IEKP KA
Observation of Orbitally
Excited B Mesons
with the DELPHI Detector
at LEP
Christof J Kreuter
Zur Erlangung des akademischen Grades eines
DOKTORS DER NATURWISSENSCHAFTEN
von der Fakult at fur Physik der Universit at TH Karlsruhe
genehmigte
DISSERTATION
Tag der mundlic hen Prufung
Referent Prof Dr W de Boer
Korreferent Prof Dr Th Mul ler
Diese Arb eit wurde gef ordert vom Land Baden Wurttem berg
Abstract
First exp erimental evidence for the existence of orbitally excited B meson states is ob
tained byinvestigating the B and B Q value distributions Q m B m B m
using Z decaydatataken with the DELPHI detector at LEP The mean Q value of the decays
B B is measured to b e stat syst MeV c The Gaussian width
of the signal is stat syst MeV c The observed shap e is consistent with the
pro duction of several broad states and several narrow states as predicted by the quark mo del
and HQET and whichhave b een observed in the D meson sector The mean mass for B
mesons is extracted to b e stat syst MeV c and the pro duction rate of
stat syst In addition the B mesons p er b jet is measured to b e
helicity distribution of B mesons is investigated
A search is p erformed for orbitally excited strange B meson states in the decay B
s
B K Atwo p eak structure in the B KQ value distribution Q m B m B
s
m K is observed which can b e describ ed by the pro duction of the predicted narrow B
s
states B and B The mass of the B state is determined to b e stat syst
s s
s
while the mass of the B state is determined to b e stat syst The pro duc
s
tion rates p er b jet are stat syst for the B state and
s
stat syst for the B state
s
First exp erimental evidence for the b eautybaryons and is presented in an anal
b b
ysis of the Q value distribution Q m m m Atwo p eak struc
b b
b
ture is observed on top of a at background which can b e describ ed by the pro duction of
is determined to b e baryons The mean Q value of the decays and
b
b b b
is determined to b e stat syst MeV c and that of the decays
b
b
stat syst MeV c The pro duction rate of and baryons p er b jet is
b
b
measured to b e stat syst The pro duction ratio
b b
b
is found to b e stat syst The helicity angle distribution of the signal
identi ed as suggests a suppression of the helicity states b
Contents
Intro duction
The Theoretical Background
The Static Quark Mo del
Mesons q q states
Baryons qqq states
Quantum Chromo dynamics
The QCD Lagrangian
The Running Coupling Constant
s
Symmetries in QCD
Heavy Quark Symmetry
Potential Mo dels
The Electroweak Phase
The Perturbative Phase
The Fragmentation Phase
Hadron Decays
B Meson Sp ectroscopy
Ground State B Mesons
B Mesons with Orbital Excitation
Motivations from the D Meson Sector
Predictions for Orbitally Excited B Mesons
Flavour Tagging and CP Violation
b Baryon Sp ectroscopy
Heavy Baryons
PresentKnowledge ab out b Baryons
Baryons Predictions for and
b
b
Summary of the Chapter
The Exp eriment
The LEP Collider
The DELPHI Detector
The Tracking System
The Calorimeters
Particle Identi cation Devices
The DELPHI Online System
The SlowControl System
The Trigger
The Data Aquisition System
The DELPHI O ine Analysis Chain
The DELANA Package
The SDST Creation
The DELPHI Event Display
The Detector Simulation
Summary of the Chapter
Analysis Tools
Hadronic Event Selection
Tagging of bb Events
Inclusive B Meson Reconstruction
B DecayVertex Reconstruction
Hadron Identi cation
V Reconstruction
Summary of the Chapter
The Analysis
Observation of Orbitally Excited B Mesons B B
Exp erimental Pro cedure and Results
Interpretation and Comparison with Predictions
B Helicity Analysis
B Charge Analysis
B Fragmentation
Comparison with other Exp eriments
Search for Orbitally Excited Strange B Mesons B B K
s
Exp erimental Pro cedure and Results
Interpretation and Comparison with Predictions
Comparison with other Exp eriments
Search for and Baryons
b b
b b
Exp erimental Pro cedure and Results
Interpretation and Comparison with Predictions
Helicity Analysis
b
Summary
References
Memb ers of the DELPHI Collab oration
Acknowledgements
List of Figures
SU Meson Multiplet
SU Baryon Multiplet
Feynman Graphs of the Fundamental Pro cesses of QCD
One lo op Contributions to the Vacuum Polarisation
From Quarks to Hadrons
Hadron Pro duction in e e Annihilation
Schematical View of the String Fragmentation Algorithm
Longitudinal Fragmentation Function
Particle Decays in the Sp ectator Mo del
Pro duction of Vector and Pseudoscalar Mesons at LEP
The Coupling Schemes of Symmetric and Heavy Light Mesons
Pro duction and Decay Prop erties of Orbitally Excited B Mesons
Flavour Change in B Decays
Decay Prop erties of Orbitally Excited B Mesons
Orbital Angular Momenta for a Light Diquark System
Lo cal Area Map of the LEP Collider
Schematic View of the LEP Injection System
Integrated LuminosityAveraged over the LEP Exp eriments
Schematic View of the DELPHI Detector
Schematic View of the DELPHI Detector along the Beam Pip e
Schematic Layout of the DELPHI Microvertex Detector
Hadronic Z Event in the DELPHI Vertex Detector
Layer Structure of the High density Pro jection Chamb er HPC
The Ring Imaging Cherenkov Detector RICH
The DELPHI O ine Analysis Chain
A Three jet Event Recorded with the DELPHI Detector
Performance of the DELPHI b Tagging Package
Inclusive B Reconstruction Algorithm
Performance of the Inclusive B Reconstruction
Iterative Pro cedure for the Vertex Reconstruction
Selected b b Event in DELPHI
Performance of the Vertex Reconstruction Algorithm
Sp eci c Energy Loss dE dx in the TPC
Average Cherenkov Angle p er Track for Liquid and Gas RICH
Performance of the DELPHI Hadron Identi cation
Q value Distribution for B Pairs
Comparison of the B Q value Distribution with Various Mo dels
Q value Distribution for B Pairs in HelicityBins
Decay Angle Distribution for B Pions
Decay Angle Distribution B Signal sub divided
Decay Characteristics for the Four B Charge States
Q value Distribution for the Four B Charge States
Total Pro duction Cross Section
b B
Inclusive B Cross Section in Bins of x
Etrue
Decay Characteristics for the Two B Charge States
s
Quark Flavour Tagging for B Decays
s
Distribution of the Q value of B K Pairs
Distribution of the Q value of B K Pairs Jet Charge Anticut
Distribution of the Q value of Pairs with and without Baryon Enrichment
b
Distribution of the Q value of Pairs with Di erentBaryon Enrichments
b
Decay Characteristics for the Four Charge States
b
Distribution of the Q value of B Pairs for the Di erent Charge States
Decay Angle Distribution for Pions b
List of Tables
Additive Quantum Numb ers of the Quarks
Selected Exp erimental Results on B and B Mesons
Excitation Sp ectrum in the Static Quark Mo del
Exp erimental Results for Orbitally Excited D Mesons
D Pro duction in e e Annihilation
Prop erties of and Baryons
b b
Numb er of Multi hadronic and bb Events in DELPHI
Cherenkov Angle Reconstruction in the RICH Detectors
Di erential Pro duction Cross Section d d cos
b
Total Pro duction Cross Section
B b
Di erential Pro duction Cross Section d dx
b Etrue
LEP B B Results
u d
LEP B B K Results
s
LEP Results
b b
Chapter
Intro duction
The present knowledge of particle physics considers the observed matter in the surrounding
nature to b e constructed from six di erenttyp es of quarks and leptons The quark typ es are
called d u s c b and t the lepton typ es are called e and Quarks and
e
leptons are fermions with spin The fundamental interactions b etween these particles are
understo o d by the exchange of so called gauge b osons The describing theory is known as the
Standard Mo del of particle physics It basically consists of the following
The theory of strong interactions which is called Quantum Chromo dynamics QCD de
scrib es the e ects of quark interactions The gauge b osons of the strong interaction the
gluons have b een discovered in three jet events at the electron p ositron ring PETRA at
DESY Since the gluon carries colour charge this leads to the observed quark gluon con ne
mentatlower energies Because of this e ect the theory QCD has to b e a non Ab elian
theory
The theory of the electro weak interactions has b een develop ed by Glashow Salam and
Weinb erg It is often called GSW theory It uni es the rst mo dern gauge theory Quan
tum Electro dynamics QED whichwas rst constructed bySchwinger and Feynman
with the weak interaction which is resp onsible for radioactive decays This electro weak
theory predicted the existence of three new gauge b osons the W and the Z They were
discovered in the predicted mass range in and in proton antiproton collisions by
the UA and UA collab orations at CERN
In order to investigate the prop erties of the electro weak gauge b osons Z and W the
Large Electron Positron LEP collider at CERN has b een built The collider pro duced in
the years approximately million multi hadronic Z events from the annihilation
of electrons and p ositrons in resonance at a center of mass energy of m GeV Four
Z
detectors ALEPH DELPHI L and OPAL collected the data from the Z decay pro ducts
In a second stage of LEP starting from the collider is b eing upgraded to an energy of
twice the W mass in order to pro duce W pairs In this way the charged electro weak
b osons can b e investigated This second stage of LEP is called LEP
PETRA Positron Electron Tandem Ring Accelerator
DESY Deutsches Electronen Synchrotron
CERN Conseil Europ een p our la Researche Nucl eaire
The pro duced Z b osons at LEP can decay either into lepton pairs Z orinto
quark antiquark pairs Z q q i e dd uu ss cc and bb TheZ b osons cannot decay
into tt pairs due to the large top quark mass The studies in this thesis fo cus on the prop
erties of the lighter b quark It was discovered in by the group of L Lederman in the
CFS exp erimentatFermilab Chicago in proton collisions with a b eryllium target They
observed a narrow resonance in the invariant mass sp ectrum of muon pairs at GeV c
p Be X This state was identi ed as the S state of the so called b ottomonium
system consisting of a bb pair It was named S Later radial excitations of this system
were discov ered e g S S S and S Furthermore states with orbital ex
citations have b een identi ed e g h P P P and P The excitation
b b b b
sp ectrum of this system was successfully describ ed using QCD inspired p otential mo dels in
analogy to the description of p ositronium
P
B mesons are b ound states of a b quark and au or d quark with spin parity J
In it was con rmed by CESR and later at DORIS that S decays into a pair of
B B mesons Several exp eriments e g ARGUS and CLEO which study the weak decays of
B mesons run at the S resonance in e e annihilation Apart from the ground state B
P P
meson with spin parity J only the B meson with J has b een exp erimentally
established Both states are investigated in Z bb decays at LEP
The main goal of this analysis is the search for and rst observation of orbitally excited B
mesons commonly lab eled as B mesons with the DELPHI detector at LEP The rst
evidence was obtained in parallel with an indep endent analysis in the OPAL collab oration
The exp ected main decaychannel of B mesons is into B The analysis starts with a
multi hadronic event selection This is followed by the tagging of bb events exploiting the long
lifetime of the b hadrons of ps The four vectors of the B or B mesons are reconstructed
in an inclusive fashion using the hard fragmentation of b hadrons Since B mesons decay
rapidly through the strong interaction decay pions originate from the primary vertex and not
from a secondary B decayvertex Due to the long lifetime of B mesons the secondary vertex
lies on average ab out mm apart from the primary eventvertex A signi cantbackground
reduction is achieved by the reconstruction of primary and secondary vertices The obtained
signal is consistent with theoretical exp ectations for B states The helicity distribution of
B fragmenta B mesons is analyzed and a charge analysis is p erformed In addition the
tion is investigated
Furthermore a search for B mesons decaying into B K is p erformed exploiting the
s
good kaon identi cation capabilities of the DELPHI RICH detector Two narrow signals
consistent with the pro duction of twonarrow B states are extracted from the data
s
Their The last part of the analysis is dedicated to a search for the baryons and
b
b
exp ected main decaychannel is into The is reconstructed in an inclusive fashion It is
b b
combined with pions from the primary vertex In order to enhance the signal to background
ratio a baryon enrichmentisachieved by using proton tagging and reconstruction First
is extracted from the data evidence for the existence of the baryons and
b
b
The presented analysis is p erformed using approximately million multi hadronic Z
events taken with the DELPHI Detector at LEP in the years The results obtained
have b een published in Refs and Some review articles are given in Ref
The top quark has recently b een discovered in proton antiproton collisions by the CDF and D collab orations
The CDF collab oration measure a mass for the t quark of GeV c The D collab oration quote
avalue of GeV c
Chapter
The Theoretical Background
This section gives the main theoretical background which is needed for the understanding of
the analysis in this thesis Starting from the static quark mo del for mesons and baryons the
basic concepts of Quantum Chromo dynamics QCD are develop ed Emphasis is given to the
symmetries of QCD Mainly heavy quark symmetry is discussed which leads to an e ective
theory of QCD the Heavy Quark E ective Theory HQET
Then the four phases of hadron formation in e e annihilation are describ ed electro
weak phase p erturbative QCD phase con nement phase and particle decay phase This is
followed by detailed descriptions of the phenomenology of B meson and b baryon sp ectroscopy
Lastly the present exp erimental status in this eld is reviewed
The Static Quark Mo del
Todayitiswell known that the proton is not an elementary particle since it consists of
three fundamental particles which are called quarks The name quarks originates from the
s when Gell Mann and Ne emen discovered symmetries in the sp ectrum of particles
which lead rst to a classi cation of all known hadrons into meson and baryon o ctets and
baryon decuplet and later to the prop osal of the existence of new fundamental particles the
quarks At that time the known hadrons could b e constructed with the three quark avours
up u down d and strange s Today three more quarks are known charm c b ottom b
and top t
Each quark has spin and baryon number Tab gives the additive quantum
numb ers except the baryon numb er of the three generations of quarks The convention is
that the avour of a quark describ ed by I S C B and T hasthesame sign as the charge
With this convention any avour carried byacharged meson has the same sign as its charge
e g the strangeness of the K is the b ottomness of the B is and the charm and
strangeness of the D are each By convention each quark has p ositive parity Thus
s
eachantiquark must have negative parity as they are fermions
Sea quarks and gluons are neglected for the moment
Prop erty Quark d u s c b t
I isospin rd comp onent
S strangeness
C charm
B b ottomness
T topness
Table Additive quantum numbers of the quarks The u and d quarks belong to the rst
family the s and c quarks to the second family and the b and t quarks to the third family
Mesons q q states
Nearly all known mesons are b ound states of a quark q and an antiquarkq the avours of
q and q can b e di erent If the orbital angular momentum of the q q system is L then the
L
parity P is A state q q of a quark and its own antiquark is also an eigenstate of
LS
charge conjugation with C where the total spin S is or The L states
P P
are the pseudoscalars J and the vectors J According to this states in the
J
S and hence CP That means normal spin parity series P must have
that mesons with normal spin parityand CP are forbidden in the q q mo del The
PC PC
J state is forbidden as well Mesons with such J values would lie outside the
additive quark mo del
PC
For xed J nine p ossible q q combinations containing u d and s quarks group themselves
into an o ctet and a singlet according to SU symmetry
P
States with the same IJ I Isospin and the same additive quantum numb ers can mix If
they are eigenstates of charge conjugation they must also have the same value of C As an
example consider the I memb er of the ground state pseudoscalar o ctet It mixes with
the corresp onding pseudoscalar singlet to pro duce the and mesons They app ear as
memb ers of a nonet whichisshown as the middle plane of Fig a The heavier charm
and b ottom quarks can b e included in this scheme b y extending the symmetry to SU The
signi cant mass di erences b etween the various avour states indicate that this symmetry is
badly broken Fig shows the SU sub group of the pseudoscalar and vector mesons made
of u d s and b quarks The drawing of the full SU multiplets would require four dimensions
All the mesons shown except the have b een observed exp erimentally The work of
b
this thesis is mainly devoted to B meson sp ectroscopy The present exp erimental status in
this eld as well as the theoretical background of B meson ground states and excited states is discussed in detail in section − − (a) ο (b) ∗ο Bs Bs − − (bs) (bs) − − − −ο ∗− − − − ∗ο B (bu) (bd) B B (bu) (bd) B ο + ∗ο ∗+ K K K K − ο − − − − (ds)π η (us) + − (ds)ρo ω (us) − − − − + π (du) (ud) π ρ (du) (ud) ρ − η η' − − Y Φ − (su)b (sd) (su) (sd) − − ο ∗− − ∗ο K K K K
ο − − + ∗ο − − ∗+ (db)− (ub) (db)− (ub) B (sb) B B (sb) B ο ∗ο
Bs Bs
Figure SU plets for a pseudoscalar and b vector mesons made of u d s and
b quarks The nonets of the light mesons occupy the central planes to which the bb have been
added The neutral mesons at the centers of these planes are mixtures of uu dd ss and bb
States involving the c quark are not shown
Baryons qqq states
All the established baryons are quark qqq states and each such state is a SU colour
singlet a completely antisymmetric state of the three p ossible colours Since the quarks are
fermions the state function for anybaryon must b e antisymmetric under interchange of any
two equal mass quarks up and down quarks in the limit of isospin symmetry Thus the
state function can b e written as
jqqqi jcolouri jspace spin avouri
A A S
where the subscripts S and A indicate symmetry or antisymmetry under the interchange of
anytwo of the equal mass quarks
The ordinary baryons are made up of u d and s quarks Assuming an approximate
avour SU symmetry for the three avours implies that baryons made of these quarks
b elong to the multiplets on the right side of
S M M A
Here the subscripts indicate symmetric mixed symmetry orantisymmetric states under in
terchange of anytwo quarks Including the c and b quarks in addition to the light quarks
would extend the avour symmetry to the badly broken SU symmetry Again it would
require four dimensions to draw the multiplets of SU The Figures a and b show
the multiplets containing only u d s and b quarks SU sub group All the particles in a
P P
given multiplet have the same spin and parity J for Fig a and J
for Fig b The ground oors of the shown multiplets represent the SU o ctet that Ω− (a) (b) bbb
− ο Ξ Ξ Ξ ∗− Ξ ∗ο bb (dbb) (ubb) bb bb (dbb) (ubb) bb − (sbb) − (sbb) Ω ο Ω ο bb Λ Σ − bb Σ* + − b, b + Σ* Σ* Σ Σ b b b b (ddb) (udb) (uub) b (ddb) (udb) (uub) (dsb) (usb) − (dsb) (usb) ο − ο Ξ* Ξ* Ξ (ssb) − − b ο (ssb) − + ++ b Ω Ξ Δ Δ Ω Δ b Δ n b b p b (udd) (uud) (ddd) (udd) (uud) (uuu) − ο + ∗− ∗ο ∗+ Σ (dds) (uds)Λ,Σ (uus) Σ Σ (dds) (uds)Σ (uus) Σ (dss) (uss) ∗− (dss) (uss) ∗ο Ξ− Ξο Ξ (sss) Ξ
Ω−
Figure SU multiplets of baryons made of u d s and b quarks a The plet with
a SU octet b The plet with a SU decuplet
contains the nucleon and the SU decuplet that contains the All these particles
have b een observed in former exp eriments Most of the baryons containing a b quark are not
yet established exp erimentally apart from the and the Parts of this thesis will fo cus
b b
on the search for the charged and baryon
b
b
Quantum Chromo dynamics
The static quark mo del successfully describ es symmetries and quantum numb ers of the known
hadrons It cannot explain why mesons q q and baryons qqq are the only b ound states
Other combinations of q andq are p ossible as well in this mo del but are not observed in
nature Inspired by this mystery a dynamical mo del for the strong interaction was develop ed
called Quantum Chromo dynamics QCD
The QCD Lagrangian
Quantum Chromo dynamics QCD the gauge eld theory which describ es the strong inter
actions of coloured quarks and gluons is one of the comp onents of SU SU U
C L Y
called the Standard Mo del As already mentioned in section a quark of sp eci c avour
such as the b ottom quark can ha veany one of three colours often called red r green g or
blue b The gluons span the colour space whichwould lead to nine di erenttyp es of
This statement is true although some exotic states are known which do not t easily in the meson baryon
picture E g the a is interpreted as K K molecule by some authors (a) (b) (c)
g
q
Figure The Feynman graphs of the fundamental processes of QCD a
quark gluon interaction b triple gluon vertex c gluon vertex
gluons However according to SU symmetry these nine states decomp ose into an o ctet
p p
r g rb g r g b br bg r r g g r r g g bb
and a singlet
p
r r g g bb
Note that the singlet combination do es not carry net colour and therefore it do es not transmit
any colour The eight other gluons involve the net transmission of colour Hadrons are colour
singlet combinations of quarks antiquarks and gluons
The Lagrangian of QCD up to gauge xing terms is given by this formula
X X
j a a
i i
L i D m F F
QC D ij q qi
q q q
q q
with
c b a a a
A g f A A A F
s abc
and
a
X
ij
a
D ig A
ij ij s
a
where g is the QCD coupling constant and the f are the structure constants of the SU
s abc
a i
algebra The are known as Gell Mann matrices The x are the comp onent Dirac
q
ij
a
spinors asso ciated with each quark eld of colour i and avour q The A x are the eight
Yang Mills gluon elds The rst term in the Lagrangian is the kinetic term the second term
corresp onds to the mass term and the third term is known as the eld term This form of the
Lagrangian leads to the three fundamental pro cesses of QCD the quark gluon interaction
the triple gluon vertex and the gluon vertex The Feynman graphs of these pro cesses are
shown in Fig
The Running Coupling Constant
s
Calculations in lowest order p erturbation theory have nite results Higher order calculations
of Feynman diagrams are divergent and would lead to unphysical results In order to obtain
nite physical values one has to p erform a regularization and renormalization pro cedure This
leads to the result that the e ective QCD coupling constant g is not constant but
s s
dep ends on an energy scale The renormalization scale dep endence of the e ective QCD
coupling is describ ed by the Renormalization Group Equation RGE
s
s
s s s
The functions contain some QCD intrinsic co e cients
n
f
n
f
n n
f
f
where n is the numb er of quark avours with mass less than the energy scale In solving
f
this di erential equation for a constantofintegration is intro duced This constantis
s
the one fundamental constant of QCD that must b e determined from exp eriment The most
sensible choice for this constantisthevalue of at a xed reference scale e g m
s Z
but it is more conventional to intro duce the dimensional parameter since this provides
QC D
a parametrization of the dep endence of The de nition of is arbitrary One way
s QC D
of de ning it is to write the solution of Eq as an expansion in inverse p owers of ln
The solution to rst order is
s
ln
QC D
The solution illustrates the prop ertyofasymptotic freedom i e that as From
s
this equation it can also b e seen that reaches in nityatthescale The increase
s QC D
of at small scales re ects the con nement prop erty of QCD This b ehaviour of is
s s
remarkably di erent from the b ehaviour in QED where a decrease of the coupling constant
with the scale is observed Fig illustrates the one lo op contribution to the vacuum
p olarisation in QCD In contrast to QED gluons also participate in these lo ops which leads
to an increase in with decreasing scale This prop erty re ects the non Ab elian character
s
of QCD The solution of the RGE in second order gives
ln ln
QC D
s
ln ln
QC D QC D
Symmetries in QCD
There are very few cases in which it is p ossible using analytic metho ds to make systematic
predictions based on QCD in the low energy nonp erturbative regime In fact QCD has b een
shown to b e so intractable to analytic metho ds that all such predictions are based not on dynamical calculations but on some symmetry of QCD + + +
+ + +
Figure One loop contribution to the vacuum polarisation All strong interacting particles
can participate in these loops In contrast to QED thereare also contributions from gluons
Isospin Symmetry Isospin symmetry was the rst such symmetry discovered It is now
understo o d as an approximate symmetry which arises b ecause the light quark mass di erence
m m is much smaller than the mass asso ciated with con nement which is set bythe
d u
scale The predictions based on isospin symmetry would in a world with only strong
QC D
interactions b e exact in the limit m m Corrections to this limit can b e studied in
d u
an expansion in the small parameter m m SU avour symmetry is similar
d u QC D
but the corrections are larger since m m is not small
s u QC D
Chiral Symmetry Chiral symmetry SU SU arises in QCD b ecause b oth
L R
m and m are small compared to It is asso ciated with the separate conservation of
d u QC D
vector and axial vector currents Although sp ontaneously broken in nature the existence of
this underlying symmetry allows the expansion of chiral p erturbation theory in which many
low energy prop erties of QCD are related to a few reduced matrix elements If the strange
quark is also treated as small compared to then the chiral symmetry group b ecomes
QC D
SU SU
L R
Heavy Quark Symmetry Over the last years there has b een progress in understanding
systems containing a single heavy quark The mass m of the heavy quark is much greater
Q
than the scale of the strong interaction It was discovered that there is a new symme
QC D
try of QCD similar to isospin and chiral symmetry in the b ehaviour of such systems This
symmetry arises b ecause once a quark b ecomes su ciently heavy its mass b ecomes irrelevant
to the nonp erturbative dynamics of the light degrees of freedom of QCD This symmetry is
called heavy quark symmetry and the underlying theory is known as Heavy Quark E ective Theory HQET
Heavy Quark Symmetry
The most imp ortant predictions from heavy quark e ective theory are for semileptonic B
meson decay form factors These play an imp ortant role in the accurate determination of the
values of the Cabibb o Kobayashi Maskawa matrix elements V and V from exp erimental
cb ub
data The prop erties of hadrons containing a single heavy quark have b een studied since a
long time using phenomenological mo dels Now it is understo o d that this physics arises from
symmetries of an e ective theory that is a systematic limit of QCD Consequently mo del
indep endent predictions are p ossible using HQET
Heavy Flavour Symmetry
As an extreme example consider twovery heavy quarks of masses one and ten kilograms
Although these quarks will live in the usual hadronic sea of light quarks and gluons they will
hardly notice it Their motion will su er only slight uctuations compared to the motion of
a free heavy quark Such quarks de ne with great precision their own center of mass system
Therefore hadronic systems containing a heavy quark can b e studied in the frame where the
heavy quark acts as static source of colour lo calized at the origin The equations of QCD
in the neighborhood of such an isolated heavy quark are therefore those of the light quarks
and gluons with the b oundary condition that there is a static triplet source of colour electric
eld at the origin Since the b oundary condition is essentially the same for b oth of our
hyp othetical heavy quarks the solutions for the states of the light degrees of freedom in their
presence will b e the same Thus the light degrees of freedom will b e symmetric under an
isospin like rotation of the heavy quark avour into one another even if the quark masses are
not almost equal In particular the heavy meson and baryon excitation sp ectra built on any
vy quark will b e the same hea
Heavy Spin Symmetry
The preceding discussion ignored the spin of the heavy quark This is appropriate in QCD
since the spin of the heavy quark decouples from the gluonic eld i e all heavy quarks lo ok
like scalar heavy quarks to the light degrees of freedom Since the avour and spin of a heavy
