Diplomarbeit - thesis/data/iekp-ka2012-3.pdf · wurden von BaBar Obergrenzen fu¨r...

IEKP-KA/2012-3

Analysis Of The SemileptonicDecay

B+ → ℓ+νγ with ℓ+ = e+, µ+

At The Belle Experiment

Andreas Heller

Diplomarbeit

Durchgefuhrt Am

Institut Fur Experimentelle Kernphysik (EKP)

Karlsruher Institut Fur Technologie (KIT)

Referent: Prof. Dr. M. Feindt

Korreferent: Prof. Dr. U. Husemann

05. 03. 2012

Deutsche Zusammenfassung

Die Diplomarbeit befasst sich mit der Analyse des semileptonischen Zerfallsdes geladenen B-Mesons in die Kanale B+ → ℓ+νγ mit ℓ+ = e+, µ+, wobeidies den ladungskonjugierten Kanal einschließt. Der τ Zerfallskanal wirdnicht untersucht, da das τ zerfallt bevor es den Detektor erreicht und dabeizusatzlich mindestens ein weiteres Neutrino emittiert, was eine ganzlich an-dere Herangehensweise an die Analyse notig macht.Die beiden Zerfalle wurden bereits vom BaBar Experiment mit einem Daten-satz von 465 × 106BB analysiert [1] und es wurde kein signifikantes Sig-nal gefunden. Aus der Analyse ging eine obere Grenze auf das Verzwei-gungsverhaltnis fur die Kombination aus beiden Kanalen von BR(B+ →ℓ+νγ) < 15.6 × 10−6 in einem Konfidenzintervall von 90% hervor. Auchwurden von BaBar Obergrenzen fur Verzweigungsverhaltnisse fur zwei ver-schiedene Zerfallsmodelle bestimmt, von denen die Theorie eines stark fa-vorisiert, so dass nur eines dieser Modelle in der hier vorgestellten Analyse inBetracht gezogen wird. Mit dem Belle Datensatz von 772 × 106BB bestehtdie Moglichkeit, dass ein signifikantes Signal gefunden wird.Fur die Theorie ist dieser Zerfall von großem Interesse, da er die Bestimmungeines schwer zu errechnenden theoretischen Parameters λB erlaubt. Diesertritt in QCD Faktorisierungsansatzen fur nicht-leptonische Zerfalle des B-Mesons bei hohen Energien auf, dabei beschreibt er die Impulsverteilung derKonstituentenquarks im Meson. Die Ermittlung des Parameters wird durchden hadronenfreien Endzustand ermoglicht, fur den nur gut verstandeneschwache und elektromagnetische Ubergange eine Rolle spielen. Der Zerfallhat im Vergleich zum rein leptonischen B+ → ℓ+ν Prozess durch die Prasenzdes Photons im Endzustand ein wesentlich hoheres Verzweigungsverhaltnis,da das Photon mit seinem Spin die Helizitatsunterdruckung des schwachenUbergangs aufhebt. Von theoretischer Seite wird ein Verzweigungsverhaltnisvon etwa 5×10−6 bevorzugt, welches aus der Berucksichtigung des wahrschein-lichsten Parmeterbereichs fur λB hervorgeht, der durch Ergebnisse von Berech-nungen nicht-leptonischer Zerfalle eingeschrankt wird. Das neuste Ergeb-nis zum differentiellen Wirkungsquerschnitt wurde in [2] berechnet und istgegeben durch

d2Γ

dEγdEℓ

=αemG

2F |Vub|2

16π2m3

B(1−xγ)[

(1−xν)2(FA+FV )

2+(1−xl)2(FA−FV )

2]

,

iii

mit xi = 2Ei

mBfur die Teilchen i = γ, ℓ, ν. Weiter gilt 0 ≤ xi ≤ 1 und

xγ + xℓ + xν = 2. mB ist die B-Meson Masse, FA der axiale Formfaktor undFV der vektorielle Formfaktor. Das Verzweigungsverhaltnis ist abhangig vonden Parametern des schwachen Zerfalls G2

F (Fermi Kopplungskonstante) und|Vub|2 (CKM Matrixelement fur u-b-Quarkubergange), die die Zerfallsampli-tude fur den Ubergang eines Quarks in den Flavor seines Partners und denanschließenden Zerfall uber ein virtuelles W-Boson angeben. Zusatzlich hi-erzu kommt die elektromagnetische Kopplungskonstante αem, die von derPhotonemission herruhrt. Das Photon kann jeweils von einem der Kon-stituentenquarks oder vom Lepton abgestrahlt werden (Abbildung 0.1). Die

Abb. 0.1: Feynman-Diagramme fur die Beitrage fuhrender Ordnung.Photonen-Abstrahlung vom Up-Quark (links). Photonen-Abstrahlung vomBottom-Quark unterdruckt mit 1

mb(rechts) [2].

Formfaktoren sind gegeben durch

FV (Eγ) =QumBfB2EγλB

R +[

ξ(Eγ) +QbmBfB2Eγmb

+QumBfB(2Eγ)2

]

FA(Eγ) =QumBfB2EγλB

R +[

ξ(Eγ)−QbmBfB2Eγmb

− QumBfB(2Eγ)2

+QlfBEγ

]

,

wobei Q die Ladung fur Lepton, Up und Bottom-Quark und mb die Bottom-Quark Masse ist. Der erste Term reprasentiert die fuhrende Ordnung im obenerwahnten QCD Faktorisierungsansatz, der die Photonemission vom leichtenQuark beschreibt. Dieser Term beinhaltet den zu bestimmenden theoretis-chen Parameter λB, die Strahlungskorrekturen R fur das Up-Quark und fB,

iv

welches den Uberlapp der Quark Wellenfunktionen im Meson parametrisiert.Die ubrigen Terme in eckigen Klammern sind von der Ordnung 1

mb, wobei

der Term mit der Qb-Ladung die fuhrende Ordnung der Emission des Pho-tons vom Bottom-Quark und die verbleibenden beiden Terme einen Prozesshoherer Ordnung fur die Photonemission vom Up-Quark beschreiben. Der Ql

Term, der nur in FA vorhanden ist, gibt die Emission des Photons vom Lep-ton an. Die Feynman-Diagramme fur die Photonemission von den Quarkssind in Abbildung 0.1 gezeigt.Fur die hier vorgestellte Analyse wird fur jeden Signalkanal ein separaterDatensatz generiert. Das Modul zur Signal-Monte-Carlo Erzeugung basiertauf den Berechnungen einer alteren Veroffentlichung [3], welche nur geringeAbweichungen zum oben gezeigten Ergebnis aufweist [2].Fur den Untergrund werden drei verschiedene Monte-Carlo Datensatze ver-wendet, von denen jeder spezifische Zerfallsmodi abdeckt. Der als generischbezeichnete Datensatz beinhaltet die haufigsten B+B− und B0B0 Zerfalle, indenen B → c-Quark ubergeht. Zusatzlich hierzu kommen noch e+e− → qqKontinuumsereignisse mit q = u, d, s, c. Der generische Datensatz enthaltdie 5-fache Menge der am Belle Experiment aufgezeichneten Daten. Einweiterer Datensatz enthalt seltenere B-Meson Zerfalle in B → s-Quark undandere Kanale, die u.A. auch die Signalzerfalle einschließen. Er beinhaltetdie 50-fache Datenmenge. Der dritte Datensatz besteht aus semileptonischenB+ → X0

uℓ+ν Zerfallen, wobei X0

u ein Meson mit einem Up-Quark ist. Erumfasst die 20-fache Datenmenge und wird im folgenden als ulnu Datensatzbezeichnet.Das Ziel dieser Analyse ist es, das Verzweigungsverhaltnis der beiden B+ →ℓ+νγ Zerfallskanale durch das Fitten der Missing-Mass-Variable (m2

miss) zubestimmen, welche die Masse des fehlenden Teilchens auf der Signalseite an-gibt. Dies ist die beste Variable zur Trennung von Signal und Untergrundund die Definition lautet

m2miss = (pBsig − plepton − pγ)

2,

wobei pBsig der Viererimpuls des B-Mesons auf der Signalseite ist. Hi-ervon werden die Viereimpulse seiner beiden detektierbaren Kinder sub-trahiert. Das Ergebnis sollte fur korrekte Signalereignisse der Masse desNeutrinos entsprechen, deshalb bilden diese einen Peak um die Null. Un-tergrunde hingegen steigen von Null zu positiven Werten hin an. Die Aus-gangsverteilung von m2

miss kann man in Abbildung 0.2 fur den Muonkanalsehen.

v

]2 [GeVmiss2m

-2 0 2 4

Num

ber

of E

ntrie

s

0.00

0.02

0.04

0.06

0.08

0.10

0.12 , 13811 entriesγ µν +µ →+signal MC B

generic MC , 268424 entries

ulnu MC , 600178 entries

rare MC (no signal decay) , 1.33912e+06 entries

, 1564 entriesγ µν +µ →+rare MC B

Abb. 0.2: Normierte m2miss Verteilung fur den Muonkanal mit Signal MC

(blau), rare MC Signalanteil (turkis), rare MC (schwarz), ulnu MC (grun)and generisches MC (rot).

Um den Impuls des signalseitigen B-Mesons zu erhalten, wird die vollstandigeRekonstruktion benutzt, welche am EKP entwickelt wurde [4]. Mit dieserTechnik werdenB-Mesonen in diversen generischen Zerfallskanalen vollstandigrekonstruiert. Aus der Y(4S)→ B+B− Zerfallsdynamik folgt mit der Kennt-nis des CMS Impulses und dem rekonstruierten B-Meson der Impuls pBsig.Die Selektion der Signalseite geschieht in zwei Schritten. Zunachst werdenlockere Vorschnitte gemacht, um einfach trennbaren Untergrund zu ent-fernen. Hierbei sind die Vorschnitte fur beide Signalkanale, bis auf denSchnitt auf die Leptonidentifikations-Variable (Lepton ID), identisch. DieVorschnitte werden qualitativ anhand der normierten Signal- und Untergrund-Monte-Carlos bestimmt. Die Vorschnitte lauten wie folgt

• Das Signalphoton soll nach der vollstandigen Rekonstruktion das hochst-energetische im Ereignis sein.

