur. Phys. J.)
ii
J.Abdallah25, P.Abreu22, W.Adam51, P.Adzic11, T.Albrecht17, T.Alderweireld2, R.Alemany-Fernandez8,
T.Allmendinger17, P.P.Allport23, U.Amaldi29, N.Amapane45, S.Amato48, E.Anashkin36, A.Andreazza28, S.Andringa22,
N.Anjos22, P.Antilogus27, W-D.Apel17, Y.Arnoud14, S.Ask26, B.Asman44, J.E.Augustin25, A.Augustinus8, P.Baillon8,
A.Ballestrero46, P.Bambade20, R.Barbier27, D.Bardin16, G.J.Barker17, A.Baroncelli39, M.Battaglia8, M.Baubillier25,
K-H.Becks53, M.Begalli6, A.Behrmann53, E.Ben-Haim20, N.Benekos32, A.Benvenuti5, C.Berat14, M.Berggren25,
L.Berntzon44, D.Bertrand2, M.Besancon40, N.Besson40, D.Bloch9, M.Blom31, M.Bluj52, M.Bonesini29, M.Boonekamp40,
P.S.L.Booth23, G.Borisov21, O.Botner49, B.Bouquet20, T.J.V.Bowcock23, I.Boyko16, M.Bracko43, R.Brenner49,
E.Brodet35,P.Bruckman18,J.M.Brunet7,L.Bugge33,P.Buschmann53,M.Calvi29,T.Camporesi8,V.Canale38,F.Carena8,
N.Castro22, F.Cavallo5, M.Chapkin42, Ph.Charpentier8, P.Checchia36, R.Chierici8, P.Chliapnikov42, J.Chudoba8,
S.U.Chung8, K.Cieslik18, P.Collins8, R.Contri13, G.Cosme20, F.Cossutti47, M.J.Costa50, B.Crawley1, D.Crennell37,
J.Cuevas34, J.D’Hondt2, J.Dalmau44, T.daSilva48, W.DaSilva25, G.DellaRicca47, A.DeAngelis47, W.DeBoer17,
C.DeClercq2, B.DeLotto47, N.DeMaria45, A.DeMin36, L.dePaula48, L.DiCiaccio38, A.DiSimone39, K.Doroba52,
J.Drees53,8, M.Dris32, G.Eigen4, T.Ekelof49, M.Ellert49, M.Elsing8, M.C.EspiritoSanto22, G.Fanourakis11,
D.Fassouliotis11,3, M.Feindt17, J.Fernandez41, A.Ferrer50, F.Ferro13, U.Flagmeyer53, H.Foeth8, E.Fokitis32,
F.Fulda-Quenzer20, J.Fuster50, M.Gandelman48, C.Garcia50, Ph.Gavillet8, E.Gazis32, R.Gokieli8,52, B.Golob43,
G.Gomez-Ceballos41, P.Goncalves22, E.Graziani39, G.Grosdidier20, K.Grzelak52, J.Guy37, C.Haag17, A.Hallgren49,
K.Hamacher53, K.Hamilton35, J.Hansen33, S.Haug33, F.Hauler17, V.Hedberg26, M.Hennecke17, H.Herr8, J.Hoffman52,
S-O.Holmgren44, P.J.Holt8, M.A.Houlden23, K.Hultqvist44, J.N.Jackson23, G.Jarlskog26, P.Jarry40, D.Jeans35,
E.K.Johansson44, P.D.Johansson44, P.Jonsson27, C.Joram8, L.Jungermann17, F.Kapusta25, S.Katsanevas27,
E.Katsoufis32, G.Kernel43, B.P.Kersevan8,43, A.Kiiskinen15, B.T.King23, N.J.Kjaer8, P.Kluit31, P.Kokkinias11,
C.Kourkoumelis3, O.Kouznetsov16, Z.Krumstein16, M.Kucharczyk18, J.Lamsa1, G.Leder51, F.Ledroit14, L.Leinonen44,
R.Leitner30, J.Lemonne2, V.Lepeltier20, T.Lesiak18, W.Liebig53, D.Liko51, A.Lipniacka44, J.H.Lopes48, J.M.Lopez34,
D.Loukas11, P.Lutz40, L.Lyons35, J.MacNaughton51, A.Malek53, S.Maltezos32, F.Mandl51, J.Marco41, R.Marco41,
B.Marechal48, M.Margoni36, J-C.Marin8, C.Mariotti8, A.Markou11, C.Martinez-Rivero41, J.Masik12,
N.Mastroyiannopoulos11, F.Matorras41, C.Matteuzzi29, F.Mazzucato36, M.Mazzucato36, R.McNulty23, C.Meroni28,
