Rare B meson decays - mathieu trocmé

UNIVERSITY OF BRISTOL
DEPARTMENT OF PHYSICS
NAME: TROCMÉ Mathieu
DEGREE: Erasmus Student
PROJECT/DISSERTATION
NUMBER:
TITLE:
PA1
YEAR OF SUBMISSION: 2003
Rare B Decays
SUPERVISOR: Dr Fergus Wilson
H. H. Wills Physics Laboratory
University of Bristol
Tyndall Avenue, Bristol BS8 1TL

Abstract 1
ABSTRACT
This report aims to describe a way to measure simultaneously the branching ratio of the
0 * + −
meson decay B → K π and its conjugate . This way, based on the analysis of 61.6 ±
0.68 millions 0
0
0
0
B and B mesons, uses a cut and count method. The B / B mesons were
generated at SLAC between 1999 and 2002 in the PEP-II collider and detected by the BABAR
* +
* −
0 +
0
−
detector. The K / K were observed via their decay to a K π / K Sπ
, which results in a
0
0
B / B having the three body charmless final state
→ π
0
B
* +
K
−
&
0 +
K Sπ
The total branching ratio was found to be:
BR
S
0 + −
0
− +
K Sπ
π / K Sπ
π :
B
0
* −
+
→ K π
0
S
−
K π
0 * + −
0 * −
+
−6
{ B → K π } + BR{
B → K π } = ( 18.
6 ± 6.
5 ± 1.
6)
× 10
with a statistical significance of 3.2 σ

Acknowledgements 2
ACKNOWLEDGEMENTS
Firstly, I would like to thank Nicole Chevalier for all she has done for us throughout the
year. Always available and always smiling, it was really a great pleasure to come and annoy
her with some not always sensible questions. I really have appreciated this.
I would also like to thank all the people that helped me from time to time when I was
randomly looking for help: Robert Frazier, Nick Barlow, Jim Burke, Wahid Bhimji, Dave
Newbold, Fergus Wilson.
Many thanks as well go to all the Particle Physics Project Work students that have
contributed to make this work more enjoyable: Meyrem, Shona, Domenico, Jamie, Chris.
Finally, ‘un grand merci à David’ for having helped me with my English.

Table of contents 3
TABLE OF CONTENTS
Abstract………………………………………………………………………………………… 1
Acknoledgements……………………………………………………………………………… 2
I- Introduction…………………………………………………………………………………. 5
II- Physical Background………………………………………………………………………. 7
II.1- Symmetries in Particle Physics……………………………………………………. 7
II.1- CP violation in the Standard Model……………………………………………….. 9
II.3- B mesons and the BABAR experiment………………………………………………. 12
0 * + −
0
* − +
II.4- The B → K π & B → K π decays.……………………………………... 15
III- Analysis Method…………………………………………………………………………... 18
III.1- Data Sample and Preselection…………………………………………………… 18
III.2- The Cut and Count Method (CCM).……………………………………………… 18
III.2.1- Principle of the CCM…………………………………………………… 18
III.2.2- Selection variables……………………………………………………… 19
III.2.2.1- Event shape variables…………………………………………. 19
III.2.2.2- Particle Identification……………………………………….. 21
* + 0 +
* + 0
−
III.2.2.3- The K → KSπ
/ K → K Sπ
resonance………….…… 22
0 − +
0
+ −
III.2.2.4- The K S → π π / K S → π π resonance………………… 24
III.2.2.5- Kinematic constraints: the ∆E-mES plane................................... 26
III.2.3- Computing Overview…………………………………………………… 29
III.3- Calculation of the Branching Ratio……………………………………………….. 29
III.3.1- Definition……………………………………………………………….. 29
III.3.2- MC Efficiency…………………………………………………………... 30

Table of contents 4
III.3.5- Background Characterisation and Subtraction………………………… 32
III.3.7- Errors on the branching ratio calculation……………………………… 36
III.4- Optimisation of the cuts…………………………………………………………... 37
III.4.1- Significance calculation………………………………………………… 37
III.4.2- Errors on the significance……………………………………………….. 38
III.5- Overall Process……….…………………………………………………………... 42
IV- Results……………………………………………………………………………………... 44
IV.1- Final selection criteria after optimisation………………………………………… 44
IV.2- MC Efficiency………… ………………………………………………………… 46
IV.3- Combinatoric background………………………………………………………... 47
0 * + −
0
* − +
IV.4- Branching ratio of the B → K π & B → K π decays ………………… 49
V- Discussion…………………………………………………………………………………... 50
VI- Conclusion…………………………………………………………………………………. 53
Appendix...……………………………………………………………………………………... 54
References…………………………………………………………………………………….. 56

I- Introduction 5
I- INTRODUCTION
We live in a matter universe. However, from the ‘Hot Big Bang’ model – the current
model explaining the beginning of the universe (Gamow, 1946, [1]) – this universe began
with an equal amount of matter and antimatter. This model being widely accepted – especially
after the random discovery of the Cosmologic Microwave Background by Penzias and Wilson
in 1965 [2] – , one question comes to mind: Where has all the antimatter gone ? Many
theories generating a matter asymmetry have been proposed, even some antigravity ones. But
the current one is due to Sakharov (1967, [3]) and based on the ‘Sakharov’ conditions, one of
which is CP violation.
Basically, to turn the properties of a particle into the ones of its antiparticle, one just
needs to process a symmetry operation called CP. If this CP operation can be successfully
observed in a decay, matter and antimatter are absolutely symmetric. Otherwise, it proves
there is an asymmetry between matter and antimatter, which could be one explanation of the
matter asymmetry in the universe.
From the middle of the sixties, it has been known that CP violation is a real
phenomenon that occurs in weak decays. Since then, a quantification work has been
undertaken to determine whether or not CP violation processes alone can lead to an
explanation of the universe matter asymmetry.
Having successfully studied K meson systems first, physicists currently track CP
violation in B meson systems. Two major recent collaboration are involved in that study: the
BELLE collaboration at the KEK-B collider in Japan and the BABAR one at SLAC in
California. These both collaborations have already observed CP violation in B mesons [4].
But there is still a lot to do…

I- Introduction 6
A way to quantify CP violation consists of measuring the branching ratio (or branching
fraction) of a specific decay (i.e. the likelihood this decay happens). This is what was
proposed in this computing project, namely measure the total branching fraction of the two
conjugate decays:
0 * + −
B → K π &
B
0
* − +
→ K π
A part of the Particle Physics Group of the University of Bristol being involved in the BABAR
experiment, the data to be analysed for this measurement come from California.

II- Physical Background 7
II- PHYSICAL BACKGROUND
II.1- Symmetries in Particle Physics:
In Particle Physics, there are three fundamental discrete symmetry operations that can
be performed on a particle to look at its behaviour.
The first one is the charge conjugation operation ‘C’ which inverts all the signs of all
the internal quantum numbers of a particle, leaving its mass, energy, momentum p r , spin s r
r r
and helicity (or ‘handedness’) h ≡ s . p unchanged:
r C r r C r
p ⎯ ⎯→ p , s ⎯⎯→
s ,
C
h ⎯⎯→
h
The second one is the parity operation ‘P’ which reverses all the space coordinates of a
particle. Therefore, all its real vectors like its position r and its momentum are reversed,
whereas all its axial or pseudo vectors like its spin are not. This implies that its helicity must
change.
r P r r P r r P r
P
r ⎯ ⎯→ −r
, p ⎯⎯→
− p , s ⎯⎯→
s , h ⎯⎯→
−h
As mentioned in the introduction, it is the combined operation CP (or PC) that changes
a particle into its antiparticle.
The third and last one is the time reversal operation ‘T’ which converts all the
properties of a particle into those of the same particle running backwards in time, that is,
moving and ‘spinning’ in the opposite direction, leaving its handedness unchanged.
r
T r r T r
p ⎯ ⎯→ − p , s ⎯⎯→
−s
,
T
h ⎯⎯→
h

II- Physical Background 8
These three symmetry transformations were originally thought to be exact symmetries,
that is, one could not differentiate between:
- a particle observed in a matter universe from its ‘antiparticle’ observed in the
same antimatter universe (C conservation)
- a ‘mirror-particle’ observed in a mirror universe (P conservation)
- a particle moving backwards in time in a universe evolving equally
backwards in time (T conservation)
However, it turned out that these symmetries can all be broken or violated in weak
decays. In 1956, Lee and Yang discovered that parity was not conserved via weak interaction
in K mesons systems whereas it was in the electromagnetic and strong ones [5]. This was also
successfully corroborated in 1957 by Ms Wu and her team [6].
Soon after, it was found that C was equally violated, especially by examining the spins of −
e
+
+
−
and e in respectively µ and µ decays [7]. Another example of C violation is the nonexistence
of these 2 potential particles that should only be sensitive to the weak interaction,
namely the right-handed neutrino ν R ( h > 0 i.
e.
θ r r
( s , p)
< 90°
) and the left-handed
antineutrino ν L ( h < 0 i.
e.
θ r r
( s , p)
> 90°
). No experiments have ever observed one or the
+
−
other. For instance, applying C to the decay of a π emitting a ν L should give a π emitting
an ν L . But only a ν R is observed.
More recently in 1998 and in K meson systems again, the CPLEAR experiment at CERN (CP
standing for CP violation and LEAR for Low Energy Anti-proton Ring) observed a case of T
violation [8].
Considering the previous example leading to C violation, one can nevertheless see that
applying P after C would turn the ν L into ν R which is observed.
L
ν does not exist
=> P violation
ν R
P C
ν L C & P ν R
C P
ν
L
Figure 1: C and P symmetry operations are violated by the weak interaction.
However, the combined CP operation seems to be conserved.
ν R does not exist
=> C violation