• Es sollen keine geladenen Spuren im Ereignis verbleiben.

vi

• Es werden Qualitatsschnitte auf die Lepton ID gemacht, wobei es einVeto auf die ID des Leptons aus dem jeweils anderen Signalkanal gibt.

• Es gibt zwei Qualitatsschnitte auf das Signalphoton. Ein Schnitt aufdie Energie im B-Meson Ruhesystem, welche uber 400 MeV liegen soll.Ein weiterer Schnitt auf ein Photonennetzwerk das in der vollstandigenRekonstruktion zum Einsatz kommt, welches richtige von falschen Pho-tonen unterscheidet.

• Die verbleibende Energie im elektromagnetischen Kalorimeter nachRekonstruktion des Gesamtereignisses soll unter 900 MeV liegen.

• Der Kosinus des Winkels zwischen Lepton und Photon im B-MesonRuhesystem soll unter 0.6 sein.

• Die Masse des vollstandig rekonstruierten B-Mesons soll uber 5.27 GeVliegen.

]2 [GeVmiss2m

-2 0 2 4

Num

ber

of e

xpec

ted

Eve

nts

0

10

20

30

40

50 generic MC , 1310 events

, 61.0099 eventsγ µν +µ →+signal MC B

ulnu MC , 446.15 events

rare MC (no signal decay) , 26.56 events

Abb. 0.3: m2miss Verteilung fur den Muonkanal nach Vorschnitten mit Gewich-

tung die der Erwartung auf Daten entspricht.

vii

Nach diesen Schnitten verbleibt vor allem Untergrund aus dem generischenund ulnu-Monte-Carlo, wie man fur den Muonkanal in Abbildung 0.3 sehenkann. In dieser Abbildung, wie auch in der weiteren Analyse, wird die Anzahlder Signalereignisse auf die von BaBar gemessene Obergrenze des Verzwei-gungsverhaltnisses normiert.Nachdem die Vorschnitte gefunden sind, wird fur die finale Selektion ein Net-zwerk mit der NeuroBayes-Software fur jeden Signalkanal trainiert, wobeizum Training fur beide Kanale ahnliche Variablen benutzt werden. Wie sichin diversen Trainings zeigt, sind die Untergrunde bestehend aus B+ → X0

uℓ+ν

mit X0u = π0, η, am schwierigsten zu trennen, da diese dem Signalzerfall am

ahnlichsten sind. Deshalb werden im Netzwerktraining mehrere Pion- undEtavetos benutzt. Zusatzlich dazu kommen Variablen, die fur die Vorschnitteverwendet wurden. Es konnen nur solche Variablen benutzt werden, dienicht zu stark mit m2

miss korreliert sind. Dies soll zu starke Angleichungender Signal- und Untergrundform vermeiden, welche das Fitten unmoglichmachen wurden.Der Schnitt auf die Netzwerkausgabe wird mit der Figure of Merit (Gutezahl)von Punzi optimiert[11], mit

FOM =εsigl

12nσ +

√

N bkgl

,

wobei εsigl die Signaleffizienz, N bkgl die erwartete Untergrundanzahl im Sig-

nalfenster und nσ die gewunschte Signifikanz ist, welche in dieser Analyse auf3 Sigma gesetzt wird. Das Ergebnis fur die Figure of Merit ist ein Schnittoberhalb 0.7 fur beide Signalkanale. Die Selektion nach allen Schnitten ist furden Muonkanal in Abbildung 0.4 gezeigt. Die Signaleffizienz fur die gesamteAnalyse liegt bei etwa 0.4% fur beide Kanale.Beim Fitten werden die Datensatze separat mit analytischen Funktionenparametrisiert, wobei fur beide Zerfallskanale die gleichen Funktionen ver-wendet werden. Der Anteil des rare-Monte-Carlos ist nach der Selektion ver-nachlassigbar klein und wird daher beim Fitten nicht berucksichtigt. In Ab-bildung 0.5 ist zu sehen, dass die Funktionen die Verteilungen gut wiedergeben.

viii

]2 [GeVmiss2m

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Eve

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0

2

4

6

8

10

Tagside-Corrected

generic MC , 276.282 events




Abb. 0.4: m2miss Verteilung fur den Muonkanal nach Netzwerkschnitt mit

Gewichtungen, welche der Erwartung auf Daten entsprechen.

]2 [GeVmiss2m

-2 0 2 4

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0

1

2

3

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5

6

Abb. 0.5: Fits fur Signal MC (rot), generisches MC (grun) und ulnu MC(blau) fur den Elektronkanal ix

]2 [GeVmiss2m

-2 0 2 4

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of e

xpec

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0

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60

80

100

]2 [GeVmiss2m

-2 0 2 4

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of e

xpec

ted

Eve

nts

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60

80

100Stacked Plot --- Tagside-Corrected --- net1<0.7


, 10.4229 eventsγ eν + e→+signal MC B



Datasample , 3011 events

]2 [GeVmiss2m

-2 0 2 4

Ent

ries

Nor

mal

ized

to U

nity

0.000

0.005

0.010

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to U

nity

0.000

0.005

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0.035Stacked Plot --- Tagside-Corrected --- net1<0.7

generic MC , 1675.48 entries

, 10.4229 entriesγ eν + e→+signal MC B

ulnu MC , 398.944 entries

rare MC (no signal decay) , 18.3423 entries


Abb. 0.6: m2miss Seitenband mit Netzwerkoutput < 0.7 fur den Elektro-

nenkanal gewichtet auf die Erwartung in Daten (links) und normiert (rechts),jeweils mit Signal MC (blau), ulnu MC (grun), generisches MC (rot), rareMC, (schwarz) und Daten (Datenpunkte).

Die Stabilitat der Fits wird mit Toy-Monte-Carlo Studien gepruft, hierbeiwerden verschiedene Verzweigungsverhaltnisse fur das Signal angenommen.Die Fits liefern fur alle Konstellationen gute Ergebnisse, wobei sich fur denFit des Signalanteils bei null Signalereignissen ein Bias zu negativen Wertenergibt.Die Ubereinstimmung der Monte-Carlo-Erwartung mit dem Belle Datensatzwird in verschiedenen Seitenbandern uberpruft. Diese umfassen die m2

miss

Variable > 1 GeV2, die vollstandig rekonstruierte B-Meson Masse < 5.27GeV und die Netzwerkausgabe < 0.7. Wie in Abbildung 0.6a zu sehen, istdie absolute Ereignisanzahl auf Daten hoher als im Monte-Carlo, deshalbwerden Daten und Monte-Carlo aufeinander normiert (Abbildung 0.6). DieSeitenbander fur den Elektronenkanal zeigen eine gute Ubereinstimmung.ImMuonkanal gibt es einen Peak auf Daten im Seitenband derm2

miss Verteilungfur B-Meson Massen < 5.27 GeV (Abbildung 0.7a). Dieser tritt nur in einemTeil des Seitenbandes auf und verschwindet im Rahmen der Fehler fur B-Meson Massen > 5.27 GeV und Netzwerkschnitte > 0.7 (Abbildung 0.7b),sowie fur eine Netzwerk Selektion > 0.7 und B-Meson Massen < 5.27 GeV.Daraus lasst sich schließen, dass eine Klasse von Ereignissen aus dem kom-

x

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0.030Stacked Plot --- Tagside-Corrected --- BTagMbc<5.27


, 4.04409 entriesγ µν +µ →+signal MC B




(a)

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Uni

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0.035 Stacked Plot --- Tagside-Corrected --- BTagMbc>5.27&&net1<0.7






(b)

Abb. 0.7: m2miss Seitenband fur den Muonkanal mit B-Meson Massen < 5.27

GeV (links) und Netzwerkschnitten < 0.7 mit B-Meson Massen > 5.27 GeV(rechts), jeweils mit Signal MC (blau), ulnu MC (grun), generisches MC(rot), rare MC, (schwarz) und Daten (Datenpunkte).

binatorischen Untergrund gute m2miss Werte liefert.

Zur Vervollstandigung der Analyse mussen systematische Studien durchgefuhrtwerden, welche im Hinblick auf die Meson-Vetos schwierig sind. Zudem musseine Abschatzung der Sensitivitat durchgefuhrt werden, bevor die Messungauf dem Belle-Datensatz erfolgen kann.

xi

Contents

1 Theoretical overview 3

1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Fundamental interactions . . . . . . . . . . . . . . . . . 3

1.1.2 Particles of the Standard Model . . . . . . . . . . . . . 7

1.2 The B+ → ℓ+νγ decay . . . . . . . . . . . . . . . . . . . . . . 11

1.2.1 Latest calculation for the B+ → ℓ+νγ decay . . . . . . 13

1.2.2 The LNUGAMMA-module . . . . . . . . . . . . . . . . 16

2 The Belle experiment 19

2.1 The KEK B collider . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 The Belle detector . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.1 Silicon vertex detector (SVD) . . . . . . . . . . . . . . 24

2.2.2 Central drift chamber (CDC) . . . . . . . . . . . . . . 24

2.2.3 Aerogel cherenkov counter system (ACC) . . . . . . . . 25

2.2.4 Time of flight counter (TOF) . . . . . . . . . . . . . . 26

2.2.5 Electromagnetic calorimeter (ECL) . . . . . . . . . . . 26

2.2.6 Extreme forward calorimeter (EFC) . . . . . . . . . . . 27

2.2.7 KL and muon detection system (KLM) . . . . . . . . . 28

2.2.8 Particle IDs . . . . . . . . . . . . . . . . . . . . . . . . 28

3 BaBar analysis of the B+ → ℓ+νγ decay 31

4 Tag side reconstruction 37

5 Signal side reconstruction 45

5.1 General outline of the analysis . . . . . . . . . . . . . . . . . . 45

5.2 Monte Carlo samples . . . . . . . . . . . . . . . . . . . . . . . 47

5.2.1 Background Monte Carlo . . . . . . . . . . . . . . . . . 47

5.2.2 Signal Monte Carlo . . . . . . . . . . . . . . . . . . . . 48

5.3 Missing mass variable . . . . . . . . . . . . . . . . . . . . . . . 51

5.4 Precuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.5 Network training . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.6 Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.7 Sideband consistency check . . . . . . . . . . . . . . . . . . . . 88