quark are irrelevant the static heavy quark symmetry is actually SU N where N is the
h h
numberofheavy quarks At the sp ectroscopic level this additional symmetry means that each
sp ectral level built on a heavy quark unless the light degrees of freedom combine to spin zero
will b e a degenerate doublet in total spin
Heavy avour symmetry is analogous to the fact that the di erent isotop es of a given
elementhave the same chemistry i e their electronic structure is almost identical b ecause
they have the same nuclear charge The spin symmetry is analogous to the near degeneracy
of hyp er ne levels in atoms and the electronic structure of the states of a hyp er ne multiplet
are almost the same b ecause nuclear magnetic moments are small
The Cabibb o Kobayashi Maskawa CKM matrix is the quark mixing matrix of the weak interactions
In rst approximation hadronic states containing a c or a b quark are treated in that way Thet quark
with its mass around GeV c would form an almost ideal heavy quark system Unfortunately it decays
rapidly through the weak interaction b efore the hadronisation takes place t Wb
The E ective Theory
In the situation describ ed ab ove where the light degrees of freedom typically have four
momenta small compared with the heavy quark mass it is appropriate to go over to an
e ective theory where the heavy quark mass go es to in nity with its four velo city xed The
heavy quark path is a straightworld line describ ed by a four velo city v satisfying v
The SU N spin avour symmetry of the heavy quark e ective theory is not presentinthe
h
full theory of QCD It b ecomes apparent only in the e ective theory where the heavy quark
masses are taken to in nity The situation is very similar to the chiral symmetry whichis
only apparent in the limit where the light quark masses are taken to zero Perturbations to
the predictions from heavy quark e ective theory with m can b e calculated in p owers
Q
of m
QC D Q
One can derivetheFeynman rules for the e ective theory by taking the ab ove limit of the
Feynman rules for QCD In the full theory of QCD the heavy quark propagator is
i p m
Q
Q
p M
Q Q
In order to go over to the e ective theory we write p m v k wherek is a residual
Q
Q
momentum that is small compared to the heavy quark mass In the limit m the heavy
Q
quark propagator b ecomes
i
v k
Furthermore in the full theory of QCD the vertex for heavy quark gluon interaction is
a
ig
s
a
where g is the strong coupling constantand are the SU colour generators Gell Mann
s
matrices For the vertex in the e ective theory one obtains
a
ig v
s
In this derivation factors of v in the numerators of propagators and in vertex def
initions havebeenmoved to the outside of anyFeynman graph where they give unity when
acting on the on shell spinors u v s Equations and can b e taken as de nitions of
the e ective heavy quark theory
A di erent but equivalent approach starts from the QCD Lagrangian Eq The
heavy quark spinor with velo city v as an approximation for m can b e written as
Q
v
im v x
q
e h
Q
Q
v
where the eld h is constrained to satisfy
Q
v v
v h h
Q Q
Inserting this in Eq leads to the Lagrangian of heavy quark e ective theory
v j v i
a a
v D h F L ih F
ij HQET
Q Q
For simplicity the Lagrange densityisgiven for a system containing just one heavy quark
The e ective Lagrangian repro duces the Feynman rules in Eqs and The
heavy quark e ective theory has symmetries which are not manifest in the Lagrangian of
QCD Since there is no pair creation in the e ective theory there is a U symmetry of
the e ective Lagrangian asso ciated with heavy quark conservation Since gamma matrices no
longer app ear in the gluon heavy quark interaction the spin of the heavy quark is conserved
Asso ciated with this is a SU symmetry group of the Lagrangian in Eq
Potential Mo dels
The quark p otential mo del is the most successful to ol enabling physicists to calculate masses
and prop erties of mesons and baryons However p otential mo dels su er from the fact that
although motivated by QCD so far they have not b een derived from basic theory The most
general non relativistic ansatz for a quark antiquark system with masses m and m leads
to the Breit Fermi Hamilton function
p
V H H H H
LS SS T
The rst term represents the kinetic energy with m m m m The sp eci c p otential
mo del enters in V which usually contains an attractive and a repulsive term The remaining
terms re ect the couplings b etween total spin S and orbital angular momentum L and the
coupling b etween the quark spins S and S H is known as tensor term Some examples for
T
frequently used p otential mo dels are given b elow The di erent mo dels have certain domains
of applicability
Authors Potential
s
ar Eichten V
r
Quigg Rosner V a ln r r
Martin V A Br
R
q
s
V Buchmuller d q exp i q r
q
The energy levels of a quark antiquark system can b e calculated by solving the eigenvalue
equation
H j i E j i
where E is the energy level and j i the wave function of the state In the early times of p oten
tial mo dels sp ectroscopywas very successful in heavy quark systems e g charmonium cc or
b ottomonium bb since non relativistic approaches were justi ed Then the spin dep endent
terms in the Hamilton function can b e treated by p erturbation theory For light mesons a
non relativistic approach cannot b e justi ed Furthermore p erturbation theory for the spin
Explicit expressions for these terms can b e found in Ref
s
Describing the charmonium system with a p otential of typ e V ar leads to v c The
r
b ottomonium system will b e even less relativistic
The non relativistic approachinlight meson systems is normally only justi ed by its phenomenological success
dep endent terms cannot b e used since e g spin spin e ects cannot b e treated as small The
imp ortance of spin spin e ects can b e seen in the system where the pion with spin
has a mass of MeV c and the meson with spin has a mass of MeV c
An interesting application of p otential mo dels is to study the di erence of the squared
masses b etween spin singlet and triplet states m m S m S From exp eri
ment one nds nearly constantvalues for m GeV m K K GeV
m D D GeV m D D GeV and m B B GeV
s
s
Potential mo dels predict m h V r i Demanding the result to b e mass in
s
s
ar dep endent as motivated by observation and by using a p otential of typ e V
r
leads to m a This means that the light quarks in this systems mainly feel the
s
linear term of the p otential From this the strong coupling constant is extracted to b e
s
For practical calculations it is sometimes useful to knowhow the energy of a state changes
with a parameter This means that one is interested in the derivative of the energy with
resp ect to the parameter This leads to the so called Feynman Hel lmann Theorem
E H
h j j i
The pro of of this theorem can b e found in Ref If we consider e g a linear p otential
p
H ar
the Feynman Hellman Theorem leads to
E a
hr i
a
Since the right side of the equation is always p ositive it is evident that the energy rises with
increasing parameter a
From Quarks to Hadrons
The formation of hadrons from highly energetic quarks is theoretically not understo o d in all
details A combined mo del consisting of exactly calculable parton cross sections phenomeno
logical algorithms and a variety of exp erimentally known hadron decay prop erties is used to
describ e the evolutionofamulti hadronic Z decay
The mo del can b e divided into four time ordered phases which are schematically shown in
Fig The pro cess starts with e e annihilation into the strongly interacting quark and
antiquark Phase I in Fig is governed by the electroweak force Phase I I is the phase of
small distance strong interactions which is calculable exactly in p erturbative QCD Phase I I I
is the domain of long distance strong interaction linear con nement and hadron formation
Due to the large strong coupling constant no p erturbative calculations are p ossible for this
s
p erio d Phase IV is the era in which the primary hadron resonances formed in phase I I I
decayinto the nal state particles hadrons leptons photons which are observable in the
detector
Quarks and gluons are partons − γ q e+ g
γ / Z0 − e q
I II III IV
Figure The four phases of e e annihilation I electro weak phase with initial state
radiation II perturbative QCD phase with gluon radiation o the leading quarks III con
nement phase wherecolour singlet hadrons emerge and IV decay into nal state particles
The Electroweak Phase
The rst phase in e e annihilation is governed by the Standard Mo del of electroweak in
teractions which has b een develop ed by Glashow Salam and Weinb erg It is often called
GSW theory For QCD studies at LEP the pro cess e e q q is of main imp ortance In
rst order Born approximation this pro cess is describ ed by the exchange of a photon or a
Z b oson By neglecting fermion masses the total cross section can b e derived as
Q Q e e q q N
C
e q
s
V A V A j j
e e q q
Q Q V V Re
e q e q
where
s
iM s M
sin cos
Z Z
w w
Z
The rst term originates from exchange the second from Z exchange and the third from
Z interference V I Q sin and A I are the vector and axial vector
f f f w f f
couplings of the fermions to the Z where sin is known as the weak mixing angle The
w
ne structure constantis e and N is the numb er of colours Fig shows
C
Details on this theory can b e extracted from many standard textb o oks ] nb
[ 1 Z0 exchange (a) (b) 10 0.8 hadrons)
→ total 0.6 -
e 1 +
(e 0.4 σ γ exchange -1 10 0.2 Z0 / γ interf. γ exchange 0 Contribution to total cross section 20 60 100 140 180 20 60 100 140 180 [ ] [ ]
ECM GeV ECM GeV
Figure Hadron production in e e annihilation a The total hadronic cross section
as a function of center of mass energy E b The relative contributions of Z exchange
CM
and Z interference to the total hadronic cross section
the total cross section for hadron pro duction in Born approximation as a function of center of
mass energy aswell as the relativecontributions of Z exchange and interference term to
the total cross section At a center of mass energy which corresp onds to the Z mass
GeV the Z exchange dominates completely
Formula is mo di ed by electro weak and strong interaction corrections of higher
order These are partly virtual corrections vertex and propagator corrections and partly
radiative corrections of photons in the initial and nal state and gluons in the nal state The
latter will b e discussed in the next section
Furthermore the Standard Mo del provides predictions for the partial widths of the Z
b oson
Br Z e e
Br Z
Br Z q q
The pro duced neutrinos will not b e observed in the detector while the other decays are
exp erimentally accessible Roughly of the hadronic Z decays will go into bb pairs
The study of these events is the sub ject of this thesis
The PerturbativePhase
Two p erturbative approaches are commonly used to calculate the quark and gluon cross
sections in phase I I The rst metho d is the complete second order QCD matrix element ME
calculation and the second is the parton shower PS approach in leading log approximation
QCD Matrix Elements
The Born term annihilation pro cess e e q q is mo di ed through the p ossible gluon radi
ation o coloured quarks The exact cross section in second order for three parton nal
s
states e e q qg has b een calculated byseveral groups Two of these ME calcula
tions are available in the jetset program The four parton nal states e e q qg g
or e e q qq q cross section in second order contain just the tree level diagrams With
s
the total cross sections known from the optical theorem the two parton cross section follows
from a unitarity argument once the three and four jet cross sections are calculated by di
rect Feynman graph techniques Thus the ME calculation is able to describ e two three
and four parton nal states i e cross sections for the pro cesses e e q q e e q qg
e e q qq q and e e q qgg
Parton Shower Mo del
In order to calculate multi parton nal states a vast numberofFeynman diagrams has to
b e considered An alternative to these excessive calculations is available in terms of the
leading logarithm approximation In this approach only the leading terms of the p erturbative
expansion are kept thus neglecting non leading terms The parton shower mo del PS is
based on the picture of a time ordered cascade of subsequent splitting pro cesses of the partons
q qg g q q and g gg The allowed splittings coincide with the O vertices which
s
are displayed in Fig Instead of calculating a single transition amplitude A e e
q qggq qggg two primary quarks are pro duced according to a mo di ed electroweak muon
cross section including initial state radiation Then the massless quarks are assumed to
s During the b e at rest and thus completely o shell maximal virtuality Q m
q
following chain of incoherent parton splittings the probability P for a branching a bc
a bc
results from splitting functions which are taken from the Altarelli Parisi equations
The main di erence b etween ME and PS lies in the fact that ME cannot takeinto account
higher order e ects since it is restricted to a maximal numb er of four partons PS pro duces
multi gluon events with an average of nine comparably soft gluons p er Z event
The Fragmentation Phase
The formation of b ound state systems from quarks and gluons cannot b e calculated with
p erturbativetechniques even if all higher orders could b e obtained easily b ecause of the
large coupling constantif Q is of the order of Therefore the hadronisation is describ ed QC D
by QCD motivated phenomenological mo dels The commonly used mo dels are independent
string and cluster fragmentation which are discussed in this section Emphasis is given to the
string fragmentation mo del since the standard DELPHI Monte Carlo generator is based on
that
Indep endentFragmentation
One of the rst fragmentation mo dels was the so called indep endent fragmentation mo del
The ansatz assumes that every parton fragments into hadrons indep endently of the other
partons in the event The algorithm is based on an iterative ansatz in which the available
energy is divided in a branching according to a longitudinal splitting function The iteration
stops when the remaining energy is b elow a certain cuto energy E whichistypically ab ove
IF
the pion mass The fragmentation is p erformed in the center of mass frame of the whole
pro cess Therefore the indep endent fragmentation mo del is not Lorentz invariant Also the
remaining energy of each individual jet has to b e balanced at the end of each fragmentation
pro cedure
String Fragmentation
The simplest version of string fragmentation starts with a pair of massless quarks and
antiquarks moving in opp osite directions with v c The self coupling of the gluons leads to
a linear eld con guration of typical size of fm which is spanned b etween the quarks This
ob ject is called string The idea originates from the magnetic ux tub es in sup erconductors
The e ect is therefore called the chromoelectric Meissner e ect The linear energy densityin
GeV leading to a linear growing p otential the colour eld is a constant a GeV fm
between the quarks As so on as the energy stored in the eld exceeds the quark pair creation
threshold a new meson is formed leaving the rest of the string as an exact copy of the original
scaled down by the energy taken by the meson Figure shows schematically this pro cedure
The fraction of energy and momentum z whichisgiven to the meson is distributed according
to the longitudinal fragmentation function f z Exp erimental data for the heavy avours c
and b can b e describ ed b est bythePeterson function
f z
z z z
and for the light avours u d and s by the Lund symmetric function
a
z bm
T
f z exp
z z
The Peterson function has the free parameter It is the squared ratio of the masses of
heavy to light quarks However since the light quark masses are not precisely known in
practice the value of is evaluated from the data Once it is known for one heavy avour the
appropriate value for the other can b e obtained from the quark mass relation m m
b c
c
b
The Lund symmetric function has two parameters a and b whichhave to b e tted to the data colour string − qq
− q q − qq
(1−z) · p z · p
Figure Schematical view of the string fragmentation algorithm The self interaction of
the colour eld leads to a linear eld of constant energy density the string The string breaks
and a meson is formed The rest of the string is left as an exact copy of the original scaled
down by the energy taken by the meson
The transverse mass m m p is calculated from the mass and the average transverse
T T
momentum of the pro duced meson Fig shows the longitudinal fragmentation functions
for the di erent quark avours The heavy avours are describ ed bythePeterson function
with and For the light avours the Lund symmetric function is plotted
b c
with the values a b MeV c and the masses of pion and kaon as
p
T
typical representations for a light and strange meson
The gluons can b e incorp orated into the string fragmentation picture in an universal and
simple way They are treated as transverse excitations of the colour ux tub e Without the
intro duction of additional free parameters anynumb er of soft and hard gluons can b e mo deled
as a string with several kinks
The avour content of the new hadrons dep ends on the probability of creating a quark
antiquark pair within the thin linear colour ux tub e The rest mass m of the pro duced pair
has to b e provided by the eld energy stored in the string Assuming constant linear energy
density a the two new quarks havetobeatadistance l with l m a when app earing
as on shell particles If the mo del includes also the transverse movement of the pro duced
ob ject this additional energy requires an even further separation The probability for such
a pair creation pro cess can b e calculated by a simple quantum mechanical approach treating
the e ect as a tunneling phenomenon The tunneling feature b ecomes evident if the reaction
is imagined to pro ceed in the time reversed direction starting with two quarks at rest at
l attached to two strings of string constant a By a short violation of energy conservation
they travel a distance l meeteach other at the middle and connect the two strings thereby
restoring the amount of p otential energy la they b orrowed in their annihilation A wave
function intruding a linearly growing p otential exceeding the classical turning p oint will have
an exp onentially decreasing intensity This yields for the pair creation probability
m p
T
P exp
a
The tunneling picture predicts in a natural waya unique Gaussian p distribution for all
T
is a free parameter since neither the string constant nor the quark hadrons The width
p
T
masses are precisely known It automatically accounts for the suppression of heavy avours beauty
up and down charm
fragmentation function strange
fragmentation variable z
Figure The longitudinal fragmentation functions for the di erent quark avours The
heavy avours are described by the Peterson function with and For
b c
the light avours the Lund symmetric function is plotted with the values a b
MeV c and the masses of pion and kaon as typical representations for a light and
p
T
strange meson
during the fragmentation The exp ected rates are
u d s c b
This means that c and b quarks are practically never pro duced by the soft hadronisation
mechanism Since the light quark masses are only known with large errors the s quark
suppression is a free parameter of the mo del
The creation of a diquark in the fragmentation phase leads to baryon pro duction For this
case the same statement is true ab out the suppression factors for heavy avours In order to
conserve quantum numb ers a second diquark has to b e pro duced near to the rst diquark It
can either b e pro duced immediately next to the rst diquark or with some mesons in b etween
The latter case is known as pop corn e ect
Cluster Fragmentation
A particular version of the so called cluster fragmentation is implemented in the HERWIG
program The basic idea is the following The parton shower evolution develops up to
a certain virtuality Q Then all gluons are forced to split into quark antiquark pairs thus
ef f
is intro duced to enforce this pro cess forming clusters of partons An e ective gluon mass m
g
The heavy quarks can either b e pro duced primarily or during the p erturbative phase
ef f
m is a parameter whichmust b e adjusted in order to t the mo del to the data Conservation
g
ef f
of energy and momentum requires m to b e at least twice the mass of the lightest quarks
g
If the mass of a formed cluster is ab ove a certain cluster mass C it will decayinto two
max
clusters by creation of a q q pair The clusters are colour singlets which then turn into hadrons
ef f
for the quarks The invariant mass of a cluster M is calculated by using e ective masses m
i
in a cluster The e ective masses for up down strange charm and b ottom quarks are
and GeV c resp ectively
Hadron Decays
After the fragmentation phase no particles created during the p erturbative phase have sur
vived They were con ned in primary mesons and baryons whichnow start to decayinto
stable nal state particles The commonly used simulation programs here refer to experimen
tal ly measured branching ratios However at LEP energies esp ecially within the domain of
b ottom hadrons a numb er of states are pro duced where only a few or no exp erimental data
exist The mo deling of their pro duction and decay is inspired by predictions observations in
analogous systems quantum numb er conservation and simple spin and state counting ar
guments Fig gives two examples for particle decays visualized in the so called sp ectator mo del
+→ ∗ο +ν + ∗∗+→ οπ+ (a) B D e e e (b) B B u + + π W ν − − − e d b c u d + ∗ο ∗∗+ ο B D B B − −
u u b b
Figure Two examples for particle decays in the spectator model a Weak decay of a
B meson in a D and a e pair b Strong decay of an orbital ly excited B meson B
e
into a B meson and a pion
The only exception are initial or nal state photons which are colourless and thus escap e from con nement
The D meson and its excitations e g can serve as a mo del for the B system
Quantity Exp eriment Measurement Ref
MeV c m PDG
B
ps PDG
B
L
DELPHI
m MeV c ALEPH
B B
PDG
average
L publ
pro duction ratio L up date
DELPHI
B B B
ALEPH
average
Table Selectedexperimental results on B and B mesons as given by the Particle Data
Group and the LEP col laborations
B Meson Sp ectroscopy
For hadrons containing a heavy quark Q quantum chromo dynamics displays additional sym
metries in the limit as the heavy quark mass m b ecomes large compared with a typical QCD
Q
scale These heavy quark symmetries are p owerful aids in understanding the sp ectrum and
decayofheavy light Qq mesons see also section Because m heavy quark
b QC D
symmetry should provide an excellent description of the B and B meson and their excited
s
states It is plausible that the prop erties of the D mesons and even of the K mesons should
also re ect approximate heavy quark symmetry
Ground State B Mesons
P P
The pseudoscalar B meson J andthevector B meson J have b een
established exp erimentally for several years The B meson decays electromagneticallyinto
a B meson and a photon B B A fraction of the exp erimentally available results is
shown in Tab The Hilb ert space of these states can b e represented conveniently in a
tensor pro duct notation j i where the rst is the rd comp onent of the spin
of the heavy quark and the second is the rd comp onent of the light degrees of freedom
jB i j i
p
jB i j i j i
jB i j i
p
jB i j i j i * B/B spin counting V : P = 3 : 1 V/(V+P) D/D*
K/K* π/ρ
< >
(MV-MP)/ M
Figure Production ratio V V P of vector V and pseudoscalar P mesons as a
function of M M hM i at LEP The triangles show the ratio including primary and
V P
secondary produced mesons The squares give the same ratio wheresecondary mesons
from particle decays have been subtracted using the jetset model with DELPHI
tuning A vector meson suppression is evident for the light mesons
It can b e seen that the pseudoscalar B meson b elongs to a singlet while the vector B meson
b elongs to a triplet From a simple spin counting argument one would exp ect a pro duction
ratio of B B mesons of in e e collisions This exp ectation is in accord with LEP
measurements see Tab
B B B
ting argument which seems to work well in the B B However this simple spin coun
system fails for light meson systems Avector meson suppression is observed here The
pro duction ratio V V P of vector V and pseudoscalar P mesons as a function of M
V
M hM i is shown in Fig The triangles show the ratio including primary and secondary
P
pro duced mesons The squares give the same ratio where secondary mesons from particle
decays have b een subtracted
B Mesons with Orbital Excitation
For the discussion of orbitally excited meson states the usual sp ectroscopic notation is used
S
n L where n is the principle quantum number S the total spin L the orbital angular
J
momentum b etween the quarks and J L S Tab gives the suggested q q quark mo del
assignments for most of the known mesons
In the strict sense this notation is valid only if S and L are conserved quantum numbers
In the limit of equal mass quarks q q this situation is rather well ful lled rst column in
Fig In this case the total spin S s s and the orbital angular momentum L are
q q
This simple argument needs slight corrections due to the pro duction of higher excited states e g B mesons This will b e discussed in the next sections e they s s bs B B I d b B B cial ly of the u e b I P P P d in this table sinc S b b b b b I e not liste s s c D I s s s Some assignments esp D D D d D u c c I D D D S P P P P c ws the suggestion of the PDG Other authors suggest these states to b e c c c c c c I h J K sd oversial Some of the light mesons ar A B K su K K ontr I K K K K K K K cules or other exotic states and mole e stil l c K K s K s d h f f f I u d u mixtures of o del assignments for most of the known mesons andidates f f h f al l c d quark mo u d q q u I d d b a a dasglueb u molecules a are nearly equal ete K B K t of these particles is still under discussion The classi cation follo K PC J Suggeste and A J L K S S P P P P D D D D terpreted as S in The The assignmen e usual ly interpr N able T multiplet and for somear of the higher multiplets ar
conserved separately For the case of u or d quarks the ground state pseudoscalar and vector
P P
meson corresp ond to the pion J and the meson J Orbital excitations are
formed by coupling the total spin S to the orbital angular momentum L leading to a singlet
and a triplet For the case of L the b is identi ed as the singlet and the particles a a
and a are identi ed as b elonging to the triplet see Fig
This situation changes drastically if one quark b ecomes muchheavier than second
QC D
column of Fig One essential idea of the heavy quark limit is that the spin of the
heavy quark s and the total spin orbital angular momentum j s L of the light
Q q q
degrees of freedom are conserved separately Accordingly each energy level in the excitation
sp ectrum of Qq mesons is comp osed of a degenerate pair of states characterized by j and
q
J j s The ground state pseudoscalar and vector mesons the total angular momentum
q Q
P
which are degenerate in the heavy quark limit corresp ond to j with J B and
q
P
J B Orbital excitations lead to two distinct doublets asso ciated with j L
q
For the sp ecial case of L four di erent states are exp ected
P
J B
j
q
P
J B
P
J B
j
q
P
J B
The o cial notation for the four states is given in the third column All four states are com
monly lab eled as B In order to describ e whether the b quark in the meson is accompanied
byau d or as quark the notation is extented by the subscript u d or s B B and B
u s
d
In the literature the symbol B usually refers to the states B and B sometimes it also
u
d
includes the state B The meaning b ecomes apparent from the context Before the start of
s
the work describ ed in this thesis none of the B mesons was observed exp erimentally The
main part of this thesis will fo cus on the search for and observation of these states
Prop erties of Orbitally Excited B Mesons
Orbitally excited B mesons will decay due to the strong interaction The exp ected main decay
mo des of B mesons are B and B If the B meson mass is ab ove the BK or B K
s
u d
y mo des since the decayinto B is forbidden by threshold these will b e the prominentdeca
s
isospin conservation The memb ers of the rst doublet j should b e narrow compared
q
to the typical strong decay width b ecause only L d wave decays are allowed This is
due to the conservation of angular momentum and parityforthe state and a dynamical
prediction of HQET for the partner The memb ers of the second doublet j are