II- Physical Background 9
This combination of operations looking invariant reassured all the community, but a
new surprise arose. In 1964, still in K mesons, Cronin and Fitch discovered the first laboratory
evidence of CP violation [9].
Nowadays, only the combination of the three symmetry operations all together (the
‘CPT combination’) is believed to be invariant. That is, the backwards observation of a
phenomena filmed through a mirror in an antimatter universe would be indistinguishable than
the same phenomena observed in ‘natural’ conditions [10].
II.2- CP Violation in the Standard model:
One of the first attempts to explain CP violation came from Wolfenstein in 1964 [11].
His theory was implying a new unknown force, the “weak superforce”. Although simple and
elegant, it was abandoned, not being able to explain new phenomena. It was only in 1973 that
a valid explanation, based on the work of Cabibbo [12], was proposed by Kobayashi and
Maskawa [13]. Cabibbo first realised that the weak interaction does not ‘see’ the flavour of
the then 4 known quarks (u/d, c/s) as the electromagnetic or the strong interactions do.
Instead, it feels a mixture of quarks. To express his idea, he so created a 2x2 matrix (still only
4 quarks) comprising a real parameter θ c – today known as the Cabibbo angle – that must be
found by experiment.
⎛d
'⎞
⎛V
⎜ ⎟ = ⎜
⎝ s'
⎠ ⎝V
ud
cd
V
V
us
cs
VCabibbo
⎞⎛d
⎞ ⎛ cos( θ c )
⎟⎜
⎟ = ⎜
⎟ ⎜
⎠⎝
s ⎠ ⎝−
sin( θ c )
d'
= (cosθ
). d + (sinθ
). s
c
s'=
( −sinθ
). d + (cosθ
). d
c
sin( θ ⎞⎛d
c ) ⎞
⎟
⎜ ⎟
cos( θ ⎠⎝
s c ) ⎠
where the dashed letters represent the quark eigenstates seen by the weak interaction (called
flavour eigenstates), and the undashed ones the ‘normal’ quark eigenstates as felt by the
electromagnetic or the strong interaction (the mass eigenstates).
c
c

II- Physical Background 10
s
b
gWVus
Figure 2: Feynman diagram of a weak quark flavour changing process. The coupling
strength at the vertex is given by the weak coupling constant gW times the corresponding
element in the Cabibbo matrix.
But once again, this could not completely explain the observation of new phenomena.
Some years later, Kobayashi and Maskawa realised that with the introduction of a third
generation of quarks - thus leading to a 3x3 matrix with 4 independent parameters having
equally to be found by experiments (3 real ones -3 other ‘mixing angles’- and one non-trivial
complex phase) - these phenomena could be explained. This matrix is known as the Cabibbo-
Kobayashi-Maskawa matrix (or CKM matrix), and it is the aforementioned complex phase
parameter that is indeed the source of CP violation in the Standard Model of Particle Physics.
Similarly, this physically translates to:
⎛d
'⎞
⎛V
⎜ ⎟ ⎜
⎜ s'
⎟ = ⎜V
⎜ ⎟ ⎜
⎝ b'
⎠ ⎝V
ud
cd
td
gWVcb
V
V
V
us
cs
ts
VCKM
V
V
V
W -
tb
u
ub
cb
W -
c
⎞⎛d
⎞
⎟⎜
⎟
⎟⎜
s ⎟
⎟⎜
⎟
⎠⎝
b ⎠
Figure 3: Feynman diagram of a weak quark flavour changing process. The coupling
strength at the vertex is given by the weak coupling constant gW times the corresponding
elements in the CKM matrix.

II- Physical Background 11
This matrix being unitary, some very useful relations can be inferred. One of special interest
experimentally speaking is the following one:
Im
V
V
td
cd
V
V
V
tb
*
cb
ud
V
*
*
ub + VcdVcb
+ VtdVtb
*
As a matter of fact, if divided by V , it becomes:
cdVcb
V
V
ud
cd
V
V
*
ub
*
cb
+
γ
V
td tb
1 + *
VcdVcb
Each term being complex, they can be drawn as vectors in the complex plane. Once arranged
head-to-tail, they form a triangle (their sum giving 0). Since one side of this triangle is 1, it
lies on the real axis and has a modulus of 1. Thus, only the coordinates of the top point need
to be specified, i.e. once two of the α, β and γ angles are known, the triangle is perfectly
defined. This visual help is called the “Unitarity triangle”.
?
(0,0) (1,0)
Figure 4: The unitary triangle
V
V
V
= 0
= 0
ud
cd
V
V
α β
Basically, the goal of any CP violation experiments is to accurately measure these three
angles (to assure they do sum to 180°), by as many independent means as possible. Leading to
the determination of the CKM matrix elements and so to its non-trivial complex phase, the
expected amount of matter in the universe could be inferred and if this does not tally with
what is observed, then there should be some new physics underneath, i.e. physics beyond the
Standard Model.
*
ub
*
cb
Re

II- Physical Background 12
II.3- B mesons and the BABAR experiment:
In order to confirm the idea of Kobayashi and Maskawa, a run for the third generation
of quarks started. In 1977, the b quark was discovered in a Y resonance also called bottonium
( Υ = bb
) [14] an in 1995, the CDF collaboration (Collider Detector at Femilab) discovered
the top quark [15]. The third generation of quarks was complete.
Mesons with b quarks therefore appeared to be natural new candidates to investigate CP
violation. B mesons, first discovered by the CLEO Collaboration in 1983 [16], are a bound
±
0
state of a b quark and a light anti-quark ( B = ub
, bu
, B = db
). Made up of a third
generation quark and so having a large mass, they are a good environment to study CP
violation. Many decays are possible, which offer many different avenues of research. The
CKM matrix elements can almost be all measured, especially the third generation related ones
(3 rd columns and 3 rd ±
rows). This is not possible with K mesons ( K = us,
su
and
0 0 0
±
K , ( K S , K L ) = ds
) or D mesons ( D = cd
, dc
not made up of third generation quarks.
0
, D = cu
±
and = cs,
sc
), since they are
B mesons look like perfect candidates. However, unlike the C and P violation that are
said to be violated ‘maximally’ – ν R and ν L do not exist – CP violation is rather a small effect
in B decays. Although branching ratios of K mesons can at most be of order 10 -3 , B meson
ones are usually at a 10 -6 level. Thus, many millions of B mesons need to be produced to
ensure any accuracy.
To generate this massive quantity of particles, several devices has been used or
designed. The two first collaborations trying to measure CP violation in B decays were: CDF
at Fermilab and CLEO at CESR (Cornell Electron Storage Ring) (CLEO is not an acronym, it
is just the short for Cleopatra, a suitable companion for CESR - pronounced “Caesar”)
Despite not having obtained any relevant results, they paved the way for two new experiments
that, as said in the introduction, have already observed CP violation in B mesons. These two
current collaborations are: BELLE (B standing for B mesons, EL for electrons and LE for anti
electrons EL = LE ) at the KEK-B collider (Koh-Enerugii Kasokuki kenkyu kikou - High
Energy Accelerator research organization) in Japan and BABAR (standing for B B ) at SLAC
(Stanford Linear Accelerator Center) in California.
D s

II- Physical Background 13
BABAR is also the name of the detector that has primarily been built to study CP violation
in B meson decays. However, comprising all the elements of a general purpose detector,
namely :
- a high resolution silicon vertex tracker,
- a drift chamber for general tracking and momentum measurement,
- a Čerenkov detector to distinguish particles,
- an electromagnetic calorimeter enclosed in a 1.5 T solenoid to measure
photons and electrons energy
- a kind of hadronic calorimeter to detect muons and neutral kaons
it can be used for many other tasks and is so an excellent opportunity to look at many parts of
the Standard Model.
Čerenkov Detector
Tracking Chamber
Muon/Hadron Detector
Silicon
Vertex Detector
Figure 5: Schematic diagram of the BABAR detector
Magnet Coil
EM calorimeter
(Electron/Photon Detector)

II- Physical Background 14
To create B mesons, BABAR uses the PEP-II SLAC accelerator (PEP stands for Positron
Electron Project). This ‘B factory’ is an +
e
−
e collider constructed with the express purpose of
producing large quantities of B mesons. To produce these B mesons, +
e and −
e are collided
with a centre-of-mass energy equal to that necessary to create the Y(4s) resonance (10.58
GeV). This forms a Y(4s) approximately one quarter of the time, generating a high signal to
background ratio. The energy of this Y(4s) being just above the production threshold required
+ −
to form a BB pair, it decays in almost 100% of the cases to produce either a B B pair or a
0
0
B B pair:
e
+
+ e
−
→
Υ
+ −
0
0
( 4s)
→ B B or B B
If the +
e and −
e have the same energy, the Y(4s) is created at rest and because of the
small difference of mass between this and a pair of B B , the B B pair is produced almost at
rest too. This inhibits an accurate measurement of the decay length between the Bs. Thus, to
allow a better resolution, +
e and −
e of different energy (respectively 3.1 GeV and 9.0 GeV)
are collided. The PEP-II collider is indeed an asymmetric collider.
Figure 6: Schematic diagram of the PEP II collider showing the BABAR detector