5.8 Comparison between the BaBar analysis and this diploma thesis 91

1

6 Appendix 936.1 Precuts electron channel . . . . . . . . . . . . . . . . . . . . . 936.2 Network training results for the electron channel . . . . . . . . 996.3 Fitting results electron channel . . . . . . . . . . . . . . . . . 1026.4 Monte Carlo study muon channel . . . . . . . . . . . . . . . . 1046.5 Monte Carlo study electron channel . . . . . . . . . . . . . . . 1096.6 Sidebands Monte Carlo vs. data plots for the electron channel 1146.7 Sidebands Monte Carlo vs. data plots for the muon channel . 118

2

1 Theoretical overview

1.1 The Standard Model

The Standard Model is the base of particle physics, which defines a frameworkfor all particles and their interactions. It has been tested for over fortyyears in countless experiments and it has always been able to reproducethe experimental results. The numerical predictions have been tested tosmallest perturbative corrections in high precision experiments. These wereunable to reveal any deviation from theoretical predictions. It is thereforeone of the best tested theory that ever existed. Nevertheless the discoveryof neutrino oscillations, which can not be described with massless StandardModel neutrinos, and also dark energy and dark matter, who are constitutedof unknown particle types, call for an extension of the Standard Model.In addition, several theoretical concerns arise, like the missing concept ofquantum gravity, the baryogenesis in the early universe, the 26 parameterswhich can not be determined mathematically but have to be measured inexperiments and their in some cases peculiar values. As for example, themixing-angles of the weak CKM matrix exhibit a strong hierarchical orderwhere none is expected, also no difference between the charges of leptonsand protons could be found. All of this are compelling arguments for physicsbeyond the Standard Model.A short overview of the Standard Model will be given in the following.

1.1.1 Fundamental interactions

Interactions in the Standard Model are described by the exchange or emissionof bosons. The Standard Model comprises three interactions: the weak,strong and electromagnetic. Gravity is not contained and despite intensiveefforts no viable theory including it into the model has been found so far.The three interactions can mathematically be ”derived” by invoking certaingauge invariances of the quantum mechanical equations.The electromagnetic field for example naturally follows, from demanding alocal invariance of the Dirac equation towards transformations of the U(1)group. The exchange boson is then identified with the generator of thisgroup. Specifically the solutions of the Dirac equation are wave functionswhose physical meaning lies in their absolute values. Since absolute valuesare independent of phase factors of the like eiχ(~x,t) (the ~x and t dependence

3

is the defining property of a local gauge invariance), they can be multipliedto the function without changing physics. These functions are no longersolutions to the ungauged equation, because derivatives of the phase factorare introduced into it. These additional terms have to be compensated witha modification of the derivative, by replacing ∂µ with Dµ = ∂µ− i e

~Aµ, where

Aµ denotes the relativistic four potential. This leads to an interaction term inthe Dirac equation, describing the coupling to the electromagnetic field. Theother two interactions can be obtained by a similar procedure, with the weakinteraction obeying a SU(2) and the strong interaction a SU(3) symmetry.Because a SU(n) Lie group has n2 − 1 generators the weak interaction hasthree exchange bosons with W+, W− and Z0, and the strong interaction haseight gluons. The three interactions have very different characteristics.The electromagnetic interaction has one massless and uncharged exchangeboson with a spin of one, endowing it with an infinite interaction range.The potential behaves like α

r. The coupling constant, which is also called

the fine structure constant, has a value of α ≈ 1137

at low energies. Theconstant becomes larger with rising energy, it is a running constant. Thischaracteristic applies to all three interaction constants. Higher energies ormomentum translate through Heisenberg‘s Uncertainty Principle ∆p∆x ≥ ~

2

to a more precise distance resolution, making smaller processes like vacuumquantum fluctuations visible. Since electron positron pairs are constantlycreated in these fluctuations, a particle’s electrical charge will be shielded bypolarization of these pairs, resulting in an effective charge at low energies.At high energies the vacuum processes are resolved and the naked charge isuncovered.The weak interaction has three very massive exchange particles with massesof about 80 GeV for the W’s and 91 GeV for the Z. If the energy of thereaction is low energetic the exchange boson is a virtual particle and due toits high mass it is very far off the mass shell. These masses lead to very smallpropagator terms 1

MW/Z−q2, where the progator is a measure for the distance,

the virtual boson has to bridge. In a low energy regime the interaction ispoint-like with ranges of 10−17 − 10−16m. The overall strength of the weakinteraction at low energies is given by the Fermi constant

GF

(~c)3=

√2

8

α2W

M2W

≈ 10−5

which comprises the propagator contribution from the heavy gauge bosonand the weak coupling constant αW . This parameter is only valid at tree

4

level order processes. For higher energies the gauge boson mass in the de-nominator of the propagator is compensated by the momentum transfer. Atdistances of 10−18m, the strength of the interaction becomes comparable tothe electromagnetic. Above the gauge boson threshold, the naked couplingconstant emerges with a value of αW ≈ 1

30. This naked constant is again

a running coupling like in the electromagnetic case. The overall interactionstrength increases greatly with the energy, mostly due to the overcoming ofthe gauge boson threshold. Only the weak interaction is capable of chang-ing particle flavors, introducing a CKM mixing matrix that describes thetransition amplitudes between the quarks. A classical example of such atransition is the beta decay of the neutron which is depicted in figure 1.1.

Figure 1.1: Neutron Beta Decay Neutron [6]

The free neutron has a meanlife time of approximatelyeight minutes before weaklydecaying into a proton. Inthis process one of the downquarks emits a W−-boson andchanges into an up quark.The quark content of thebaryon changes from (udd)to (uud). The W-boson de-cays into an electron and elec-tron anti-neutrino. The quarkmixing is hierarchical and itstrongly favors decays withinor to neighboring generations.The weak interaction violates parity maximally, by coupling to masslessleft-handed particles (spin and momentum anti-parallel) and massless right-handed antiparticles exclusively. It couples to the weak charge called isospin,which is conserved in the interaction. Fermions carry isospins of ±

12and

bosons ±1 or 0. The interaction has two charged and one neutral boson.The convergence of the coupling strengths of weak and electromagnetic forceis no coincidence, but reveals a higher symmetry. The two forces are unifiedinto the electroweak interaction at ∼ 100GeV with a gauge symmetry groupSU(2)×U(1). The symmetry breaking is caused by the Higgs mechanism,which mixes the original unbroken bosons W 0 from the (W+,W 0,W−) SU(2)triplet with B0 from the U(1) singlet. The two mixed bosons are two newstates, the Z0 and the photon, where the boson content of the photon equals

5

|γ〉 = cosΘW |B0〉 + sinΘW |W 0〉. The mixing angle is called the Weinbergangle and its value is sin2ΘW ≈ 0.2312. The electromagnetic and weakcoupling constants and the charges are also connected through this angleby αem = αW · sin2ΘW and e = g· sinΘW . The weak gauge bosons gainmass through interaction with three Higgs fields ascribed to the three mas-sive bosons. The interacting particle is the Higgs boson which is the onlyparticle of the Standard Model yet to be discovered. The Higgs Mechanismis needed to explain massive gauge bosons, because a gauge theory aloneproduces solely massless gauge particles.The strong interaction couples via eight gluons, each of them carrying atleast two different strong charges called colors. Beside the gluons, quarksare the only particles who carry color charges. Colors come in blue red andgreen, and their anti colors. It is required by nature that every particle com-pounded of quarks has to be color-neutral, i.e. either equal amounts of allthree colors or anti colors, or equal amounts of color and anti color whichcancel, have to be combined. This behavior is called confinement. So far onlytwo-quark combinations found in the mesons and three-quark combinationsfound in the baryons have been observed. The strength of the potential lookslike VS = −4

3αS

r+ kr. For short ranges this force behaves similar to the elec-

tromagnetic, but for long ranges it has a linear slope leading to divergence.When a quark is removed from a compound particle the field strength riseswith distance between the quarks, this is often compared to rubber bandholding the quarks together. When the field energy is above the energy oftwo quarks masses, hadronization occurs, which means that the field tubebreaks and a quark anti-quark pair is created. This pair couples with theoriginal quarks in two separate compound particles, thus shortening the dis-tances between the constituent quarks. The linear rise of the field strength iscaused by self interaction of the gluons, who themselves carry color, thereforecausing an increasing interaction cloud with rising distance. This self inter-action is also prevalent in the compound particle’s, which leads to complexprocesses, that spawn a cloud of gluons and quark anti-quark pairs. Theresult is a non negligible number of sea quarks and gluons accounting forlarge parts of the compound particles mass. The strong coupling has also arunning constant moving with the energy scale. At low energies the couplingis about hundred times stronger, than the electromagnetic with αS ≈ 1, butit decreases with increasing energy. This fact makes convergent perturbativecalculations in powers of αS for low energies impossible. The strong inter-action also binds nuclei, showing up in a residual interaction between the

6

protons and neutrons. The color exchange is mediated through color-neutrallight meson, predominantly pions. The color-neutrality of the exchange par-ticles allow for longer range interaction, by avoiding high field energies overlong distances, although this interaction is orders of magnitude lower thandirectly via gluons.Gravity is not included in the Standard Model, but taking into account its es-timated coupling strength of the order 10−39−10−45, disregarding it, is a verysafe approximation for energies accessible to current and future experiments.

1.1.2 Particles of the Standard Model

The particles of the Standard Model are categorized under several aspects.All particles are either bosons with integer spin or fermions with half-integerspin values. Fermions are, in contrast to bosons, not able to populate one sin-gle state more than once. This is known as Pauli’s exclusion principle. Eachparticle has an antiparticle with all charges the particle carries conjugatedand if weakly interacting an opposite chiral coupling, but otherwise identicalproperties. At a fundamental level particles are either: gauge bosons, leptonsor quarks.As discussed in the previous section there are twelve gauge bosons: threemassive weak bosons with two of them oppositely charged, one masslesselectromagnetic boson and eight massless strong bosons. All of them carry aspin of one and the strong and weak gauge bosons their respective couplingcharges. The photon carries no charge, therefore the electromagnetic inter-action has an infinite range. Further two weak gauge bosons W+ and W−

carry an additional electromagnetic charge.Fermions are divided into three generations each containing two leptons andtwo quarks. The six leptons contribute to each generation one charged mas-sive and one neutral massless particle (in the Standard Model). The chargedparticles: electrons, muons or taus, are each paired with a neutrino. Allleptons have a spin of one half. Electrons and all neutrinos are assumed tobe stable. Muons and taus decay into electrons and anti-neutrinos. The lep-ton number is a preserved quantity in the Standard Model and it is definedas the difference between the number of leptons and anti-leptons. In parti-cle generation and decay the lepton number of each generation is preserved.Thus every decay in which a lepton is created, an anti-lepton of the samegeneration must be generated, which is in most cases the charge conjugateneutrino.