q
exp ected to b e broad of the order of the typical strong decay width MeV c b ecause
L s wave decays are allowed HQET predicts the two eigenstates to b e mixtures
of the states with S and S This results in the prop erty that the j
q
state decays via s wave while the j state decays via d wave The situation is
q
ern the p ossible decay mo des for similar to the D and K meson sector Spin parity rules gov
the di erent states In general
symmetric mesons heavy lightmesons
u u u
q q q
Q
conventional quark mo del Heavy Quark E ective Theory
m m m m m
q q q Q Q
L
Parity P
LS
Charge Conjugation C C not de ned
s s S s L j
q q q q
L S J s j J
Q q
ground state orbital angular momentum L
B
B
excited state orbital angular momentum L
B
b
B
a
a
B
a
B
Figure The di erent coupling schemes of symmetric and heavy light mesons For
symmetric mesons rst column the total spin S and the orbital angular momentum L are
conserved separately Heavy light mesons second column are governed by HQET The spin
of the heavy quark s and the total angular momentum of the light degrees of freedom j are
Q q
conservedseparately
b
Q
Q
Q
Q
pickfromvacuum
Q
Qs
q q q
H
H
H
mesons baryons
H
H
H
H
H
H
Hj
L L
B B B
B B B
B B B
B B B
R
BN
B B
B B B B
B B
B B
P
H
P Q
Z
P H
B B
P Q
Z H
P
P Q H
Z
B B
P
H
P Q
P Z H
B B
P Q
H
P
Z
P Q H
B B
P
Z H
P Q
strong decays
P H
Z
B B
P Q
H
P
P Q Z H
B B
P
H
Q P
Z
P H
B B
P Q
Z H
R P Z
BN BN
Hj
P Q
P
Qs
Pq
B B
Figure Production and decay properties of orbital ly excited B mesons Details con
cerning this diagram are given in the text
B B B BK broad states
s
B B B B K s wavedecay
s
B B B B K narrow states
s
B B B B K d wavedecay
s
where the symbol B denotes B or B meson Fig gives an overview of pro duction
and decay prop erties of orbitally excited B mesons A primary pro duced b quark will picka
quark q from the vacuum of the time to form a meson while of the time a baryon
is formed From the D meson sector it is exp ected that roughly of the mesons will b e
pro duced with L with L According to simple spin counting rules the states
with L will b e manifest in of the cases as B mesons and in as B mesons The
four B states and withL will decay according to spin parity rules into
B and B mesons Dep ending on the pro duction mechanism assumed for these states spin
counting state counting oranything in b etween the ratio of B
B mesons pro duced from B decays can vary from to For this
calculation it is assumed that the state decays only in B mesons for the spin counting
argument and only into B mesons for the state counting argument The B meson then decays
electromagneticallyinto a B meson and a photon
In uence of B Pro duction on the Ratio B B
As discussed in section the pro duction ratio of B mesons p er primary pro duced meson
was measured by the LEP exp eriments to b e In the absence of
B B B
B pro duction this ratio is equal to the parameter V V P inthejetset fragmentation
mo del where V and P are the pro duction rates of primary vector and pseudoscalar B
mesons However pro duction of a sizeable amountofB mesons can alter the ratio of B to
B mesons dep ending on the relative pro duction rates and branching fractions into B and
B of the four individual B spin parity states A further complication arises from the way
jetset treats the pro duction of the two states one state is made from the P S
fraction and the other state together with the and the states is made from the V
S fraction However HQET predicts the two eigenstates to b e equal mixtures of
S and S Di erent assumptions such as relative pro duction ratios
varying b etween state counting and spin counting and unknown
decay branching ratios into B maychange the e ective branching fraction of B to B
to anything within the range to This implies that
V
B
f Br B B
V P f
B B
where f denotes the pro duction ratio of B mesons p er primary pro duced meson
In uence of B Pro duction for Mixing Studies
s
The avour change in B decays is shown schematically in Fig According to isospin
rules B and B will decay of the time with the emission of a charged pion and in
u
d
with the emission of a neutral pion for the moment the B channel is neglected In
the analysis presented here only the charged pion decaychannel is investigated It is worth
noting that B mesons cannot decayinto B since it is forbidden by isospin conservation
s
s
B mesons decay with the emission of a kaon K K
s
This fact is imp ortant for B mixing studies which are b eing p erformed at LEP
s
These analyses lo ok for oscillations of a primary pro duced B to a B meson The Standard
s s
K system with box diagrams Inthe Mo del describ es such pro cesses in analogy to the K
B B system clear evidence for time dep endent and integrated mixing has b een extracted
d d
from data at LEP Assuming the usual strangeness suppression factor
u d s
for the pro duction of B mesons in B events leads to a pro duction ratio of
s B B B
s s
mesons are This pro duction ratio has to b e corrected if sizeable amounts of B
s
The avour here refers to the quark antiquark which forms the B meson together with the b b quark
B B B
s u
d
H
H
H
K K
H
H
H
H
H
H
H
H
H
H
H
H
H
H
Hj R R
B B B
s u
d
Figure Flavour change in B decays According to isospin rules B and B wil l
u
d
decay of the time with the emission of a charged pion and with the emission of a
mesons since this is forbidden by isospin neutral pion B mesons cannot decay into B
s
s
conservation
pro duced since they do not decayinB mesons One obtains
s
B
s
f
s
B B
s
where f is the pro duction ratio of B mesons p er primary pro duced bs state This e ect
s s
makes it more di cult to observe B mixing at LEP
s
The decay prop erties and susp ected mass relations of orbitally excited B and B mesons
s
are summarized in Fig The ordinate shows schematically the mass of the di erent
states The arrows give the p ossible decay mo des The decays of the ground state mesons
L are not shown
Motivations from the D Meson Sector
Orbitally excited D and D mesons have b een established exp erimentally for the past few
s
years The evidence has b een obtained by exp eriments running on the S resonance
mainly CLEO and ARGUS The results from the CLEO collab oration dominate the world
P
average All narrow orbitally excited D meson states j with J have b een
q
observed in the channels D and D Furthermore in the D meson sector all the narrow
s
states have b een identi ed in the channels DK and D K Spin parity and decaycharacter
istics have b een shown to b e in accord with HQET predictions bystudyingdecay angular
P
distributions However until now none of the broad states j with J has
q
b een identi ed Tab summarizes the measurements of masses and widths for the known
excited D meson states as published by the CLEO collab oration The observed mass
splitting b etween and states is given as well
Heavy quark symmetry predictions e g byEichten Hill and Quigg use the mea
masses as input and predict the masses of the corresp onding B states This sured D and D
Note that only B mesons live long enough to mix It do es not matter if a B meson is primary or comes
s s
from the decay ofaprimaryB meson B B
s
s s * * Bs2 Bsο Bs1Bs1 ∗ο ∗+ ο + ο ∗ο + ∗+ B2 B2 Bο Bο B1 B1 B1 B1 L = 1
* Bs ∗ο ∗+ B B B π emission s L = 0 ο + K emission B B
J=0 J=1 J=2
Figure Decay properties and suspected mass relations of orbital ly excited B mesons
The ordinate shows schematical ly the mass of the di erent states The arrows give the possible
decay modes The decays of the ground state mesons L are not shown
will b e discussed in the following section Furthermore they predict masses and decay widths
for the D and D mesons Their prediction for the D meson lies MeV c b elow
s s
s
the level observed at MeV c The prediction for the D meson lies
s
MeV c below the level observed at MeV c It was suggested by the authors
to take the discrepancies b etween the calculated and the observed masses as a measure of the
limitations of their mo del The accuracy for the B system predictions is lower since none of
s
the unknown orbitally excited B states could b e used as input at the time the mo del was
u d
develop ed
Recently the LEP exp eriments rep orted evidence for D pro duction in c events as well
as in b events The D mesons in b events app ear due to weak decays of B mesons
e g B D The measured pro duction ratios of the LEP exp eriments are summa
rized in Tab together with the corresp onding measurements from ARGUS and CLEO
Although exp erimental errors are large it b ecomes clear that sizeable fractions of D mesons
are pro duced in B meson decays roughly Moreover sizeable fractions of D mesons
roughly are observed in c quark fragmentation thus proving that quark fragmentation
is capable of pro ducing mesons with orbital excitation These facts motivate a search for B
mesons at LEP
State Channel Mass Width Ref
MeV c MeV c MeV c
D D
D D
D D
D D D
D D K D K c l
s
D D K
s
Table Experimental results for orbital ly excited D mesons obtained by the CLEO col
laboration Given are masses widths and mass splitting between and states
Quantity Exp eriment Measurement Ref
ARGUS
CLEO
c D X Br D D
c jet
DELPHI
ALEPH
ALEPH
b D X Br D D
b D X
DELPHI
ARGUS
CLEO
Br B D
Br B D D D
DELPHI
OPAL
Table D production in e e annihilation experiments Note that ARGUS and CLEO
run on the S resonance while the ALEPH DELPHI and OPAL experiments operate at
the Z pole
Predictions for Orbitally Excited B Mesons
Predictions of Masses
The heavy spin symmetry can b e combined with the heavy avour symmetry to predict masses
of the narrow orbitally excited B mesons in terms of meson masses in the charm sector The
relevant derivation may b e found in a pap er byFalk and Mehen The splittings b etween
excited doublets and the ground state should b e indep endentofheavy quark mass while the
spin symmetry violating splitting within the doublet scales like m If one de nes the spin Q
averaged masses and mass splittings to b e
m m m
B B B
m m m
B B B
m m m
B B B
and analogous relations for charm mesons the heavy quark symmetries predict that
m m m m
D B D B
m
c
m m
B D
m
b
With the assumption m m and averaging over the charged and neutral charmed
c b
mesons these relations yield
m B MeV c
m B MeV c
m B MeV c
s
m B MeV c
s
are of the order The leading corrections to the predictions form andm
B B
s
MeV
QC D
m m
c b
where a QCD scale of MeV has b een assumed It b ecomes evident that heavy
QC D
quark symmetry together with measurements in the charm system provide p owerful to ols for
predictions in excited B systems The simpleness of these considerations increases the con
dence in the predictions
A more sophisticated mo del has b een develop ed in twopapersbyEichten Hill and
Quigg In a more general concept they write the mass of a heavy light meson in
the from
C nL j
J q
m nL j m S E nL j
J q q
m
Q
where m S m S m S is the mass of the ground state E nL J is the
q
excitation energy and C nL j are constants The excitation energy E nL j has a weak
J q q
dep endence on the heavy quark mass Referring to non relativistic Buchmul ler type p otential
mo dels to estimate the variation of the excitation sp ectrum as a function of heavy quark mass
and using meson masses of already observed states the following mass predictions have b een
determined for orbitally excited B mesons
The following particles were used as an input K K K K D D D D D D B and B
A s
s
m B MeV c
m B MeV c
m B MeV c
s
m B MeV c
s
Thus the mass splitting b etween the and the state is predicted to b e MeV c for
the B case and MeV c for the B case Similar mass splittings MeV c for the
s
u d
B and MeV c for the B are predicted byFalk and Mehen although their absolute
s
u d
mass predictions are signi cantly di erent from the ab ove
There are no detailed predictions for the masses of the broad j B states
q
since they decay immediately via s wave due to strong interactions In rst approximation
they should have the same masses as the narrow j states Other mo dels predict
q
their masses to split from the narrow states by an amount of the order of MeV c
whose magnitude and sign gives valuable information on the spin structure of the long range
interquark force
Predictions of Decay Widths
It is somewhat more delicate to make predictions for the widths of the excited B mesons than
for their masses since the widths dep end on the available phase space and hence on the values
of the heavy meson masses The argument presented here follows the ideas of Eichten Hill and
Quigg Consider the decay of an excited heavy lightmeson H characterized by L j
J q
to a heavy light meson H L j and a light hadron h with spin s The amplitude for
h
q
J
the emission of h with orbital angular momentum l relativeto H satis es certain symmetry
relations b ecause the decay dynamics b ecomes indep endent of the heavy quark spin in the
m limit of QCD The decay amplitude can b e factored into a reduced amplitude A
Q R
times a normalized j symb ol
J s j
Q
q
s j J j
q
Q h
A j l j j A H H h C
R h q
q
j J j
q
h
where
q
s s j J j J
Q Q
q q
C J j
q
j Jj j J j
q q
h h
and
j s l
h h
The co e cients C dep end only up on the total angular momentum j of the light hadron and
h
not separately on its spin s and the orbital angular momentum wave l of the decay The
h
two b o dy decay rate may b e written as
s j J j j
q
Q
q q
l H H h
C p F p
j l
j J j j l
h
q
h h
where p is the three momentum of a decay pro duct in the rest frame of H Heavy quark
j j
q
q
p for a particular decay symmetry do es not predict the reduced A or the related F
R
j l h
However once determined from the strange and charmed mesons these dynamical quanti
ties are used to predict related decays e g those of orbitally excited B mesons For each
indep endent decay pro cess a mo di ed Gaussian form is assumed
l
M
j j j j
q q
q q
exp p p F F
j l j l
h h
M p
and the overall strength of the decay and the momentum scale is determined by tting to
existing data The ability to predict decay rates dep end on the quality of the information used
to set these parameters The following list gives the predicted decay widths for orbitally
excited B mesons
B B MeV c
B B MeV c
B B MeV c
B B MeV c
B al l MeV c
B B MeV c
B B MeV c
B B MeV c
B al l MeV c
B B K MeV c
s
B BK MeV c
s
B al l MeV c
s
B B K MeV c
s
Chiral symmetry and heavy quark symmetry combined suggest that the heavy light j
q
states should have large widths for pionic decay to the ground states MeV c
This will make the discovery and study of these states challenging and will limit their utility
for B tagging
Flavour Tagging and CP Violation
Inclusive studies of particle antiparticle mixing and CP violation for neutral B mesons require
that the quantum numb ers of the meson have to b e identi ed at the time of pro duction This
identi cation can b e made by observing the decayofaB B pro duced in asso ciation with
the neutral B B ofinterest The e ciency of avour identi cation might b e signi cantly
enhanced if the neutral B mesons under study were self tagging
Charmed mesons have b een observed as strong decay pro ducts of orbitally excited cq
states in the decaychannels D D and D D The charge of the pion signals the
tnumber of B mesons were pro duced avour content of the charmed meson If a signi can
through one or two narrow excited states then the strong decay B B tags the
neutral meson as bq or bq ThisB tagging may resolve kinematical ambiguities in semilep
tonic decays of charged and neutral B mesons bycho osing b etween two solutions for the
momentum of the undetected neutrino In hadron colliders and Z factories this technique
may make high statistics determination of the form factors in semileptonic decays p ossible
and would enable precise measurements of V and V
cb ub
However the primary application of B tagging would b e in the exp ected large CP
violation asymmetry Theoretically these asymmetries can b e interpreted most easily
in the decays of the neutral B meson into CP eigenstates f suchasJ K A state whichwas
s
pro duced as B at time t decays into a CP eigenstate f with probability D while a state
f
whichwas B at t decays into f with probability D The time integrated asymmetry
f
can b e written as
B f B f D D
f f
t t
A f
B f B f D D
f f
t t
For the nal state f J K it has b een shown that the asymmetry A f measures the
s
angle of the unitarity triangle a fundamental parameter of the CKM matrix to a very
go o d approximation for notation see e g Ref
x
d
A J K sin
s
x
d
since a single amplitude contributes to eachdecay B J K and B J K The
s s
parameter x is known as the mass mixing parameter and has b een extracted from time inte
d
mixing analyses B grated B
d d
This discussion shows the imp ortance of B tagging for future exp eriments on CP
violation in the B system The work of this thesis is dedicated to the rst observation of
the B meson and to the investigation of its prop erties
b Baryon Sp ectroscopy
Heavy Baryons
Heavy baryons are b ound states formed from a heavy quark and a light diquark system The
P
spin parity quantum numbers J of the light diquark system are determined from the spin
and orbital degrees of freedom of the twolight quarks that make up the diquark system
From the spin degrees of freedom of the two light quarks one obtains b oth spin and spin
states The total orbital state of the diquark system is characterized bytwo angular degrees
of freedom whichw etake to b e the two indep endent relative momenta k p p and
K p p p which can b e formed from the two light momenta p and p and the
heavy quark momentum p Thek orbital momentum describ es relative orbital excitations of
the twolight quarks and the K orbital momentum describ es orbital excitation of the center
of mass of the twolight quarks relative to the heavy quark as shown in Fig
The wave function may b e viewed as if the heavy quark charm or b ottom at the center
is surrounded by a cloud corresp onding to a light diquark system The only communication
between the cloud and the center is via gluons But since the gluons are avour blind the light
cloud knows nothing ab out the avour of the center Also for in nitely heavy quarks there
Up till now CP violation has only b een observed in the K K system
q y
L L
K k
Q
q y
Figure Orbital angular momenta of a light diquark system L describes relative orbital
k
momentum of the two light quarks and L describes orbital momentum of the center of mass
K
of the light quarks relative to the heavy quark
is no spin communicationbetween the cloud and the center Thus one concludes that in the
heavy mass limit a b ottom baryon at rest is identical to a charm baryon at rest regardless
of the spin orientation of the heavy quarks First order corrections to this limit would b e
prop ortional to m as discussed in section
Q
The ground state heavy baryons L L are made from the heavy quark Q
k K
P
with spin parity J and a light diquark system with spin parity and moving
in an s wave state relative to the heavy quark When one combines the diquark spin with the
heavy quark s spin one obtains the ground state heavy baryons and according to
Q Q
Q
the following coupling scheme
P
J
Q
P
J
Q
P
J
Q
The two states and are exactly degenerate in the heavy quark limit since the heavy
Q
Q
quark p ossesses no spin interaction with the light diquark system as m Parts of the
Q
work on this thesis will fo cus on the search for the charged and baryons with quark
b
b
They are exp ected to decay strongly and ddb for the content uub for the
b b
into
b
PresentKnowledge ab out b Baryons
The present exp erimental knowledge ab out b baryonsisvery limited First measurements
show that roughly of primary b quarks in e e annihilation fragmentinto
baryons while the remaining b quarks fragmentinto B mesons see also Fig Fig
shows the SU baryon multiplets made of u d s and b quarks where picture a corresp onds
A comprehensive theoretical review ab out heavy baryons is given in Ref
Quantity Exp eriment Measurement Ref
ALEPH
MeV c Mass m DELPHI
b
PDG Average
ALEPH
Lifetime ps DELPHI
b
OPAL
Polarisation P ALEPH
b
DELPHI
Rate f b Br X
b b
OPAL
ALEPH
Rate f b Br X
b b c
DELPHI
Lifetime ps DELPHI
b
ALEPH
Rate f b Br X DELPHI
b b
OPAL c l
Table Present know ledge about b baryons Properties of and baryons as measured
b b
by the LEP experiments
P
to the plet with SU o ctet J and picture b corresp onds to the plet with
P
SU decuplet J The present knowledge on b baryons is summarized in Tab
From the b baryons only the state is exp erimentally established Most of the b baryons
b
are exp ected to decayinto by strong or electromagnetic interactions Since the is the
b b
lightest b baryon it decays weakly It has b een observed in the nal states J
b
X and X Note that the lifetime is roughly pD
b
c c
lower than the lifetime of the B meson Some evidence has also b een obtained
for the existence of the baryon otherwise there is nothing known ab out excited b
b
baryons
The sp ectroscopyinthec baryon sector can serve as a guide in the searches for new
b baryons The has b een observed in manychannels e g pK pK
c c
pK and It has a mass of MeV c Furthermore
the has b een identi ed decaying to almost hundred p ercentinto The follow
c c
ing masses ha ve b een measured m MeV c m
c c
MeV c and m MeV c The has not yet b een
c
c
discovered
Baryons Predictions for and
b
b
Predictions of Masses
The simplest approach in predicting the mass di erence b etween and consists of a
b b
simple extrap olation from the c baryon sector ignoring all m corrections Taking the
b
Particle Data Group mass values for the and leads to
c c
m m MeV c
b b
As already said in this simple approach the state would have the same mass as since
b
b
there is no spin communicationbetween the b quark and the diquark
A more sophisticated mo del for the masses of and dealing with corrections in
b
b
m has recently b een published by Roncaglia Dzierba Lichtenb erg and Predazzi
b
They argue that the quark p otential mo del has b een the most successful to ol enabling
physicists to calculate the masses of normal mesons and baryons containing heavy quarks
However p otential mo dels su er from the fact that although motivated by QCD they have
not b een derived from basic theory QCD Therefore predictions ab out hadron masses are
made with complementary metho ds which use general prop erties of the p otential but not its
sp eci c form Complementar y constraints are obtained from hadron and quark masses
from the Feynman Hellman theorem theorems which relate the ordering of b ound state
energy levels to certain prop erties of p otentials and regularities in known hadron masses
which yield estimates of undiscovered hadrons using either interp olation or semi empirical
mass formulae Exploiting these metho ds the following mass predictions for the and
b
b
baryon are obtained
m m MeV c
b b
m m MeV c
b
b
A similar mass prediction for the baryon has already b een obtained in a pap er from
b
by A Martin
m m MeV c
b b
Predictions of Widths
can b e estimated in the nonrelativistic quark The widths for the transitions
b b
b
mo del by using a pion quark coupling estimated from the Goldberger Trieman relation This
computation has b een done byYan et al They nd
g p
A
p MeV c
f MeV c
where p is the pion three momentum in the rest frame f MeV c andg is the
A
b
axial vector coupling of the constituent quark In the numerical estimate we take g
A
to give the correct g for the nucleon The and the have the same decay rate up
A b
b
to kinematic factors since the decaymechanism do es not directly involve the heavy quark
Summary of the Chapter
The static quark mo del describ es nearly all exp erimentally known meson and baryon
states Furthermore predictions for the quantum numb ers of unknown meson and
baryon states can b e derived
The dynamic theory of the strong interaction is Quantum Chromo dynamics QCD
The non Ab elian structure of the theory provides the key p oint for the understanding
of con nement and asymptotic freedom
Quantum chromo dynamics reveals additional symmetries in the limit of m m
d u
Isospin Symmetry as well as in the limit of m Chiral Symmetry and in
q
the heavy quark limit m Heavy Quark Symmetry The latter symmetry is
Q
describ ed mathematically byHeavy Quark E ective Theory HQET
In the heavy quark limit the spin of a heavy quark decouples from the light quark
degrees of freedom Heavy Spin Symmetry and the avour of the heavy quark b ecomes
irrelevant to the system Heavy Flavour Symmetry Heavy Quark E ective Theory can
b e constructed by taking the limit m with four momenta xed of the Feynman
Q
rules of QCD In an equivalent approach the same limit is taken for the QCD Lagrangian
leading to the same Feynman rules
The non relativistic quark p otential mo del is the most successful to ol enabling physicists
to calculate masses and prop erties of mesons and baryons The most general non
relativistic ansatz for a quark antiquark system starts with the Breit Fermi Hamilton
or heavy quark systems e g charmonium cc or b ottomonium bb spin function F
dep endent terms in the Hamilton function can b e treated by p erturbation theory
Hadronic Z decays in e e annihilation can b e describ ed by four phases which are
implemented in the jetset simulation program Electroweak Phase Perturbative
Phase Fragmentation Phase and Particle Decay Phase The p erturbative phase of
short distance QCD is mo deled either by the parton cross sections obtained by the
exact second order QCD matrix element at an optimized scale or by the parton shower
algorithm The low Q QCD pro cesses of hadron formation in jetset are describ ed by
the string fragmentation mo del
Quark mo del and dynamical implications from HQET provide predictions for orbitally
excited B mesons They are commonly lab eled as B B mesons and are group ed
s
P P
Twoof into two doublets with j J andj J
q q
these states j are exp ected to havenarrowwidth MeV c since they
q
decay through d wave transitions The exp ected main decaymodesareB B
B B K Masses and decay widths of these states have b een predicted Obser
s
vations from the D meson sector motivate the search for orbitally excited B mesons
The present knowledge ab out b baryons is very limited Only the is exp erimentally
b
are made using constraints established Predictions for the baryon masses of and
b
b
on hadron and quark masses from the Feynman Hellman theorem theorems which
relate the ordering of b ound state energy levels to certain prop erties of p otentials and
is exp ected regularities in known hadron masses The principal decaymodefor and
b
b
be into b
Chapter
The Exp eriment
This chapter describ es the exp erimental setup of the Large Electron Positron LEP collider
at CERN After an intro duction to the LEP machine the DELPHI detector one of the four
LEP exp eriments is discussed in more detail This is followed by a description of the DELPHI
online and o ine systems
The LEP Collider
The LEP storage ring with a circumference of ab out km is installed in the LEP tunnel
which has a diameter of m and lies to meters b elow the surface across the frontiers
between France Pays de Gex and Switzerland Canton Gen eve A schematic map of the
lo cal area is given in Fig The LEP ring consists basically of a b eam pip e a set of magnets
acceleration sections and their p ower supplies The magnets either b end or fo cus the electron
b eam while the acceleration sections consisting of several radio frequency cavities provide
the energy for the acceleration of the electrons and p ositrons In total there are dip ole
magnets for b ending and quadrup ole sextup ole and correction magnets for
fo cussing Since the electrons and p ositrons have opp osite electric charge and equal mass
they can circulate in opp osite directions in a single b eam pip e with the same arrangementof
fo cussing and b ending magnets Therefore unlike proton proton colliding b eam accelerators
LEP has only one b eam pip e
p
The energy of the electrons and p ositrons in the LEP phase is around GeV s
m This is achieved in a several step pro cedure as shown in Fig In the rst step of
Z
p ositron generation electrons are accelerated at the LEP Injector Linacs LIL to an energy
of ab out MeV Collisions with a target of high atomic numb er Z lead to the pro duction
of p ositrons with an average energy of MeV A small fraction of the p ositrons
is accelerated by the second stage LIL to MeV The electrons for the electron b eam are
pro duced by a MeV electron gun and are injected directly into the second stage LIL In the
next step the electrons and p ositrons are accumulated in the Electron Positron Accumulator
EPA to increase the currentofeach b eam The Proton Synchrotron PS then accelerates
the b eams to GeV followed by the Sup er Proton Synchrotron SPS which accelerates
Figure Schematic map of the local areanear the LEP col lider PS SPS and the LEP
rings are shown together with the four LEP experiments ALEPH DELPHI L and OPAL