II- Physical Background 15
0 * + −
+
II.4- The B → K π & B → K π decays:
A way to measure the CKM matrix elements (or to measure the angles of the unitary
triangle) is to measure the asymmetric parameter ACP . This is proportional to the difference
between the branching ratio BR of a B meson decay – i.e. the likelihood the decay happens –
and that of the conjugate process. For instance, if the decay studied is of the form:
B → X + Y , the conjugate process will be: B → X + Y and the asymmetric parameter will
be such that: ACP ∝ BR{
B → X + Y}
− BR{
B → X + Y } . Formally, the asymmetric parameter
is defined as the ratio of the difference of the conjugate decays branching ratios to their sum,
that is:
A CP
BR
=
BR
0
* −
{ B → X + Y}
− BR{
B → X + Y }
{ B → X + Y}
+ BR{
B → X + Y }
0 * + −
* − +
The B decay studied in this project is B → K π so its conjugate is B → K π .
Distinguishing two conjugate neutral B mesons and ensuring they come from the same Y(4S)
is not a trivial task. Actually, this would require a whole other project. Thus, no calculation of
the asymmetric parameter was required. The aim of this project was only to determine a
global branching ratio for the two conjugate decays simultaneously. This corresponds to the
denominator of A CP .
0
Let us consider the B decay first. To detemine an accurate branching ratio for this
* +
decay, the K decay into a +
0
π and a K S is of special interest. Indeed, the final state
produced consists of three particles and is referred to as a three body charmless state
− + 0
+
−
0
( π π K where π = ud
, π = ud
, and K S = ds
, no charm quark)
S
But other physical processes occur, namely:
B
0 * + −
→ K π
B
0 * + −
→ K π
0
K S
+
π
( K
( K
0
S
0
L
π )
+ −
π
π )
+ −
π
+ 0 −
( K π ) π
0

II- Physical Background 16
As a result, the total branching ratio of the
these 3 possible decays:
BR
0
B decay is given by the sum of those of
{ } { } { } { } − +
− +
− +
− +
0 *
0 *
0 *
0 *
B → K π = BR B → K π + BR B → K π + BR B → K π
+
K π
0
S
+
K π
0
K L
+
+
K
0
= = =
0
L
+ 0
K π
As shown by the three following Feynman diagrams, all these second branching ratios are
equally likely:
BR
BR
{ } { } { } − +
− +
− +
0 *
0 *
0 *
B → K π = BR B → K π = BR B → K π
+
K π
0
S
+
K π
0
L
+ 0
K π
{ } { } { } − +
− +
− +
0 *
0 *
0 *
B → K π
BR B → K π
BR B → K π
+
K π
0
S
{ } − +
0 *
BR B → K π
{ } − +
0 *
BR B → K π
{ } − +
0 *
BR B → K π
Therefore, { } { } − +
− +
0 *
0 *
BR B → K π = 3⋅ BR B → K π
π
+
K π
Calculating the main branching ratio amounts to measuring one of the three possible
secondary ones and multiply it by a factor of 3.
The approach is exactly the same for the
by antiparticles. Hence, the total branching ratio for the both conjugate decays is:
BR
0
S
0
B decay. One just need to replace particles
0 * + −
0 * −
+ ⎡ 0 0 −
0 0
+ ⎤
{ B → K π } + BR{
B → K π } = 3 ⎢ BR{
B → KSπ
} + BR{
B → K Sπ
} ⎥⎦
⎣
+
K π
0
S
π
0
1
3
−
K
Sπ

II- Physical Background 17
* +
K
* +
K
* +
K
* +
K
s s
d
d
u u
s s
d
d
u u
s s
u
u
u u
s s
u u
u
u
0
K S
+
π
0
K L
+
π
+
K
0
π
+
K
0
π
Figure 7: Feynman diagrams of all the possible decays coming from
* +
0 * + −
the decay of the K in the channel B → K π . The last decay is
forbiddenbecause of Zweig suppression.

III- Analysis Method 18
III- ANALYSIS METHOD
III.1- Data Sample and Preselection:
The data sample on which this analysis is performed was collected at BABAR between
0
0
1999 and 2002 and is made up of 61.6 ± 0.68 millions of B B events. In order to reduce the
0
0
overall analysis time, the data is firstly skimmed at BABAR by discarding all the B / B
0
0
candidates that are irrelevant to the decay under study. For each B / B candidate,
discriminating variables are calculated. If they satisfy a loose set of selection conditions, the
0
0
B / B candidate is integrated to a data structure called ‘Ntuple’. Over 200 variables are
dumped into the Ntuple. This therefore contains all the relevant information concerning a
0
0
B / B candidate, such as its mass, energy, momentum, …, as well as those of its daughter
particles, and some event shape and particle identification information. This pre-processing of
data is called preselection. The Ntuple used here contains 7 893 939
III.2- The Cut and Count Method (CCM):
III.2.1- Principle of the CCM:
0
0
B / B candidates.
At the Ntuple level, another set of selection requirements or ‘cuts’ is applied to remove
0
0
all the irrelevant background events. If all the conditions are satisfied by a B / B candidate,
this is counted. Formally, such an analysis is referred to as a ‘selection cut based counting
analysis’. The discriminating variables used in this analysis can be divided in 5 categories.
These are described hereafter.

III- Analysis Method 19
III.2.2- Selection variables:
III.2.2.1- Event shape variables:
Two event shape variables are used in this analysis: the thrust angle (or more precisely
its cosine) and the Cornelius Fisher discriminant. They both aim at rejecting the continuum
0
0
background events coming from qq random production (with q=u,d,c,s). The B / B mesons
being produced almost at rest in the centre-of-mass frame, they decay isotropically
(spherically) in this frame. In contrast, continuum events are very jet-like. Therefore, if a
0
0
B / B candidate appears to have a jet-like decay, it is more likely to have been reconstructed
from random continuum events. This feature provides a powerful tool to discrimate between
(real) signal and continuum background events.
Practically, the thrust angle is defined as the angle between the direction of thrust of the
0
0
three particles constituting the decayed B / B and the direction of thrust of all the other
events (in the centre-of-mass frame) Taking the cosine of this angle leads to a flat distribution
0
0
for real B / B and a very peaked one near cos(θt)=±1 (θt≈±π) for dummy candidates.
Concerning the Cornelius Fisher discriminant (‘fisherCrn’), its physical representation
is hazier. It combines several event shape variables together. Namely it includes the summed
0
0
energy of the aforementioned rest of events in nine cones around the thrust axis of the B / B
0
0
candidate, as well as the cosine of the B / B thrust axis with respect to the beam axis and
0
0
the cosine of the B / B decay axis with respect to the beam axis [18].
As shown hereafter on Monte Carlo simulated data, typical values for these cuts are:
. cos( θ t ) < 0.
7
. fisherCrn
< −0.
5

III- Analysis Method 20
Number of events
Number of events
600
500
400
300
200
100
MC Data: | cos θt
| cut
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
| cos θ |
1800
1600
1400
1200
1000
Figure 8: |cos(θt)| distribution before (solid line) and after (dashed line) all the cuts.
Here, |cos(θt)| < 0.65
MC Data: FisherCrn cut
800
600
400
200
0
-2 -1 0 1 2 3
Fisher Crn
t
Figure 9: Cornelius Fisher Discriminant (‘fisherCrn’) distribution before
(solid line) and after (dashed line) all the cuts. Here, fisherCrn < -0.4

III- Analysis Method 21
III.2.2.2- Particle Identification:
Several PID (Particle IDentification) information are enclosed in the Ntuple. The three
0
0
desired decay products of the B / B (the three-body final state) can thus be selected. Each of
this decay product is referred to as a track. Thus, three track variables are defined: trk1, trk2
and trk3. The Ntuple is built in a way that the 3 rd 0
0
track always contains the S / S K K . The other
tracks can only be those of either a kaon K or a pion π .
− + 0 + −
The three-body final state studied being π π KS
/ π π K S , a prior cut exists in order to
0
0
discard all the B / B candidates for which the tracks 1 or/and 2 refers to a kaon (or may refer
to a kaon, the preselection process leading to these variables not being perfect)
The Ntuple is not built for only one secondary decay. Many secondary decays are
m
available. In the Ntuple used, three different final states can be studied: π π K
±
0
, K K
m ±
π or
0
K S and
± m 0
K K KS
(no distinction is made between
2, this provides 8 possible combinations that are recorded in an array as shown below.
0
0
K S ). With permutation around track 1 and
0 1 2 3
Trk1 trk2 trk3 trk1 trk2 trk3 trk1 trk2 trk3 trk1 trk2 trk3
π π
0
K S π K
0
K S K π
0
S
0
K S π π
4 5 6 7
trk1 trk2 trk3 trk1 trk2 trk3 trk1 trk2 trk3 trk1 trk2 trk3
π K
0
K S π π
0
K S π K
0
K S K K
Table 1: Final states available in the Ntuple. The 2 particles constituting one
resonant state are shaded.
Second cuts can thus be applied to only look at the variables belonging to the secondary
0 +
0
−
decay of interest, namely in this project, the resonant state: K Sπ
/ K Sπ
. From the array
above, only the indices 3 and 5 will therefore be used.
0
K S
0
K S
S

III- Analysis Method 22
III.2.2.3- The
* + 0 +
* + 0
−
K → K Sπ
/ K → K Sπ
resonance:
Using what has been said beforehand, 2 cuts are performed on the resonant non
0
differentiated connjugate states K
− +
→ π π /
0
+ −
K S → π π .
S
* +
The first one concerns the mass of the K / K for which the Particle Data Group
(PDG) [17] cites a nominal value of 0.896 GeV/c 2 0
0
* +
* −
. Any B / B candidate having a K / K
with a mass too different from this value is therefore discarded. This mass is calculated by
0
0
summing those of S / S K
±
K (trk3) and π (trk1 or trk2). The result is then put in an array
variable called resMass[]. As explaimed, the cuts therefore test the value of resMass[3] and
resMass[5] with a certain tolerance.
A typical value for this tolerance is: m m < 0.
10 GeV/c 2
Number of events
Number of events
3500
3000
2500
2000
1500
1000
500
4500
4000
3500
3000
2500
2000
1500
1000
+ 0 +
MC Data: K* →Kspi
Mass cut
1
* −
* − * +
−
0 +
0
−
K / K K Sπ
/ K Sπ
0
0 1 2 + 3 0 +
m {K* →Kspi1}
4 5 6
500
+ 0 +
MC Data: K* →Kspi2
Mass cut
0
0 1 2 + 3 0 +
m {K* →Kspi2}
4 5 6
Figure 10: * +
K
0 +
→ K Sπ
/ K
−
→ K Sπ
resonance mass
distribution before (solid line) and after (dashed line) all the cuts.
* +
0