W.T.Meyer1, E.Migliore45, W.Mitaroff51, U.Mjoernmark26, T.Moa44, M.Moch17, K.Moenig8,10, R.Monge13,
J.Montenegro31, D.Moraes48, S.Moreno22, P.Morettini13, U.Mueller53, K.Muenich53, M.Mulders31, L.Mundim6,
W.Murray37, B.Muryn19, G.Myatt35, T.Myklebust33, M.Nassiakou11, F.Navarria5, K.Nawrocki52, R.Nicolaidou40,
M.Nikolenko16,9, A.Oblakowska-Mucha19, V.Obraztsov42, A.Olshevski16, A.Onofre22, R.Orava15, K.Osterberg15,
A.Ouraou40, A.Oyanguren50, M.Paganoni29, S.Paiano5, J.P.Palacios23, H.Palka18, Th.D.Papadopoulou32, L.Pape8,
C.Parkes24, F.Parodi13, U.Parzefall8, A.Passeri39, O.Passon53, L.Peralta22, V.Perepelitsa50, A.Perrotta5, A.Petrolini13,
J.Piedra41, L.Pieri39, F.Pierre40, M.Pimenta22, E.Piotto8, T.Podobnik43, V.Poireau8, M.E.Pol6, G.Polok18,
P.Poropat†47, V.Pozdniakov16, N.Pukhaeva2,16, A.Pullia29, J.Rames12, L.Ramler17, A.Read33, P.Rebecchi8, J.Rehn17,
D.Reid31, R.Reinhardt53, P.Renton35, F.Richard20, J.Ridky12, M.Rivero41, D.Rodriguez41, A.Romero45, P.Ronchese36,
E.Rosenberg1, P.Roudeau20, T.Rovelli5, V.Ruhlmann-Kleider40, D.Ryabtchikov42, A.Sadovsky16, L.Salmi15, J.Salt50,
A.Savoy-Navarro25, U.Schwickerath8, A.Segar35, R.Sekulin37, M.Siebel53, A.Sisakian16, G.Smadja27, O.Smirnova26,
A.Sokolov42, A.Sopczak21, R.Sosnowski52, T.Spassov8, M.Stanitzki17, A.Stocchi20, J.Strauss51, B.Stugu4,
M.Szczekowski52, M.Szeptycka52, T.Szumlak19, T.Tabarelli29, A.C.Taffard23, F.Tegenfeldt49, J.Timmermans31,
L.Tkatchev16,M.Tobin23, S.Todorovova12, B.Tome22, A.Tonazzo29,P.Tortosa50,P.Travnicek12, D.Treille8,G.Tristram7,
M.Trochimczuk52, C.Troncon28, M-L.Turluer40, I.A.Tyapkin16, P.Tyapkin16, S.Tzamarias11, V.Uvarov42, G.Valenti5,
P.VanDam31, J.VanEldik8, A.VanLysebetten2, N.vanRemortel2, I.VanVulpen8, G.Vegni28, F.Veloso22, W.Venus37,
F.Verbeure2, P.Verdier27, V.Verzi38, D.Vilanova40, L.Vitale47, V.Vrba12, H.Wahlen53, A.J.Washbrook23, C.Weiser17,
iii
D.Wicke8, J.Wickens2, G.Wilkinson35, M.Winter9, M.Witek18, O.Yushchenko42, A.Zalewska18, P.Zalewski52,
D.Zavrtanik43,V.Zhuravlov16,N.I.Zimin16,A.Zintchenko16,M.Zupan11
1DepartmentofPhysicsandAstronomy,IowaStateUniversity,AmesIA50011-3160, USA
2PhysicsDepartment,UniversiteitAntwerpen,Universiteitsplein1,B-2610Antwerpen, Belgium
andIIHE,ULB-VUB,Pleinlaan2,B-1050Brussels,Belgium
andFacult´edesSciences,Univ. del’EtatMons,Av. Maistriau19,B-7000Mons,Belgium
3PhysicsLaboratory,UniversityofAthens,SolonosStr. 104,GR-10680Athens,Greece
4DepartmentofPhysics,UniversityofBergen,All´egaten55,NO-5007Bergen,Norway
5DipartimentodiFisica,Universita`diBolognaandINFN,ViaIrnerio46,IT-40126Bologna,Italy
6CentroBrasileirodePesquisasF´ısicas,ruaXavierSigaud150,BR-22290RiodeJaneiro,Brazil
andDepto. deF´ısica,Pont. Univ. Cato´lica,C.P.38071BR-22453RiodeJaneiro,Brazil