7

Like the leptons, six quarks are separated into three generations with two

Figure 1.2: Standard Model Particles [6]

quarks each. Every generation has an up-type quark: up, charm or top, withan electrical charge of 2

3and a weak isospin of 1

2and a down-type quark:

down, strange or bottom, with an electrical charge of −13and an opposite

isospin. Quarks have a spin of one half and the number of quarks minusanti quarks is a preserved quantity. If not bound in a proton or neutron,only the lightest up quark is stable. The remaining quarks decay weaklyinto lighter quark flavors. Because of weak isospin and charge conservation,up-type quarks can only decay in down-type and vice versa. The decay ismediated by the weak interaction with the emission of a W+ or W− boson.The strength of the decay amplitudes are given in the CKM matrix, whichdisplay a strong tendency for decays within one generation.

VCKM =

|Vud| |Vus| |Vub||Vcd| |Vcs| |Vcb||Vtd| |Vts| |Vtb|

=

0.97459 0.2257 0.003590.2256 0.97334 0.04150.00874 0.0407 0.999133

The fundamental particles of the Standard Model are summarized in fig-ure 1.2.

8

Confinement forces quarks to be bound in baryons in three quarks or mesonsin two. To ensure color-neutrality baryons must consist of three particlesor three anti-particles and mesons of one particle and one antiparticle. Thespins in a baryon can either couple to 3

2or to 1

2and in a meson 1 and 0. With

these combinatorics many particles can be constructed, but because of theincreasing instability of the bound state with rising mass, only the lighterones were found so far. Furthermore combinations with a top do not exist,since the top decays so rapidly, due to its big mass, that it can not engage ina bound state with other quarks. Figure 1.3 shows baryons with spin 3

2and

meson with spin 0 from the uds-sector.The Ω is made up of three strange quarks with same spin up. Since the

Figure 1.3: Flavor mixtures for baryons (left) and mesons (right) [6]

omega is a fermion, this state is a direct proof for an additional quantumnumber the color. The quantum numbers known to the Standard Model donot forbid tetra quarks with two quark anti-quark pairs or penta-quarks withthree quarks combing to white and one quark anti-quark pair. Neverthelessthese states have not yet been discovered.The up, down and strange quark masses are very close together. That meansthey are quasi degenerate and accordingly they mix similarly like the colorcharges with a SU(3) symmetry. This symmetry can be reduced to an octetand singlet, yielding nine particles as shown on the right panel of figure 1.3.The resulting quark flavors mixtures for the mesons with spin and chargezero are the superpositions π0 = uu−dd√

2, η = uu+dd−2ss√

6and η′ = uu+dd+ss√

6.

9

Due to the mass discrepancies the SU(3) symmetry is not exact. The etaparticles are in fact linear combination of the unbroken SU(3) eta states

η = ηoctetcosΘ− ηsingletsinΘ

η′ = ηoctetsinΘ+ ηsingletcosΘ.

The breaking of the symmetry becomes stronger for larger quark mass dif-ferences, leading to an effective decoupling of the two heavy flavors charm,bottom. The upsilon for example is a clean bb state.

10

1.2 The B+ → ℓ+νγ decay

The semileptonic B+ → ℓ+νγ decay with ℓ+ = e+, µ+ is rare, with atheoretically expected branching fraction of the order of 10−6. A BaBarmeasurement in 2009 yielded an upper limit for the branching fraction ofB(B+ → ℓ+νγ) < 15.6 × 10−6 combined for both the electron and muonchannel. The decay consists of a weak component and the photon emissionwith an electromagnetic and a strong component. As seen in figure 1.4 inthe weak part of the decay, one quark of the constituents emits a virtualW-boson and makes a transition into the anti-flavor of its partner and theyannihilate. The W-boson decays into a lepton and a neutrino. The photon isemitted from either one of the meson constituent particles or from the finalstate lepton. The decay would be helicity suppressed without the presenceof the photon as will be discussed in the following.The B meson has a angular momentum of J = 0, thus for the purely weak

Figure 1.4: Feynman diagrams for the leading order contributions. Leftpanel: Leading order contribution for the photon emission off the up quark.Right panel: Power suppressed contribution for the emission off the bottomquark [2]

decay B+ → ℓ+ν, the spins of the lepton and the neutrino must be anti par-allel in the B meson rest frame to ensure angular momentum conservation.The weak interaction couples to right handed anti-particle and left handedparticle chiralities. The chirality has to be Lorentz invariant to ensure theLorentz invariance of the weak interaction. For massive particles it does not

11

commute with the free particle Hamiltonian of the Dirac equation, so everyparticle is an oscillating superposition of left and right handed chiralities.Therefore the chirality is an intricate concept which can not be easily visu-alized, except for massless particles where the chirality equals the helicity,which is defined as

H =~S ~p

|~p| = ~S ~n.

where ~S is the spin vector. The helicity is the normalized projection of thespin on the momentum. If a particle is massless, this parameter is Lorentzinvariant, i.e. no reference frame can be found in which the particle is over-taken which would cause the momentum to flip and therefore lead to a signchange of the helicity. If we assume the lepton and anti neutrino to be mass-less in the B meson decay the anti neutrino has to be right handed, thatmeans its spin has to point in momentum direction, and the lepton on theother hand has to be left handed to couple weakly. Both conditions are notbe satisfiable at once since both particles are right handed. However formassive particles the helicity is not equal to the chirality and even if bothparticles appear right handed in the B meson rest frame, their chiralities arenot purely right handed states. Every massive particle has a left and a righthanded admixture and their magnitudes can be understood as the amountof reference frames in which the particle has a left or right handed helicity.In the B+ → ℓ+ν decay the anti neutrino, which is nearly massless, is almostpurely right handed and the massive lepton has a right handed helicity inthe B meson rest frame. However the lepton has a left handed admixturethat couples to the weak current, which is dependent on its velocity. The lefthanded component is proportional to (1− β) and with increasing velocity ofthe lepton this left handed admixture diminishes and becomes zero at thespeed of light. This causes a helicity suppression for lighter particles whichare created at higher velocities, reducing their weakly coupling chiral com-ponent.The purely weak B+ → ℓ+ν decay has therefore a branching fraction

BR(B+ → ℓ+ν) =G2

FmBm2ℓ

8π(1− m2

ℓ

m2B

)2f 2B|Vub|2τB

with a factor proportional to m2ℓ(1 −

m2ℓ

m2B). The velocity of the lepton is de-

termined by its mass and the energy of the decay is given by the B mass.The less massive the lepton or the larger its velocity, the less likely the decay.

12

This dynamic favors muons over electrons even though their phase space fora transition is smaller. Otherwise the transition amplitude is determined bythe Fermi constant GF , the matrix element Vub in the CKM matrix whichconnects up and bottom quark flavors and fB which is a parameter quanti-fying the quark overlap in the B meson.The presence of the photon in B+ → ℓ+νγ lifts the helicity suppression.The photon carries a spin and the process becomes a three body decay,which causes the phase space for parity violating transitions to grow consid-erably. Even though the electromagnetic interaction introduces an additionalα2em factor into the equation, the overall branching fraction increases largely

compared to the photon-less case. The weak process in this decay is lowenergetic and therefore point-like, which makes it precisely calculable. Thephoton emission on the other hand is more complicated to obtain. It depends

strongly the inverse moment 1λB

=∫∞0

dωΦB+ (ω)

ω, which is a theoretical pa-

rameter needed in a QCD factorization approach, which is commonly appliedfor non-leptonic B decays. ΦB+(ω) describes the B meson constituents’ mo-mentum distribution function in a high energy limit and it is instrumental tomany calculations involvingB mesons. This parameter is difficult to calculatetheoretically and therefore suitable to be determined through measurement.The B+ → ℓ+νγ is especially appropriate for such a measurement since thereare no hadrons in the final state, thus delivering a potentially clean result.Phenomenology in non-leptonic B decays prefers values of λB ≈ 200MeV asstated in [2].Generally, decays with low branching fraction are always sensitive to newphysics. This is because unobserved effects must have small branching frac-tions and they become observable if the branching fraction predicted in theStandard Model is equally small.

1.2.1 Latest calculation for the B+ → ℓ+νγ decay

The ensuing results are taken from the latest theoretical paper [2] dealingwith this decay. The calculation assumes massless leptons, thus precludingtaus, applying only to electrons and muons. Due to this assumption thedecay amplitudes of the two modes are identical. The decay amplitude iscomputed to all orders in the strong and to first order in electromagneticinteraction. The factorization approach assumes photon energies of 2Eγ ∼mb. The authors of the paper therefore consider photon energies below 1GeV

13

as unsafe. The result of the calculation is

d2Γ

dEγdEℓ

=αemG

2F |Vub|2

16π2m3

B(1−xγ)[

(1−xν)2(FA+FV )

2+(1−xl)2(FA−FV )

2]

(1)with xi =

2Ei

mBwith i=γ, ℓ, ν and 0 ≤ xi ≤ 1, xγ + xℓ + xν = 2, mB the

B meson mass, FA axial form factor and FV vector form factor. Since theform factors are independent of the lepton mass an integration over Eℓ canbe performed yielding

dΓ

dEγ

=αemG

2F |Vub|2

48π2m4

B(1− xγ)x3γ

[

F 2A + F 2

V

]

(2)

with

FV (Eγ) =QumBfB2EγλB(µ)

R(Eγ, µ) +[


+QumBfB(2Eγ)2

]

and

FA(Eγ) =QumBfB2EγλB(µ)

R(Eγ, µ) +[


− QumBfB(2Eγ)2

+QlfBEγ

]

, where Qi is the charge for i=lepton, up- and bottom quark and µ de-notes the energy scale at which the corrections to the form factors are beinginvestigated (value suggested in the paper µ ∼ O(mbλQCD)