III- Analysis Method 23
* +
The second one deals with the helicity of this resonant state. The K / K is
longitudinally polarised, which means that its helicity angle θh – defined as the angle between
0
0
its line of flight and its direction decay – is small. A good B / B candidate will therefore
have a cos(θh) greater than 0.
A typical value for this cut is: cos( θ ) > 0.
4
Number of events
Number of events
2500
2000
1500
1000
500
1800
1600
1400
1200
1000
+ 0 +
MC Data: cos ( θ {K* →Kspi
} ) cut
h
1
h
0
0 0.1 0.2 0.3 0.4 0.5+ 0 +
cos ( θh{K*
→Kspi1}
)
0.6 0.7 0.8 0.9 1
800
600
400
200
+ 0 +
MC Data: cos ( θh{K*
→Kspi2}
) cut
0
0 0.1 0.2 0.3 0.4 0.5+ 0 +
cos ( θh{K*
→Kspi2}
)
0.6 0.7 0.8 0.9 1
Figure 11: * + 0 +
K → K Sπ
/
* + 0
−
K → K Sπ
cos(θh) distribution
before (solid line) and after (dashed line) all the cuts.
* −

III- Analysis Method 24
III.2.2.4- The
0 − +
0
+ −
K S → π π / K S → π π resonance:
The same procedure can be performed on the resonant decay
0
K
0 − +
0
+ −
S → π π / K S → π π
0
The first cut is about the mass of the S / S K K for which the Particle Data Group (PDG)
[17] cites a nominal value of 0.498 GeV/c 2 0
0
0
0
. Any B / B candidate having a S / S K K with a
mass falling outside this value (within a certain tolerance) is therefore discarded. This mass is
calculated by summing those of the + −
π and π . The result is then put in a variable called
* +
* −
gkMass (‘gk’ standing for Grand Kids, the Kids being then K / K ).
A typical value for this tolerance is: m m < 0.
01
Number of events
3500
3000
2500
2000
1500
1000
500
MC Data: K
0
s
→π+
π-
0 0 − ±
/ π π
m
KS
K S
Mass cut
GeV/c 2
0
0.46 0.47 0.48 0.49 00.5
0.51 0.52 0.53 0.54
+ -
m {K →π
π }
s
Figure 12: 0 − +
K S → π π /
+ −
K S → π π mass distribution
before (solid line) and after (dashed line) all the cuts.
0
.

III- Analysis Method 25
0
0
S / S K
The second one concerns the measured flight length of the K , i.e. its decay length
calculated from its decay time: ldecay = cτ
decay (where c is the speed of light). In order to be
dimensionless and for more efficiency, the quantity used is indeed the ratio of the decay
length to its error: c τ / σ c τ . The variables associated with these values are called: gkCtau
(decay length) and gkCtaue (error on the decay length).
cτ
A typical value for this cut is: > 5.
0
σ
Number of events
500
400
300
200
100
MC Data: K
0
s
→π+
π-
cτ
Decay length cut
0
0 2 4 6 8 10 0 12 14 16 18 20
+ -
(cτ/
∆cτ)
{K →π
π }
0
0 − +
Figure 11: K S → π π /
+ −
K S → π π decay length distribution
before (solid line) and after (dashed line) all the cuts.
s

III- Analysis Method 26
III.2.2.5- Kinematic constraints, the ∆E-mES plane:
0
0
Due to the great efficiency of BABAR , the kinematics of the B / B mesons is well
+ −
defined. It is then possible, with the help of some initial information about the e e beam, to
use this as new selection criteria. As implied by the title, 2 kinematic constraint variables are
used in this final event selection.
The first one, ∆ E , is the difference between the reconstructed energy of the
0
0 / B
B
meson B E and that expected from the beam termed “beam-energy constrained energy” E bc :
∆ E = E − E
EB is derived from the momentum measurement of the three daughter particles
0
− + 0
π π K S /
+ −
π π K S (actually that of these two pions and that of the two pions coming from
the
0
0
S / S K K decay since measuring a momentum requires charged particles) and a
hypothesised mass associated with each momentum. This mass hypothesis is necessary
because only the momentum of each daughter particle is known. Thus, here, one momentum
0
must be associated with a K /
0
S mass and the other two with a pion one. In natural units:
S K
E
B
=
∑ = i 3
i 1
B
bc
= ⎭ ⎬⎫
⎧ 2 2
⎨ pi
+ mhyp
i
⎩
As for E bc , it is calculated from the 4-momentum of the beam ( beam , beam ) p E and the
0
0
momentum of the B / B meson B pr , which is equal to the sum of those of its three daughter
particles. Still in natural units, Ebc is given by:
E
bc
=
E
2
beam
2 r
− p beam − 2(
p
2E
If the chosen mass hypothesis is correct, ∆E should be centered around 0.
beam
beam
r
. p
B
)

III- Analysis Method 27
The second kinematic variable used, m ES , known as the “beam-energy substituted
mass”, is, with the same notation, defined as:
m = E − p
ES
0
0
This therefore tests whether the momentum of the reconstructed B / B fits with the expected
energy for the beam to give the correct mass. In that case, the mass found should be
0
0
2
approximately that of a B / B meson, namely: 5.279 GeV/c . If this is not the case, either
0
0
0
0
the B / B candidate was not a real B / B , or it has been reconstructed incorrectly, that is,
from random particles.
It is worth noting that contrary to ∆ E , m ES , since using E bc and not E B , does not depend on
the mass hypothesis.
Usually, these 2 kinematic variables are used in pairs. A very common visual
construction in Particle Physics is the ∆E - m ES plane in which ∆E is plotted versus m ES .
After having applied all the previous cuts, the surviving events are plotted in that plane and
only those which lie around ∆E = 0.
0 and m ES = 5.
279 GeV/c 2 are finally counted. All the
others are discarded. Practically, this is achieved by defining a box in the plane termed ‘signal
region’ (SR). The size of that box is generally defined in such a way that 99% of the events
generated with Monte Carlo simulated data fall inside.
Typical values for these cuts (i.e. typical size for the SR) are:
. ∆E = 0 . 0 ± 0.
1
. = 5 . 279 ± 0.
010
m ES
GeV/c 2
As one can see hereafter, another box is defined in the ∆E - mES plane. This box,
termed the Grand Side Band (GSB) is bigger than the SR and lies on its left. Its interest is the
following. Once all the selection criteria have been applied, several non-signal events still
remain in the SR as one can see by the fact that all the events do not fall inside the SR. There
are two sources of parasitic events. The first one is background from other decay channels.
0
0
This is negligible in the decay studied. The second one comes from the fact that a B / B
meson can be reconstructed in more than one way as shown by the sketch hereafter. This kind
of background is called random combinatoric background.
2
bc
2
B

III- Analysis Method 28
0
B ?
0
B ?
0
B ?
0
B ?
0
B ?
In order to subtract this background events from the final counting, a statistical
assessment on their density is performed on a neighbouring region: the GSB.
E
∆
E
∆
0
K
S
0.4
0.2
0
-0.2
-0.4
-0.6
MC Data: DeltaE-MES Plane
-0.8
5.18 5.2 5.22 5.24
mES
5.26 5.28 5.3
0.4
0.2
0
-0.2
-0.4
-0.6
+
π
0
B
−
π
MC Data: DeltaE-MES Plane
−
π
0
K S
+
π
0
0
Figure 12: Illustration of random combinatoric background. A B / B can be
reconstructed from 3 random particles (major source of combinatoric background) or a
mixing of random particle(s) and daughter particle(s) or a mixing of daughter particles
0
0
belonging to different B / B .
-0.8
5.18 5.2 5.22 5.24
mES
5.26 5.28 5.3
0
B
−
π
Figure 13: The ∆E - mES plane before (on top) and after (on bottom) all the cuts.
The SR is the small box on the right, the GSB, its left neighbour.
−
π
0
K S
+
π

III- Analysis Method 29
III.2.3- Computing overview:
This analysis has been performed within the CERN software to process particle physics
data, namely ROOT. ROOT is a C++ interpreter with many inbuilt functions and classes that
allow an easy analysis of such data.
As on could have guessed, the basis of the programme is just a big loop within which
several conditional structures (‘if’ statements) lie:
potential_real_B0 = 0 ;
for i=1 to total_Number_Of_B0_Candidates
{
if ( cut1 ok ) then
if ( cut2 ok ) then
...
potential_real_B0 = potential_real_B0 + 1 ;
}
For further details, please refer to the Appendix (p.54), in which this loop is fully given.
III.3- Calculation of the Branching Ratio:
III.3.1- Definition:
As everything said above may suggest, the branching ratio BR of a decay, i.e. its
occurring likelihood, is given by:
where N 0 is the total number of
B
N
BR =
N
real
sig
0
B
0
0
B / B events and
real
N sig is the final number of events
counted (i.e. after the aforementioned statistical subtraction). The subscript real is just here to
remind that this branching ratio must be calculated using real data (or on-line resonance data)
MC
and not MC simulated one for which this final number will therefore be noted: N sig .