andInst. deF´ısica,Univ. EstadualdoRiodeJaneiro,ruaS˜aoFranciscoXavier524,RiodeJaneiro,Brazil
7Coll`egedeFrance,Lab. dePhysiqueCorpusculaire,IN2P3-CNRS,FR-75231ParisCedex05,France
8CERN,CH-1211Geneva23,Switzerland
9InstitutdeRecherches Subatomiques, IN2P3-CNRS/ULP-BP20,FR-67037StrasbourgCedex,France
10NowatDESY-Zeuthen,Platanenallee 6,D-15735Zeuthen, Germany
11Institute ofNuclearPhysics,N.C.S.R.Demokritos,P.O.Box60228,GR-15310Athens,Greece
12FZU,Inst. ofPhys. oftheC.A.S.HighEnergyPhysicsDivision,NaSlovance2,CZ-18040,Praha8,CzechRepublic
13DipartimentodiFisica,Universita`diGenova andINFN,ViaDodecaneso 33,IT-16146Genova, Italy
14InstitutdesSciences Nucl´eaires,IN2P3-CNRS,Universit´edeGrenoble1,FR-38026GrenobleCedex,France
15HelsinkiInstituteofPhysics,P.O.Box64,FIN-00014UniversityofHelsinki,Finland
16JointInstituteforNuclearResearch,Dubna,HeadPostOffice,P.O.Box79,RU-101000Moscow,RussianFederation
17Institutfu¨rExperimentelleKernphysik,Universita¨tKarlsruhe,Postfach6980, DE-76128Karlsruhe,Germany
18Institute ofNuclearPhysics,Ul. Kawiory26a,PL-30055Krakow,Poland
19FacultyofPhysicsandNuclearTechniques,UniversityofMiningandMetallurgy,PL-30055Krakow,Poland
20Universit´edeParis-Sud,Lab. del’Acc´el´erateurLin´eaire,IN2P3-CNRS,Baˆt. 200,FR-91405OrsayCedex,France
21SchoolofPhysicsandChemistry,UniversityofLancaster,Lancaster LA14YB,UK
22LIP,IST,FCUL-Av. EliasGarcia,14-1o,PT-1000LisboaCodex,Portugal
23DepartmentofPhysics,UniversityofLiverpool,P.O.Box147,LiverpoolL693BX,UK
24Dept. ofPhysicsandAstronomy,KelvinBuilding,UniversityofGlasgow,GlasgowG128QQ
25LPNHE,IN2P3-CNRS,Univ.ParisVIetVII,Tour33(RdC),4placeJussieu,FR-75252ParisCedex05,France
26DepartmentofPhysics,UniversityofLund,So¨lvegatan 14,SE-22363Lund,Sweden
27Universit´eClaudeBernarddeLyon,IPNL,IN2P3-CNRS,FR-69622VilleurbanneCedex,France
28DipartimentodiFisica,Universita`diMilanoandINFN-MILANO,ViaCeloria16,IT-20133Milan,Italy
29DipartimentodiFisica,Univ. diMilano-BicoccaandINFN-MILANO,PiazzadellaScienza2,IT-20126Milan,Italy
30IPNPofMFF,CharlesUniv.,ArealMFF,VHolesovickach2,CZ-18000,Praha8,CzechRepublic
31NIKHEF,Postbus41882, NL-1009DBAmsterdam,TheNetherlands
32NationalTechnical University,PhysicsDepartment,ZografouCampus,GR-15773Athens,Greece
33PhysicsDepartment,UniversityofOslo,Blindern,NO-0316Oslo,Norway
34Dpto. Fisica,Univ. Oviedo,Avda. CalvoSotelos/n,ES-33007Oviedo,Spain
35DepartmentofPhysics,UniversityofOxford,KebleRoad,OxfordOX13RH,UK
36DipartimentodiFisica,Universita`diPadovaandINFN,ViaMarzolo8,IT-35131Padua,Italy
37RutherfordAppletonLaboratory, Chilton,DidcotOX11OQX,UK
38DipartimentodiFisica,Universita`diRomaIIandINFN,TorVergata, IT-00173Rome,Italy
39DipartimentodiFisica,Universita`diRomaIIIandINFN,ViadellaVascaNavale84,IT-00146Rome,Italy