12 ). The first

term represents the leading order contribution of the QCD heavy-quark ex-pansion, describing the photon emission off the light quark, containing thealready mentioned λB parameter. This term is corrected for radiative ef-fects given by the R(Eγ,µ) factor. This factor represents higher order masscorrections of the up quark that equal one at tree level. This radiative cor-rections reduce the leading order amplitude by roughly 20% − 25%. Theremaining terms are 1

mbpower corrections. The term containing the bottom

quark charge, represents the photon emission off the heavy quark, which issuppressed due to the quarks higher mass. This process can be seen in fig-ure 1.4. The propagator joining the W and the photon becomes much largerfor the emission off the heavy quark (p − q)2 ∼ m2

b , than in the leading or-der contribution featuring the up quark (q − l)2 ∼ mbλQCD. The Ql-termrepresents the photon emission off the lepton, this term is only present inthe axial form factor. The Qu-term in square brackets and the ξ(Eγ)-term

14

Figure 1.5: Form Factor Photon Energy Dependence [2]

are higher order correction for the photon emission off the up quark, wherethe ξ(Eγ)-term is an unknown contribution to this emission process, whichis being parametrized.The double differential branching ratio’s (1) second term in square bracketsis power suppressed in the heavy quark limit FV −FA

FV +FA∼ λQCDmb due to helic-

ity conservation, but becomes very large at small photon energies, renderingthe calculation increasingly invalid. Especially the contribution of the vec-tor current, which does not have oppositely signed terms in higher orders isbecoming large. The form factor behavior can be seen in figure 1.5. Thebranching fraction plotted against the λB parameter is shown in figure 1.6adjusted to an analysis made by the BaBar collaboration [1]. The theoreti-cal prediction lies just above BR(6 × 10−6) for λB ≈ 200MeV and declineswith rising values for this parameter. Illustrated in the picture are also dif-ferences in the branching fraction prediction for: lower order models where“LO“ denotes just leading order calculation, “NLL“ next to leading loga-rithm radiative corrections added to the leading order and “NLL + powercorrections“ the complete result with higher order processes.

15

Figure 1.6: λB Dependence of the Branching Fraction [2]

1.2.2 The LNUGAMMA-module

The B+ → ℓ+νγ analysis performed in this thesis uses the LNUGAMMAmodule [7], provided by the event generator software, for the simulation ofsignal events. The module implements a calculation, which is based on apaper from 2000 [3]. The result given in this paper is coarser compared tothe one given in the previous paragraph. Specifically it neglects radiativecorrections to the up quark mass for the leading order term. Furthermoreit does not contain the higher order photon emission processes off the upquark, but it includes the leading order

λQCD

mbterm for the bottom quark

photon emission. However the paper uses a wrong sign for this leading ordercorrection in the vector current (minus instead of plus), rendering the twoform factors fV and fA equal. The formula for the two currents reads

FV,A =QufBmB

2Eγ

R− QbfBmB

2Eγmb

.

R denotes the intergral over the light-cone B meson wave function and is es-timated in this paper to an model-independent lower limit 3

4λB, which yields

apart from the prefactor of 34an identical result to the calculation above.

16

The remaining terms match the ones in the previous section.The LNUGAMMA module offers two modes in which it can operate in. Thevector and axial current can either as a default be chosen as equal, conformingto the formula above, or the FA current can be set to zero. This accommo-dates for the fact, that the decay is theoretically not perfectly understood.Since the calculation does not apply to low final state photon energies, themodule provides an option for a lower bound for the photon energies pro-duced in the B mesons rest frame. Furthermore a variable for the R-valueand the bottom quark mass has to be set. The EvtGen guide’s recommendedvalues are used in this thesis, which are: a photon energy cutoff at 35MeV,an R-value of 3 GeV and a bottom quark mass of 5 GeV. Additionally theform factors are chosen to be equal.

17

2 The Belle experiment

The Belle Experiment consists of the Belle detector which is mounted onthe KEKB accelerator. It is located at Tsukuba Japan at the KEK researchfacility. It was conceived in 1994 and in operation since 1999. The exper-iment has several aims, but its primary goal is to measure mixing inducedand time-integrated CP -Violation in B meson systems. To accomplish thistask it has to be highly precise. Aside from CP -violation the experiment isadditionally fit to investigate a multitude of further topics. These includeprecision measurements of τ , B meson and D meson particles, the search forrare decay modes, one of which is performed in this thesis, and the searchfor new exotic particles.The CP -violation has been discovered in several decay channels like for ex-ample B → J/Ψ K0. This decay is also called the golden decay because it isvery clean to measure. It reveals a CP -Violation in the interference of mix-ing and decay, short mixing-induced CP -Violation. The time-independentor direct CP -asymmetry has first been found in charged and neutral decaysof B± → K±π0 and B0 → K+−π−+. This asymmetry is caused by differentdecay probabilities of CP conjugated states. Together with BaBar, the Bellediscoveries of CP -violating decays in B meson systems, paved the way tothe bestowal of the Nobel Prize to Nambu, Kobayashi and Maskawa for theCKM-Mechanism. The experiments results were explicitly mentioned in thereasoning for the award.The Belle Experiment collected 772 ×106 BB Pairs at the Y(4S)-resonance.Additionally 10% of the data was taken 40-60MeV below the resonance forthe study of continuum backgrounds. This background contains e+e− → qqevents with q=(u,d,s,c). In addition Belle recorded smaller amounts of Y(5S)data at an energy of 10.865 GeV for BS meson research. These are mesonscontaining a bottom and a strange quark. Also considered were events atthe Y(3S) resonance with an energy of 10.335 GeV to search for exotic darkmatter candidates and the Higgs boson. Belle has been shut down in 2010and it is being replaced by the Belle II experiment, which is scheduled tostart operations in 2014 with two orders of magnitude higher luminosity.

19

2.1 The KEK B collider

The accelerator collided electron positron pairs with nominal energies ofE+=8 and E−=3.5 GeV and thus operated at center of mass energy of

√s ≈

√

4E+E− = 10.58GeV,

what corresponds to the mass of the Y(4S)-Resonance and thus producingthe Y(4S) with very high efficiency. The Y(4S) is the third radial excitation ofthe bound b− b-system. Its high mode of excitation decays into two B meson,through the creation of uu or dd pairs that couple with the bottom quarks.This results either in charged B+B− pairs or neutral B0B0s. The Y(4S)decays almost entirely into these two channels and their branching ratios areapproximately equal. Since the Y(4S) has barely enough energy to createthe B mesons they are nearly at rest in the CM frame with a momentumof p ≈ 325MeV/c. As mentioned above the Belle experiment was primarilyconstructed to measure a possible CP -Violation in the B meson system andmany design considerations were made to attain this goal. Most importantlythe collider is asymmetric, which means that the electron and positron beamhave different energies. The two beams are contained in separate rings, alow and a high energetic one. These rings run parallel to each other witha crossing point for the interaction region. The accelerator ring is depictedin figure 2.1. The energy discrepancy between the beams leads to a boostedproduction of the B meson pairs in the lab frame with βγ = 0.43 along thebeam axis. This is important for decay-time difference measurements of thetwo mesons. Decaying at different times, the boost ensures that the particlestravel different distances before decaying. The larger the boost the larger thedistance and therefore the more accurate the decay-time resolution. At KEKB the traveled distance is on average ∆z ≈ 200µm. This yields an averagedecay-time resolution of

< ∆t >≈ < ∆z >

cβγ≈ 1.55ps.

The traveling distances of a few hundred µm require for the vertexing to beas accurate as possible. The positions of the decay-vertices are determinedwith the silicon vertex detector.Decay time differences are crucial for the measurement of mixing-inducedCP -Violations of neutral B0 mesons. Being produced in a quantum mechan-ically entangled state, the decay of the first B0 (B0) determines the flavor

20

Figure 2.1: KEK B Accelerator [8]

of its partner, thus serving as a trigger for the life-time measurement of thenow disentangled meson, which is displaying oscillations into its anti-particlevia weak box-diagrams. The CP -Violation shows up in a different time evo-lution of particle and anti-particle decay probabilities.KEK B collides particles at a crossing angle of 11 mr instead of head on, whichhelps to avoid parasitic collisions with subsequent particle bunches. Thehigher-energetic beam crosses the detector’s magnetic field at a 22 mr angle,the lower-energetic one, being more prone to bending in the magnetic field,is injected perpendicularly. The finite crossing angle setup reduces beamrelated background by a significant amount, obviating separation-bend mag-nets near the interaction region. With the help of crab cavities the bunchesare warped accordingly, that the collision virtually happens head on. Theaccelerator is filled with 1582 bunches at a time, each bunch containing 1010

particles, colliding them with a frequency of ∼500 MHz. The luminosityachieved with this collider, is with 2.1083×10−34cm−2s−1 a world record.As already explained, the precision of the vertexing is crucial. The demandfor precision makes it necessary to move the silicon vertex detector (SVD) as

21

close as possible to the beam pipe. This lead to two challenges. The beambackground has to be diminished significantly with an intelligent beam pipegeometry and the beam pipe is heated at the interaction point necessitatingan active pipe cooling with helium and a heat shielding for the SVD.

22

2.2 The Belle detector

The Belle Detector is constructed in a layered structure around the beampipe. It has a near cylindrical symmetry, only deviating from it due to theasymmetric beam energies. The opening angle in boost-direction is smallerthan in reverse direction, otherwise it is a 4-π-detector covering a large solidangle around the interaction point. The detector is built around a supercon-ducting solenoid with a radius of 1.8 m and a magnetic field of 1.5 T. Themagnet encloses the central drift chamber, introducing curved trajectories tocharged particles, enabling momentum and charge measurement. The struc-ture of the detector can be seen in figure 2.2. In the following a summary

0 1 2 3 (m)

e- e+8.0 GeV 3.5 GeV

SVD

CDC

CsIKLM

TOF

PID

150°

17°

EFC

Belle

Figure 2.2: Belle Detector Side View [8]

of the most important detector compents will be given. A Detailed reportabout the detector can be found in the Belle Technical Design Report [8].