III- Analysis Method 30
III.3.2- MC Efficiency:
In fact, this last formula is not exactly true. The preselection and cuts being rather tight,
0
0
real
many real B / B mesons are not counted in N sig . Therefore, the branching ratio must be
scaled up by a corrective factor k to take this matter into account. In order to assess this, a MC
0
0
simulation is performed on events which are exclusively B / B mesons. The simulated
mesons thus created pass the same preselection and cuts as the real ones. The probability of a
0
0
B / B falling inside the SR, in other words, the efficiency of the computing process, is
consequently given by:
MC
Nsig
ε MC =
N
where ε MC stands for ‘MC Efficiency’
Note that no statistical subtraction of the combinatoric background is done. This feature can
be taken into account with simulated data for which almost everything can be known
(particles can be tagged, …) This can also be seen on the previous schemes (figure 13) on
which there are no events in the GSB.
The scale-up factor k is so given by:
As a result,
k
BR =
1
=
ε
N
MC
real
sig
B
0
N
=
N
However, it is not so simple. The MC Efficiency thus calculated must be corrected to
take into account any inconsistencies with real data. The major source of correction lies in a
poor modelling of the detector. It is therefore this corrected MC Efficiency ε MC, corr and not
the prior calculated one ε MC that must finally be used in the calculation of branching ratio:
N
BR =
real
sig
×
×
N
N
real
0
B
1 ε
MC
O
B
MC
sig
1 ε
MC
MC,
corr
real
0
B

III- Analysis Method 31
The corrected MC Efficiency ε MC, corr is given by:
ε =
MC, corr kcorrε MC
where the correction k corr depends on many other factors that are associated with the cuts
applied :
k k k k k k × k
corr
= evtShp × PID × trk × 0 × K ∆
S
The k evtShp factor is a correction on the event shape modelling process, the k PID one on the
0
PID process, the k trk one on the tracking process, the k 0 one on the K K
S selection and the k∆ E
S
and the km ones on the ∆ E and m ES
ES calculations. Except for k trk which must be calculated
from the data used, all the other correction factors have been previously calculated, especially
by N. Chevalier [18].
Two kinds of error therefore come from the corrected MC efficiency: a statistical one
MC
due to the counting method used to calculate ε MC ( N sig is just a counter) and a systematical
one due to the above corrections (the error on the k factors being only systematical) used to
calculate the ‘real’ MC Efficiency (the corrected one). This mathematically leads to the
following errors:
σ
σ
= ε
ε =
MC, corr kcorrε MC
×
⎛σ
⎜ k
⎜
⎝
stat
corr
⎞
⎟
⎟
⎠
2
⎛σ
+ ⎜
⎜ ε
⎝
stat
ε
MC
⎞
⎟
⎟
⎠
E
= ε
m
ES
⎛σ
× ⎜
⎜
⎝
stat
ε
stat corr
MC
MC
ε MC , corr
MC,
corr
k
MC,
corr
ε
syst
ε
MC , corr
= ε
MC,
corr
×
⎛σ
⎜ k
⎜ k
⎝
syst
corr
corr
⎞
⎟
⎟
⎠
2
⎛σ
⎜ ε
+
⎜ ε
⎝
syst
MC
MC
⎞
⎟
⎟
⎠
2
2
= ε
MC,
corr
⎛σ
⎜ k
×
⎜ k
⎝
stat
Since as aforementioned σ kcorr = 0.
0 and since
MC
B O N being fixed by the
MC
programmer ( N
syst
= 50 , 000 ± 0 ± 0 ), σ = 0.
0 (since
MC
N = ε / N )
B O
ε
MC
MC
MC
syst
corr
corr
sig
⎟ ⎟
⎞
⎠
⎟ ⎟
⎞
⎠
MC
B O

III- Analysis Method 32
With,
MC
Nsig
1) ε = ⇒ MC
MC
N 0
B
stat
σ ε
MC
= ε MC ×
stat
stat
2
MC
⎛σ
MC ⎞
⎛σ
⎞
N
N ⎜ B
0
⎜
⎟
sig ⎟
+
⎜ MC ⎜ MC ⎟
N ⎟
sig ⎜ N 0
⎝ ⎠ B ⎟
⎝ ⎠
=
MC
(since N = 50 , 000 ± 0 ± 0 )
2) k corr = kevtShp
× kPID
× ktrk
× k 0 × k K ∆E
× k
S
mES
⇒
σ
B O
2
2
2
2 syst
2 syst
syst ⎛ ⎞ syst
syst ⎛ ⎞ syst
σ ⎛ ⎞ ⎛ ⎞
⎛ ⎞
⎛
0
⎜ ⎟
σ σ σ
⎟
⎜ k
⎜
⎟ σ
σ
⎜ ⎟
⎜ ⎟
⎜ k
syst
kevtShp
k
K
m
PID
ktrk
S
k∆E
ES
= k × + + + ⎜ ⎟ + +
k corr ⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎜ ⎟
⎜
corr kevtShp
kPID
ktrk
0 ⎜ kK
⎟ k∆E
S
⎜ k
mES
⎝
⎠
⎝
III.3.3- Background Characterisation and Subtraction:
As previously mentioned, the background events remaining in the whole ∆E - mES plane
once all the cuts have been applied, are mainly of a random combinatoric nature, i.e. they are
0
0
in fact B / B candidates reconstructed from completely random particles. Thus, for one real
0
0
B / B , many
⎠
⎝
0
0
B / B candidates exist. To avoid multi-counting, a special variable called
nevent is used. This is associated with all the
same real decay:
0
0 / B
⎠
2
⎝
ε
N
⎠
MC
MC
sig
⎝
⎠
⎝
2
⎞
⎟
⎟
⎟
⎠
0
0
B / B candidates assumed to come from the
0
0
B / B candidate # 0 1 2 3 4 5 6 7 8 9
nevent 1 1 2 2 2 2 3 4 5 5
Table 2: To avoid multi-counting, the ‘nevent’ variable is used.
0
0 / B
Amongst all these B candidates, only one or zero can be a real B . In order to
only keep one candidate and not to underestimate the number of combinatoric background
events in the GSB (this will be of great help later), a candidate is usually chosen completely at
random.

III- Analysis Method 33
This process being unfortunately quite cumbersome and time-consuming, it has not
been applied here. Instead, only the first candidate of each nevent sequence is kept (e.g. in the
example above, the candidates 0,2,6,7,8), which remains somewhat random if the data
ranking is itself random.
Nevertheless, combinatoric background events can still remain in the SR. As already
said, this background must be subtracted from the number of events observed in the SR to
correctly calculate the BR. A basic way to estimate this background is to characterise the
background distribution in both the GSB and the SR using ‘off-line resonance’ data, i.e. with
0
0
data collected during a phase where no B / B mesons can be created, the energy of the beam
being too small to form the Y(4s) necessary to their creation. This can sound odd, but the
combinatoric background is mainly due to completely random particles from continuum
events (such as massive massive q q production) rather than rare different daughter particles
association.
The ∆E and mES background distributions thus generated being almost independent,
they can reasonably be studied separately.
The ∆ E background distribution is (weakly) quadratic:
2
N∆ E = a(
∆E)
+ b(
∆E)
+ c
(where N is the number of counts)
Whereas the mES one has the shape of an Argus function [19]:
⎛ m
= C ⋅
⎜
⎝ m
⎞
⎟ ×
⎠
⎛ m
1−
⎜
⎝ m
2
⎞ ⎪
⎧ ⎡ ⎛ m
⎟ × exp⎨
− ξ . ⎢1
−
⎜
⎠ ⎪⎩
⎢
⎣ ⎝
ES
ES
ES
N
mES MAX
MAX
mMAX
2
⎞ ⎤
⎪
⎫
⎟ ⎥ ⎬
⎠ ⎥
⎦ ⎪⎭
(where mMAX is the maximum possible value of mES and ξ and C are respectively the “Argus
background shape parameter” and the “scale factor”. mMAX is actually the same as that of the
on-line resonance data (real data) i.e. 5.29 GeV/c 2 which corresponds to half the energy of the
beam (10.58 GeV), the 0
B and the 0
B sharing it equally. The off-line resonance data being
obtained with a beam energy of 40 MeV less (that is, 20 MeV less by B mesons), the
mES values must so be plotted shifted of 20 MeV/c 2 to keep the same SR and GSB size values.

III- Analysis Method 34
By integrating the fitted function of these distributions with respect to the size of the SR
and the GSB, the ratio R of the number of combinatoric background events in the SR to that in
the GSB, can be calculated:
Number of counts
Number of counts
n
R =
n
bg _ SR
bg _ GSB
=
∫
SR
∫
GSB
N
N
∆E
∆E
d(
∆E)
×
d(
∆E)
A visual insight of all this characterisation process is given below.
GSB
∫
SR
∫
GSB
N
N
m
m
ES
ES
5.279 5.29
d(
m
d(
m
Figure 14: mES Argus-shaped background distribution used to assess
the proportion of combinatoric background in the SR.
GSB
SR
-0.2 -0.1 0.0 +0.1 +0.2
Figure 15: ∆E quadratic background distribution used to assess the
proportion of combinatoric background in the SR.
SR
ES
ES
)
)
mES (GeV/c 2 )
∆E