40DAPNIA/ServicedePhysiquedesParticules,CEA-Saclay,FR-91191Gif-sur-YvetteCedex, France
41InstitutodeFisicadeCantabria(CSIC-UC),Avda. losCastross/n,ES-39006Santander, Spain
42Inst. forHighEnergyPhysics,SerpukovP.O.Box35,Protvino,(MoscowRegion),RussianFederation
43J.StefanInstitute, Jamova39,SI-1000Ljubljana,SloveniaandLaboratoryforAstroparticlePhysics,
NovaGoricaPolytechnic, Kostanjeviska16a,SI-5000NovaGorica,Slovenia,
andDepartmentofPhysics,UniversityofLjubljana,SI-1000Ljubljana,Slovenia
44Fysikum,Stockholm University,Box6730, SE-11385Stockholm,Sweden
45DipartimentodiFisicaSperimentale,Universita`diTorinoandINFN,ViaP.Giuria1,IT-10125Turin,Italy
46INFN,SezionediTorino,andDipartimentodiFisicaTeorica,Universita`diTorino,ViaP.Giuria1,
IT-10125Turin,Italy
47DipartimentodiFisica,Universita`diTriesteandINFN,ViaA.Valerio2,IT-34127Trieste,Italy
andIstitutodiFisica,Universita`diUdine,IT-33100Udine,Italy
48Univ. FederaldoRiodeJaneiro,C.P.68528CidadeUniv.,IlhadoFunda˜oBR-21945-970RiodeJaneiro,Brazil
49DepartmentofRadiationSciences,UniversityofUppsala,P.O.Box535,SE-75121Uppsala,Sweden
50IFIC,Valencia-CSIC,andD.F.A.M.N.,U.deValencia,Avda. Dr. Moliner50,ES-46100Burjassot(Valencia),Spain
51Institutfu¨rHochenergiephysik, O¨sterr. Akad. d. Wissensch.,Nikolsdorfergasse18,AT-1050Vienna,Austria
52Inst. NuclearStudiesandUniversityofWarsaw,Ul. Hoza69,PL-00681Warsaw,Poland
53FachbereichPhysik,UniversityofWuppertal, Postfach100 127,DE-42097Wuppertal, Germany
† deceased
1
1 Motivation and Overview
In addition to testing models of b-hadron decay, knowledge of b-hadron lifetimes is of
importance in the determination of other Standard Model quantities such as the CKM
matrix element V and in measurements of the time dependence of neutral b-meson
cb
oscillations.
The Spectator Model provides the simplest description of b-hadron decay. Here, the
lifetime depends only on the weak decay of the b-quark with the other light-quark con-
stituent(s) playing no role in the decay dynamics. This, in turn, leads to the prediction
that all b-hadron species have the same lifetime. Non-spectator effects however such
as quark interference, W exchange and weak annihilation can induce lifetime differences
among the different b-hadron species. Models of b-hadron decay based on expansions
in 1/m predict that, τ(Λ ) < τ(B0) τ(B ) < τ(B+),1 and this lifetime hierarchy has
b b s
∼
already been confirmed by experiment. There is a growing consensus between models
that a difference in lifetime of order 5% should exist between the B+ and B0 meson [1]
and it is currently measured to be, τB+ = 1.085 0.017 [2]. Clearly, more precise life-
τB0 ±
time measurements of all b-hadron species are valuable in order to test developments in
b-hadron decay theory.