23

2.2.1 Silicon vertex detector (SVD)

Situated on the inner most layers is the SVD. The SVD measures the tracksof short lived particles decaying inside the beam pipe, which is important in-formation for the subsequent vertexing. A charged particle passing throughthe silicon semiconductor lifts electrons from the valence to the conductingband, creating an electron-hole-pair. Due to the voltage applied to the sili-con, the pair drifts to the electrode and causes a signal. Particles decayingin short distance from the interaction point are among others τs, D mesonsand B mesons. The design constraints on the SVD are given by the the flightdistance of B mesons it has to resolve well. The resolution has to be of theorder of tens of micrometers to resolve CP -Violations.Since most particle energies are below 1 GeV, multiple coulomb scatteringdominates as a disturbing influence, therefore scattering sources are mini-mized, by employing thin materials for the beam pipe and the synchrotonradiation mask, and by moving the readout electronics for the SVD out ofthe inner volume. To maximize accuracy the SVD is moved close to thebeam, which increases the strain on the material. Its degradation reduces itsefficiency over time. The SVD has a polar angle coverage of 23 < θ < 139.It is built in a ladder geometry, providing complete azimuthal coverage. Theladders are read out by double-sided strip detectors with high yields and highS/N-ratios, allowing for a matching of SVD clusters to CDC tracks with anefficiency above 98.8%. The SVD1 has three layers of silicon with 8/10/14ladders at 30/45.5/60.5 mm distance from the IP respectively. It was re-placed by the SVD2, due to declining performance caused by high radiationdamage. The SVD2 has been improved with respect to its predecessor, withfive layers of double-sided silicon at distances of 15/21.1/44/70/90 mm fromthe IP.

2.2.2 Central drift chamber (CDC)

The CDC is located on the layer next to the SVD. The CDC performs amomentum measurement of charged particles, by measuring their curvaturein the magnetic field. The trajectory is determined with a gas-filled chamberinterspersed with high voltage wires, which create a strong electrical field.A charged particle passing through the CDC, releases charge from the gas,which accelerates and multiplies in the field until it reaches the closest wirecreating a signal. With the wire hits nearest to the particle trajectory, a track

24

can be interpolated. The CDC momentum resolution necessary to meet theexperiments requirement, was determined to be

σpt

pt= 0.5%√

1+p2tfor charged

particles above 100 MeV. Additionally to the tracking, the dEdx

energy loss aparticle is experiencing by passing through the tracking-gas, is another im-portant parameter determined by the CDC. This quantity is particle specificand allows for a particle identification. The particles energy is determinedwith the amount of charge it releases and the time the charge needs to driftto one of the wires. Furthermore the CDC gives information for the trigger-system.Like in the SVD the result is improved through the reduction of multiplecoulomb-scattering. For the tracking-gas a compromise has to be made be-tween low scattering cross-sections, demanding a low nuclear charge, and agood dE

dxresolution. The choice has been made for a gas-mixture of half he-

lium and half ethane, where the ethane ensures a good particle ID.The CDC covers a polar angle between 17 < θ < 150 and its chamberextends 103.5-874mm from the IP. Without any walls in-between, scattering,especially for low pt tracks, is kept at a minimum. The shape of the chamberis asymmetric in beam-direction, employing a conical structure around the IPwith two differing opening angles. This accounts for the differently boostedbeam components. The purpose is to avoid beam background, while maxi-mizing the angular coverage. The CDC is constructed of 50 cylindrical layerscontaining 8400 drift cells arranged nearly parallel to the beam, with somehaving a tilt of 40-70 mr. This deviation gives z-positioning information,complemented with additional cathode stripes glued to the inner cylinder ofthe chamber and between layer two and three.

2.2.3 Aerogel cherenkov counter system (ACC)

The ACC is situated on the subsequent layer in the Belle Detector. It de-livers a contribution to the particle identification by distinguishing betweencharged mesons, especially pions and kaons. This is done through velocitymeasurement, which in combination with the momentum information frommagnetic bending in the CDC, allows for inferences on the mass. The de-tector captures Cherenkov light which is created in materials, in which thephase velocity of light lies below the particle’s own velocity. This preventsthe normally occurring negative interference of light-waves which are createdby polarization in the material, caused by the passing particle. The light is

25

emitted in a cone around the particle trajectory, with a velocity dependentopening angle cosΘ = 1

nβ, where n denotes the materials refractive index and

the beta equals vc. The speed of light in materials is given by c = c0

n. Since all

the particles generated in the accelerator are near speed of light, the refrac-tive index has to be very low to make a sensible distinction between them. Itchosen such that pions and the more massive kaons can be efficiently sepa-rated. Kaons tend to be slower, therefore only pions emit Cherenkov light ina momentum range of 1.2 - 3.5 GeV for the material parameters used,whichrange from n=1.01-1.03.The ACC consists of three parts, a barrel region with 960 counter modulesin 60 cells and concentric forward and backward cap with 228 modules in 5layers.

2.2.4 Time of flight counter (TOF)

The TOF is mounted radially outside the CDC on the inner ECL-wall andit provides additional particle identification. It measures the time it takes aparticle to travel the 1.2 m distance from the IP to its scintillators. The timeresolution of ∼ 100 ps covers the momentum range below 1.2 GeV, whataccounts for 90% of the particles created at Y(4S).The system consists of 128 TOF counters and 64 trigger scintillator counters.The scintillators are thin and of plastic, ensuring quick response times. Theangle covered is 34 < θ < 120 and the minimal momentum is pt ∼ 0.23GeV.

2.2.5 Electromagnetic calorimeter (ECL)

The ECL wraps around the CDC and measures particle energies. It is pre-dominantly constructed to measure photon energies but it is also able to giveinformation about electrons, charged pions and kaons. Particles travelingthrough the silicon, interact electromagnetically in different ways dependingon their type. The interaction causes a cascade in the crystals, which resultsin a particle shower, that produces photons as end products. The so calledscintillation light is captured with silicon photodiodes attached to the backof the material. A sensitivity towards incoming photons below 500 Mev is ofimportance, since most photons are products of decay cascades and thereforeexperience energy fragmentation before reaching the ECL. Equally significantis a good position resolution, as for example daughter photons in π0 decays

26

tend to be highly boosted, resulting in a small angular separation. Besidethe energy determination of photons the ECL provides a particle identifi-cation for electrons, by combining its energy measurement with momentummeasurements of the other detector parts, providing a powerful particle dis-crimination parameter with the E

pratio. The shower shape can also be taken

into account, although it is correlated to Ep. Most commonly used is the ratio

that divides the energy deposition in a three by three tile array through theenergy deposition in the larger five by five tile array. The reason these vari-ables serve as good discriminators, is due to the different types of interactionthe primary particles exhibit within the silicon. Electrons interact via pairproduction and bremsstrahlung creating a large shower, losing all their en-ergy in the ECL. Hadrons interact with the nucleus and are also detectable.Muons lose energy only through ionization and excitation of atoms creatingnearly no shower at all.The ECL consists of 8736 tower-shaped CsI crystals pointing to the IP withslight tilts, that close gaps between them. The detector is split in three parts,a barrel region, forward region and an end cap. These three parts have gapsin-between, thus the polar angle 17 < θ < 150 is not entirely covered. Thesize of the crystals has to be a compromise of position and energy resolu-tion, because smaller tiles enhance position determination, but shrinking thecrystals increases the gaps in-between. This increases the amount of inactivedetector material, and further too small crystals can not contain the showers.The energy resolution of the barrel is 1.7%, the forward region 2.85% andthe backward region 1.74%.

2.2.6 Extreme forward calorimeter (EFC)

The EFC is mounted on the faces of the cryostat of the compensation solenoidmagnets. It extends the angular coverage of the ECL to 6.4 < θ < 11.5 infoward and 163.3 < θ < 171.2 backward direction. Apart of calorimetricmeasurement as it is done in the ECL, the EFC, being close to the beam,provides a mask for the CDC and it serves as a beam and luminosity monitorfor the experiment.Due to its vicinity to the beam, it is exposed to large amounts of radia-tion, therefore this detector component has to be very durable. Bismuth-Germanate crystals (Bi4Ge3O12) were determined to fulfill these require-ments. The energy resolution is (0.3− 1)%/

√

E(GeV ).

27

2.2.7 KL and muon detection system (KLM)

The KLM is the outer most part of the detector, capturing KLs and µs, theleast reactive detectable particles who manage to pass through all other com-ponents without decaying or losing much of their energy. The KLM showersparticles similarly to the ECL, however the KLM is much less precise thanthe ECL. The calorimeter needs a much larger interaction length to captureless interacting particles and signal is much less consistent compared to theECL. The KLM efficiently distinguishes between kaons and muons, coveringmomenta above 600 MeV. The discrimination is done by evaluating energydepositions in the KLM and by matching charged tracks from the CDC tothese energy clusters. This delivers a positive results only in the muon case,since the KLs lack of a charged track. The direction of KLs can solely bedetermined from the shower shape in the KLM. Apart from this the mea-surement of KL energies is not possible, due to fluctuating and thereforeunreliable shower sizes.The KLM consists of alternating iron and detection layers. The iron provides3.9 interaction lengths for KL, in addition to the ECL with 0.8 interactionlengths. The detector layers are made of glass-electrode resistive plate coun-ters. The glass serves as a highly resistive bulk, which is set under voltage bythe electrodes. The room between two glass plates is filled with gas, whichis ionized, when traversed by charged particles stemming from the showeringin the iron, causing a discharge on the glass plate. Like the ECL, the KLM issplit into three parts, a barrel with 15 detector and 14 iron layers, a forwardcap and an end cap with 14 layers of detectors and iron each. The coveredangle amounts to 20 < θ < 155.