III- Analysis Method 35
The final number of signal in the SR is therefore given by:
real
N sig = ntot
_ SR − nbg
_ SR
where ntot _ SR is the total number of events falling down the SR as counted once all the cuts
have been applied and nbg _ SR the estimated number of combinatoric background defined from
what has been said above by:
nbg _ SR = R × nbg
_ GSB = R × ntot
_ GSB
where nbg _ GSB is the number of combinatoric background in the GSB, that is simply the
number of events counted in the GSB once all the cuts have been applied ntot _ GSB .
real
So finally, = n − ( R × n )
N sig tot _ SR
tot _ GSB
The systematical error on ntot _ SR and ntot _ GSB is zero (these are just counters) as well as
the statistical one on R. The systematical error on this is also obtained by playing with the
different parameters offered by the fit function of ROOT. The value of R is taken as the best
fit value with an error equal to the half of the maximum deviation to this value:
Concerning N ,
With,
real
sig
1 ⎧
= Rbest
_ fit ± MAX ⎨ Rbest
_ fit − Rmax_
fit , Rbest
_ fit − R fit
2 ⎩
R min_
stat
stat 2 stat 2
σ real = ( σ ) + ( σ ) =
n
n
SR +
n ( σ
N sig
tot _ SR
bg _ SR
nbg
_ SR
syst
syst 2 syst 2
σ real = σ ) + ( σ ) =
n
n
( σ
syst
n
N sig SR
bg _ SR
bg _ SR
σ
stat
n
bg_SR
= n
bg_SR
×
⎛ σ
⎜
⎝ R
stat
R
⎞
⎟
⎠
2
⎛ σ
+
⎜
⎜ n
⎝
stat
n
tot _ GSB
tot _ GSB
⎞
⎟
⎟
⎠
2
stat
=
)
2
n
n
bg_SR
tot _ GSB
= R
n
tot _ GSB
syst
2
syst
2
syst
⎛σ
⎞ ⎛ σ ⎞
R
n
R
n
⎜
⎛
tot GSB
σ ⎞
_
=
⎟
bg _ SR × ⎜ + = nbg
SR × = ntot
GSB
R ⎟
n
⎜
tot GSB
R ⎟
⎜ ⎟ _
_
_
syst
σ × σ
nbg
_ SR
⎝ ⎠ ⎝ ⎠ ⎝ ⎠
⎫
⎬
⎭
syst
R

III- Analysis Method 36
III.3.4- Errors on the branching ratio:
As previously seen, the calculation of the branching ratio requires the following stages:
⎛
BR = ⎜ N
⎜
⎝
real
sig
Hence, the errors on that branching ratio are such that:
σ
σ
stat
BR
= BR ×
⎛σ
⎜ N
⎜ N
⎝
⎝
stat
real
sig
real
sig
⎞
⎟
⎟
⎠
⎠
2
⎛ σ
+
⎜
⎜ ε
⎝
⎝
×
stat
ε MC , corr
MC,
corr
1
⎞
⎟
⎠
N 0
real
B
ε MC,
corr
⎞
⎟
⎟
⎠
⎠
2
⎛σ
⎜
+ ⎜
⎜ N
⎝
⎛ σ
⎝
stat
real
N
B
0
real
0
B
2
2 syst
syst
syst
real
⎛σ
⎞ ⎛ σ ⎞ ⎜ N 0
⎜ N
B
syst
sig ⎟ ⎜ ε MC , corr
= × +
⎟
BR BR
⎜ ⎟
+
⎜ ⎟
⎜ real
N sig ε MC,
corr ⎜ N 0
B
( since
2
⎞
⎟
⎟
⎟
⎠
2
⎞
⎟
⎟
⎟
⎠
= BR ×
real
N 0 = 61 600 000 ± 0 ± 680 000 given )
B
⎛σ
⎜ N
⎜ N
⎝
stat
sig
sig
⎞
⎟
⎟
⎠
2
⎛ σ
+
⎜
⎜ ε
⎝
stat
ε MC , corr
MC,
corr
Where all the intermediate calculations to arrive to the final results can be found in
looking at the previous parts. It is nonetheless worth noting that the statistical error comes
from ntot _ SR and ntot _ GSB whereas the systematical one comes from the background
charaterisation ratio R and the corrective factor for the MC Efficiency k corr (and to a lesser
extent from
real
N 0 ). B
real
N sig = ntot
_ SR − nbg
_ SR
nbg _ SR = R × ntot
_ GSB
ε =
MC, corr kcorrε MC
ε
MC
N
=
N
MC
sig
MC
0
B
⎞
⎟
⎟
⎠
2

III- Analysis Method 37
III.4- Optimisation of the cuts:
III.4.1- Significance calculation:
All the cuts values, except for ∆E and m ES , are optimised by maximising an
approximation of the statistical significance of the branching ratio σ defined by:
σ =
s
s + b
where b is the number of background in the signal region (by analogy from above, it
corresponds to nbg _ SR )
b = R × ntot
_ GSB
and s is the estimated final number of events in the signal region (by analogy from above, it
real
corresponds to N sig )
real '
= N × BR × ε
s 0
B
MC,
corr
(since still by analogy
s × 1
' ε
BR = )
N
MC,
corr
real
0
B
s is said estimated since the branching ratio BR’ used to calculate it must be assumed (for
reason given later – Cf III.5, p.42) Although this may not completely reflect the true
branching ratio for the channel under study, the optimisation is usually not heavily affected. A
sensible value for it is usually the previous value found by someone else. The last person
having studied this decay being N. Chevalier, the BR she found was used.
Practically, each time a cut varies, 2 values change: the MC Efficiency appearing in s
first, the number of events in the GSB leading to b secondly. Thus, by recalculating the
corrected MC Efficiency and recounting the number of events in the GSB for each different
value of one cut, the significance can be plotted versus these changing values and the
maximum then found.

III- Analysis Method 38
All the selection cuts are thus varied independently in order of their use.
Unfortunatelly, the cuts being not completely independent (or orthonormal), changing the
value of one can change the others. For example, imagine the optimisation of cos(θt) leads to
a value of 0.6 for a fisherCrn value of -0.5. Using this new value of 0.6 for cos(θt) within the
fisherCrn optimisation gives a fisherCrn of -0.2. But reusing this new value of -0.2 for the
fisherCrn within the cos(θt) optimisation will not yield a cos(θt) of 0.6 but, say, 0.7. The cuts
are not orthonormal. It can be difficult to deal with such a process but it is usually (rapidly)
convergent
.
At last, this may provide several sets of cuts values, the ‘winning’ one being that
yielding the best sensitivity.
III.4.2- Errors on the significance:
The calculation of the statistical and systematical errors on the branching ratio statistical
significance is given below.
s
σ =
with
s + b
∂σ
∂σ
By definition, d σ = ( ) ds + ( ) db
∂s
∂b
where
⎛ ∂σ
⎞
⎜ σ s ⎟
⎝ ∂s
⎠
2
⎛ ∂σ
+ ⎜ σ
⎝ ∂b
σ σ = b
∂σ s / 2 + b
=
∂s
( s + b)
real '
s = N 0 × BR × ε
B
MC,
corr
b = R × ntot
_ GSB
3 / 2
∂σ s / 2
= −
∂b
( s + b)
3 / 2
2
⎞
⎟
⎠

III- Analysis Method 39
Hence,
σ σ
real '
With, 1 s = N 0 × BR × ε MC,
corr
σ
σ
stat
s
syst
s
B
= s ×
= s ×
⎛σ
⎜
⎜
⎜ N
⎝
stat
real
N
B
0
real
0
B
⎛σ
⎜ N
⎜
⎜ N B
⎝
And where
And, 2 b = R × ntot
_ GSB
σ
stat
b
= b ×
syst
real
B
0
real
0
⎛σ
⎜
⎝ R
1
=
( s + b)
2
⎞
⎟
⎟
⎟
⎠
2
⎞
⎟
⎟
⎟
⎠
ε
stat
R
⎛σ
+
⎜
⎜ BR
⎝
stat
'
BR
'
3 / 2
⎞
⎟
⎟
⎠
2
2
⎛ s ⎞ 2 ⎛ s ⎞
⎜ + b⎟σ
s + ⎜ ⎟σ ⎝ 2 ⎠ ⎝ 2 ⎠
⎛ σ
+
⎜
⎜ ε
⎝
syst ⎛σ
' ⎞ ⎛ σ
⎜ BR ⎟
+
⎜ ε
+
⎜ '
BR ⎟ ⎜ ε
⎝ ⎠ ⎝
MC,
corr
⎞
⎟
⎠
2
⎛ σ
+
⎜
⎜ n
⎝
syst
ε MC , corr
MC,
corr
syst
MC , corr
MC,
corr
⎞
⎟
⎟
⎠
⎞
⎟
⎟
⎠
2
2
= s ×
MC ⎛ N ⎞ sig
= k = ⎜ ⎟
corrε
MC kcorr
⎜ MC ⎟
⎝ N 0
B ⎠
stat
n
tot _ GSB
tot _ GSB
⎞
⎟
⎟
⎠
2
=
n
b
tot _ GSB
= R
2
b
⎛σ
⎜
⎜ BR
⎝
n
stat
'
BR
'
⎞
⎟
⎟
⎠
2
tot _ GSB
syst
2
syst
2
syst
syst ⎛σ
⎞
⎛ σ ⎞
R
n
R
b b
⎜
⎛
tot GSB σ ⎞
_
= ×
⎟
⎜
= b × = ntot
GSB
R ⎟ +
n
⎜
tot GSB R ⎟
⎜ ⎟
_
_
σ × σ
⎝ ⎠
⎝ ⎠
⎝ ⎠
⎛ σ
+
⎜
⎜ ε
⎝
syst
R
stat
ε MC , corr
MC,
corr
This gives the exact error on the statistical significance σ. Nonetheless, the interest of
the optimisation process is not to accurately calculate this value. Its interest is, via this σ
calculation, to be able to say which of 2 following values is the best if any differences
between them. Thus, the error must be taken into account and especially the variation of error
between these 2 points instead of the total error itself in which this variation may be (is)
drowned.
⎞
⎟
⎟
⎠
( See previous parts
for errors calculation )
2