them to an energy of GeV Finally the b eams are injected into LEP where the particles
are accelerated to ab out GeV The energy loss U due to synchrotron radiation is given
by
m E
U
r
GeV
where E is the b eam energy and r the b ending radius of the ring The synchrotron radiation
loss in LEP is not negligible and consumes ab out MW of p ower It is the ma jor constraint
on the maximum b eam energy for LEP with the present accelerator sections
Each b eam is concentrated in short time bunches with a length of cm The transverse
dimensions are mand m corresp onding to an elliptic b eam pro le
x y
Each bunch contains roughly electrons or p ositrons and circulates around the ring
times a second Until mid four bunches for electrons and p ositrons were used
Starting in LEP also op erates in an eight bunch so called pretzel mode andithas
b een tested successfully to run with bunch trains Both bunch systems are synchronized so
that they cross each other at the four interaction p oints each of which is surrounded by one
of the detectors ALEPH DELPHI L and OPAL The rate of pro duction of Z events at
the interaction p oints is increased b ecause the transverse size of the bunches is squeezed by
strong sup erconducting quadrup ole magnets close to the detectors
The running with bunches dividing each bunchinto a train of several mostly bunches is called bunch train mo de
Figure Schematic view of the LEP injection system which shows the two stage LEP
Injector Linacs LIL the Electron Positron Accumulator EPA the Proton Synchrotron
PS the Super Proton Synchrotron SPS and the LEP ring itself The MeV electron gun
close to the e e converter is not shown
From the physics p oint of view two imp ortantmachine parameters are the center of mass
p p
s and the luminosity L The center of mass energy s of an e e storage ring of two energy
b eams with exactly the same energy is twice the b eam energy This is the most economical
wayofachieving the highest p ossible center of mass energy In order to get a stable b eam
several e ects such as b etatron oscillations or b eam b eam interactions must b e considered
An additional small e ect which in uences the b eam energy on the p er mill level is the phase
of the mo on The surface of the earth is sub ject to the gravitational attraction of the mo on
It moves since the ro cks that make it up are elastic At the new mo on and when the mo on
is full the earth s crust rises by some cm in the Geneva area under the e ect of these
tides This movement causes a variation of mm in the circumference of LEP for a total
circumference of km which shifts the b eam energy up to E MeV
The luminosity L can b e de ned by
n L
where n is the numberofevents p er second of a given pro cess and is the corresp onding cross
section The luminosity dep ends on some sp eci c machine parameters and can b e expressed
Oscillations of the b eam around the ideal orbit of the machine are called b etatron oscillations
Electromagnetic interactions b etween the b eams lead to an increased b etatron frequency
Figure Integrated luminosity averaged over the LEP experiments in the years and
The horizontal plateaus correspondtotechnical stops and machine developments
in the following way
N N k f
L
x y
where N denotes the numb er of electrons or p ositrons in a bunch k is the numb er of bunches
f is the revolution frequency and and are the horizontal and vertical widths of the b eams
x y
at the collision p oint The maximum luminosity obtained at LEP in was approximately
nb s The integrated luminosityaveraged over the four LEP exp eriments for the years
and is shown in Fig In summary anintegrated luminosity of roughly
pb has b een collected in the years byeach exp eriment The b eam currentforan
e e collider is de ned as
I N k f e
where e is the elementary charge of the electrons and p ositrons Typical b eam currents for
LEP during the running p erio d were mA
The op erational phase of LEP ended in Octob er Starting from the cen
ter of mass energy of LEP will b e increased up to GeV in order to pro duce W W pairs
With a scheduled integrated luminosityof pb roughly W pairs are exp ected
p er exp eriment The main physics goals are investigations of the prop erties of the W boson
e g a precise measurement of its mass and searches for new physics e g Higgs or sup ersym
metric particles A serious problem for LEP is the energy consumption of the ring Due
to synchrotron radiation an energy loss of ab out MW is exp ected for running in the eight
bunch mo de This corresp onds to roughly of the pro duction of a mo dern p ower station
In order to optimize the acceleration sections of LEP the conventional radio frequency RF
cavities are b eing exchanged with sup erconducting RF cavities
The DELPHI Detector
The DELPHI detector is one of the four multi purp ose detectors at LEP DELPHI stands
for DEtector with Lepton Photon and Hadron Identi cation A schematic view of the appa
ratus is given in Figs and It was constructed and it is run by a collab oration of
physicists coming from di erent universities and national lab oratories The construction
time of DELPHI was roughly years The costs for the construction of DELPHI not including
the manp ower provided by the institutes were in the order of MSFr Since the op erational
b eginning of LEP in Novemb er DELPHI has collected over hadronic Z events
Forward Chamber A Barrel Muon Chambers
Forward RICH Barrel Hadron Calorimeter
Forward Chamber B Scintillators
Forward EM Calorimeter Superconducting Coil
Forward Hadron Calorimeter High Density Projection Chamber
Forward Hodoscope Outer Detector
Forward Muon Chambers Barrel RICH Surround Muon Chambers
Small Angle Tile Calorimeter
Quadrupole
Very Small Angle Tagger
Beam Pipe
Vertex Detector
Inner Detector
DELPHI Time Projection Chamber
Figure Schematic view of the DELPHI detector Vertex Detector VD Inner De
tector ID Time Projection Chamber TPC Ring Imaging Cherenkov Counter RICH
Outer Detector OD High density Projection Chamber HPC Superconducting Solenoid
Time of Flight Scintil lators TOF Hadron Calorimeter HAC Muon Chambers MUB
MUF and MUS Forward Drift Chambers FCA and FCB Smal l Angle Tile Calorimeter
STIC Forward Electromagnetic Calorimeter FEMC
Figure Schematic view of the DELPHI detector barrel part along the beam pipe
The apparatus can b e divided into three main parts the cylindrical barrel part with a
total length of m and a diameter of m which lies axially symmetric to the b eam pip e and
two large end caps m long and m diameter It has a total weight of approximately
tons The detector architecture has b esides some conventional comp onents of an e e detec
tor additional features for particle identi cation e g the Ring Imaging CHerenkov RICH
detectors whichallow a separation of kaons pions and protons in certain momentum re
gions Most of the elements in DELPHI provide direct three dimensional information which
is read out via some channels dedicated computers and one main computer This
section reviews the main barrel detector comp onents of DELPHI and provides information
concerning the p erformance More details can b e found in Refs
The Tracking System
The Solenoid
A large part of the barrel detector is emb edded in the magnetic eld T of the large
sup erconducting coil length m inner diameter m made of copp er packed Ni Ti
laments op erating at T K with a total current of A The magnetic eld allows
a precise momentum determination of charged particles from the curvature of their tracks in
the R plane Moreover it plays an essential role in reducing the transverse di usion of the
gas drift devices e g in the central Time Pro jection Chamb er TPC and in the High density
Pro jection Chamb er HPC
The Vertex Detector
The DELPHI Vertex Detector VD consists of three layers of silicon micro strip detectors
which surround the interaction p oint at radii of and cm parallel to the b eam pip e
see Fig and Eachlayer consists of mo dules covering a length of cm cm for
the closer layer In twolayers of the VD were equipp ed with double sided micro strip
detectors which provide measurements in R and Z direction The intrinsic resolution of the
VD is min R and minZ for p erp endicular tracks The short lever arm to the
interaction p oint results in an excellent impact parameter resolution in R and Z
has contributions from three indep endent sources The impact parameter uncertainty
IP
There is a purely geometric extrap olation uncertainty due to the p oint measurement
error in the VD the uncertainty due to multiple scattering in the b eam pip e and the layers
of the VD and the uncertainty on the p osition of the primary vertex Thus
MS V
The impact parameter uncertainty has successfully b een parametrized
IP MS V
for the R direction
v
u
u
GeV m c
t
R m
IP
p sin
and for the Z direction
v
u
u
GeV m c
t
m Z
IP
p sin
where p is the track momentum GeV c and the corresp onding p olar angle T oachieve
the extremely high precision which is of the order of the inhomogenities of a smo oth surface
a careful alignmentofeachlayer is necessary Measurements on high momentum particle
tra jectories e g Z aswell as the overlaps b etween the neighb oring wafers in each
layer are very useful in this resp ect
DELPHI has a cylinder co ordinate system with the Z axis coinciding with the electron b eam direction
The impact parameter is de ned as the distance of closest approachofatrack to the primary vertex
Figure Schematic layout of the DELPHI microvertex detector in cm a Projection
on the plane transverse to the beam b Perspective view
The Inner Detector
The Inner Detector ID is used for fast trigger decisions and it yields some redundancy for
the vertex reconstruction and track separation done by the VD It covers a cylindrical volume
between the radii cm and cm and a total length of m The apparatus is split into
an inner drift chamb er part with a jet chamber architecture p ointing to the interaction p oint
and an outer MWPC for radii greater cm All wires are parallel to the b eam The jet
chamb er is divided into sectors in with wires each The high voltage is chosen so
that the drift velo city rises in the same way as the drift distance e g linearly with R Due
to this architecture ideal tracks stemming from the interaction p oint lead to pulses arriving
on the wires all at once This allows a fast trigger decision s weather tracks come
from the interaction p oint Fivelayers of eld wires in the MWPC part serve to resolve
the left rightambiguity of the jet chamb er while circular catho de strips pitch mm
give Z information The resolutions obtained for Z events is R mand
mrad The two track separation is ab out mm In the shutdown the ID
was replaced by an extendet device with a total length of m
The Time Pro jection Chamber
The Time Pro jection Chamb er TPC is the main tracking device of DELPHI It covers the
activevolume from R cm to cm jZ j cm and is lled by an argone methane
gas mixture Ar CH The TPC is divided into two hemispheres of six sectors in
It is read out at the end caps by concentric pad rows and ano de wires A track passing
MWPC Multi Wire Prop ortional Chamb er XY RZ
0.0 cm 6.0 cm 0.0 cm 6.0 cm
XY RZ DELPHI 48758 / 2666 2/Jul/94 17:02
0.0 cm 1.0 cm 0.0 cm 1.0 cm
Figure The XY and the RZ projection of a hadronic Z decay observed in the DELPHI
vertex detector Circles and squares indicate vertex detector hits associatedtotracks crosses
correspond to unassociated hits
through the gas volume leaves a tub e of ionization along its way Due to a homogeneous
electric eld along the Z direction the charges are drifted in the gas with a drift velo city
of v cm s to the end caps The R resolution is governed by the segmentation of
D
the read out structure while the Z co ordinate is measured by the drift time In this wayup
to three dimensional space p oints can b e measured p er track The single p oint resolution
for tracks from multi hadronic Z decays is mintheR plane and m in the RZ
plane The two p oint separation is of the order of cm Particle identi cation with the
TPC is p erformed using the dE dx measurementforcharged tracks This is describ ed in
detail in section
The Outer Detector
The Outer Detector OD is a drift chamb er whichessentially provides a fast trigger infor
mation in R as well as in Z It consists of velayers of drift tub es at a radius b etween
o o
and cm covering an angular region in b et ween and The OD gives p oints
with go o d spatial resolution at a radius of m from the interaction p oint which increases
the lever arm for the trac k reconstruction All velayers provide precise R measurements
with a resolution of m The longitudinal information in Z is obtained by the
R
relative timing of the signals from b oth ends A resolution of cmisachieved
Z
The Performance of the Tracking System
The design of the DELPHI detector which includes the RICH detectors for particle identi
cation limits the size of the central tracking devices Therefore a system of several tracking
comp onents e g VD ID TPC and OD for the barrel part has b een constructed The align
ment of the di erent comp onents and the disentangling of systematic e ects e g shifts or
torsions is essential for a go o d momentum resolution By using Z events the total
momentum resolution in the barrel part of the detector is determined to b e
p GeV c
combining VD ID TPC and OD track elements The momentum resolution in the
o o
forward region with is
p GeV c
using at least VD and FCB information
The Calorimeters
The High Density Pro jection Chamber
The High density Pro jection Chamb er HPC is the barrel electromagnetic calorimeter in
DELPHI It is the rst large time pro jection gas calorimeter whichprovides a full
The Forward Chambers FCA and FCB are the main tracking devices in the forward region see Fig
Figure Schematic view of the layer structure of a single HPC module An entering
electron initiates an electromagnetic shower in the converter The produced charge is drifted
to a planar MWPC The ful l detector consists of such modules
three dimensional reconstruction of an electromagnetic shower It covers the angular region
The HPC consists of mo dules arranged in rings inside the cryostat of
the magnet Each ring consists of mo dules concentrically arranged around the Z axis with
an inner radius of cm and an outer radius of cm In principle each HPC mo dule is
a TPC with layers of a high dense material lead in the gas volume where electromagnetic
showers are initiated see Fig The converter thickness varies b etween and radiation
length dep ending on the p olar angle It consists of planes of lead with a thickness of
ab out mm The gas gaps are lled with an argone methane gas mixture Ar CH
The pro duced cloud of electric charge form an electromagnetic shower It is drifted
with a velo cityof v cm s in a homogeneous electric eld E V cm whichis
D
parallel to the B eld The read out of a single mo dule is p erformed at the end of eachmodule
by a planar MWPC which consists of sense wires and is segmented in pads Each pad
is read out in time buckets This leads to a total number of
ADC signals which are available p er event The energy resolution of the HPC for photons has
b een found to b e
E
p
E
E GeV
using neutral pions reconstructed from one photon converted b efore the TPC reconstructed
with high precision and one photon reconstructed in the HPC The angular resolution
in is given by the segmentation of the read out mrad The Z information is
evaluated from the drift time leading to mrad
The Hadron Calorimeter
The return yoke of the DELPHI sup erconducting solenoid is designed as an iron gas hadron
o o
calorimeter HAC The angular acceptance of the instrumentis in the
o o o o
barrel part and and in the twoforward parts The active
comp onents of the HAC consist of layers in the forward region of plastic made wire
chamb ers of cm depth interleaved by cm of iron The energy resolution obtained from
multi hadronic Z decays using the momentum information from the TPC is describ ed by
E
p
E
E GeV
The average depth of m of the HAC together with the other detectors make DELPHI
self shielding so that even during runtime the detector is accessible
The Luminosity Monitoring Detectors
The luminosity is measured via low Q Bhabha scatter events which emerge from the interac
tion largely at small p olar angles Therefore the Small angle Tile Calorimeter STIC and
the Very Small Angle Tagger VSAT are mounted m and m resp ectively from the
interaction p oint close to the b eam pip e The STIC is a lead scintillator sampling calorimeter
read out with wavelength shifting bres and photo electro de tub es VSAT is a W Si calorime
ter of radiation length sensitivebetween the p olar angles of and mrad
Particle Identi cation Devices
The identi cation of photons electrons muons and hadrons is generally done in a combined
o ine analysis of many detector comp onents This section emphasizes the sub detectors which
are dedicated to particle identi cation
The Ring Imaging Cherenkov Detectors
Charged particles traversing a dielectric medium with a velo city larger than the sp eed of light
in that medium pro duce a cone of Cherenkov light The emission angle dep ends on the
Ch
mass M and momentum p of the particle via the relation
p
M p
cos
Ch
n
where n is the refractive index of the radiator medium The numb er of photons emitted is
prop ortional to sin This information Cherenkov angle and numb er of photons is used
Ch
to evaluate masses of charged particles The main goal of the RICH detectors is to separate
The STIC detector replaced in the Small Angle Tagger SAT
Figure Schematic view of the barrel RICH detector The upper volume shows the gas
radiator system l ledwith C F The liquid radiator volume l ledwith C F is indicatedas
wel l The Cherenkov photons areconvertedin CH C H T M A E gas The converted
electrons drift for both systems to the proportional chamber indicated on the right hand side
Note that the rings of the liquid and of the gas systems aredisplacedwithrespect to each other
kaons and protons form the large pion background In the momentum range where kaons and
protons are b elow the Cherenkov threshold they do not emit light while lighter particles do
This prop erty can also b e used in the so called veto mode
The DELPHI RICH contains two radiator systems of di erent refractive indices A
liquid radiator is used for particle identi cation in the momentum range from GeV c
and a gaseous radiator is used from GeV c The full solid angle coverage is provided by
two indep endent detectors the forward and the barrel RICH Per uoro carb ons were chosen
F and in the barrel liquid as radiator media b oth in the forward liquid C F gaseous C
C F gaseous C F Photons in the range from nm are fo cused onto photosensitive
Time Pro jection Chamb ers in numb er in the barrel and in each arm of the forward
RICH A schematic view of the DELPHI barrel RICH is given in Figure More details on
the op eration of the RICH and the corresp onding particle identi cation software are given in section
The Muon Chamb ers
The DELPHI muon chamb ers are drift chamb ers which are lo cated b ehind the hadron calorime
ter They provide a muon identi cation with an e ciency of ab out The Barrel Forward
and Surround MUon BMU FMU and SMU chamb ers cover the p olar angular region b e
o o
tween and Resolution measurements on isolated tracks give mm The Z
R
co ordinate is evaluated from delay time measurements with a digitization windowof ns
obtaining a resolution of cm
Z
The Time of Flight Counters
The Time of Flight TOF system is installed on the outer surface of the solenoid It consists
ofalayer of scintillation counters The mo dules cm cross section and m long
are read out at b oth ends by photo multipliers connected by light guides In the forward part
of the DELPHI detector a similar system is installed as well In the p olar angle region from
o o
to the TOF system serves as a cosmic muon trigger as well as a cosmic veto during
b eam crossings Cosmic ray runs show the time resolution to b e ns
The DELPHI Online System
The DELPHI online system has to manage several functions during runtime analyse the
events on an elementary level and supply a fast trigger decision read out all detector com
p onents and write the data on storage media disks tap es run the p ower supplies gas and
co oling systems of the detector and control and log all slowly varying detector parameters
e g temp eratures pressures high voltages drift velo cities etc
The SlowControl System
The DELPHI slow control architecture allows a single op erator to monitor and control the
complete status high and lowvoltages gas supplies etc of the entire detector The p er
formance comprises the display of the detector status error messages and the continuous
up dating of the detector database for calibration and o ine analysis The gas lled sub de
tectors of DELPHI are supplied by a standardized gas owcontrol system including automatic
survey of relative mixtures cleaning and drying of the media This system is realized using
VAXstation computers shared with the DELPHI data aquisition The hardware link is realized
by G computers for the sub detectors connected by an ethernet link
The Trigger
The time b etween two bunchcrossovers is s s in bunch mo de The DELPHI
trigger system is designed to handle large luminosities with large background event rates
The four level hierarchy starts with twohardware triggers T and T The rst level decision
is made within s using e g the charged track condition of the ID and OD or correlated
wires in the FCA and FCB Other rst level trigger conditions are provided by scintillator
mo dules mounted inside in the HPC If T res T decides within s reanalyzing the
slow drifting devices to con rm the T decision e g the TPC for charged tracks and the
HPC for electromagnetic energies The T rate is usually around Hz the T rate around
Hz T and T are software triggers running in real time T con rms the T decision
using the full granularity and resolution rejecting roughly half of the T events The fourth
level trigger program suppresses remaining background ags events for physics analyses and
provides an online event display for monitoring purp oses There are at least di erent
trigger conditions for the levels and and further logical combinations are p ossible The
trigger system is highly redundant so that the e ciency can b e tested by data itself The
e ciency for multi hadronic events is almost
The Data Aquisition System
The heart of the DELPHI Data Aquisition System DAS is a VAX computer sup
p orted byaVAX and several VAX and DEC workstations All T events are stored
as raw data on IBM cassettes using the ZEBRA bank structure The typical size of
amulti hadronic eventis Kbyte The events are agged with the l l number of the LEP
machine and with the DELPHI run number A run is de ned as a p erio d of stable conditions
e g constant temp erature pressure high voltages and other detector parameters Each run
is a separate le on the output tap es
The DELPHI O ine Analysis Chain
This section gives an o verview over the DELPHI o ine analysis chain The main comp onents
are shown in Fig
The DELANA Package
The main reconstruction program is the DELPHI ANAlysis program DELANA It con
tains one mo dule for each sub detector which p erforms the necessary alignment and calibration
of the raw data The data format inside DELANA is based on ZEBRA and is called TANA
GRA The event reconstruction pro ceeds in the following steps
A lo cal pattern recognition is p erformed indep endently and separately for each sub
detector resulting in so called Track Elements TE s e g space p oints and directions
energy dep ositions and so on This step is known as rst stage pattern recognition
ZEBRA is a memory management program which o ers the p ossibility of handling dynamic data structures DELSIM - DELPHI Detector Simulation subdetectors FASTBUS data readout Event - generation - fragmentation Database - particle decays CARGO, DDAPP full simulation of the ONLINE detector geometry interactions and the data readout detector response calibration
MC raw-data raw-data
DELANA detectors TD und TE banks track reconstruction TK banks vertex reconstruction TV banks particle identification
DST data TANAGRA data
SHORT- and MINI- DELGRA DST production interactive graphics- Physics program Analysis
SHORT-DST data
MINI-DST data
Figure The DELPHI o ine analysis chain
The track elements from several detectors are group ed into track candidates and a rst
track t is p erformed
After resolving ambiguities the tracks are extrap olated to obtain precise estimates for
their passage through the sub detectors
A second stage pattern recognition is p erformed where the lo cal pattern recognition is
redone using the appropriate extrap olated information from the other sub detectors
Energy dep ositions in the calorimeter are either successfully linked to charged tracks or
are marked as neutral energy
Primary eventvertices are tted from the reconstructed tracks
The output of this pro cedure is the so called DST data format containing a tree structure
of banks based on the reconstructed vertices All information related to physics analysis e g
four vectors of particles calorimeter information matches to the simulation etc is stored
here The size of a multi hadronic Z DST event is roughly kbyte
The SDST Creation
In order to improve data quality and to provide reasonable particle identi cation for the
collab oration an additional pro cessing is p erformed It reduces the amount of data bya
factor of three and is called Short DST SDST It contains the following
Track and vertex ts are redone after xes for alignment and calibration have b een
applied on the TE basis DSTFIX
Running of the AABTAG package tagging of bb events
Running of the ELEPHANT package e and identi cation
Running of the MUFLAG package identi cation
Running of the RECV package and K identi cation
Running of the HADIDENT package K and p identi cation
In order to reduce the volume of data by an additional factor of three a subsample of the
SDST data is pro duced which is called Mini DST MDST The MDST data format contains
just the basic information which is needed for an analysis e g track re ts are not p ossible
using this format
The time consuming pro cessings DELANA and SDST pro duction are done on the DEL
FARM computer cluster consisting of ALPHA OSF DEC ULTRIX and VAX VMS work
stations The analyses presented in this thesis are based on the SDST data format The
programs analysing the SDST data ran on the DELPHI SHIFT system consisting of seven
HP UX and four ALPHA OSF workstations
DST Data Summary Tap e The DST data format is based on ZEBRA and is pro duced from TANA
GRA data by the program package PXDST TD TE TS TK TV ST PA DELPHI Interactive Analysis 0 86 0 27 26 0 0 Act Beam: 47.2 GeV Run: 5902 DAS : 16-Dec-1989 ( 0) ( 86) ( 0) ( 27) ( 26) ( 0) ( 0) 03:29:34 0 0 0 0 0 0 0 Evt: 879 Deact Proc: 24-Nov-1991 Scan: 19-Oct-1992 ( 0) ( 5) ( 0) ( 3) ( 16) ( 0) ( 0) 1.X-Y
Y Z
X
2.Z-X
X
Y Z
Figure A three jet event recorded with the DELPHI detector and visualized with the
DELGRA event display program Individual chargedtracks aredrawn as lines and energy
depositions in the calorimeters as boxes The upper and lower plot show the views in direction
and perpendicular to the direction of the beam pipe
The DELPHI Event Display
The DELPHI GRAphics program DELGRA is a D interactive colour display facilityto
visualize the detector resp onse of an event It is very useful for investigations of the detector
p erformance and for checks of event reconstruction programs e g shower reconstructions and
track ts Esp ecially in the LEP phase where very lowevent rates are exp ected and new
physics could show up the DELGRA program will b e of ma jor imp ortance A three jet event
visualized by DELGRA is shown in Fig
The Detector Simulation
The primary aim of a simulation program is to pro duce data for a particular reaction
which are as close as p ossible to the real raw data from the detector These data are
then pro cessed through the reconstruction program DELANA and the subsequent analysis
programs in exactly the same way as for real data This pro cedure mo dels the detailed
resp onse of the complete detector to a particular physics sub ject The DELPHI simulation
DELSIM is based on three comp onents which can b e summarized as follows
A mo del for the generation of the primary physics pro cess In most cases this is p er
formed by external programs like jetset for quark nal states dymu for
e e babamc for e e e e koralz for e e The
DELPHI collab oration uses its own parameter tuning for the di erent generators deter
mined from the latest available data
The general task of following particles through the DELPHI detector up to the p oint