2.2.8 Particle IDs

The Belle Experiment defines particle IDs for Electrons, Muons and Kaons,which comprise the gathered results of CDC, ACC, TOF, ECL and KLM.The electron and muon IDs are composed of several discriminating variablescombined into a single output. Likelihoods are computed for every singlevariable and these are combined by multiplication to the final parameter.The variables used are dE

dxfrom the CDC, ratio of ECL energy vs. CDC

momentum, the shower shape in the ECL, matching of charged tracks withECL and/or KLM clusters, light yield in the ACC and TOF measurements.The strength of electron ID was tested on e+e− → e+e−e+e− vs. KS → π+π−

28

samples, where electrons were discriminated from pions with efficiencies of90% and fake rates of 0.2%-0.3% above momenta of 1 GeV.For the kaon ID three variables were combined as above. The dE

dxin the

CDC, TOF measurement and ACC light yield. The kaon ID is given asa likelihood of not being a pion, i.e. PID(K) = PK

PK+Pπand accordingly

PID(π) = 1−PID(K), however, it is not only used for pion-kaon separationbut also for the identification of other particles. The kaon ID was tested withthe decay D∗+ → D0π+, followed by D0 → K−π+. The π+ from the firstdecay serves as a charge-tag, being low energetic it can be easily distinguishedfrom the other particles without relying on an ID. The remaining kaon andpion are identified by their charge. Thus the D0 decay can be used for ID-testing. A PID(K) cut above 0.6 yields a kaon efficiency above 80% with apion fake rate below 10%.

29

3 BaBar analysis of the B+ → ℓ+νγ decay

The latest analysis of the B+ → ℓ+νγ decay was performed by the BaBarcollaboration, in which the electron and the muon mode were considered [1].Like the Belle experiment, BaBar operated at the Y(4S) resonance and ithas accumulated a data sample of 465× 106BB pairs, which is used entirelyin this analysis. The BaBar detector is located at the asymmetric PEP-IIe+e− storage ring at SLAC.The BaBar analysis utilizes the LNUGAMMA module for signal Monte Carloproduction (just like this diploma thesis), where two decay models are sim-ulated with either FA = FV or FA = 0. This reduce the model-dependencyto the best possible level. For background simulation large generic and con-tinuum samples with e+e− → τ+τ− and e+e− → qq (q= u, d, s, c) aregenerated. Additionally exclusive B+ → X0

uℓ+ν decays are regarded, where

X0u represents a neutral meson with an up quark as one of its constituents.

The decays with X0u = π0, η turn out to be the most problematic background

sources, comprising 73% and 18% of the semileptonic background respec-tively.The BaBar analysis is done with the hadronic recoil technique, meaning thatone meson of the BB pair is reconstructed exclusively in several hadronicdecay modes, while the signal decay is searched among the other particles.This procedure provides an effective background suppression, while retain-ing a less model-dependent access to the signal decay, without the need formodel-specific constraints on signal side kinematics, especially the angulardistribution of the child particles. The decay channels in which the tag sideis reconstructed, are B’s decaying as B− → D(∗)Xhad on the top level, fol-lowed by decays into different kaon plus pion channels. After the hadronic

reconstruction the variables ∆E = EB − EBEAM and MBC =√

E∗2

c4− (pB

c)2

are demanded to lie within a range around true B meson candidates. Cutsare applied on ∆E to lie within a window of ±0.12 GeV around zero andMBC , the B meson mass, should be above 5.27 GeV. The background in theB meson sample consists of incorrectly reconstructed continuum events andcombinatoric events in which particles from both B mesons are used to forma candidate. For each channel the background shape is extrapolated fromthe sideband distribution in MBC into the signal region above 5.27 GeV andthe distribution is calibrated on data. The sample purity is derived fromfitting these distributions in the MBC mass and it is demanded that the pu-

31

rity in the signal window should be above 12% for each channel. If multiplecandidates fulfill all of theses criteria for the B tag the best one is selected.This results in a B- tag reconstruction efficiency of 0.3%. Continuum back-ground is further reduced with a cut on a likelihood ratio composed of fiveevent-shape variables. This cut also ensures the Monte Carlo and data to bein better agreement, by suppressing unmodeled backgrounds.The signal side events are selected to be consistent with a B+ → ℓ+νγ decay.It is required that the signal lepton track is the only one left after tag sidereconstruction, which removes 99% of the background with an efficiency of25%. Its charge should be opposite to the tag meson and a particle identifi-cation cut is applied. In addition bremsstrahlung photons are added to theelectron four-vector, which are found in a cone around the lepton momentum.The signal photon candidate is demanded to be the cluster with the highestcenter of mass energy. To ensure the events consistency with the presence ofa massless neutrino, the squared missing mass m2 = (pBsig − plepton − pγ)

2

is computed, where the p’s are the four momenta of the signal B meson,pBsig, and its two detectable children. It is required to be -1 GeV2/c4 <m2 < 0.46 (0.41) GeV2/c4 for the electron (muon) mode, since this variablerepresents the neutrino mass. Aside from its mass near zero, an additionalkinematic constraint is set on the neutrino. The angle taken in the frame inwhich the signal B meson recoils from the photon pBsig − pγ, is required tobe cosΘlν < −0.93. The angle Θlν is measured between the missing momen-tum and the lepton momentum. This ensures, that in the rest frame of thelepton-neutrino two body decay the two particles are emitted back to back.These neutrino quality cuts remove 99% of the background with an efficiencyof 30%(20%) for electron (muon) mode.The squared missing mass distribution after all cuts is shown in figure 3.1.The plot shows electron and muon channel. The thick perpendicular lineindicates the performed cut. The signal events are peaking around zero.The background consists of a peaking component with events that have acorrectly reconstructed tag side B meson and a less important non-peakingcontribution containing a continuum background with few events in the sig-nal region, linearly growing to higher values.The two dominant peaking backgrounds not contained in the missing massplots are B+ → π0ℓ+ν and ηℓ+ν. These are analyzed separately in exclusivesamples. The neutral mesons decay mostly into two photons, which fake thesignal photon quite efficiently. To suppress π0 background, events in whichthe signal photon can be combined with a second photon with energy Eγ2 to

32

Figure 3.1: m2miss distributions for electron (upper) and muon (lower) de-

cay channel. The five elements in the plots are: signal Monte Carlo scaled toBR = 40×10−6 (dotted), background peaking in signal region with correctlyreconstructed B tag (shaded), wrong B tag with continuum and combina-toric admixture (solid), data (dots) and the perpendicular line indicates theperformed cut. [1]

a particle with an invariant mass falling into a mass window, are rejected asfollows:

120MeV/c2 < M(π0) < 145MeV/c2 for Eγ2 > 30MeV

100MeV/c2 < M(π0) < 160MeV/c2 for Eγ2 > 80MeV

515MeV/c2 < M(η) < 570MeV/c2 for Eγ2 > 100MeV.

For B+ → ω(π0γ)l+ν, 730MeV/c2 < M(ω) < 830MeV/c2

with a π0: 115MeV/c2 < M(π0) < 145MeV/c2 for Eγ1,Eγ2 > 70MeV in CM.

These criteria reduce the pertaining backgrounds by 65% for π0 and 50% forη and ω. Additionally a veto on the lateral photon moment in the calorimeteris implemented to reject events in which two merged photon are reconstructed

33

as one. The remaining energy deposited in the electromagnetic calorimeterby background photons is required to be below 0.8 GeV, where only photonenergies above 50 MeV are taken into account.The efficiency of the whole procedure is validated with the exclusive B+ →π0ℓ+ν decay, since it is the most similar to the searched signal decay andits branching fraction has already been measured. All cuts except for theπ0 vetoes are applied. The decay peaks in the squared missing mass signalregion similarly like in the signal mode. The selection yields a branchingfraction on data of BR(B+ → π0ℓ+ν) = 7.8+1.7

−1.1 × 10−5, which is compatiblewith the world average value.The cuts are optimized by maximizing the figure of merit defined by Punziin [11]. It reads

FOM =εsigl

12nσ +

√

N bkgl

,

with εsigl as the total signal efficiency, N bkgl the expected background number

in the signal window and nσ the desired significance in standard deviations.The significance is chosen to be nσ = 1.3 without further explanation. Theanalysis is arranged as a counting experiment, where the number of signal,peaking background and continuous background events are counted sepa-rately. The branching fraction is calculated with

BR =N obs

l −N bkgl

εsigl ×NB±,

where N obsl denotes the number of events in the signal box and NB± the

number of charged BB pairs.The estimation of the uncertainties is done individually for the peaking andcombinatoric background contribution. As mentioned above the exclusiveB+ → X0

uℓ+ν decays deliver the largest part of the peaking contribution,

thus the systematic uncertainties of the peaking backgrounds are dominatedby unknown branching fractions and form factors of theses decays. The com-binatoric background’s uncertainty is comprised of errors of the sidebandshape and the method for the extrapolation of this shape into the signal re-gion of the MBC distribution. The combinatoric background is contained inthe generic Monte Carlo which has a negligible peaking component.The branching fractions are computed by the frequentist approach of Feld-man and Cousins [12], and the uncertainties for N bkg

l and εsigl are assumed to

34

be Gaussian. The branching fractions for the two lepton modes are computedseparately and combined. The combined model-independent branching frac-tion is measured to an upper limit with BR(B+ → ℓ+νγ) < 15.6 × 10−6 at90% confidence level. Moreover also a model specific analysis is provided,differing in additional kinematic cuts on angles between the signal particles.Specifically the angles in the B meson rest frame between the photon andlepton (Θγl), and between the photon and neutrino (Θγν) are considered. Forthe FA = 0 model it is required that

(cosΘγl−1)2+(cosΘγν + 1)2

3> 0.4, or (cosΘγν−1)2+

(cosΘγl + 1)2

3> 0.4,

since the lepton is preferred to be emitted with either the photon or theneutrino. For the FA = FV model the lepton is preferably back to back withthe photon, thus only the first angular relationship is required. All resultsare subsumed in figure 3.2.