III- Analysis Method 40
For example in the first case of the figure below, the points 1, 2 and 3, for which the
total error is plotted, cannot really be differentiated, whereas in the second case, in which only
the error variation is plotted, only the points 2 and 3 can be seen as similar.
.1 .2 .3
In order to only take into account this variational error, all the constant errors must be
removed, that is:
stat ⎛σ
⎞
⎜ '
BR ⎟
⎝ ⎠
⎛ σ
⎜ ε
⎝
⎛σ
⎜ ε
⎝
( ) ⎟ ⎟
'
stat ' ⎜ BR
= ×
⎟
+
⎜ ε MC , corr ⎟
→ ×
⎜ ε MC , corr
σ s
s
s
⎛σ
⎜
⎜ N
⎝
syst
2
2
stat
MC,
corr
⎞
⎟
⎠
2
stat
MC,
corr
real
N
' B
0
'
syst
,
( ) ⎜ BR
+
⎟
+
⎜ ε MC corr
σ = s ×
⎟
⎜ ⎟
→ 0.
0
s
real
0
B
⎞
⎟
⎟
⎠
2
syst ⎛σ
⎞
⎜ '
BR ⎟
⎝ ⎠
( stat '
b ) = R ntot
_ GSB → R ntot
_ GSB
syst '
( σ ) = ×
syst
→ 0.
0
⎛σ
⎜ ε
⎝
syst
MC,
corr
σ unchanged
b ntot _ GSB σ R
.1 .2 .3
Figure 16: Illustration of the optimisation interest via the error calculation
of the statistical significance σ.
⎞
⎟
⎠
2
⎞
⎠

III- Analysis Method 41
Practically, this leads to the following schemes:
s+b
s /
s+b
s /
4
3.5
3
2.5
2
1.5
1
0.5
s/
s+b
vs |cosθt|
0
0 0.2 0.4 0.6 0.8 1
| cos θ |
3
2.5
2
1.5
1
0.5
s/
s+b
vs |cosθt|
0
0 0.2 0.4 0.6 0.8 1
| cos θ |
Figure 17: Real example of the optimisation interest via the error calculation of the
statistical significance σ. The second scheme obviously contains more relevant
information than the first one. A relevant value for the cut can thus be determined.
t
t

III- Analysis Method 42
III.5- Overall process:
The policy of the BABAR collaboration states that such an analysis must be blind,
which means that the number of candidates within the SR must remain unknown until the
selection cuts are optimized and frozen: once the signal region is exposed, the analysis cannot
be modified in any way (hence the use of an assumed branching ratio in the optimisation
process). This is done to prevent any biases in the analysis. As a matter of fact, one could be
tempted to use the branching ratio first obtained (BR1) as a new seed for the optimisation and
so generate a new set of cuts that could be more appropriate to the decay studied. Like the
assumed branching ratio (BR0) used to generate the first branching ratio (BR1), this branching
ratio (BR1) could in turn be used to create a new set of cuts and then a new branching ratio
(BR2). And so on, BRn giving BRn+1 that would give BRn+2 that would give… However, such
an iterative procedure is very dangerous. If the optimisation acts in a region of large
fluctuation, this feed-back process will tend to misidentify fluctuations as maxima, which will
completely warp the analysis.
Nonetheless, the optimisation process does introduce biases into the estimation of the
number of background events in the SR. As a matter of fact, maximising σ =s/(s+b) 1/2 is
equivalent to minimising b, that is, minimising the background in the GSB and so its estimate
in the SR. As a result, any fluctuation of the number of background events will be minimised,
thus leading to a biased analysis since tending to reduce the effect of this fluctuation by the
use of a ‘special’ set of cuts. To avoid this, the set of background events counted in the GSB
(on which the calculation of background events in the SR is based) is not the same during the
optimisation phase and the BR calculation phase. Only the even-numbered events are taken
into account during the optimisation phase. For the BR calculation phase, the number of
background events in the GSB is counted by using these optimised cuts on the other half of
the events, the odd-numbered events. This number should therefore be scaled by two to
estimate the number of background in the SR. The point being to not favour any one of the 2
sets, all the events are used to count the number of events in the SR.

III- Analysis Method 43
Optimisation
BR Calculation
b Even-numbered events
s Even-numbered events
n Odd-numbered events
tot _ GSB
n Every event
tot _ SR
Table 3: Counting processes used during the optimisation and the
BR calculation phases. This is done to avoid any fluctuation to be
underestimated.
Consequently, the final branching ratio is given by:
BR =
N
real
sig
×
N
1 ε
MC,
corr
real
0
B
real
where = n − [ R × ( 2 × n ) ]
Nsig tot _ SR
tot _ GSB

IV- Results 44
IV- RESULTS
IV.1- Final selection criteria after optimisation:
As previously said, the optimisation has been performed using the branching ratio found
by N. Chevalier [18], namely:
BR
0 * + −
0 * −
+
−6
{ B → K π } + BR{
B → K π } = ( 16.
1±
8.
5 ± 3.
0)
× 10
So, the branching ratio BR’ used in the optimisation procedure is:
BR
'
0 * + −
0 * −
+ 1 −6
{ B → K π } + BR{
B → K } = × ( 16.
1±
8.
5 ± 3.
0)
× 10
= BR
π
+
K π
This leads to the following set of cuts:
0
S
0
S
−
K π
Selection Criteria Cut Value
cos (θthrust) cos( θ t ) < 0.
65
Cornelius Fisher Discriminant fisherCrn < −0.
4
* + 0 +
* + 0
−
K → K Sπ
/ K → K Sπ
resonance mass * 0 = 0.
896 ± 0.
075
* + 0 + − −
K →K Sπ
/ K →K
Sπ
3
m GeV/c 2
* + 0 +
* + 0
−
K → K Sπ
/ K → K Sπ
resonance cos (θhelicity) cos( θ h ) < 0.
45
0 − +
0
+ −
KS → π π / K S → π π resonance mass 0 = 0.
498 ± 0.
010
0 + −
− +
K S →π π / K S →π
π
m GeV/c 2
0 − +
0
+ −
KS → π π / K S → π π resonance ‘decay length’ > 4.
0
σ cτ
Table 4: Final optimised selection criteria.
cτ

IV- Results 45
s+b
s /
s+b
s /
s+b
s /
3
2.5
2
1.5
1
0.5
s/ s+b
vs |cosθt|
0
0 0.2 0.4 0.6
| cos θt
|
0.8 1
3
2.5
2
1.5
1
0.5
s/ s+b
vs
∆resMass
0
0 0.02 0.04 0.06 0.08 0.1
∆ resMass (GeV)
0.12 0.14 0.16
3
2.5
2
1.5
1
0.5
s/ s+b
vs
∆gkMass
0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
∆ gkMass (GeV)
s+b
s /
s+b
s /
s+b
s /
3
2.5
2
1.5
1
0.5
0
3
2.5
2
1.5
1
0.5
s/ s+b
vs fisherCrn
-1 -0.5 0 0.5 1
fisherCrn
s/ s+b
vs |cosθB|
0
0 0.2 0.4 0.6
| cos θB
|
0.8 1
3
2.5
2
1.5
1
0.5
s/ s+b
vs gkCtau/gkCtaue
0
0 2 4 6
gkCtau / gkCtaue
8 10
Concerning the size of the SR (in which 99% of the MC signal does fall inside) and
that of the GSB, they have been chosen as follows:
SR
GSB
Figure 18: Optimisation cuts schemes
∆E =
0 . 0 ±
0.
1
m = 5 . 279 ± 0.
010 GeV/c 2
ES
∆E =
0 . 0 ±
0.
2
m = 5 . 240 ± 0.
020 GeV/c 2
ES
Table 5: Size of the
SR and the GSB.

IV- Results 46
IV.2- MC Efficiency correction:
ε MC = k ε
, corr corr MC with
MC
Using the previous cuts, it is found that: N sig = 3104 ± 56 ± 0 .
MC
So, as N = 50000 ± 0 ± 0 fixed,
B
0
ε MC
The values of the k correction factors are:
(*) k trk ktrk
_1 × ktrk
_ 2
ε
=
k evtShp
k PID
k∆ E
k
k
mES
0
KS
k trk
k corr
( 6 . 34 ± 0.
11±
0.
00)
%
Consequently, ( 5.
99 0.
11 0.
52)
%
MC,
corr
=
= 0 . 928 ± 0.
000 ±
= 0 . 963 ± 0.
000 ±
= 1 . 000 ± 0.
000 ±
= 1 . 000 ± 0.
000 ±
= 1 . 080 ± 0.
000 ±
= 0 . 979 ± 0.
000 ±
= 0 . 945 ± 0.
000 ±
±
±
0.
051
0.
045
0.
025
0.
010
0.
026
0.
030
0.
081
σ k
σ σ σ
trk _ i
k k _1
k
trk
trk
trk _ 2
= with = 1.
5%
[18] ⇒ = + = 3.
0%
k
k k k
Ntuple variables,
ktrk is the mean of the Gaussian fit
to the ktrk_1 ktrk_2 distribution
trk _ i
ε
N
MC
sig
MC = MC
N 0
B
k × k
corr = kevtShp
× kPID
× ktrk
× k 0 × k K ∆E
S
trk
[18]
[20]
(*)
trk _1
trk _ 2
mES

IV- Results 47
IV.3- Combinatoric background:
. ∆ E background distribution:
. m ES background distribution:
⎛ m
= C ⋅
⎜
⎝ m
N∆ E
⎞
⎟ ×
⎠
= a(
∆E)
⎛ m
1−
⎜
⎝ m
2
+ b(
∆E)
+ c
2
⎞ ⎪
⎧ ⎡ ⎛ m
⎟ × exp⎨
− ξ . ⎢1
−
⎜
⎠ ⎪⎩
⎢
⎣ ⎝
ES
ES
ES
N
mES MAX
MAX
mMAX
Hence, as
R =
∫
SR
∫
GSB
N
N
a = 4339 ± 0 ± 186 GeV -2
with b = −9300
± 0 ± 39 GeV -1
c = 7011 ± 0 ± 13
∆E
∆E
d(
∆E)
×
d(
∆E)
∫
SR
∫
GSB
R = 0 . 162 ± 0.
000 ±
4
( 57 . 99 ± 0.
00 ± 2.
50)
× 10
C =
with ξ = −24
. 84 ± 0.
00 ± 0.
11
m = 5.
29 GeV/c 2
MAX
N
N
m
m
ES
ES
0.
001
d(
m
d(
m
ES
ES
)
)
2
⎞ ⎤
⎪
⎫
⎟ ⎥ ⎬
⎠ ⎥
⎦ ⎪⎭

IV- Results 48
Another common notation is to express R as a function of the size of the SR (ASR) and
that of the GSB (AGSB). As a result, as here AGS=4.ASR
12000
10000
No of events
8000
6000
4000
2000
0
⎛ A
⎜
⎝ A
( ) ⎟ SR
0 . 647 ± 0.
000 ± 0.
× ⎜
R =
003
DeltaE Fit to 2nd Order Polynomial using OffRes Data deltaEfit
10000
No of events
8000
6000
4000
2000
0
GSB
-0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4
DeltaE (GeV)
mes Fit to Argus Function using OffRes Data mesfit
⎞
⎠
deltaEfit
Nent = 897274
Mean = -0.1173
RMS = 0.2238
x^2 parameter = 4339
x parameter = -9300
Constant term = 7011
Figure 19: ∆E quadratic background distribution used to assess the
proportion of combinatoric background in the SR.
mesfit
Nent = 897274
Mean = 5.237
RMS = 0.02662
Constant C = 2.449e+04
Xi parameter = -24.84
5.2 5.22 5.24 5.26 5.28 5.3
mes (GeV)
Figure 20: ES
m Argus-shaped background distribution used to assess the
proportion of combinatoric background in the SR.