where they hit an active detector comp onent This is done by stepping through the
magnetic eld including the p ossibility that these particles give rise to secondary in
teractions In order to reach the required accuracy for the results a very detailed
description of the material inside the detector is necessary
Following the particles inside the active detector comp onents and the simulation of the
detector resp onse as recorded in reality This part is sp eci c to every detector comp onent
and the mo dularity of the co de is suchthateach of them corresp onds to an indep endent
software mo dule
The particle tracking through the DELPHI detector includes energy loss multiple scattering
and the following secondary pro cesses
the photo electric e ect
the emission of Delta rays
bremsstrahlung
annihilation of p ositrons
pair pro duction
Compton scattering
weak decays
nuclear interactions using GEANTH
The material parameters which determine the rates of the ab ove pro cesses are extracted from
the CARGO data base When a particle enters an active detector comp onent the control
of the track following is given to the corresp onding software mo dule Most mo dules follow
the particles by using to ols provided by the general routines outlined ab ove Some mo dules
use di erent metho ds for example the HPC whichneedsavery accurate description of the
electromagnetic e ects and is based on EGS When a particle crosses the sensitive
volume of a detector the relevant information is stored to compute the detector resp onse in
the form of electronic signals as for real data
The simulation of events for physics analyses and detector studies is pro duced in several
pro duction centers in the DELPHI memb er states The achieved statistics is comparable with or larger than the statistics for the actual LEP data
Summary of the Chapter
LEP is the largest storage ring ever built The luminosity of nb s was reached
using bunches p er e e b eam in pretzel orbits LEP is op erating on the Z resonance
with go o d p erformance close to the design values
DELPHI is one of the four LEP exp eriments It is equipp ed with a large sup erconducting
coil pro ducing a magnetic eld of T The electromagnetic calorimeter HPC and the
RICH systems are lo cated inside the sup erconducting coil which restricts the volumes
of the central tracking devices
In the years DELPHI collected an integrated luminosity of roughly pb
Ab out million hadronic Z decays have b een recorded on tap e
The track resolution is dominated by the DELPHI vertex detector consisting of three
layers of silicon microstrip dio des The impact parameter resolution can b e parametrized
r
as R m p sin for R The corresp onding resolution in the
IP
r
p sin Z direction is given by Z m
IP
The momentum resolution of the DELPHI tracking system was determined to b e p
GeV c for the barrel and p GeV c for the forward
region
The energy resolution of the electromagnetic calorimeter HPC was found to b e E
E
p
E GeV The energy resolution of the hadron calorimeter is describ ed
p
by E E GeV
E
Sp ecial emphasis during the construction of DELPHI was given to the particle identi
cation devices Go o d separation b etween kaons protons and pions is achieved by using
the barrel and forward RICH detectors Furthermore DELPHI is equipp ed with
muon chambers
The DELPHI online system manages several functions during runtime analyse the
events on an elementary level and supply a fast trigger decision read out all detector
comp onents and write the data on storage media run the p ower supplies gas and co oling
systems of the detector and control and log all slowly varying detector parameters
The o ine analysis DELANA SDST pro duction is done on the DELFARM computer
cluster consisting of DEC ALPHA workstations The pro cessed data are stored for
physics analysis in the DST Data Summary Tap e SDST Short DST and MDST
Mini DST format The presented analyses were p erformed at CERN using the SDST
format and the DELPHI SHIFT computer system
The simulation for physics analyses and detector studies is pro duced in several pro duc
tion centers in the DELPHI memb er states The achieved statistics is comparable with LEP statistics
Chapter
Analysis To ols
The main goal of this thesis is the search for and observation of orbitally excited B mesons
in the decaychannel B B or B B This chapter describ es the main analysis
to ols while the next chapter is dedicated to the actual analysis The analysis starts with a
multi hadronic event selection section followed by a tagging of bb events section
The four vectors of the B or B mesons are reconstructed in an inclusive fashion using an
algorithm based on a simple rapidityargument section Since B mesons decay rapidly
through the strong interaction decay pions originate from the primary vertex A signi cant
reduction of background from B decay pro ducts is achieved by using a vertex reconstruction
algorithm section
Furthermore a searchforB mesons decaying into B K as well as a search for the b
s
baryons and is p erformed Signi cantkaon identi cation is essential for the observation
b
b
B mesons section In order to achievebaryon enrichment for the analysis of
s
b
metho ds of proton tagging and reconstruction are used sections and
Hadronic Event Selection
The hadronic event selection in DELPHI is based on the reconstruction of charged particle
tracks and neutral energy dep osition in the calorimeters Prior to the actual event selection
a track selection takes place which removes badly reconstructed tracks or tracks originating
from secondary interactions with the detector material The following track quality cuts are
applied
track length cm
track momentum GeV c
radius of rst measured p oint cm
R impact parameter cm
relative error on R impact parameter
Z impact parameter cm
Electromagnetic showers are selected by using the default quality cuts from the ELEPHANT
package Neutral showers reconstructed in the hadron calorimeter HAC are accepted
if their energy exceeds GeV The multi hadronic event selection comprises the following
standard selection cuts for details see Ref
number of charged tracks in the event
numb er of neutral particles in the event
jp ositive negativej charged particles in the event
charged energy in the event GeV
total energy in the event GeV
After these cuts one obtains a sample of K multi hadronic events taken with the DELPHI
detector in the years The following SDST data sets are used F K D
K C Kand B K Background originating from beam gas and beam
wal l events is signi cantly suppressed The contribution of these backgrounds to the event
sample is estimated to b e of the order of The background from events is of the
order of
For eachmulti hadronic event the main event axis given by the thrust axis t is calculated
The quantity thrust T is de ned by
P
j n p j
i
i
P
T max
j p j
j nj
i
i
and the thrust axis t is given by the vector n for which the maximum is attained The allowed
range is T with a two jet event corresp onding to T and an isotropic event
to T Eachevent is divided into two hemispheres as de ned by the thrust axis The
analysis is restricted to the barrel region where there is complete vertex detector coverage
j cos j with b eing the angle b etween the thrust axis t and the Z axis
thr ust thr ust
Furthermore the jet structure of eachevent is analyzed using the LUCLUS algorithm
with a transverse momentum cuto of GeV c leading to a classi cation of all events into
two three four or ve jet event samples In simulation studies this transverse momentum
cuto is found to give the b est reconstruction of the initial b hadron direction Dep ending on
t cuts for the numb er of jets are used the particular analysis p erformed di eren
Tagging of bb Events
The cross section for bb pro duction in e e annihilation on the Z resonance is nb which
corresp onds roughly to of the hadronic cross section Z q q Several metho ds
The following parameter settings are used for the LUCLUS algorithm PARU MSTU MSTU and MSTU
are used by the LEP collab orations in order to isolate bb events from the remaining multi
hadronic backgrounds Z cc ss uu and dd Ab hadron can either b e reconstructed in a
fully exclusiveway from its decay pro ducts or it can b e tagged by a measured high p lepton
t
from its weak decay These metho ds su er from low e ciencies and small branching ratios in
the observable decaychannels e g Br B e X
e
The metho d used in this analysis is based on the long lifetime of b hadrons ab out ps
for the mixture of B mesons and b baryons pro duced at LEP their large mass GeV c
and their sizeable energy hE i E These facts lead to a mean ight distance for b
b beam
hadrons in the lab oratory frame of d c mm In order to identify bb events one may
try to reconstruct a secondary b decayvertex from charged particle tracks in a hemisphere
see section However studies of impact parameter distributions of b decay pro ducts lead
to metho ds with higher tagging e ciencies Such metho ds are standard in DELPHI and
are discussed b elow
The impact parameter is de ned as the distance of closest approach of the tra jectory
of a charged particle to the primary reconstructed vertex It is evaluated separately in the R
plane and in Z The sign of the impact parameter is de ned with resp ect to the jet direction
It is p ositive if the vector joining the primary vertex and the p oint of closest approachto
the track lies in the same direction as the jet to which the given track b elongs The sign is
computed in two dimensions when only R measurements from the VD are available other
wise it is done in three dimensions The sign of R and Z impact parameters are the same
for a given track The impact parameter error arises from the error on the p oint of closest
approach and the error on the vertex p osition The signi cance S ofagiven track is de ned
as the impact parameter divided by its error
The impact parameter is used as the only tagging variable for the separation of events
with b quarks from the rest of the hadronic events With the given de nition of the impact
parameter and of its sign it follows that the tracks from the decays of b hadrons have p ositive
impact parameters whereas non zero impact parameters arising from the inaccurate recon
struction of particle tra jectories are equally likely to b e p ositive or negative Therefore the
use of tracks with p ositive impact parameters increases the tagging e ciency
For the tagging of b hadrons the probability metho d prop osed originally in is used
It gives the p ossibility of constructing one tagging variable from all impact parameter values
observed in the event This is achieved by the following algorithm The negative signi cance
distribution mainly re ects the detector resolution and is used to build the track probability
function P S whichisby de nition the probabilityfora track from the primary interaction
to have a signi cance with absolute value S or greater By construction the distribution of
P S for tracks with p ositive impact parameters should haveapeakatlowvalues Using the
track probability function the probabilityforeach track in the event can b e computed accord
ing to the value of the signi cance Thus for any group of N tracks the N track probability
is de ned as
N N
Y X
j
ln j where P S P
i N
j i
This variable giv es the probability for a group of N tracks with the observed values of sig
ni cance to come from the primary vertex By construction a at distribution of P is
N
The impact parameter and the obtained resolutions in DELPHI are also discussed in section
Starting from the DELPHI vertex detector provides b oth R and Z information 1 0.9 (a) 0.8 0.7
efficiency 0.6 0.5 0.4 0.3 event probability PE 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 purity
1 0.9 (b) 0.8 0.7
efficiency 0.6 0.5 0.4 0.3 hemisphere probability PH 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
purity
Figure b tagging e ciency as a function of purity for di erent values of the cut on
a the event probability and b on the hemisphereprobability for three dimensional VD ful l
line and for two dimensional VD dashed line
exp ected for a group of tracks from the primary vertex provided the signi cances of these
tracks are uncorrelated while tracks from b hadron decays should have a sharp p eak at In
the case that the Z impact parameter is measured the probability P S is computed in
Z
the same wayasforthe R impact parameter The N track probability is then given bya
combination of b oth P and P probabilities The event probability P is the probability
R Z E
computed using all the N tracks of the event and similarly the hemisphere probability P
H
is the probability computed from the tracks b elonging to that hemisphere Furthermore in
order to decide if a single track originates from the primary vertexorfroma b decayvertex
the track probability P is provided bytheb tagging package Fig shows the b tagging
T
e ciency as a function of purit y for the event probability and for the hemisphere probability
for three dimensional VD full line and for two dimensional VD dashed line It can b e seen
that the p ossibility to measure b oth R and Z increases the e ciency for a given purity The
year multi hadronic bb events bb events
Z events purity purity
K K K
K K K
K K K
K K K
Table Number of multi hadronic Z events and b tagged events for DELPHI data taken
in the years
results have b een extracted from simulation for a sample of multi hadronic events selected
within the acceptance of the vertex detector jcos j The working p oints for
thr ust
the di erentpresented analyses are stated explicitly in the next chapter Some typical values
for eventnumb ers and purities are given in Tab A cut on the event probability P
E
corresp onds to an e ciency of and a purityof A cut P leads
E
to an e ciency of and a purity of
Inclusive B Meson Reconstruction
The algorithm of inclusive B meson reconstruction was develop ed and successfully applied
in the DELPHI B analysis combining inclusive reconstructed B mesons with converted
Additionally itleadtoaninclusive measurement of the B fragmentation photons B B
function in DELPHI
The algorithm is based only on the measured momenta and angles of the B decay pro ducts
This works well for B mesons due to their large mass and their hard fragmentation function
Simulation studies at the Z resonance show that the rapidity y log E p E p
z z
of B mesons along the event thrust axis should b e strongly p eaked at y with some
spread towards lower jy j due to hard gluon radiation see Fig a Another observation
is that the B meson decay pro ducts should have a Gaussian distribution in rapidity space
with a width of ab out units In b events the fragmentation pro cess generates particles
mostly at low rapidity and their distribution can b e describ ed bytwo Gaussians of width
units centered at The mo del dep endence of these distributions has b een analyzed b y
comparing the predictions of jetset and herwig with the jetset particle
decays b oth with default parameters In general these two predictions di er by less than
at anyvalue of y in the inclusive y distribution from fragmentation and by less than
in the distribution from B decays
Detector acceptance and resolution e ects have only a small in uence on these distribu
tions the most imp ortant e ect b eing that the loss of low energy particles leads to a suppres
sion of the p opulation at low jy j The inclusive rapidity distributions for DELPHI data and
simulation are shown in Fig b Excellent agreement is observed for b oth charged and
neutral particles
The de nition of the rapidity originates from a parametrization of the Lorentz invariant phase space element
for a single particle A longitudinal Lorentz b o ost is a linear transformation in dLips dy d dp
rapidity
Figure a Rapidity distributions for B mesons shadedarea particles stemming from
B decay solid curve and particles from fragmentation dotted curve in bb events as expected
from the jetset model
b Comparison between the rapidity distributions of al l particles upper curves and charged
particles lower curves in a b enriched sample of data points and Monte Carlo simulation
lines
c Reconstructed B mass spectrum for data points and simulation solid line
d Correctedfractional B energy spectrum for data points and simulation solid line The
shadedarea in c and d corresponds to the background due to non bb events
Eachevent is divided into two hemispheres as de ned by the thrust axis The rapidityof
each reconstructed charged particle assuming the pion mass and neutral particle assuming
the photon mass with resp ect to the thrust axis is calculated Particles outside a central ra
pidity windowof units are considered to b e B meson decay pro ducts The four momenta
of these particles are added together in each hemisphere to arriveataB meson energy esti
mate E for each side of the event
y
Given the inclusive nature of this reconstruction technique there are events that are not
well reconstructed However most of these p o orly reconstructed events are removed by re
quiring that
a minimum energy of GeV is reconstructed for the B candidate in the rapidity
gathering algorithm
the reconstructed mass m lies within GeV c of the average reconstructed B
y
meson mass
the ratio of hemisphere energy E to b eam energy E lies in the range
hem beam
x E E
h hem beam
Enforcing these requirements results in a loss of of B decays Studies using simulation
showed a strong correlation b etween the generated B meson energy E and the initial
Btrue
estimate E from the rapidity gathering algorithm describ ed ab ove There is a further corre
y
lation b etween the energy residuals E E E and the reconstructed B meson mass
y Btrue
m which is approximately linear in m Also a correlation b etween E and the ratio of the
y y
energy seen in the hemisphere to the b eam energy x E E is observed re ecting
h hem beam
global ine ciencies and neutrino losses Since the mass and hemisphere energy dep endences
are not indep endent a correction technique taking into account their correlations is applied
The correction function is determined using simulated events in the following way Af
ter applying all cuts the simulated data are divided into several samples according to the
measured ratio x For each of these classes the energy residual E is plotted as a func
h
tion of the reconstructed mass m The median values of E in each bin of m are cal
y y
dep endence tted by a second order p olynomial E m x bin culated and their m
y y h
a b m hm i c m hm i The three co e cients in the t a b and c ineach
y y y y
x class are then plotted as function of x and their dep endence tted using second order
h h
p olynomials a x a a x a x and similarly for b x and c x Thus one obtains
h h h h
h
a smo oth correction function describing the mean dep endence on m and the hemisphere en
y
ection is applied ergy characterized by parameters a b c i Finally a small bias corr
i i i
for the mean remaining energy residual as a function of the corrected energy as determined
from simulation
The go o d agreementbetween data and Monte Carlo simulation for the reconstructed B
mass m and corrected fractional B energy x distributions is shown in Figs c and
y E
d The attainable precision of this inclusivetechnique dep ends on the cuts on the b
tagging probability the event shap e variables e g thrust and numb er of jets and on the B
quality E m and x For the standard cuts describ ed ab ove the energy precision is for
y y h
of the B mesons the remainder constituting a non Gaussian tail towards higher energies
The angular resolution in and can b e parameterized as double Gaussians with widths of
mrad for of the data and mrad for the remaining Fig shows the energy
and angular resolutions of the inclusive reconstruction metho d (a) (b) entries entries
-0.2 -0.1 0 0.1 0.2 -0.2 -0.1 0 0.1 0.2 Φ −Φ [ ] Θ −Θ [ ] ( rec MC) rad ( rec MC) rad
(c) entries
-1.5 -1 -0.5 0 0.5 1 1.5 −
(Erec EMC)/EMC
Figure Inclusive B reconstruction algorithm a b and c
rec MC rec MC
E E E The angular resolutions can beparametrized by double Gaussians the
rec MC MC
energy resolution consists of a Gaussian part with a tail towards higher energy
The simulation prediction of the resolutions of the inclusive B reconstruction algorithm is
veri ed by the go o d agreement in the width of the B B mass di erence p eak
B DecayVertex Reconstruction
In order to reconstruct orbitally excited B meson in the decaychannel B B the
four vectors of the reconstructed B or B mesons are combined with p ossible B decay pi
ons This section describ es a to ol for the reduction of the combinatorial background from the
Figure Iteration procedure for the reconstruction of two B decay vertices and one pri
mary vertex The rapidity assignment serves as a starting point for the iteration
many fragmentation pions present Since B mesons decay due to the strong interaction
decay pions originate from the primary vertex and not from the B decayvertex which lies on
average ab out mm away from the primary vertex An iterative pro cedure is describ ed which
provides a t of three vertices in an event two B decayvertices and one primary vertex In
the analysis only pion candidates are accepted which are assigned to the primary vertex
Only well measured tracks with momentum greater than GeV c and two asso ciated
vertex detector hits are used for this algorithm The alignment of the various tracking detec
tor comp onents as well as an accurate description of e ciencies resolutions and covariance
matrix elements of charged tracks which are crucial for the analysis are monitored and ad
justed using Z decays and primary vertex ts of non bb hadronic events
The algorithm is as follo ws All well measured tracks are classi ed into three vertices
the primary vertex which has to b e compatible with the known b eam sp ot and two B decay
vertices The rapidity classi cation serves as a starting p oint all particles with jy j are
assigned to the primary vertex and those with y andy to the two secondary
vertices resp ectively Three vertex ts are then p erformed In a rst step all tracks are re
assigned to the three vertices according to their impact parameters with resp ect to primary
and secondary vertex Three vertex ts are p erformed with the new assignments The track
contributing the largest is then tried at the other kinematically allowed vertex i e the
primary vertex if it was a secondary b efore and vice versa The new vertex distribution is
accepted if the gets b etter otherwise the old distribution is kept If the trackgives the
largest contribution in b oth situations it is discarded The iteration pro cess is illustrated
in Fig This pro cedure is continued until no trackgives a contribution larger than
On average ab out sixteen iteration steps are p erformed Fig shows an example for an
event where a primary and two B decayvertices hav e b een reconstructed
In order to get a sensible distinction b etween primary and secondary vertices the recon
structed decay length in the signal hemisphere is required to exceed d mm Additional
cleaning is achieved by placing a cut on the acolinearity de ned by the co ordinates of the two DELPHI 26024 / 1730
0.0 cm 7.5 c DELPHI 26024 / 1730
0.0 cm 2.0 c
Figure Selected event with reconstruction of a primary vertex and two B decay vertices
The vertices are marked with stars The upper plot also shows the three layers of the DELPHI
vertex detector The lower plot magni es the situation near to the interaction point (a) (b) entries entries
-0.2 -0.1 0 0.1 0.2 -0.4 -0.2 0 0.2 0.4 Φ Φ [ ] Θ Θ [ ] ( rec- MC) rad ( rec- MC) rad 1 1 (c) (d) 0.8 purity 0.8 efficiency 0.6 0.6
0.4 0.4
0.2 0.2
0 0 0246810 0246810
p [GeV/c] p [GeV/c]
Figure Performance of the vertex reconstruction algorithm a and b
rec MC
obtainedfrom the coordinates of the reconstructed vertices c E ciency for
rec MC
particles originating from fragmentation to be assigned to the primary vertex as a function
of momentum d Purity as a function of momentum
B decayvertices and the primary vertex cos The p erformance of the algorithm
V
dep ends on the required event top ology e g on the numberofjetsintheevent
The following quantities have b een extracted from a Monte Carlo sample containing two
and three jet events P A mean numb er of particles p er hemisphere b elonging
E
to the primary vertex is found For the B decayvertex a mean numb er of particles is
observed Both numb ers are in agreement with the results in real data The angular res
olution in can b e parameterized as a double Gaussian with a width of mrad for
of the data and mrad for the remaining see Fig a It is compatible with the
The cut on the numb er of jets is di erentineach particular analysis and is stated explicitly in chapter
resolution obtained from the inclusive B reconstruction algorithm The angular resolution in
is somewhat w orse It can b e parameterized as a double Gaussian with a width of mrad
for of the data and mrad for the remaining see Fig b Furthermore the
resolution on the ight distance of the reconstructed B meson has b een studied By using a
double Gaussian function one obtains a resolution of cm for of the data and of
cm for the remaining The e ciency for particles from fragmentation to b e assigned to
the primary vertex as a function of momentum is shown in Fig c It is approximately
constant at The purityoffragmentation particles which are assigned to the main
vertex reveals a strong dep endence on momentum see Fig d For particles b etween
GeV c a purityof is found
Hadron Identi cation
In order to obtain evidence for B mesons inclusively reconstructed B mesons are com
bined with pions Since the dominant fraction of charged particles in an event are pions no
sophisticated hadron identi cation is needed However B mesons are exp ected to decay
s
into B K Go o d particle identi cation is essential for this kind of analysis Furthermore
in order to study and baryons an enrichmentinbaryons can b e achieved by proton
b
b
tagging The algorithm and p erformance of the DELPHI hadron identi cation is discussed in
this section It is based on the sp eci c ionization measured by the TPC and the reconstructed
Cherenkov angles in the RICH detectors
Sp eci c Ionization from the TPC
In addition to providing a three dimensional track reconstruction the DELPHI TPC is useful
for charged particle identi cation by measuring the energy loss p er unit length dE dx The
sense wires of its prop ortional chamb ers provide up to ionization measurements p er track
The signals collected by the sense wires are asso ciated to the tracks reconstructed by the
TPC pads This asso ciation is done by comparing the time of arrival of the pad and sense
wire signals Hits to o close in time to b e correctly separated are not used for the dE dx
calculation This requirement corresp onds for tracks orthogonal to the drift direction Z to
a separation of at least cm
It should b e noted that an average of of the signals collected by the sense wires are
b elow the electronic threshold The fraction of the Landau distribution lost due to this e ect
is a function of the drift length and gap size To reduce this dep endence an e ective threshold
is applied which dep ends on these quantities
To b e used in the physics analysis the truncated dE dx is required to have at least
measurements The e ciency obtained after these requirements is for tracks in multi
hadronic events with momentum greater than GeV c and jcos j The
thr ust
measured signals are corrected to takeinto account the usual dep endence on parameters like
gap size or drift length The dep endence of dE dx on the ratio p m of the track is measured
from the data using various samples and the nal result can b e seen in Fig The p osition
These quantities have b een extracted with a vertex detector providing full three dimensional information
Figure Speci c energy loss dE dx in the TPC as a function of momentum The ful l
lines correspond to the expectations for e K and p tracks
of the Fermi plateau when normalized to the minimum ionizing particle is found at
The resolution on dE dx estimated from data is for pions p GeV c coming
from K decays in multi hadronic events and for muons p GeV c from dimuon
s
events Z With the obtained resolution and dep endence of dE dx on p m
the separation b etween electron and pion is ab ove standard deviations for momenta b elow
GeV c A pion kaon separation can b e achieved at the level ab ove GeV c
Detection of Cherenkov Radiation
The detection of Cherenkov light with the RICH detectors has already b een describ ed in
section In the data taking p erio d million events were recorded with a fully
op erational RICH detector In previous years the Barrel RICH recorded million events
with b oth radiators and million events with the gas radiator only The identi cation