This paper reports on the measurement of the B+ and B0 meson lifetimes from data
taken with the DELPHI detector at LEP I, in sub-samples separately enriched in B+ and
B0 mesons. In addition, a measurement of the mean b-hadron lifetime τ (i.e. with
b
Λ ,B0,B ,B+ unseparated) is obtained, which is a quantity of importance for many b-
b s
physics analyses at LEP e.g. in the extraction of the CKM matrix element V .
cb
| |
The analysis proceeds by reconstructing the proper time of b-hadron candidates (t =
Lm /pc where L,p and m are the decay length, momentum and rest mass respectively)
0 0
and fitting the t distribution in simulation to the data distribution in a χ2–minimisation
procedure. In the fit for the B+ and B0 lifetimes, the B and Λ lifetimes are set to
s b
their measured values whereas in the fit for τ , all B-species are assumed to have the
b
same lifetime and τ is the only free parameter in the fit. The approach used is highly
b
inclusive and based on the DELPHI inclusive B-physics package, BSAURUS [3]. Aspects
of BSAURUS directly related to the analysis are presented in a summarised form but the
reference should be consulted for full details of the package.
After describing parts of the DELPHI detector essential for this measurement in Sec-
tion 2, the data sets are described in Section 3 and relevant aspects of BSAURUS are
highlighted in Section 4. Section 5 describes the reconstruction of the B-candidate proper
time from measurements of decay length and momentum. Samples with a 70% purity
∼
in B+ or B0 mesons were achieved by use of a sophisticated neural network approach
which is described in Section 6. Section 7 shows the results of the lifetime fits and finally,
systematic uncertainties on the measurements are dealt with in Section 8.
2 The DELPHI Detector
A complete overview of the DELPHI detector [4] and of its performance [5] have been
given in detail elsewhere. This analysis depends crucially on precision charged particle
tracking performedbytheVertexDetector(VD),theInner Detector, theTime Projection
Chamber (TPC) and the Outer Detector. A highly uniform magnetic field of 1.23 T
parallel to the electron beam direction, was provided by the superconducting solenoid
1Note that the corresponding charge conjugate state is always impliedthroughout this paper. B0 always refers to the
B0d stateandΛb referstoany,weaklydecaying,b-baryon.
2
throughout the tracking volume. The momentum of charged particles was measured with
a precision of σ /p 1.5% in the polar angle region 40◦ θ 140 and for p < 10 GeV/c.
p
≤ ≤ ≤
The VD was of particular importance for the reconstruction of the decay vertices of
short-lived particles and consisted of three layers of silicon microstrip detectors, called
the Closer, Inner and Outer layers, at radii of 6.3cm, 9cm and 11cm from the beam line
respectively. The VD was upgraded [6] in 1994 and 1995 with double-sided microstrip
detectors in the Closer and Outer layers providing coordinates2 in both rφ and rz. For
polar angles of 44◦ θ 136◦, a track crosses all three silicon layers of the VD. The
≤ ≤
measured intrinsic resolution is about 8 µm for the rφ coordinate while for rz it depends
on the incident polar angle of the track and reaches about 9 µm for tracks perpendicular
to the modules. For tracks with hits in all three rφ VD layers the impact parameter
resolution was σ2 = ([61/(p sin3/2θ)]2 + 202) µm2 and for tracks with hits in both rz
rφ
layers and with θ 90◦, σ2 = ([67/(p sin5/2θ)]2 + 332) µm2. Before the start of data
≈ rz
taking in 1995 the ID was replaced with a similar device but with a larger polar angle
coverage in preparation for LEP 2 running. The impact of this change on the current
analysis is relatively minor.