IV- Results 49
IV.4- Branching ratio of the
BR
BR
∆E
0.4
0.2
0
-0.2
-0.4
-0.6
mES
∗+
−
B K
0 ∗−
+ & B → K π
0
→ π
Quantity Value
ntot _ SR
7 0
On Line Resonance Data: DeltaE-MES Plane
53 ± ±
ntot _ GSB (x2) 20 0
186 ± ±
nbg _ SR
. 1 3.
1 0.
1
30 ± ±
real
N sig
. 9 7.
9 0.
1
22 ± ±
Statistical Significance 3 . 2σ
{ } { } +
0 * + −
0 * −
B → K π + BR B → K π
+
K π
0
S
-0.8
5.18 5.2 5.22 5.24 5.26 5.28 5.3
0
S
−
K π
{ } { } +
0 * + −
0 * −
B → K π + BR B → K π
Table 6: Final Findings
Figure 21: Final ∆E - mES events distribution.
( 6.
20 ± 2.
15 ± 0.
54)
× 10
( 18.
6 ± 6.
5 ± 1.
6)
× 10
decays:
6
6

V- Discussion 50
V- DISCUSSION
As detailed in the previous chapter, the total branching ratio found for the neutral
0
conjugate B decays B
* + −
0
→ K π and B
* −
+
* +
* −
→ K π via the K / K decay into a
0 +
0
−
K Sπ
/ K Sπ
using 61.6 ± 0.68 millions 0
BR
B and
0
B mesons is:
0 * + −
0 * −
+
−6
{ B → K π } + BR{
B → K π } = ( 18.
6 ± 6.
5 ± 1.
6)
× 10
with a statistical significance of 3.2 σ
This measurement is, within errors, in good agreement with the previous ones, namely:
Experiment
N 0 0
B / B
(x10 6 )
CLEO, 1999 [21] 5.8
BELLE, 2001 [22] 22.8
BABAR, 2002 [18] 22.7
BABAR, 2003 61.6
Table 7: Previous measurements of the
Secondary
Decay
(conjugate implied)
* + 0 +
→ KSπ
Branching Ratio
(x10 -6 )
Statistical
Significance
K 22 . 0 ± 7.
0 ± 5.
0 5.2 σ
* + + 0
K → K π 26 . 0 8.
3 ± 3.
5
* + + 0
K → K π 16 . 1 8.
5 ± 3.
0
* + 0 +
→ KSπ
± 4.3 σ
± 2.2 σ
K 18 . 6 ± 6.
5 ± 1.
6 3.2 σ
∗+
−
B → K π
0
+
0 * −
+
B → K π branching ratio.

V- Discussion 51
As one can see hereafter, it also agrees with the nominal value of the theoretical
−6
branching ratio found by Cottingham et al. [23] which is: 15.
3×
10 .
0 5 10 15 20 25 30 35 40
∗+
−
B → K π
0
CLEO, 1999 [21]
BELLE, 2001 [22]
BABAR, 2002 [18]
BABAR, 2003
( x10 -6 )
Figure 22: Previous measurements of the
+ B → K
+
π branching ratio.
(The half length of the uncertaintiy bars is the sum of the statistical and systematical errors).
As expected from the use of a significantly larger data set, the statistical error is lower
than those found by the previous experiments. On the other hand, a systematical error almost
twice smaller than the more recent calculated ones seems rather dubious. The calculations
having been checked several times, this must be due to a too simplistic way to calculate R (the
other source of statistical error being k corr which was here almost independent of the
computing treatment performed). Many other more accurate ways (such as using several
statistical bands over both on-line and off-line resonance data) exist to estimate this. Two
other points could also be improved. First, it could be of interest to verify that the part of
* + + °
background coming from other B decays (e.g. K → K π ) is truly negligible. Second, it
could be necessary to use a real random treatment for the multiple candidates (nevent) instead
of the ‘pseudo-random’ one actually used.
Although this result is consistent with the prior ones, it is worth noting that it is still
besmirched with a quite large total error of about 45%. This error should decreases with years,
the quantity of data collected by BABAR becoming more and more important. It then could be
of interest to use an ellipse instead of a rectangle to define the signal region, the distribution in
the ∆E-mES plane assumed to be ellipsoidal as modelled in the MC data (this has not been
performed in this project, the number of signal detected being too small)
0
* −

V- Discussion 52
Concerning the optimisation process, no real problems have been encountered. The cuts
appeared to be rather orthonormal, that is, changing the value of one did not change much the
values of the others. The convergent process have thus been achieved in two steps, the first
optimisation yielding values that have been used instead of the prior ones in a second
optimisation run which lead in turn to some new values that finally appear to remain the same
after a last run. As mentioned, the cuts values found were independent of that of the branching
ratio used. Whatever the one used (the CLEO one, the BABAR 2002 one, and even the one
found here – simply used out of curiosity – ), they remained identical. Although the difference
between these branching ratios is small, the astonishing stability of the optimisation process
remains suspicious. Once again, it may come from the aforementioned too simplistic
approach used.

VI- Conclusion 53
VI- CONCLUSION
The total branching ratio measured for the conjugate neutral B decays
0 * + −
B → K π and
0 * −
+
B → K π is consistent with both previous experimental results and theoretical prediction.
To the best of the author’s knowledge, this result should be the most accurate yet achieved,
since being derived from the larger data set ever. In time, its accuracy should improve, the
data gathered at BABAR increasing day after day.
A study of both channels separetely with respect to their mother particle Y(4s) is now
expected. The asymmetric parameter ACP could therefore be calculated and lead to the value
of some of the CKM matrix elements. This will contribute to the appraisal of the Standard
Model by checking whether or not it could predict the matter-antimatter asymmetry in the
universe.
Currently, it is believed that CP violation as predicted by the Standard Model is not
large enough to create the amount of matter observed in the universe today. Thus, continuing
to study CP violation is very important, since it may pave the way for exciting new physics
whether this model is not the whole story.

Appendix 54
APPENDIX
This appendix displays a skimmed version of the main loop of the code used to count
the number of events falling down the Signal Region and the Grand Side Band with respect to
the cuts discussed beforehand.
Int_t nSR = 0 ; // Number of events falling down the Signal Region
Int_t nGSB = 0 ; // Number of events falling down the Grand Side Band
lastEvt = -1 ; // To avoid double counting since each event can refer
// to the same original BB decay
nbytes = 0 ; // buffer variable
for ( Int_t i=0 ; i GetEntry(i) ; // Loads the next entry from the ntuple
// and records the number of bytes loaded
if ( TMath::Abs(cosTTB) < cut_cosTTB ) // cos theta thrust CUT
{
if ( fisherCrn < cut_fisherCrn ) // Cornelius fisher CUT
{
if ( trk1K==0 && trk2K==0 ) // first PID CUT
{
// second PID CUT & mass of the Ks0-pi+ resonance checking
if ( ( resMass[3] > cut_resMassMin ) && ( resMass[3] < cut_resMassMax ) )
{
// second PID CUT & helicity angle of the Ks0-pi+ resonance checking
if ( TMath::Abs(resCosB[3]) > cut_resCosB )
{
// Ks0->pi+pi- mass checking
if ( ( gkMass[0] > cut_gkMassMin ) && ( gkMass[0] < cut_gkMassMax ) )
{
// Ks0->pi+pi- decay length checking
if ( gkCtau[0]/gkCtaue[0] > cut_gkCtauCtaue )
{
// nGSB counting: candidate in the GSB box?
// (Embc corresponds to mES & des[0] corresponds to deltaE)
// and no double counting checking (lastEvt!=nevent)
if ( (Embc>mesGSBMin && EmbcdeltaEGSBMin && des[0]

Appendix 55
// nSR counting: candidate in the SR box?
// (Embc corresponds to mES & des[0] corresponds to deltaE)
// and no double counting checking (lastEvt!=nevent)
if ( (Embc>mesSRMin && EmbcdeltaESRMin && des[0] cut_resMassMin ) && ( resMass[5] < cut_resMassMax ) )
{
if ( TMath::Abs(resCosB[5]) > cut_resCosB )
{
if ( ( gkMass[0] > cut_gkMassMin ) && ( gkMass[0] < cut_gkMassMax ) )
{
if ( gkCtau[0]/gkCtaue[0] > cut_gkCtauCtaue )
{
if ( (Embc>mesGSBMin && EmbcdeltaEGSBMin && des[0]mesSRMin && EmbcdeltaESRMin && des[0]

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