power of the RICH dep ends on the accuracy of the Cherenkov angle measurement and on
the detected numb er of photo electrons Stable op eration of the di erent subsystems and
monitoring of the relevant detector parameters is therefore very imp ortant Table shows
averaged resolutions for b oth single photo electrons and the resulting average Cherenkov angle
B liquid B gas F liquid F gas
numb er of photo electrons p er track
resolution p er photo electron mrad
resolution average angle mrad
Table Number of photoelectrons and angular resolutions in mrad for the Barrel B
and Forward F RICH obtainedwith Z events
p er track A detailed simulation program that takes into account all known detector e ects
was tuned to repro duce the data
Several particle identi cation algorithms havebeendevelop ed in order to ful ll very di er
ent requirements Some physics analyses need individual track tagging while others measure
statistically the content of a given sample without asso ciating tags to each track For track
by track tagging the observed signal is compared with that exp ected for known particle typ es
namely e K and p at the measured momentum Dep ending on the decay mo de ana
lyzed the prioritymay b e high rejection or high e ciency The requirements also dep end on
the dominant source of combinatorial background pion rejection only or proton kaon sepa
ration For statistical analyses one needs a continuous estimator of the observed Cherenkov
angle indep endentofanymasshyp othesis such that the numb er of particles of a given typ e
can b e determined
In a hadronic even t the main di culty is to deal with the background under the Cherenkov
signal whose shap e and level is di erent for eachtrack and is a priori unknown The algo
rithms develop ed so far followtwo mains approaches In the rst a at background is tted
and no attempt is made to separate it from the signal For eachmasshyp othesis the exp ected
signal is calculated A at background is adjusted in order to build and maximize a likeliho o d
probability The probabilities corresp onding to the known particle typ es are then used for
tagging For statistical analyses the likeliho o d probability is computed as a function of the
Cherenkov angle and the b est one is retained For further details on the HADSIGN algorithm
see Ref
In the other approach one uses a clustering algorithm to distinguish b etween background
and signal photo electrons Photo electrons are group ed into clusters and given a weight ac
cording to quality criteria such as measurement errors or p ossible ambiguities b etween several
tracks The b est cluster is retained and weights are used to measure the average Cherenkov
angle its error and the estimated numb er of photo electrons Quality ags are set to allow
di erent rejection levels They are based on the detector status and the cluster quality For
further details on the RIBMEAN algorithm see Refs
The distribution of the average Cherenkov angle as a function of the momentum in multi
hadronic events is shown in Fig for the liquid top and gaseous b ottom radiators 0.8 ch Θ 0.7
0.6
0.5
0.4
0.3 liquid RICH
0.2 0.7 0.8 0.9 1 2 3 4 5 6 7 8 p [GeV/c] 0.08 ch
Θ 0.07
0.06
0.05
0.04
0.03
0.02 gas RICH
0.01 3 4 5 6 7 8 9 10 20 30 40
p [GeV/c]
Figure Average Cherenkov angle per track as a function of the momentum in
multi hadronic events in the Barrel RICH for the liquid top and gaseous bottom radi
ators The threebands on both plots correspond to pions upmost band kaons midd le and
protons lowest band
Combination of TPC and RICH
The information originating from TPC and RICH are combined providing three di erent
tagging levels lo ose standard and tight for the separation of protons and kaons from pion
background Since the analysis presented is restricted to the barrel part of the detector
this discussion leaves out the p erformance in the forward part of DELPHI The algorithm
discussed is based on the o cial DELPHI hadron identi cation software HADSIGN The
liquid radiator is used for particle identi cation in the momentum range from GeV c 1 100 (a) (b) 0.8 80 efficiency 0.6 60 pion rejection
0.4 40
0.2 20
0 0 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 p [GeV/c] p [GeV/c] 1 100 (c) (d) 0.8 80 efficiency 0.6 60 pion rejection
0.4 40
0.2 20
0 0 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20
p [GeV/c] p [GeV/c]
Figure Performance of the DELPHI hadron identi cation HADSIGN in
multi hadronic events a E ciency and b pion rejection power for the three di erent
kaon tags as a function of momentum ful l circles loose tag open circles standard tag
triangles tight tag c E ciency and d pion rejection power for proton identi cation
and the gaseous radiator is used from GeV c Di erent op erational mo des of the
RICH detector have to b e considered e g for the kaon tag it must b e considered that the
kaon band in the gas RICH starts at GeV c see Fig which means that the gas
RICH information b elow GeV c can b e used only in the so called veto mo de In the
region b etween and GeV c kaons can b e tagged p ositively from the kaon band The
p erformance of the tagging routines has b een tested using a multi hadronic Monte Carlo
sample The e ciency and pion rejection p ower for kaon tagging lo ose tag KTAG
standard tag KTAG and tighttag KTAG as a function of track momentum is
shown in Fig a and b Analogous data for proton tagging lo ose tag PTAG
standard tag PTAG and tight tag PTAG are given in Fig c and d For
atypical multi hadronic momentum sp ectrum ab ove GeV c one obtains by demanding a
standard kaon tag KTAG a sample containing approximately kaons The
average e ciency is estimated to b e Similar estimations for the standard proton
tag PTAG lead to a sample comp osition containing approximately protons
The main background in this case originates from misidenti ed kaons The average e ciency
is estimated to b e All these quantities have b een extracted from simulation
Systematic studies comparing data and simulation show the misidenti cation probability for
kaon identi cation in Monte Carlo to b e approximately a factor of twolower than in data
V Reconstruction
This section describ es the standard DELPHI algorithm for and K reconstruction
s
By demanding a reconstructed in a hemisphere a baryon enriched sample can b e obtained
similar to demanding an identi ed proton This metho d is used in the and analysis
b
b
describ ed in the next chapter
Candidate V decays in the sample of hadronic events are found by considering all pairs of
opp ositely charged particles The vertex de ned byeach pair is determined such that the
obtained from the distances of the vertex to the extrap olated tracks considered as ellipsoids
in D space of p erigee parameters is minimized
The V decayvertex candidates are required to satisfy the following criteria
The angle in the XY plane b etween the V momentum and the line joining the
primary to the secondary vertex is less than p rad where p GeV c is
t t
the transverse momentum of the V candidate relative to the b eam axis
The radial separation R of the primary and secondary vertex in the XY plane is greater
than standard deviations
The probability of the t to the secondary vertex is larger than
The transverse momentum of each particle of the V with resp ect to the line of ight
is greater than GeV c and the invariant mass for the e e hyp othesis is less than
GeV c
When the reconstructed decay p ointofthe V is b eyond the VD radius there is no
yvertex signal in the VD consistent with asso ciation to the deca
The and p p invariant masses attributing the proton mass to the particle of
larger momentum are calculated When a pair is consistent within three standard deviations
with b oth K and hyp otheses the pair with the smaller mass pull the absolute value
of mass shift with resp ect to the nominal mass divided by the overall resolution is selected
Finally K and samples are de ned if the probabilitytohave decayed within the tted
Acharged particle track can b e describ ed as a helix de ned by ve parameters and Z These
parameters evaluated at the p oint of closest approach to the primary vertex are called p erigee parameters
distance lies b etween and and if the di erence b etween the invariant mass and the
nominal mass is within two standard deviations The mean resolution de ned as the FWHM
of the tted distributions is MeV c for K s and MeV c for s using B data
The e ciency is strongly dep endent on the V momentum For s the e ciency rises from
at GeV c to at GeV c and then drops to at GeV c For K s the
e ciency rises from at GeV c to at GeV c and then drops to at
GeV c The e ciency for K in this selection averaged over the momentum
sp ectrum is ab out with a contamination of The average e ciency for p is
with a contamination of ab out
Summary of the Chapter
The presented analysis starts with a sample of K multi hadronic events taken with
the DELPHI detector at LEP in the years The multi hadronic event selection
is based on the reconstruction of charged particle tracks and neutral energy dep ositions
in the calorimeters
The top ology of eachevent is analyzed by calculating the thrust axis and evaluating the
jet structure with the LUCLUS algorithm
Exploiting the long lifetime ps and the large mass GeV c ofb hadrons and
using the go o d spatial resolution of the DELPHI vertex detector a sample of bb events is
enriched With a purity of one obtains approximately K K events
The inclusive reconstruction of B mesons is based on the measured rapidity distribution
of charged and neutral particles in an event The rapidity of a particle is de ned as
y log E p E p where E is the energy and p is the longitudinal
z z z
momentum with resp ect to the thrust axis
Motivated bysimulation studies a rst estimate for the B four vector is given bythe
sum over all particles in a hemisphere with rapidity greater than The estimated
B energy E is corrected by a function determined from simulation which dep ends on
y
the reconstructed mass m and the reconstructed energy E in the hemisphere
y h
For standard cuts E GeV jm hm ij GeV c and E E
y y y hem beam
an energy resolution for B mesons of for of the data is achieved the remain
der constituting a non Gaussian tail towards higher energies The angular resolution in
and can b e parameterized as double Gaussians with widths of mrad for of
the data and mrad for the remaining
Avertex reconstruction algorithm is used in order to separate B pions originating
from the primary vertex from B decay pro ducts All well measured tracks with at least
twovertex detector hits asso ciated are classi ed into three vertices the primary vertex
which has to b e compatible with the known b eam sp ot and two B decayvertices The
rapidity classi cation serves as a starting p oint An iterative pro cedure reassigns tracks
between the three vertices until a minimal is found
The vertex reconstruction algorithm provides a resolution in compatible with the
resolution from the inclusive B reconstruction algorithm mrad for of the data
The e ciency for particles from fragmentation to b e assigned to the primary vertex
is approximately constantat The purity of fragmentation particles whichare
assigned to the main vertex reveals a strong dep endence on momentum For particles
between GeV c a purity of is found
The DELPHI hadron identi cation is based on the dE dx measurement of the TPC and
the Cherenkov angle reconstruction of liquid and gas RICH For a typical multi hadronic
momentum sp ectrum ab ove GeV c one obtains a sample containing approximately
kaons protons by demanding a standard kaon proton tag The
average e ciency for kaons protons is estimated to b e
Chapter
The Analysis
The main goal of this thesis is the search for and observation of orbitally excited B mesons
in the decaychannel B B The analysis starts with a multi hadronic event selection
mesons are reconstructed followed by the tagging of bb events The four vectors of the B or B
in an inclusive fashion using an algorithm based on a simple rapidity argument The combina
tion of inclusively reconstructed B mesons with pions from the primary vertex leads to the
rst observation of B mesons The obtained signal can consistently b e describ ed with
theoretical exp ectations for B states The helicity distribution of B mesons is analyzed
andacharge analysis is p erformed In addition the B fragmentationisinvestigated
A search for B mesons decaying into B K is p erformed exploiting the go o d kaon iden
s
ti cation capabilities of the barrel RICH detector Twonarrow signals consistent with the
states are extracted from the data pro duction of two narrow B
s
The third part of this chapter is dedicated to a search for the baryons and Their
b
b
exp ected main decaychannel is into The is reconstructed in an inclusive fashion
b b
using the rapidity algorithm In order to enhance the signal to background ratio a baryon
enrichmentisachieved by using proton tagging and reconstruction An indication for the
baryon and rst evidence for the baryon are extracted from the data
b
b
Observation of Orbitally Excited B Mesons
B B
If the mass of B mesons is ab ovetheB but b elow the B threshold B mesons decay
mainly into B or B Heavy Quark E ective Theory groups the di erent B states
into two doublets p er B avour according to the vector sum of the light quark s spin and
P
the orbital angular momentum j s L where if j then J and
q q q
P
if j then J The memb ers of the rst doublet should b e very narrow
q
compared to typical strong decay widths b ecause only L decays are allowed This is due
to angular momentum and parityconservation for the state and a dynamical prediction of
HQET for the partner Parity conservation also restricts the exp ected main decay
The rst evidence for B Mesons was obtained in parallel bytwo indep endent analyses in DELPHI and
OPAL The DELPHI analysis is presented here
mo des of the single states The spin parity state would decayinto B s wave the two
states into B s or d wave and the state into b oth B and B b oth d wave
Before the start of this work none of the orbitally excited B meson states was exp erimentally
known In the D meson sector the twonarrow states have b een identi ed exp erimentally
and spin parity and decaycharacteristics have b een shown to b e in accord with the HQET
predictions see section
Exp erimental Pro cedure and Results
Most of the exp erimental to ols e g multi hadron selection b tagging inclusive B recon
struction and vertex reconstruction which are needed for this analysis have b een discussed
in the previous chapter The analysis concentrates on the decaychannels B B and
tum is evaluated using the inclusive B reconstruction B B TheB or B four momen
algorithm describ ed in section Note that with the present exp erimental metho ds there
is no distinction b etween B and B mesons Therefore they are lab eled as B BoththeB
decay particles as well as the B decay pion have large rapidities However since the B
decays strongly the pion should originate from the primary vertex and not from the B decay
vertex see section The cuts used in this analysis are the following
Multi hadron event selection see section
Event top ology cuts see section
restrict analysis to barrel j cos j
thr ust
accept only two jet events NJET
Tagging of b hemispheres see section
eventtagP e ciency purity
E
hemisphere tag P e ciency purity
H
Inclusive B reconstruction see section
quality cuts E GeV jm hm ij GeV c and E E
y y y hem beam
restrict B vector to barrel jcos j jcos j
B B
Vertex reconstruction algorithm see section
qualityofvertex reconstruction jcos j
V
ight distance d mm
Pion track selection cuts see sections and
accept only pions which are assigned to the primary vertex
cut on the b tagging signed track probability P
T
restrict pion vector to barrel jcos j jcos j
veto kaons and protons KTAG PTAG HADSIGN
standard veto on electrons or muons
pion momentum cut p GeV c
originates from the b tagging package see section It is de ned as the P for tracks The quantity P
T
T
with p ositive impact parameter and P for tracks with negative impact parameter where P is the
T T
probability for a track to originate from the primary vertex
The quantity which is b est accessible exp erimentally with inclusive B reconstruction metho ds
is the Q value of the decay
Q m B m B m m B m B m
The resolution of the present metho d as obtained from simulation can b e parameterized as
Q MeV c MeV c Q GeV c It is dominated by the energy and angular
resolution of the B meson Whether the decaywas actually into B or B and whether the
B decay photon has b een reconstructed only has a negligible e ect on the resolution in the
Q value However the decayofaB of a given mass to a B gives rise to a Q value which
is shifted downwards by the B B mass di erence of MeV c compared to the Q value of
a B decay Therefore for the determination of a B mass from the measurable Q value an
assumption ab out the B B ratio in the signal has to b e employed
The distribution of the measured B Q values obtained with the DELPHI detector is
shown as data p oints in Fig a The analysis is p erformed with a sample of K multi
ts taken with the DELPHI detector in the years using the SDST data hadronic even
sets F K D K C K and B K see section There
is a large excess of combinations on top of a smo othly falling background The background
describ ed by the Monte Carlo prediction in which B decay pions have b een suppressed is
shown as the shaded area in Fig a The normalization is extracted from the sideband
in the range b etween GeV c and GeV c The Monte Carlo statistics corresp onds to
times the data statistics
Deviations of the background mo del from the measured data are observed at low Q value
The origin of this di erence is not yet fully understo o d but it might b e related to the rate
of inclusive D mesons the relative b baryon to B meson pro duction p ossible decays of B
mesons into B the mo delling of yet unmeasured B hadron decays or to general limitations
of the jetset string fragmentation mo del It is worth noting that the herwig generator
predicts a much less steep rise of the background at small Q values The reason for this
originates from the fragmentation mo del cluster instead of string rather than the di erent
mo delling of the parton shower This has b een inferred from a Monte Carlo study with
the herwig parton shower generator interfaced to lund string fragmentation The di erence
between the jetset and herwig generator is larger than the observed deviation b etween data
and jetset However note that the whole excess of entries originating from B B
decays was not known b efore the start of this analysis and thus was not simulated in the
Monte Carlo
Fig b shows the background subtracted B pair Q value distribution obtained
from Fig a The solid line originates from a mo del containing two narrow and twobroad
states Details of this mo del and further comparisons with predictions are discussed in section
The yield of the signal and its mean Q value can b e extracted using di erent metho ds
e g the signal can b e tted to a simple Gaussian or a Breit Wigner function A t of the
signal to a simple Gaussian with central value
Q B B stat syst MeV c
and Gaussian width
Q stat syst MeV c
In the calculation of the Q value the pion candidate is excluded from the inclusive B reconstruction ) 900 2 800 (a) 700 DELPHI 600 ∗∗ (∗) B → B π 500 Counts / (20 MeV/c 400
300
200
100
0
250 (b)
200
150
100
50
0
-50 0 0.2 0.4 0.6 0.8 1 (∗)
Q(B π) [GeV/c2]
Figure a Distribution of the Q value of B pairs data points along with
the Monte Carlo expectation without B production shadedarea Qisde nedas
Q m B m B m b Background subtracted B pair Q value distribu
tion The solid line originates fromamodel containing two narrow and two broad states see Fig f
contains
N stat syst
events This corresp onds to a statistical signi cance of approximately standard deviations
The main systematics on the number of events and on the width of the Gaussian originates
from the mo delling and the normalization of the background
B Pro duction Rate
Extracting the acceptance for B pions from simulation the total B pro duction cross
u d
section is determined to b e
stat syst
B b
u d
In this rate calculation it is assumed that ofallB decayinto charged pions and
into unobserved according to isospin rules for an I decayinto an isovector and an
isospinor From this the total number of B mesons p er hadronic Z decay is determined to
u d
be
N Z stat syst
B had
u d
Assuming the b baryon rate to b e and the B rate to b e see section
s
the relative amountof B mesons which originate from B decayis
u d
u d
stat syst
B B
u d
u d
Systematic Uncertainties
Systematic uncertainties dominate in the measurements of all these quantities Di erent
systematic checks have b een p erformed leading to a determination of the systematic errors
The main sources are discussed here
The mo delling and the normalization of the background is the dominantsourceofthe
systematic error Di erentbackground shap es originating from simulation and various
a
phenomenological background mo dels e g f Q a Q exp a Q a Q a
Q are tted to the data The normalization is extracted from the sideband in the
range b etween GeV c and GeV c These b ounds are varied by GeV c
Furthermore the normalization is extract from the left sideband Q
GeV c and the right sideband Q GeV c of the B signal This metho d
ulation at low Q values Employing the su ers from deviations b etween data and sim
simulation prediction for the background shap e the normalization has to b e adjusted
by the factor stat syst dep ending on cuts see b elow in order to
describ e well the data at large Q values These studies lead to a systematic error of
entries on the yield MeV c on the Q value and MeV c on the width
The complete analysis is rep eated several times with di erentsetsof B and selection
cuts This is realized in an automatic pro cedure providing hundreds of histograms
with di erent cuts and automatic tting algorithms The minimum B momentum cut is
varied b etween GeV and GeV the cut on the di erence b etween the reconstructed
and the mean B mass is varied b etween GeV c and GeV c Furthermore the
cut on the momentum of the pion candidate is varied b etween GeV c and
GeV c The quoted systematic errors on the Q value Q and the number of events
N corresp ond to half the observed width in each case The systematic error on the
yield is the error on the Q value is MeV c and the error on the width is
MeV c
A further systematic uncertainty originates from the way the yield is extracted from the
data The result of a simple Gaussian t to the signal are given ab ove consistent with
the results of a Breit Wigner t or a simple counting metho d The systematic error on
the yield from this source is
The limited Monte Carlo statistics of million multi hadronic Z events as well as the
mo delling of B decays in simulation account for a systematic error of entries on
the yield MeV c on the Q value and on MeV c on the width Q
Tocheck whether the signal could b e an artifact of the employed vertex pro cedure
since it dep ends crucially on the correct mo delling of the p erigee parameter and the
covariance matrices of the tracks the selection cuts are varied over wide ranges The
cut on the ight distance is varied from cm to cm while the cut on jcos j is
V
varied b etween and Furthermore by using simpler analysis techniques without
vertex reconstruction based on di erent cuts on P a clear excess with the same
T
characteristics is observed but it is on top of a larger combinatorial background The
systematic errors are on the yield MeV c on the Q value and MeV c on
the width Q
In order to test the stability of the results as a function of b purity the cut on the
event b tagging probability P is varied in the range b etween and This range
E
corresp onds to a variation in b puritybetween and The extracted
systematic error on the yield is and the error on the mass is MeV c
Possible re ections from B B K decays are exp ected to contribute in the Q value
s
range b etween and MeV c in the order of to the exp ected B signal
u d
Additional uncertainties are intro duced by the p ossible pro duction of and
b b
B Their p ossible in uence in the and re ections from the decay B
b
u d b
signal region is found to b e small
In addition the helicity distribution of the B signal is investigated by dividing it into eight
helicity bins The distribution is compared with theoretical exp ectations This is discussed in
detail in section The charge symmetry of the signal is tested by dividing the sample ac
cording to p ositive and negativepioncharge and p ositive and negative jet charge More details
are given in section All tests have b een passed successfully no cut b eing found where
the b ehaviour of the data was di erent from that exp ected from the simulation prediction for
a strongly decaying isospin I B resonance
Interpretation and Comparison with Predictions
If the signal were due to a single very narrow resonance the exp ected Gaussian width would
b e around MeV c asshown in Fig a This interpretation is unlikely In order
to describ e the observed signal with a single resonance its full width would havetobe
MeV c
A comparison of the signal with a single resonance of this width is shown in Fig b The
signal could b e broadened by the fact that di erent resonances with p ossibly di erent masses
contribute and that some decayinto B and others into B leading to a MeV c shift
in Q value The observed signal shap e is consistent with predictions for orbital excitations
According to this mo del the signal would consist of two narrow and and twobroad
and resonances of roughly the same mass splittings at the MeV c level and
decays into B or B as dictated by spin parity rules The is predicted to decayinto
b oth B and B with ab out equal rates
There is no prediction ab out the relative pro duction rates of the four B states but
reasonable assumptions range b etween spin counting and state counting
for the states In the D meson sector the pro duction ratios D D
D D D D have b een measured by CLEO to b e roughly This is
compatible with the state counting picture for the narrow states It also con rms the ratio
D D D D decaybranching ratio prediction from HQET These
facts motivate the use of state counting and HQET predictions
Fig c and d compare the background subtracted Q value distribution with mo d
els of two narrow states of width MeV c based on the HQET predictions of Eichten
et al In order to obtain b etter agreement with observations the predicted masses are
shifted downwards by MeV c In Fig c state counting is assumed for the relative
pro duction ratio b etween and states Fig d shows the same
comparison but using the spin counting mo del Both mo dels give fairly go o d
descriptions of the data However aneven b etter agreementwould b e obtained by implying
a somewhat larger mass splitting b etween the two states
The observed signal could also contain broad resonances with a full width of ab out
o narrow states with a width of roughly MeV c and twobroad MeV c Assuming tw
states with a width of MeV c and a pro duction ratio of for the four B
states leads to rather go o d agreement as shown in Fig e The broad states are assumed
to have the same mass as the narrow states Similar go o d agreement is obtained by using the
spin counting mo del leading to a pro duction ratio of for the four B states see
Fig f
Furthermore mo dels with large mass splittings of the order of MeV c between
narrow and broad states also lead to fairly go o d descriptions of the data Such large mass
splittings b etween the j and stateshavebeenproposedby Rosner et al
q
With the current exp erimental sensitivity the di erentinterpretations in the mo dels in
Figs b f cannot b e distinguished and neither can any of them b e discarded However
due to the large freedom consistent results can b e achieved in a numb er of p ossible scenarios
based on quark mo del and HQET
The measured Q value is somewhat lower than the predictions byEichten et al but it is consistent within
the errors if one assumes a theoretical uncertainty of roughly MeV c ) 300 2 (a) (b)
200
100 Counts / (20 MeV/c
0 300 (c) (d)
200
100
0 300 (e) (f)
200
100
0
0 0.2 0.4 0.6 0 0.2 0.4 0.6 (∗)
Q(B π) [GeV/c2]
Figure Comparison of the background subtracted Q value distribution data points with
various models solid lines The shadedareacorresponds to the generated distribution scaled
by a factor prior to detector resolution e ects The di erent models in the histograms
a f are discussed in the text
Assuming a B to B ratio of the mean mass di erence b etween the B meson
and the cross section weighted mean of the four exp ected B resonances is determined to b e
u d
m B m B stat syst MeV c
u d
u d
corresp onding to a mass of
m B stat syst MeV c
u d