Calorimeters detected photons and neutral hadrons by the total absorption of their
energy. TheHigh-density ProjectionChamber (HPC) provided electromagneticcalorime-
try coverage in the polar angle region 46◦ < θ < 134◦ giving a relative precision on the
measured energy E of σ /E = 0.32/√E 0.043 (E in GeV). In addition, each HPC
E
⊕
module is essentially a small TPC which can chart the spatial development of showers
and so provide an angular resolution better than that of the detector granularity alone.
For high energy photons the angular resolutions were 1.7 mrad in the azimuthal angle
±
φ and 1.0 mrad in the polar angle θ.
±
The Hadron Calorimeter was installed in the return yoke of the DELPHI solenoid and
provided a relative precision on the measured energy of σ /E = 1.12/√E 0.21 (E in
E
⊕
GeV).
Powerful particle identification (see Section 4.4) was possible by the combination of
dE/dx information from the TPC (and to a lesser extent from the VD) with information
from the DELPHI Ring Imaging CHerenkov counters (RICH) in both the forward and
barrel regions. The RICH devices utilised both liquid and gas radiators in order to
optimise coverage across a wide momentum range: liquid was used for the momentum
range from 0.7 GeV/c to 8 GeV/c and the gas radiator for the range 2.5 GeV/c to 25
GeV/c.
3 Data Samples
3.1 Hadronic Event Selection
Hadronic Z0 decays were selected by the following requirements:
at least 5 reconstructed charged particles,
•
the summed energy of charged particles (with momentum > 0.2 GeV/c) had to be
•
larger than 12% of the centre-of-mass energy, with at least 3% of it in each of the
forward and backward hemispheres defined with respect to the beam axis.
Due to the evolution of the DELPHI tracking detectors with time, and run-specific de-
tails such as the RICH efficiency, the data were treated throughout this analysis as two
2DELPHI has a cylindrical polar coordinate system. The z-axis points along the beam direction and r and φ are the
radialandazimuthal coordinatesinthetransverseplane.
3
independent data sets for the periods 1994 and 1995. The hadronic event cuts selected
approximately 1.4 million events in 1994 and 0.7 million events in 1995.
3.2 Event Selection
Hadronic events were enhanced in Z0 bb¯ events, by cutting on the DELPHI com-
→
bined b-tagging variable described in [7]. In the construction of the b-tag, the following
four variables were selected that are highly correlated with the presence of a b-hadron
but only weakly correlated between themselves:
1. The mass of particles included in a reconstructed b-hadron secondary vertex.
2. The probability that if a track originated from the primary vertex, it would have
a positive lifetime-signed impact parameter, with respect to this vertex, at least as
large as that observed.
3. The fraction of the total jet energy contained in the tracks associated with a sec-
ondary vertex, fitted with an algorithm run only on the tracks associated with the
jet.
4. Therapidity,withrespecttothejetaxisdirection(seeSection4.1),oftracksincluded
in the secondary vertex.
These variables were combined in likelihood ratios (which assumes they areindependent),
to give a single b-tag variable that can be applied to tag single jets, hemispheres or the
whole event. The event b-tag, comparing data and simulation, is shown in Figure 1
together with the contributions of b- and u,d,s,c-events from the simulation. The arrow
indicates the position of the cut made to enhance the sample in Z0 bb¯ events.
→
Figure 1: The event b-tag variable in 1994 data and simulation, normalised to the number
of entries.
4
In addition to the b-tag requirement it was demanded that events be well contained
in the barrel of the DELPHI detector by making the following cut on the event thrust
axis vector: cos(θ ) < 0.65. After applying the event selection cuts the purity in
thrust
Z0 bb¯ eve|nts was ab|out 94% and the data samples consisted of 285088(136825)
→ ∼
event hemispheres in 1994(1995) respectively.
3.3 Simulated Data
Simulated data sets were produced with the JETSET 7.3 [8] package with tunings
optimized to DELPHI data [9] and passed through a full detector simulation [5]. Both
Z0 qq¯ and Z0 bb¯ events were used and separate samples were produced for com-
→ →
parison with 1994 and 1995 data. The same hadronic and event selection criteria were
applied to the simulation samples as for the data resulting in 640888(239061) events of
¯
qq¯ Monte Carlo in 1994(1995) and 1581499(422304) events of bb Monte Carlo.