Part of the systematic error is due to the uncertainty in the ratio of decays into B and B
in the mapping from Q value to mass di erence Tt can accommo date the two reasonable
assumptions and see section This value is somewhat lower than the predicted
values of MeV c for the B and MeV c for the B mass di erences but
it is consistent within the errors if one adds a theoretical uncertainty of roughly MeV c
for the predictions see section
B Helicity Analysis
The angular distribution of the decay pions in the B helicity frame is investigated To
ensure acceptance in the backward hemisphere the cuts of the original analysis are lo osened
e g the cut on the pion momentum is removed The analysis uses the following cuts
Multi hadron event selection see section
Event top ology cuts see section
restrict analysis to barrel j cos j
thr ust
accept only two jet events NJET
Tagging of b hemispheres see section
event tag P e ciency purity
E
Inclusive B reconstruction see section
quality cuts E GeV jm hm ij GeV c and E E
y y y hem beam
restrict B vector to barrel jcos j jcos j
B B
Vertex reconstruction algorithm see section
qualityofvertex reconstruction jcos j
V
ight distance d mm
Pion track selection cuts see sections and
accept only pions which are assigned to the primary vertex
cut on the b tagging signed track probability P
T
ector to barrel jcos j jcos j restrict pion v
veto kaons and protons KTAG PTAG HADSIGN
standard veto on electrons or muons
pion candidate b elongs to the two most energetic particles
at the primary vertex in a hemisphere ) ∗ 2 ∗ -1.0 < cosΘ < -0.75 -0.75 < cosΘ < -0.5
(a) (b) Counts / (20 MeV/c ∗ ∗ -0.5 < cosΘ < -0.25 -0.25 < cosΘ < 0.0
(c) (d) ∗ ∗ 0.0 < cosΘ < 0.25 0.25 < cosΘ < 0.5
(e) (f) ∗ ∗ 0.5 < cosΘ < 0.75 0.75 < cosΘ < 1.0
(g) (h) 0 0.25 0.5 0.75 1 (∗)
Q (B π) [GeV/c2]
Figure a h Q value distribution of B pairs data points along with Monte Carlo
expectations without B production shadedarea in helicity bins * 0.3 Θ
0.25 DELPHI /dcos
σ ∗∗ (∗) d
b → π 0.2 B B σ 1/
0.15
0.1
0.05
0 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
cosΘ*
Figure Decay angle distribution for B pionsintheB rest frame The solid line is
the best t to the model of Falk and Peskin leading to w The dashed
line corresponds to w
The total data sample is divided into eight bins of cos where is the angle b etween the
decay pion in the B rest frame and the B line of ight in the lab oratory TheB signal
is extracted separately for each bin in cos by simple counting of the yield in the Q value
range b etween GeV c and GeV c From simulation the resolution on cos is
found to b e Even without reconstruction of the B helicity the B B helicity
angle distribution is not exp ected to b e at for all helicity states However if all contributing
states are completely unp olarized the distribution will b e at
The Q value distributions for the eight helicity bins are shown in Figs a h A
signi cantchange in the shap e of the background in di erent bins is evident from the distri
butions Note that low energetic particles p GeV c and particles close to the thrust
axis contribute mainly in the backward hemisphere at low Q values Since the lower end of
the particle momentum sp ectrum and its angular distribution with resp ect to the thrust axis
in b events are not precisely known this leads to inaccurate descriptions of the background
Deviations of the simulated background from the data esp ecially at low Q values are visible
The dominant systematic error in the extraction of the yield originates from these deviations
and the background normalization The background has b een normalized from the right and
left sideband thereby allowing only smo oth variations b etween neighb ouring helicity bins
This fact and p ossible reasons have already b een discussed in section * 0.14
Θ (a) 0.12 0.14 GeV/c2 < Q < 0.28 GeV/c2 /dcos 0.1 σ d b 0.08 σ 1/ 0.06
0.04
0.02
0 (b) 0.12 0.28 GeV/c2 < Q < 0.42 GeV/c2 0.1
0.08
0.06
0.04
0.02
0 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
cosΘ*
Figure Decay angle distribution for B pions in the B rest frame for the rst and
second half of the signal The solid lines are the best ts to the modelofFalk and Peskin
leading to a w and b w
The di erential pro duction rate d d cos in the eight helicity bins is consistent
b
with b eing at as shown in Fig a If the mo del assumption shown in Fig c or d
is correct the upp er half of the Q value distribution should contain mainly the signal from
B B whereas the lower half is a mixture of B B and B B Ifany of the
resonances is pro duced in a preferred helicity state one exp ects a deviation from a at angular
distribution Therefore the angular distributions are also evaluated separately in the regions
Q GeV c and Q GeV c In b oth energy regions the angular
distributions are consistent with b eing at as shown in Fig
The ARGUS collab oration has obtained some evidence that the helicity state of D
pro duction is suppressed in low energy GeV c quark fragmentation which leads
to an enrichmentatvery forward and backward angles Falk and Peskin attribute the
ARGUS result to a suppression of the maximally aligned helicity states of the
j q
helicitybin d d cos d d cos d d cos
b b b
all st half nd half
cos
cos
cos
cos
cos
cos
cos
cos
Table Di erential cross section d d cos for eight helicity bins The second
b
column gives the obtainedproduction rates for the whole signal while the third and forth
columns give the rates for the rst and second half of it
total angular momentum of the light quark system j s L describ ed byaweight
q q
factor w which according to the ARGUS result should b e near zero If this mo del is valid
then the same suppression should hold here for the narrow and states Translating
from the D to the B system Falk and Peskin predict the angular distribution of b oth the B
and B whether decaying into B or B to b e of the form
d
B B cos w cos B B
dcos
A t to the measured angular distribution leads to
w stat syst
shown as a solid line in Fig a The systematic error has b een estimated from uncer
tainties in the background mo delling in the di erentcos bins The angular distribution
corresp onding to the ARGUS result w isshown as dashed line in Fig a It clearly
do es not describ e the data well If the observed B signal were due to mainly narrow B
states there would b e a severe disagreement with either the mo del prediction or with the
ARGUS data The angular distributions of the rst and second half of the B signal are
also consistent with b eing at corresp onding to
w stat syst
for the rst region and
w stat syst
for the second region see Fig The systematic error has b een estimated from uncertainties
in the background mo delling in the di erentcos bins The measured di erential cross
sections d d cos are summarized in Tab The second column corresp onds to
b
the pro duction rates in the whole signal while the third and forth columns give the rates for
the rst and second half of it
The CLEO collab oration which dominates the present D world average do esn t makeany statement con
cerning the D helicity distribution yet
q
b
B B B B
bd bu ud bu bd du
q
B B B B
bu bd du bd bu ud
Figure Decay characteristics for the four B charge states decaying into charged pions
The horizontal axis denotes the pion charge while the vertical axis denotes the charge of the
involved b quark
B Charge Analysis
The charge symmetry of the extracted B signal is investigated Positively charged pions can
come from decays of the I states B containing a b quark and B containing
a b quark Therefore avour tagging with e g inclusive leptons or jet charge cannot b e used
to enhance the ratio of B signal to background
However metho ds based on avour tagging and pion charge can b e used to check the
consistency of the signal Therefore the observed signal is divided into four subsamples
according to the jet charge of the hemisphere containing the B candidate and the pion
charge If the signal stems from an I resonance the pro duction rates extracted from all
ejetcharge negative pion B four charge combinations B enriched by p ositiv
p ositive jet charge p ositive pion B negative jet charge negative pion and B
negative jet charge p ositive pion are exp ected to b e the same The four p ossible charge
combinations are shown in Fig The horizontal axis denotes the pion charge while the
vertical axis denotes the charge of the involved b quark
The analysis is based on the same selection cuts as describ ed in section Furthermore
an additional momentum cut for the B pion candidate is applied p GeV c in order
reduce uncertainties in the background mo delling at low Q values The jet charge j is de ned
c
as the longitudinal momentum weighted charge average of all charged particles in an event
hemisphere i e
P
q j p t j
i i
i
P
j
c
j p t j
i
i
where p and q are the three momentum and charge of a particle with index i in a given
i i
hemisphere The vector t denotes the thrust axis as de ned in section For this summation
only particles passing the track selection cuts describ ed in section are considered A
An enhancement of signal to background can b e achieved by tagging the B meson charge Such an algorithm
is presently under construction in the DELPHI collab oration ) 2
∗∗+ (∗)0 + ∗∗0 (∗)+ − → π B → B π B B Counts / (20 MeV/c
(a) (b)
∗∗− −(∗)0 − − ∗∗0 (∗)− + B → B π B → B π
(c) (d)
0 0.25 0.5 0.75 1 (∗)
Q(B π) [GeV/c2]
Figure Distribution of the Q value of B pairs data points along with the Monte
Carlo background expectation for four di erent charge combinations a B b
B c B and d B
minimal momentum cut of p GeV c was chosen in that analysis The free tuning
min
parameter allows one to give di erentweights to the di erent parts of the momentum
sp ectrum The width of the jet charge distribution rises with This comes from the fact
that a large value of the exp onent results in a situation in which the leading particle in the
hemisphere completely dominates the value of j In the limit j b ecomes a binary
c c
op erator with the p ossible values resulting from the charge of the leading particle In the
verage charge in the hemisphere For this analysis limit of j simply re ects the a
c
avalue of ischosen In order to increase sensitivity to the charge of the primary b 0.5 σ
/ DELPHI ∗∗
B 0.4 ∗∗ (∗) σ B → B π
0.3
0.2
∗∗+ (∗)0 + − ∗∗0 (∗)− + B →B π B →B π 0.1 ∗∗0 (∗)+ − ∗∗− −(∗)0 − B →B π B →B π
0
decay
Figure Total production cross section obtainedfrom the four di erent charge
B b
combinations B B B andB The enrichment for B is
and for B it is
quark the di erence b etween the jet charge in opp osite hemispheres is formed resulting in
the de nition of the so called charge ow
q j j
b c same c oppo
where j denotes the jet charge in the hemisphere of the B candidate and j denotes
c same c oppo
the jet charge in the opp osite hemisphere From simulation one exp ects that a p ositivecharge
ow will select of B and of B The four p ossible charge subsamples
of the B signal based on pion charge q and charge ow q are shown in Figs a d
b
The extracted total cross sections are shown graphically in Fig The numerical
B b
results are given in Tab The data are consistent with the assumption that the B signal
stems from an I resonance i e the pro duction rates extracted from the four charge
combinations B B B and B are the same within errors
B Fragmentation
The di erential cross section d dx is analyzed The analysis starts with the same
b Etrue
cuts as already describ ed in section The data sample is divided into seven equally
p opulated bins in x E E E b eing the corrected energy as describ ed in section
Erec B beam B
charge state cut enrichment
B b
B q q
b
B q q
b
B q q
b
B q q
b
Table Total production cross section evaluated for the four di erent charge
B b
combinations B B B andB
The B B Q value plot is tted in each of these bins An unfolding pro cedure is
applied that uses a simulated B sample to generate the reconstructed energy sp ectrum x
Erec
in eachof ve bins of true energy x A t to the data histogram is p erformed using the
Etrue
ve simulation histograms The t parameters determine the normalization co e cients of the
simulation histograms such that the resulting histogram of the reconstructed energies b est
describ es the data In order to avoid spurious oscillations that are typical in such unfolding
pro cedures regularization is enforced by adding to the a term prop ortional to the
curvature of the unfolding result as follows
Z
n
X
jf x j dx jf f f j
i i i
i
The regularization parameter ischosen so as to minimize the condition numb er i e the
ratio of the largest to the smallest eigenvalue of the correlation matrix Much
smaller values lead to oscillating solutions and large negative correlations whereas to o large
values lead to to o at solutions to o small errors and strong p ositive correlations However
the results are stable in the range b etween and
The nal di erential cross section as a function of the true energy is obtained bymulti
plying these relative deviations from the simulation prediction by the simulation input cross
section The results are shown as p oints in Fig The shaded histogram gives the exp ecta
tion from simulation jetset with DELPHI tuning The measured fragmentation
is somewhat harder than in simulation It is also harder than the average b hadron fragmen
tation The measured di erential cross section is given separately for each bin in Tab
It has b een checked that the result is indep endent of the fragmentation function used in
the simulation by rep eating the unfolding pro cedure with Monte Carlo events weighted as a
function of x
Etrue
x bin d dx
Etrue b Etrue
Table Di erential cross section d dx for ve bins of x The data are
b Etrue Etrue
obtained by using an unfolding procedure 0.12
E true 0.11 /dx
σ 0.1 d b
σ 0.09 DELPHI 1/ ∗∗ 0.08 B fragmentation 0.07
0.06
0.05
0.04
0.03
0.02
0.01
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
xE true
Figure Inclusive B cross section in bins of x Thepoints are unfolded data The
Etrue
curve shows the expectation from the simulation
Comparison with other Exp eriments
First evidence for B mesons was obtained in parallel bytwo indep endent analyses in the
DELPHI and OPAL collab oration Additional evidence was rep orted later by the
ALEPH collab oration using a technique similar to the DELPHI analysis presented here
Furthermore ALEPH observed B mesons using fully exclusive metho ds All the results
are compatible with each other and are summarized in Tab
For the B mass values quoted in Tab a pro duction ratio B B mesons of in
B decays is assumed The mass values given by the OPAL and ALEPH collab oration are
corrected in this way This leads to a world average of MeV c
Quantity Exp eriment Measurement Ref
OPAL stat
DELPHI
mass m MeV c
B
u d
ALEPH
ALEPH excl
average
DELPHI
uncorr width MeV c ALEPH
ALEPH excl
OPAL
single resonance MeV c
DELPHI
OPAL
DELPHI
rate B B
u d
u d
ALEPH
ALEPH excl
hel param w all DELPHI
hel param w st half DELPHI
hel param w nd half DELPHI
Table LEP B B results Masses arerecalculatedfrom mass di erences or from
u d
Q values using an upward shift of MeV c in order to account for the average B B
contribution
The uncorrected width of the B signal is consistent in the inclusive analyses of DELPHI
and ALEPH Di erences in this quantity arise from the di erent mo dels of the background
rather than from signi cant di erences in the data The exclusive ALEPH analysis reveals
amuch smaller uncorrected width for the signal whichfavours the interpretation of narrow
resonances The observed signal in all analyses can b e describ ed consistently by the pro duction
of two narrow B states with a mass splitting of the order of MeV c Aninterpretation
of the B signal as stemming from only one resonance leads to a width of in
the OPALandawidthof in the DELPHI analysis
B is found to b e approximately The The pro duction cross section B
u d
u d
dominan t uncertainty in extracting the rate originates from the mo delling and normalization
of the unknown background
The helicity parameter w as wellasthe B fragmentation have b een investigated only in
the DELPHI analysis A con rmation of the DELPHI results on the B helicity distribution
and the B fragmentation by the other LEP collab orations would b e welcome
Search for Orbitally Excited Strange B Mesons
B B K
s
This section rep orts on a search for orbitally excited strange B mesons usually lab eled B
s
in the decaymodeB B K If the B meson mass is ab ove the B K threshold
s s
is forbidden by isospin then this will b e the dominantdecay mo de since the channel B
s
conservation Parity conservation restricts the exp ected main decay mo des of the single states
the spin parity state will decayinto BK s wave the two states will decayinto B K
s or d wave and the state will decayinto b oth BK and B K b oth d wave If the
B meson mass is b elowtheB K threshold then the decay will b e electromagnetic The
s
exp ected strangeness suppression factor of for B mesons compared to B mesons
s
u d
makes an observation of these states challenging see section
Exp erimental Pro cedure and Results
The analysis presented here is very similar to the original B analysis as discussed in section
Most of the exp erimental to ols b tagging inclusive B reconstruction vertex reconstruc
tion and hadron identi cation which are needed for the analysis have b een describ ed in the
previous chapter
Since the B meson decays rapidly through the strong interaction the kaon should orig
s
inate from the primary vertex and not from the B decayvertex The decaychannel B K
s
is di cult to observe exp erimentally due to the limited K reconstruction e ciency and to
s
the dominant K background from B decays Therefore the search fo cuses on B states
s s
ying into charged kaons K deca
Charged kaons are identi ed using the dE dx information measured by the TPC and the
Cherenkov angle reconstruction in the gas and liquid RICH In the momentumrange to
GeV c a kaon ring in the liquid RICH is required HADSIGN KTAG liquid ring re
quired while the veto mo de of the gas RICH RIBMEAN KTAG or dE dx measured
by the TPC Prob K Prob is used in the momentum range ab ove GeV c Monte
Carlo studies show an approximately constantkaon tagging e ciency of with an
average pion rejection factor of This corresp onds to an average purity of the sample
of Details of the DELPHI hadron identi cation software have b een discussed in
section
In the B analysis quark avour tagging can b e used to suppress background A B can
s s
decayinto B K and B K but not into B K Thus the K will b e accompanied
s
byaB meson containing a b quark and the opp osite hemisphere will contain a b quark
This fact is illustrated in Fig The horizontal axis gives the kaon charge while the vertical
axis denotes the charge of the b quark To enhance the signal to background ratio a cut on
j j q is applied where j denotes the jet charge calculated using an energy
c same c oppo K c
weighting exp onent see section The symbol j refers to the jet charge
c same
in the signal hemisphere while j refers to the jet charge in the opp osite hemisphere In
c oppo
the signal hemisphere the kaon itself is excluded from the jet charge calculation Fig
The reconstruction of the origin primary or secondary vertex of a K from the decay K afew
s s
tens of centimeters away from the interaction p oint is not p ossible
q
b
B B K
s
bs bu us
q
K
B B K
s
bs bu us
Figure Decay characteristics for the two B charge states decaying into charged kaons
s
The horizontal axis denotes the kaon charge while the vertical axis denotes the charge of the
involved b quark
shows the distribution of j j q for simulated B kaons and background from
c same c oppo K
s
fragmentation The signal accumulates mostly at negativevalues while the background is
almost symmetrically distributed around zero A cut j j q is applied
c same c oppo K
Approximately of the B decays ful ll this criterion whereas only of
s
the background pass this cut
In summary the analysis uses the following cuts
Multi hadron event selection see section
Event top ology cuts see section
restrict analysis to barrel j cos j
thr ust
accept two jet events and most energetic jet in three jet events
Tagging of b hemispheres see section
eventtagP e ciency purity
E
Inclusive B reconstruction see section
quality cuts E GeV jm hm ij GeV c and E E
y y y hem beam
restrict B vector to barrel jcos j jcos j
B B
Kaon track selection cuts see sections and
accept only tracks which are assigned to the primary vertex
restrict koan vector to barrel jcos j jcos j
K K
standard veto on electrons or muons
kaon momentum cut p GeV c
K
p erform kaon tagging
e ciency purity
jetcharge cut j j q
c same c oppo K
e ciency background rejection ** kaons from B s
background
cut
-1.5 -1 -0.5 0 0.5 1 1.5 ⋅
(jq,same-jq,oppo) qK
Figure Distribution of j j q from simulation for kaons originating from
c same c oppo K
B decays and for background An enhancement of the signal to background ratio is achieved
s
by demanding j j q
c same c oppo K
The quantity which is b est accessible exp erimentally with inclusive B reconstruction metho ds
is the Q value of the decay
Q m B K m B m K m B m B m K
s
The symbol B denotes b oth B and B states which cannot b e distinguished with the
present metho d The resolution on the Q value is MeV c at Q MeV c This
numb er has b een determined from simulation The resolution is dominated by the energy and
angular resolution of the B meson Whether the decaywas actually into B or B and whether
the B decay photon has b een reconstructed has only a negligible e ect on the resolution on
the Q value However the decayofaB of a given mass to B K gives rise to a Q value
s
which is shifted downwards bytheB B mass di erence of MeV c as compared to the
Q value of a BK decay
The Q value plot for DELPHI data taken in the years is shown in Fig
pro duction The data distribution together with the Monte Carlo exp ectation without B
s
shows two narrow p eaks containing a total of stat syst events Simple
Gaussian ts to the signal lead to Q stat syst MeV c with a width of
stat syst MeV c for the rst p eak and Q stat syst
MeV c with a width of stat syst MeV c for the second p eak The
evaluation of the systematic errors is discussed in the next section
The p eaks are naturally explained by B pro duction The strong pion rejection and the
s
narrowness of the signals exclude an interpretation as a re ection due to B decays Several
u d
cross checks have b een p erformed in order to check the consistency of the result
In the calculation of the Q value the kaon candidate is excluded from the inclusive B reconstruction ) 900 2 (a) 800 DELPHI 700 ** (∗) B s → B K 600
500 Counts / (12 MeV/c 400
300
200
100
0 (b) 100
75
50
25
0
-25
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 (∗)
Q(B K) [GeV/c2]
Figure a Distribution of the Q value of B K pairs data points along with
the Monte Carlo expectation without B production shadedarea Qisde nedas
s
Q m B K m B m K b Background subtracted B K pair Q value dis tribution The t is to two simple Gaussians ) 450 2 400 jet-charge anticut
350
300
250 Counts / (12 MeV/c 200
150
100
50
0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 (∗)
Q (B K) [GeV/c2]
Figure Distribution of the Q value of B K pairs data points along with the Monte
Carlo expectation without B production dotted line for j j q The
c same c oppo K
s
shadedarea shows the expectation including B production The B production characteris
s s
tics is simulated in such a way to reproduce the observed signal in Fig
Tocheck whether the signal could b e an artifact of the employed vertex pro cedure
since it dep ends crucially on the correct mo delling of the p erigee parameter and the
covariance matrices of the tracks the vertex reconstruction pro cedure is replaced by
a simpler analysis techniques without vertex reconstruction based on di erent cuts on
P see section The same two p eak structure with the same characteristics is
T
observed
Di erentkaon enrichmenttechniques based on the dE dx measurements of the TPC
v angle reconstruction in gas and liquid RICH have b een used thereby and the Cherenko
varying the purity of the kaon sample b etween and For di erent purities a
similar two p eak structure as shown in Fig is extracted from the data These
tests are based on the RIBMEAN and HADSIGN software packages see section
Another cross check consists in reversing the jet charge cut i e j j q
c same c oppo K
In that way of the signal originating from B decays is suppressed while
s
is retained Fig shows the Q value distribution for data along with the
Monte Carlo exp ectation including B pro duction The B pro duction characteristics
s s
are simulated in suchaway to repro duce the observed signal in Fig by adding
two appropriate Gaussian distributions Although some uctuations are visible around
Q MeV c the agreementbetween data and exp ectation is reasonable
Interpretation and Comparison with Predictions
If the observed two p eak structure in Fig is correct it can b e describ ed consistently by
the pro duction of twonarrow B states The rst p eak is slightly broader than the exp ected
s
resolution at that low Q value It may b e explained as stemming from the narrow B decay
s
ing into B K whereas the second p eak could b e due to the B decaying into BK
s
Accepting this interpretation the masses and widths of the two states are determined to b e
m B stat syst MeV c
s
m B stat syst MeV c
s
B MeV c at c l
s
B MeV c at c l
s
The measured masses of these states are in go o d agreement with HQET predictions derived
in section A mass of MeV c is predicted for the state and MeV c for
the state The theoretical uncertainties on these predictions are of the order of MeV c
The measured masses do not agree p erfectly with the more sophisticated HQET predic
tion of Eichten et al of MeV c for the state and MeV c for the
meson mass already di ers by MeV c from state However their prediction for the B
u d
the observation Furthermore the original mo del predicts the D D and D D
s s s s
mass di erences to b e MeV c lower than the corresp onding nonstrange mass di erences
whereas they have b een observed to b e MeV c higher The up dated mo del pre
dicts these mass di erences to b e ab out the same as in the nonstrange case i e ab out
MeV c below the observed values The same pattern is observed in the B sector Thus it
s
seems that the mo del has problems in predicting the in uence of the non negligible strange
quark mass on the orbital excitation energy If the given interpretation is correct then the
mass splitting b etween the and states would b e MeV c which should b e
compared to the predicted MeV c
The pro duction cross sections p er b jet are measured to b e
Br B B K stat syst
B s b
s
Br B BK stat syst
b B
s
s
Assuming the b baryon rate to b e and the B rate to b e the relative
s
amountof B mesons which is pro duced with orbital excitation is
s
Br B B K stat syst
B s B
s
s
Br B BK stat syst
B B
s
s
s
and B analyses one can evaluate the pro duction ratio Combining the results of the B
s
u d
B
B
s
s
stat syst
B
u d
which is consistent with the exp ected strangeness suppression factor of if one assumes
signal For the calculation totally uncorrelated that the narrow resonances dominate the B
u d
errors have b een assumed
The B state is allowed to decayinto b oth BK and B K The ab oveinterpretation do es
s
not givemuch ro om for the latter decay This is in agreement with exp ectation since the
L
partial widths scale roughly like Q Q which leads to a ratio B BK B
s s
B K at the measured Q value
Systematic Uncertainties
Systematic uncertainties dominate in the measurements of all these quantities Di erent
systematic checks have b een p erformed leading to a determination of the systematic errors
The main sources are discussed here
The complete analysis is rep eated several times with di erent sets of B and K selection
cuts This is realized in an automatic pro cedure providing hundreds of histograms with
di erent cuts and automatic tting algorithms The minimum B momentum cut is
varied b etween GeV and GeV the cut on the di erence b etween the reconstructed
and the mean B mass is varied b etween GeV c and GeV c Furthermore
the cut on the momentum of the kaon candidate is varied b etween GeV c and
GeV c Two and three jet event top ologies are studied separately Di erentkaon
enrichmenttechniques based on the dE dx measurements of the TPC and the Cherenkov
angle reconstruction in gas and liquid RICH have b een used therebyvarying the purity
of the kaon sample b etween and
Di erentbackground shap es originating from simulation and various phenomenological
a
background mo dels e g f Q a Q exp a Q a Q a Q are tted to
the data The normalization is extracted from the sideband in the range b etween
GeV c Additionally GeV c and GeV c These upp er b ound is varied by