4 General Tools
The identification of b-hadron candidates and the reconstruction of their decay length
and momentum (or equivalently their energy), was made in a completely inclusive way;
i.e. the analysis was sensitive to all b-hadron decay channels. This section describes
briefly some tools that were essential in being able to decide whether the data were
likely to contain a b-hadron and what the probability was, for that b-hadron, to be a
B+,B0,B0 or b-baryon. Two specially constructed neural networks (the TrackNet and the
s
BD-Net, described below) made it possible to distinguish whether a particle was likely
to have originated from the primary vertex (in the fragmentation process or the decay
of an excited state), from the weakly decaying b-hadron secondary vertex or even from
the B D cascade tertiary vertex. The reconstruction of the b-hadron secondary vertex
→
position was essential in order to reconstruct the decay length, which in turn tags the
presence of a long-lived b-hadron state. Exploiting the excellent particle identification
abilityoftheDELPHIdetector wasanother aidtob-hadronreconstruction. Thepresence
ofhigh-momentumelectrons ormuonsisapowerfulsignatureofab-hadrondecay andthe
detection of kaons or protons also provides valuable information on the type of b-hadron.
4.1 Rapidity
Events were split into two hemispheres using the plane perpendicular to the thrust
axis. A reference axis was defined in each hemisphere along a jet reconstructed via
the routine LUCLUS [8] with p as a distance measure and the cutoff parameter
⊥
d (PARU(44))=5.0 GeV/c. In simulation studies this was found to give the best re-
join
construction of the initial b-hadron direction. For hemispheres where two or more jets
were reconstructed (about 16% of the cases), the b-tag applied at the jet level was used
to discriminate the b-jet from the gluon jet. With this scheme, the probability to select
correctly the two b-jets in a three-jet event was about 70%.
The rapidity, with respect to the reference axis, was defined as
1
y = ln (E +P )/(E P ) ,
k k
2 · −
(cid:0) (cid:1)
where identified particles were assigned their respective masses and all others were as-
signed a pion mass. Figure 2, shows the rapidity distribution for real and simulated data
5
after the event selection cuts have been applied. Particles originating from the decay
chain of a b-hadron are seen to have higher mean rapidities than particles originating
from the primary vertex. This property made the rapidity a useful input quantity to the
TrackNet (Section 4.2) and for b-hadron decay vertex reconstruction (Section 4.3). In
addition, a Rapidity Algorithm was defined that summed (p~ ,E ,m ) for particles with
i i i
y > 1.6 in order to form an estimate of the weakly decaying b-hadron four-vector.
Figure2: Distributions of rapidity from 1994 data and simulation where the normalisation
is to the number of entries. From the simulation, tracks originating at the primary vertex
and tracks from the b-hadron decay chain are also plotted.
4.2 The TrackNet
The TrackNet is the output of a neural network which supplied, for each track in the
hemisphere, the probability that the track originates from the decay of the b-hadron.
The network relied on the presence of a reconstructed secondary vertex (see Section 4.3)
providing an estimate of the b-hadron decay position in the event hemisphere. The b-
hadron four-vector was reconstructed by the Rapidity Algorithm described above. The
most important inputs to the neural network were:
the magnitude of the particle momentum in the laboratory frame,
•
the magnitude of the particle momentum in the B-candidate rest frame,
•
the track helicity angle, defined as the angle between the track vector in the B-
•
candidate rest frame and the B-candidate momentum vector in the lab frame,
a flag to identify whether the track was in the secondary vertex fit or not,
•
the primary vertex track probability (defined as in Point 2. of Section 3.2),
•
the secondary vertex track probability (defined as in Point 2. of Section 3.2),
•
the particle rapidity.