the normalization is extracted from the left and the right sidebands of the B signal
s
Furthermore di erent techniques of extracting the yield are used e g replacing the
tting of two Gaussians by simple counting metho ds
Possible re ections from B B decays are exp ected to contribute in the Q
value range b etween and MeV c in the order of to the background Their
in uence in simulation and their p ossibly larger in uence in data due to uncertainties in
the mo delling of the pion rejection capabilities have b een considered in the systematic
errors Additional but smaller uncertainties are intro duced by the p ossible pro duction
of and and re ections from the decay B B
b b b
b u d
For cross section calculations the acceptance is extracted from simulation jetset
with DELPHI tuning Uncertainties in the mo delling of the B decays as well as
s
ents account for the limited Monte Carlo statistics of million multi hadronic Z ev
the systematic errors
Comparison with other Exp eriments
The present exp erimental knowledge ab out orbitally excited strange B mesons is very limited
It is summarized in Tab First exp erimental evidence for B mesons was rep orted bythe s
Quantity Exp eriment Measurement Ref
MeV c m OPAL stat
B
s
m DELPHI MeV c
B
s
m MeV c DELPHI
B
s
width B MeV c OPAL stat
s
width B MeV c DELPHI at c l
s
width B MeV c DELPHI at c l
s
rate B B OPAL stat
s
s
rate B B DELPHI
s s
rate B DELPHI B
s
s
Table LEP B B K results The OPAL result is interpreted as an indication for
s
the production of the narrow B states B and B
s
s
s
OPAL collab oration Additional results are provided by the DELPHI collab oration If
the interpretation given in the previous section is correct then the OPAL signal yields from
the narrow B states B and B The DELPHI analysis resolved b oth states separately
s
s s
The mass measurement for the total B signal of stat MeV c from the OPAL
s
analysis agrees rather well with the DELPHI results of stat syst MeV c for
the state and stat syst MeV c for the state The published OPAL
B the error mass has b een shifted by MeV c to account for the average e ect of B
s
do es not contain the uncertainty on this pro cedure
The pro duction cross sections in the DELPHI and the OPAL analyses are somewhat
di erent but consistent within errors OPAL B B stat DELPHI
s
s
B B stat syst and B B stat syst
s s s
s
and B Combining the results from the DELPHI B analyses one obtains the pro duction
s
u d
syst which is consistent with the ratio stat
B B B
s
s
u d
exp ected strangeness suppression factor of All these measurements are in agreement
with exp ectations for the pro duction of orbitally excited strange B mesons However further
studies by the LEP collab orations are necessary to con rm these states
Baryons Search for and
b b
b
b
which are exp ected to decay and This section rep orts on a search for the b baryons
b b
into Their quark content in the static quark mo del is buu for the baryon and
b
b
bdd for the baryon The baryon b elongs to an isospin triplet I with total
b
b
angular momentum J mixed wave function while the baryon b elongs to a triplet
b
with J symmetric wave function For further details see section It is exp ected
that approximately of all primary pro duced b quarks in Z decays fragmentinto b
baryons The uds is the lightest suchbaryon and thus it decays weakly Most other b
b
baryons are exp ected to decayinto by strong or electromagnetic interactions only the
b b
states and the probably decayweakly There is evidence for and pro duction at LEP
b b b
see section otherwise nothing is known exp erimentally ab out excited b baryons
Exp erimental Pro cedure and Results
Most of the exp erimental to ols b tagging inclusive B reconstruction vertex reconstruction
and hadron identi cation which are needed for this analysis have b een describ ed in the pre
vious chapter
The analysis presented here is very similar to the original B analysis Inclusively recon
structed baryons are combined with charged pions Since the baryons decay rapidly
b
b
through the strong interaction the pion should originate from the primary vertex and not
from the decayvertex The inclusive B reconstruction algorithm is mo di ed in suchaway
b
as to force the mass of the reconstructed b hadron to the mass GeV c In the
b
wever this change original algorithm the mass is forced to B meson mass GeV c Ho
has only a very small in uence on the reconstruction of the Q value
The main di erence to the original B analysis consists in an enrichmentof decays
b
This is accomplished by demanding that there is either a reconstructed a neutral hadron
shower ab ove GeV or that the most energetic particle in the hemisphere is identi ed
as a proton The reconstruction achieves an average e ciency of with a back
ground contamination of see section Protons are identi ed using the standard
DELPHI hadron identi cation co de employing the gas RICH the liquid RICH and dE dx
measurements by the TPC HADSIGN PTAG For the multi hadronic momentum
sp ectrum the working p ointchosen leads to an average proton e ciency of with a
purity of approximately see section
In summary the analysis uses the following cuts
Multi hadron event selection see section
Event top ology cuts see section
restrict analysis to barrel j cos j
thr ust
accept two jet events and most energetic jet in three jet events
Tagging of b hemispheres see section
ent tag P e ciency purity ev E
Inclusive b reconstruction see section
mass forced to mass m GeV c
b
b
quality cuts E GeV jm hm ij GeV c and E E
y y y hem beam
restrict B vector to barrel jcos j jcos j
B B
Pion track selection cuts see sections and
accept only tracks which are assigned to the primary vertex
restrict pion vector to barrel jcos j jcos j
standard veto on electrons or muons
veto kaons and protons KTAG PTAG HADSIGN
pion momentum cut p GeV c
Baryon enrichment see sections and
most energetic particle in hemisphere is identi ed as proton
e ciency purity
reconstructed lamb da in hemisphere
e ciency purity
reconstructed neutral hardron shower ab ove GeV in hemisphere
The quantity which is b est accessible exp erimentally with inclusive reconstruction metho ds is
the Q value of the decay
Q m m m m m m
b b b
b
The resolution on the Q value using the presentmethodis MeV c at Q MeV c
This value has b een determined from simulation The resolution is dominated by the energy
and angular resolution of the baryon The distribution of the measured Q values of
b b
pairs is shown as the data p oints in Fig a There is a clear excess on top of an almost
constant background which is naturally explained by the pro duction of and baryons
b
b
The background from simulation has a at distribution in the signal range but a slightly larger
slop e towards lower Q values than is observed in the data The origin of this di erence is not
yet fully understo o d but it might b e correlated to the rate of inclusive D meson pro duction
the relative b baryon to B meson pro duction ratio the mo delling of yet unmeasured B hadron
decays or general limitations of the jetset string fragmentation mo del It is worth noting
that the herwig generator predicts a less steep rise of the background at small Q
values The reason for this seems to come from the fragmentation mo del cluster instead of
string rather than from the di erent mo delling of the parton shower This has b een inferred
from a Monte Carlo study with the herwig parton shower generator interfaced to lund string
fragmen tation
However the background as shown in Fig a has b een determined from real data
by reversing the baryon enrichment cut This pro cedure is motivated by the simulation Fig
b shows the corresp onding Q value distribution where no signi cant excess is observed
a
exp a Q a Q a Q is tted to the baryon depleted A function f Q a Q
sample and shown as background in Fig a The signal to background ratio in the baryon
depleted sample is exp ected to b e a factor of three less than in the baryon enriched sample
The e ciency for the baryon enrichment is approximately
Several cross checks have b een p erformed in order to check the consistency of the result ) 1400 2 (a) DELPHI 1200 Σ(∗) → Λ π b b 1000
800
Counts / (7.5 MeV/c 600
400
200
0 (b) 5000 baryon anti-cut
4000
3000
2000
1000
0 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 Λ π [ 2]
Q( b ) GeV/c
Figure a Distribution of the Q value of pairs data points The background
b
is extractedfrom the baryon anti cut shadedarea The solid line results froma tofthe
background and two Gaussians to the data Q is de nedas Q m m m
b b
b Distribution of the Q value of pairs data points with a baryon anti cut b ) 2 800 (a)
600
400 enrichment with protons Counts / (7.5 MeV/c 200
0 (b) 150
100
enrichment with lambdas 50
0 (c) 400
300
200 enrichment with neutrons 100
0 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 Λ π [ 2]
Q( b ) GeV/c
Figure Distribution of the Q value of pairs data points for a enrichment with
b
protons b enrichment with lambdas and c enrichment with neutrons The background
shadedarea is extractedfrom the baryon anti cut
Tocheck whether the observed two p eak signal could b e an artifact of the employed
vertex pro cedure since it dep ends crucially on the correct mo delling of the p erigee pa
rameter and the covariance matrices of the tracks the vertex reconstruction pro cedure
is replaced by a simpler analysis techniques without vertex reconstruction based on
di erent cuts on P see section The same two p eak structure with the same
T
characteristics is observed
The total sample is divided into three subsamples according to the way the baryon
enrichmentisachieved a enrichment with protons b enrichmentwithlambdas
and c enrichment with neutrons Due to the small yield of the total signal the
subsamples are exp ected to show only non signi cant structures The corresp onding
Q value distributions for pairs are shown in Figs a c In each case the
b
background is extracted from the data by reversing the baryon enrichment cut Fig
a corresp onding to an enrichment with protons and Fig b corresp ond
ing to an enrichment with lambdas show the same two p eak characteristics as ob
served in the total sample Some small indications for the two p eak structure can also
b e observed in Fig c corresp onding to an enrichment with neutrons How
ever this b ehaviour is exp ected due to the crude resolution of the hadron calorimeter
p
E E GeV which sp oils the resolution on the baryon
E b
Another cross check consists in dividing the signal according to jet charge and pion
charge The four charge states and their decaycharacteristics are shown in Fig
b
The jet charge is calculated using an energy weighting exp onent If the
signal stems from an I resonance the observed structure is exp ected to app ear
in all four charge combinations enriched by negative jet charge p ositive pion
b
negative jet charge negative pion p ositivejetcharge p ositive pion and
b b
p ositivejetcharge negative pion The achieved enrichmentis The
b
exp ectation is con rmed by the data as shown in Fig
Interpretation and Comparison with Predictions
The observed two p eak structure in Fig a can b e describ ed consistently by the pro
rst p eak and second p eak Guided by exp ectations the duction of the b baryons
b
b
excess is tted to two Gaussians of widths exp ected from detector resolution at the approxi
mate masses MeV c and MeV c with masses and pro duction rates allowed to vary
The results of this t are
stat syst N
b b
stat syst MeV c Q
b
b
stat syst MeV c Q
b
b
stat syst
b
b
b
stat syst
b b
b
According to isospin rules the observed rate has b een multiplied by to account for
b
pro duction The pro duction cross sections also havebeenevaluated separately for the
b
b
This relation is extracted from the simulation The correct mo delling of the hadron calorimeter resolution
is still the sub ject of intensive studies within the DELPHI collab oration
q
b
b b
b b
buu bdu du bdd b du ud
q
b b
b b
bdd bdu du buu bdu ud
Figure Decay characteristics for the four charge states decaying into charged
b
pions The horizontal axis denotes the pion charge while the vertical axis denotes the charge
of the involved b quark
and baryon leading to and
b b
b b
b
The statistical signi cance for the signal corresp onds to standard deviations
b
b
The quoted statistical errors are uncorrelated errors i e they have b een determined from the
evolution as a function of the deviation from the minimum re tting with resp ect to all
other parameters In particular ts without signal for or result in values larger by
b
b
ever systematic errors dominate in the measurements of all these and resp ectively How
quantities Their evaluation will b e discussed b elow Adding the pion mass to the measured
Q value leads to the following mass di erences
m m stat syst MeV c
b
b
m m stat syst MeV c
b
b
which compare well with the simple exp ectations from section m m
b b
MeV c and with previous m m MeV c and the latest predictions
b b
m m MeV c m m MeV c
b b b
b
The default mass di erences in jetset m m MeV c m
b b
b
m MeV c are somewhat lower than the measured values whereas the DELPHI
b
jetset parameter setting used to calculate acceptances uses and MeV c The
rates predicted by b oth mo dels are and
b
b b b
b b
From the observed widths of the signals and the known exp erimental resolution the upp er
limits on the full width of the resonances are calculated
MeV c at c l
b
MeV c at c l
b
The observed small widths are consistent with a calculation byYan et al who nd
MeV c and MeV c for the and at the observed Q values section
b
b
For this discussion only the mass di erences are considered since the present exp erimental uncertainties on
the mass are larger than the obtained resolution on the mass di erences m MeV c
b b ) 2 (a) (b)
Counts / (7.5 MeV/c −− −− Σ(∗)− → Λ π− Σ(∗)+ → Λ π+ b b b b
(c) (d)
Σ(∗)− → Λ π− Σ(∗)+ → Λ π+ b b b b
0 0.05 0.1 0.15 0.2 Λ π [ 2]
Q( b ) GeV/c
Figure Distribution of the Q value of pairs data points for the four di erent
b
b
charge combinations a b c and d The achieved enrichment
b b b b
in the four states is
The interpretation presented leads to consistent results and to go o d agreement with pre
dictions However the total signi cance of the rst p eak is only two standard deviations
Thus one could also try to ascrib e the second p eak to the pro duction of the baryon
b
This interpretation is excluded by the observed non at helicity distribution of the second
p eak see section since the helicity distribution for the baryon is exp ected to b e
b
at Furthermore there is no evidence for an additional enhancementabove the second
pro duction in this interpretation p eak whichwould b e exp ected from
b
Another hyp othesis for the observed signal could b e a p ossible re ection from the decay
The udb is the lightest baryon with orbital excitation denoting two
b
b b
P P
states with J L L andJ L L The orbital
k K k K
angular momentum L describ es the relative orbital excitations of the two light quarks and
k
the orbital angular momentum L describ es orbital excitation of the center of mass of the
K
baryon has not yet two light quarks relative to the heavy quark as shown in Fig The
b
b een observed exp erimentally Since the baryon is orbitally excited it is exp ected to b e
b
suppressed compared to the pro duction of and baryons In addition the may also
b
b b
have signi cant radiativebranching ratio These facts already disfavour an
b
b
interpretation of the observed signals as originating from re ections In the charm sector
b
the two baryon states and have b een observed exp erimentally in the exp ected de
c
caychannel It is found that their decays are mainly non resonant in the
c c
subsystem which pro ofs that narrow re ections cannot b e created by this system
Systematic Uncertainties
Systematic uncertainties dominate in the measurements of all the calculated quantities Dif
ferent systematic checks have b een p erformed leading to a determination of the systematic
errors
The complete analysis is rep eated several times with di erentsetsof B and selection
cuts The minimum B momentum cut is varied b etween GeV and GeV the cut
on the di erence b etween the reconstructed and the mean B mass is varied b etween
GeV c and GeV c Furthermore the cut on the b tagging event probabilityisvaried
between and Two and three jet event top ologies are studied separately
Di erent proton enrichmenttechniques based on the dE dx measurements of the TPC
and the Cherenkov angle reconstruction in gas and liquid RICH have b een used thereby
varying the purity of the proton sample b etween and The uncertainties in
the mo delling of the baryon enrichmenthave b een assumed to b e of the order of
Di erentbackground shap es originating from the baryon anti cut and various phe
a
nomenological background mo dels e g f Q a Q exp a Q a Q a Q
are tted to the data The normalization is extracted from the sideband Di erent
techniques of extracting the yield from the signals are used e g replacing the tting of
two Gaussians by simple counting metho ds
The in uence of the smaller lifetime ps compared to the B
b
meson lifetime on the p erformance of the b tagging and the vertex separation algorithm
is investigated It is found to b e smaller than for the b tagging and for the vertex
reconstruction algorithm
For cross section calculations the acceptance is extracted from simulation jetset
with DELPHI tuning Uncertainties in the mo delling of the decays of the
b
baryons as well as the limited Monte Carlo statistics of million multi hadronic Z
ev ents account for systematic errors
The in uence on the background shap e in the signal region of p ossible re ections from
B K decays has b een investigated and it is found to b e B B and B
s
u d negligible ∗ Θ DELPHI
/dcos * σ Σ → Λ π
d b b b σ 1/
∗
cosΘ
Figure Decay angle distribution for pions in the rest frame with respect to the
b b
line of ight in the laboratory The curve is a t of the expression given by Falk and Peskin
b
resulting in w
Helicity Analysis
b
An interesting consequence of a large and rate is the dep olarization of the If
b b
b
all s were primary particles the standard mo del predicts a large p olarization of
b
This would b e reduced if a substantial fraction of s came from decays of heavier
b
baryons In the quantitative mo del of Falk and Peskin the resulting p olarization is
expressed as function of two parameters A related to the pro duction rate of and and
b
b
w describing the p opulation of the spin alignmentstate of the light quark system The
pro duction ratio in this mo del is which is smaller than but consistent with the
b
b
pro duction present measurement w can b e deduced from the angular distribution of the
b
rate in the helicity frame
d
cos w cos
b
b
dcos
The measured helicity angle distribution is shown in Fig The parameter w deduced
from a t to this distribution is
w stat syst
Quantity Exp eriment Measurement Ref
Q MeV c DELPHI
b
Q MeV c DELPHI
b
MeV c DELPHI at c l
b
MeV c DELPHI at c l
b
DELPHI
b
b
b
DELPHI
b b
b
helicity parameter w DELPHI
Table LEP results
b
b
Negative w are unphysical w corresp onds to a complete suppression of the helicity
states According to Falk and Peskin large and rates and small values of
b
b
w lead to a substantial reduction of the observable p olarization in Z decays This is in
b
qualitative agreement with the apparently small p olarization P stat
b b
syst as measured by the ALEPH collab oration
The decay angle distribution for pions in the rest frame with resp ect to the line
b b b
of ight in the lab oratory is exp ected to b e at
d
b b
dcos
Within the present sensitivity the data are consistent with this exp ectation
This section rep orted on the search and rst evidence for baryons in the DELPHI
b
exp eriment The data obtained are also consistent with the pro duction of the baryon
b
The results are summarized in Tab Further studies by other exp eriments are needed to con rm these results
Chapter
Summary
First exp erimental evidence for the existence of orbitally excited B mesons B B is
obtained in parallel with an indep endent analysis bytheOPAL collab oration from the B
Q value distribution using approximately million multi hadronic Z events taken with the
DELPHI detector at LEP in the years By using an inclusive B reconstruction
metho d and secondary vertex reconstruction a large signal is observed in the B Q value
distribution at
Q B stat syst MeV c
with a Gaussian width of Q stat syst MeV c The signal can b e describ ed
consistently as originating from several narrow and broad B resonances as predicted by
quark mo dels and HQET and observed in the D meson sector The mass of orbitally excited
B mesons is extracted to b e
m B stat syst MeV c
The signal can also b e describ ed as a single resonance of full width MeV c
The pro duction rate of B mesons p er b jet is measured to b e
stat syst
b B
The helicity distribution of the signal is investigated and found to b e at within errors Fur
thermore the B fragmentation function is extracted from the data The charge symmetry
of the signal is found to b e in agreement with the exp ectations for an I resonance In
conclusion the existence of orbitally excited B mesons has b een exp erimentally established
The results are in general agreement with predictions and with measurements of other LEP
exp eriments The existence of B mesons might op en the p ossibility for future exp eriments
of observing CP violation in the B system by avour self tagging
Furthermore a search has b een p erformed for orbitally excited strange B mesons in the
decay B B K Inclusive B reconstruction metho ds secondary vertex reconstruction
s
and the DELPHI particle identi cation capabilities lead to the observation of a two p eak
structure in the B KQ value distribution at Q stat syst MeV c and
Q stat syst MeV c It can consistently b e interpreted as originating
from the predicted narrow B states B and B Accepting this interpretation the masses
s
s s
of the two states are determined to b e
m B stat syst MeV c
s
m B stat syst MeV c
s
Upp er limits at c l for the widths of these states havebeenevaluated B
s
MeV c and B MeV c The corresp onding pro duction rates are measured to b e
s
Br B B K stat syst
B s b
s
Br B BK stat syst
B b
s
s
Combining the results from the DELPHI B and B analyses one obtains the pro duction
s
ratio
stat syst
B B B
s
s
which is consistent with the exp ected strangeness suppression of The measurements
are in general agreement with predictions Additional analyses are needed by the LEP exp er
iments in order to con rm these results A sizeable pro duction of B mesons will makean
s
observation of B mixing harder at LEP since it reduces the B pro duction rate
s s
First exp erimental evidence for the b eautybaryons and is presented in an analysis
b b
of Q value distribution using an inclusive reconstruction metho d secondary vertex
b b
reconstruction and baryon enrichmenttechniques The observed structure in the Q value dis
tribution can consistently b e describ ed by the pro duction of and baryons leading to
b b
the following mass di erence measurements
m m stat syst MeV c
b
b
m m stat syst MeV c
b
b
The widths of b oth p eaks are compatible with detector resolution leading to
b
MeV c and MeV c at c l The total pro duction rate of and
b
b
b
baryons p er b jet and the relative fraction of each state are measured to b e
stat syst
b
b
b
stat syst
b b
b
baryon seem to b e suppressed The sizeable pro duction The helicity states of the
b
rate and the suppression of the helicity states could account for the small measured
b
p olarisation The results are in general agreement with predictions Additional analyses are
needed by the LEP exp eriments in order to con rm these results
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Memb ers of the DELPHI Collab or at io n
AUSTRIA VIENNA
W Adam W Bartl R Fruhwirth J Hrub ec M Krammer G Leder D Liko J MacNaughton
W A Mitaro N Neumeister H Pernegger M Pernicka M Regler J Strauss
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M L Andrieux R Barate F Dup ont F Ledroit F Naraghi L Ro os G Sa jot
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J E Augustin P Bambade B Bouquet J L Contreras G Cosme B Dalmagne
F Fulda Quenzer G Grosdidier B Jean Marie V Lep eltier A Lipniacka P Paganini
S Plaszczynski P Reb ecchi F Richard P Roudeau A Sto cchi A Trombini G Wormser
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R Aleksan Y Arnoud J Baudot T Bolognese C De Saint Jean P Jarry J P Laugier
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D Blo ch F Djama M Dracos J P Engel D Gele J P Gerb er P Juillot V Nikolaenko
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W D Ap el A Daum W De Bo er R Ehret D C Fries U Haedinger M Hahn M Kaiser
C Kreuter G Maehlum H Mueller W Ob erschulte Beckmann O Po dobrin H Schneider
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K H Becks M Blume J Dahm J Drees K A Drees M Elsing F Hahn S Hahn
K Hamacher P H Kramer P Langefeld G Lenzen R Lindner T Maron W Neumann
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P P Allp ort P S L Bo oth T J V Bowco ck L Carroll A Galloni M Gibbs M Houlden
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G J Barker S Blyth S Bosworth N Demaria F J Harris P J Holt J G Loken L Lyons
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T Adye M J Bates D Crennell P D Dauncey B Franek G Gopal J Guy G Kalmus
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M Verlato
ROMA
V Bo cci V Canale L Cerrito L Di Ciaccio G Matthiae P Privitera
SANIT A
A Baroncelli C Bosio P Branchini E Graziani C Mariotti A Passeri E Spiriti C Stanescu
L Tortora
TORINO
F Bianchi M Bigi R Chierici D Gamba E Migliore G Rinaudo A Romero G Sciolla
TRIESTE UDINE
F Cossutti G Della Ricca B De Lotto L Lanceri C Petridou P Poropat M Prest F Scuri
L Vitale F Waldner
NETHERLANDS NIKHEF
E Agasi A Augustinus W Hao D Holthuizen P Kluit B Ko ene M Nieuwenhuizen
W Ruckstuhl I Siccama J Timmermans D Z To et G W Van Ap eldo orn P Van Dam
J Van Eldik
NORWAY BERGEN
S J Alvsvaag G Eigen A G Fro desen A Klovning B Stugu
OSLO
L Bugge T Buran M Dam A L Read T B Skaali S Stapnes
POLAND KRAKOW
P Bruckman Z Ha jduk P Jalo cha K Korcyl W Krupinski W Kucewicz B Muryn H Palka
G Polok A Zalewska
WARSZAWA
K Doroba R Gokieli M Gorski J Krolikowski R Sosnowski K Stepaniak M Szczekowski
M Szeptycka P Zalewski
PORTUGAL LIP
P Abreu F Barao M Espirito Santo R Henriques A Maio L Peralta M Pimenta
T Spassov B Tome
SLOVAKIA BRATISLAVA
P Cho chula R Janik P Kubinec B Sitar
SLOVENIA LJUBLJANA
V Cindro B Erzen B Golob D Zavrtanik D Zontar
SPAIN MADRID
J A Barrio J Sanchez
SANTANDER
M Berggren A J Camacho Rozas J Garcia J M Lop ez M A Lop ez Aguera J Marco
C Martinez Rivero F Matorras A Ruiz
VALENCIA
M V Castillo Gimenez E Cortina A Ferrer J Fuster C Garcia J J Hernandez E Higon
C Lacasta F Martinez Vidal S Marti i Garcia S Navas J Salt
OVIEDO
J Cuevas Maestro
SWEDEN LUND
S Almehed O Barring E Falk V Hedb erg G Jarlskog L Jonsson P Jonsson I Kronkvist
B Lo erstad U Mjo ernmark G T ranstromer C Zacharatou
STOCKHOLM
B A sman K Canko cak G Eksp ong P Gunnarsson S O Holmgren K Hultqvist
R Jacobsson E K Johansson M Karlsson T Moa P Niss C Walck G C Zucchelli
UPPSALA
O Botner T Ekelof M Gunther A Hallgren J Medb o K Woschnagg
SWITZERLAND CERN
U Amaldi P Baillon Yu Belokopytov C Bourdarios R C A Brown A Buys T Camp oresi
F Carena A Cattai V Chabaud Ph Charp entier V Chorowicz P Collins M Davenp ort
A De Angelis H Dijkstra M Donszelmann M Feindt H Fo eth F Formenti H Furstenau
C Gaspar Ph Gavillet D Gillespie H Herr T L Hessing H J Hilke C Joram H Klein
M Koratzinos A Lop ez Fernandez J C Marin M Mc Cubbin K Mo enig L Pap e D Reid
E Rosso F Stichelbaut D Treille W Trischuk A Tsirou O Ullaland E Vallazza
P Weilhammer A M Wetherell M Witek
USA AMES
H B Crawley D Edsall A Firestone L Gorn T S Hill J W Lamsa D W Lane C K Legan
R Mc Kay W T Meyer E I Rosenberg
Acknowledgements
Iwould like to thank Prof Dr W de Bo er for his continuous supp ort and providing me
with the p ossibilitytowork in the DELPHI group at CERN I am grateful to Prof Dr Th
M uller for accepting to b e my Korreferent
Many thanks go to Dr M Feindt for the exciting working topics manyvaluable discus
sions and the go o d working atmosphere It is also a pleasure to thank Dr O Po dobrin for
his close collab oration
I am grateful to my colleagues in DELPHI esp ecially to D Edsall Dr M Feindt Prof Dr
A Firestone D Lane W Ob erschulte Dr O Po dobrin A Seitz C Weiser and M Wielers
Furthermore I would like to thank Prof Dr A Firestone D Lane Dr O Po dobrin
and C Weiser for carefully reading the manuscript
Iwould esp ecially like to thank my family and friends Their supp ort was essential for my
studies and for the work on this thesis