•
Figure 3, shows the TrackNet distribution for real and simulated data after the event
selection cuts have been applied. The simulation distribution is divided into contribu-
tions from Z0 bb¯ events representing 94% of the total and the remaining 6%, shown
→ ∼
6
in black, is due to tracks in u,d,s-quark and c-quark Z0 decays. The b-events are fur-
ther divided into ‘signal’ and ‘background’. The signal consisted of tracks originating
from the b-hadron weak decay chain and this class of track formed the target for the
neural network training. The background consisted of everything else in b-events such as
fragmentation tracks and decay products of excited b-hadrons. Figure 3 illustrates the
excellent separation, of b-hadron decay products from other tracks, possible using the
TrackNet and shows a good overall agreement in shape between data and simulation. As
aresult oftheb-taggingcut, thecontributionfromu,d,s,c-events isdominatedbyc-events
( 80%) which account for the spike around TrackNet= 1.0 in the u,d,s,c distribution.
∼
Figure 3: Distributions of the TrackNet from 1994 data and simulation, normalised to
the number of entries.
4.3 Secondary Vertex Finding
For each hemisphere an attempt was made to fit a secondary vertex from charged
particle tracks that were likely to have originated from the decay chain of a weakly
decaying b-hadron. Tracks were first selected by imposing the following set of standard
quality cuts:
impact parameter in the rφ plane δ < 4.0 cm,
r−φ
• | |
impact parameter in the z plane δ < 6.0 cm,
z
• | |
cosθ < 0.94,
• | |
∆E < 1.0,
• E
at least one r φ track hit from the silicon vertex detector(VD),
• −
7
tracks must not have been flagged as originating from interactions with detector ma-
•
terial by the standard DELPHI interaction vertex reconstruction package, described
in [10].
Inaddition, allcharged particleswere required to have rapiditygreater thanthevalue1.6,
giving gooddiscrimination between tracks orginating from the fragmentation process and
those originating from the b-hadron decay chain (see Figure 2). In order to be considered
further for vertex fitting, charged particles were selected using a procedure based on:
The likelihood to be an electron, muon or kaon.
•
The ‘lifetime’ content of the track based on the three-dimensional crossing point of
•
thetrack with the estimated b-hadrondirection vector fromthe Rapidity Algorithm.
The direction vector was forced to pass through the event primary vertex position.
Particle rapidity.
•
If at least two tracks are selected, these tracks are fitted to a common secondary vertex in
three dimensions with the constraint that the secondary vertex momentum vector must
point back to the primary vertex error ellipse. If the fit did not converge3 the track
making the largest χ2 contribution was stripped away, in an iterative procedure, and the
fit repeated. In a final step, tracks with a large TrackNet value, which had not already
been selected by theinitial track search, were added tothe vertex tracklist andthe vertex
re-fitted.
The secondary vertex described above refers to the ‘standard’ vertex fit which was an
essential input to the calculation of other b-physics quantities used in the analysis e.g.
the BD-Net described in Section 4.5. More sophisticated secondary vertexing algorithms
developed specifically for the extraction of B lifetimes are described in Section 5.2.
4.4 Particle Identification
The MACRIB package [11] provided separate neural networks for the tagging of kaons
and protons which combined the various sources of particle identification in DELPHI. An
efficiency forthecorrect identificationofK± of90%(70%)wasattainedwithacontamina-
tion of 15%(30%) for p < 0.7 GeV/c (p > 0.7 GeV/c). The corresponding contamination
for proton identification at the same efficiencies was, 2%(40%) forp < 0.7 GeV/c (p > 0.7
GeV/c).
Electron and muon candidates were defined according to the standard DELPHI lepton
identification criteria. Only muon and electron candidates with energy larger than 3 GeV
were selected.
4.5 The BD-Net
In selecting tracks for inclusion in the B secondary vertex fit, there is inevitably some
background from tracks that originate not from the B decay vertex directly, but from
the subsequent D cascade decay. When such tracks are present the vertex is in general
reconstructed somewhere in the region between the B decay point and the D vertex and
the reconstructed decay length will be biased to larger values. The resolution of the B
decay vertex is therefore improved if these tracks can be identified and removed from the
secondary vertex. In order to identify these tracks a neural network (the BD-Net) was
developed based on the following discriminating variables:
3Non-convergencemeans: theχ2wasabove4standarddeviationsattheendofthefirst10iterationsorabove3standard
deviations attheendofthenext10iterations ortookmorethan20iterationsintotal.