Figure 3.2: BaBar results for different decay models [1]

35

4 Tag side reconstruction

The analysis performed in this diploma thesis employs the full reconstructionor hadronic recoil technique. The events are in a first step processed withthe full reconstruction tool which was developed at the EKP [4]. The goal isto reconstruct the whole event with both B mesons, where one of the mesonsdecays generically and the other one decays into the signal mode. This isadvisable because of the presence of an undetectable particle in the decay,necessitating a check on the decay kinematics which have to be consistentwith a missing particle, which can only be achieved with knowledge of theentire event. The two B mesons in an event originate from decays of theY(4S) resonance, where the so called tag side B meson is reconstructed inseveral generic decay channels and the other B meson remains as the signalside meson. Quark anti-quark pairs that stem from hadronization processesand do not originate from Y(4S) decays are called continuum events and theyshow a jet like structure due to less massive child particles and therefore anexcess of energy. These continuum events are not correctly reconstructedby the full reconstruction and produce false B meson candidates resultingin a continuous background. They can efficiently be rejected by requiringthe reconstructed B tag meson mass to be correct within a certain window,moreover the signal side selection also decreases these continuous contribu-tions.With this approach the data can be processed in a first step regardless ofthe signal side, looking for these generically decaying particles. After thetag side is successfully reconstructed the momentum of the signal side B isknown due to the simple two-body decay structure. Additionally the numberof tracks in the event is reduced significantly, facilitating the analysis greatly,because all tracks left in the detector have to be counted to the signal side.The tag side mesons are reconstructed in many decay channels, which arechosen by high branching fractions and/or good signal to noise ratio, with de-cay channels comprising less than six children. The total number of channelsis mainly restrained by limited computer resources. The B+ channel includes17 decay channels among the most important, seven D0 channels with one tofour pions, four DS-D

0 modes and four J/Ψ channels with a kaon and zeroto two pions. These modes are processed hierarchically in four steps. In thefirst step the detected decay products from the Belle detector are searchedand basic quality cuts are applied. Afterwards a classification with neuralnetworks is performed for each basic particle type delivering seven networks.

37

These nets are trained by the NeuroBayes software [5] to distinguish betweendifferent particle types and its outputs can be interpreted as probabilities forcertain particle hypotheses with values between zero and one. The inputvariables used in the training are standard particle identification parametersfrequently used in Belle analyzes like, momenta, energies and impact param-eters for the particles considered. After the initial classification the particlesare combined to mother particles and theses mothers are again classified byseparate neural networks. For every particle type and decay channel a sepa-rate network is trained. Afterwards the mother particles are again combinedto heavier particles. This procedure is repeated until at the fourth and laststage the B meson candidate is reached. This approach needs 71 neural net-works to be trained, as opposed to 1104 classification problems a conventionalanalysis had to solve. This reduction is achieved by looking at the differentdecay channels separately only at each stage and then use every stage’s resultas an input parameter for the subsequent one, rather than follow each decaymode through all stages individually. An additional advantage of this proce-dure is the improved discrimination of the networks. Due to the focus on asubproblem the networks are able to get hold of more relevant information,compared to training over the entire problem.On each reconstruction stage soft cuts are applied to reduce the problem. Ingeneral the selection is required to be as universal as possible, to cover thewidest possible range of analyzes on the signal side. The cuts have to balancebetween incurred computing time on subsequent stages, and the number offinally produced B meson candidates. Computing time is a constraint be-cause the number of particle candidates rises exponentially with the levels,what results in a unprocessible amount of data.On the first stage rough cuts on charged kaon PID, a mass constraint forthe π0s and a cut on the impact parameters dz and dr for charged tracksare performed, since only tracks originating from the interaction point are ofinterest.

dr < 2cm, dz < 4cm, ATC PID (Kaon Id)(K, π) > 0.1

0.115 GeV/c2 < m(π0) < 0.153 GeV/c2, Eγ > 30MeV

On the second stage, cuts on the D meson momenta in the Y(4S) frame areintroduced, as high momenta are a clear sign for non-resonant jet-like pro-cesses. Also mass windows are defined for the D mesons, which are looser for

38

lower and tighter for higher background decay channels. Moreover the massdifferences between D∗ and D mesons are cut on.

M(D±,0(s) ± 40MeV/c2and± 60MeV/c2

p∗(D) < 2.6GeV/c

135MeV/c2 < Mdiff(D∗±) < 150MeV/c2

132MeV/c2 < Mdiff(D∗0) < 152MeV/c2

110MeV/c2 < Mdiff(D∗±s ) < 175MeV/c2

On the final stage cuts are applied on the ∆E = EB −EBEAM variable, whichis the energy difference between the B meson candidate’s energy and the

nominal beam energy, and MBC =√

E∗2

c4− (pB

c)2, which is the B meson’s

mass determined from its child momenta and the nominal beam energy.

−150MeV < ∆E < 100MeV

5.22MeV/c2 < MBC < 5.30MeV/c2

All these precuts are chosen to have a signal efficiency of nearly 100%. Apartfrom these precuts a systematic procedure for the precut determination onthe network outputs is introduced. Each mother particle is classified by theproduct of its child particles’ network outputs. Precuts are now performedon theses weights. The cut values are determined to affect each decay modeequally, by demanding a fixed number of additional background events persignal event added for all decay channels. Exemptions from this rule aremade for certain decay modes based on their importance for the subsequentstages and their total event number, where smaller or more important modesare favored with looser cuts. This systematic approach gives a unified mea-sure for decay mode classification and other than the kinematic and particlequality precuts it is meant as a stronger measure to skim the data amountat the expense of not optimal B meson candidates. Compared to the oldfull reconstruction software the luminosity of the Belle experiment has beendoubled with this procedure as can be seen in table 4.1. Furthermore theEKP full reconstruction delivers an additional network output for the B me-son candidate as a quality parameter.

The tag side efficiencies for the full reconstruction are found to differ on

39

Table 4.1: Comparison old vs. new full reconstruction [9]

data and Monte Carlo samples. The discrepancies arise predominantly dueto not precisely known branching fractions, hadronic decay dynamics. A tagside correction function is provided on the Belle web page, rectifying thesediscrepancies between Monte Carlo and data, which is based on [10]. In thepaper the behavior is studied for well known signal side decays, which mini-mizes the uncertainty on the part of the signal side and thus reveals the tagside deviations to the best possible level. As signal side signature charmedsemileptonic decays are used, due to the large branching ratios. In the fol-lowing only the results for charged B mesons are presented, since only theseare of interest in the ensuing analysis. Specifically the following decays areconsidered on the signal side for the charged B meson modes:

B+ → D0(K−π+)lν

D0(K−π+π0)lν

D∗0(D0(K−π+)π0)lν

D∗0(D0(K−π+)γ)lν.

To check the agreement of the tag side between data an Monte Carlo, theevent number ratios NData

NMCfor each channel are evaluated, where the event

numbers factorize as

N(B+ → had,B+ → Xclν) =NBB × BR(B+ → had)× BR(B+ → Xclν)×× εrec(B+ → had,B+ → Xclν).

NBB is the number of reconstructedBB-pairs and εrec describes the combinedefficiency for the signal and tag side decay. The assumption is made that thisjoint efficiency factorizes into separate signal and tag side efficiencies, and acorrelation factor

εrec(B+ → had,B+ → Xclν) = εrec(B+ → had)× εrec(B+ → Xclν)× C.

40

It is further assumed that the behavior for the signal side efficiency and thecorrelation is well described by the Monte Carlo, making only an adjustmentof the hadronic part of the efficiency necessary.The branching fractions for the semileptonic decays in the Monte Carlo arecorrected for the PDG values. The slightly lower number of BB-pairs in theMonte Carlo, some of whom are missed out of unknown reasons, is also takeninto account. For every decay mode on the signal side the squared missingmass distribution is fitted. The found discrepancies for the integrals betweenMonte Carlo and data yield the weighting factor which is averaged over allsemileptonic modes. The results for the single modes plus the averaged valueare seen figure 4.1. The errors in the plot are purely statistical and it is ev-ident that for the high efficiency modes, the factor lies significantly belowone, meaning less reconstructed events in data than in Monte Carlo.The correction factor is furthermore found to be dependent on the net-

Figure 4.1: Data tag side reconstruction efficiencies for different signal sides[10]

work output of the pertaining B meson candidate. The correction factor’sdependency is computed in the following way:

c(x) =fData(x)

fMC(x)= C(x)− FMC(x)

fMC(x)

dC(x)

dx,

where f(x) describes the function of the network output distribution, F (x) is

the integral of the distribution above a cut value x and C(x) = FData(x)FMC(x)

. The

41

result for this weighting function can be seen in figure 4.2 for two exemplaryvery common decay modes with high statistics.All distributions show in principle the same behavior, with a negative sloped

Figure 4.2: Reconstruction efficiency network output dependency [10]

function dropping below one for high network outputs.Aside from statistical errors, also systematics are taken into account. Thesecomprise uncertainties on the branching fraction, the ratio of neutral andcharged B mesons and particle identification cuts which are applied for D∗

meson and kaon selection. The uncertainties for the particle identificationare taken from the tables of the Belle PID group.A function provided by the authors [10], delivers a value which is dependenton the tag sides decay mode and the network output of the full reconstruction.The weight removes all shown biases within the margin of error. The signalto data ratios for the separate signal side decay modes after correction areshown in figure 5.1.

42

Figure 4.3: Data tag side reconstruction efficiencies after weighting [10]

The inner error bars indicate the statistical uncertainty, while the outerones show the combined error. The average ratio of Monte Carlo to dataover all modes for the charged tag side is

NData

NMC

= 1.003± 0.013± 0.034.

43

5 Signal side reconstruction

The signal side decay B+ → ℓ+νγ is analyzed in two decay modes withℓ+ = e+, µ+. The analysis is performed blindly, meaning that the whole pro-cedure is determined and tested on Monte Carlo experiments, before applyingthe findings to the data sample. The τ decay mode is not considered due towidely different decay characteristics of the τ lepton. It has a lifetime shortenough to decay before reaching the detector components. This makes a lep-ton reconstruction necessary, requiring a fundamentally different approachto the analysis, which at the same time decreases the selection efficiency sig-nificantly. Furthermore the τ decay emits at least one additional neutrino.The increase in the number of missing particles to more than one changes themissing mass variable radically, which is a crucial ingredient to this analysiswith one missing particle. Since the B+ → ℓ+νγ branching fractions withℓ+ = e+, µ+ are expected to be of the order of a few times 10−6, a τ decaychannel reconstruction is not accessible with today’s available luminositiesat B-factories. Taking into account the low branching fraction, even for theelectron and muon decay channels considered here, a significant signal is notnecessarily expected to be observed with Belle’s full dataset of 772 ×106BBpairs. BaBar was able to determine an upper limit on the combined branch-ing fractions of both decay channels of 15.6 × 10−6 at 90% confidence levelwith its sample of 465× 106BB pairs.

5.1 General outline of the analysis

The procedure for the signal side analysis is as follows. First of all, signalevents are generated with the LNUGAMMA module for the electron andmuon decay channel. The shape of the generated kinematic distribution iscompared with the latest theoretical prediction. For the background threedifferent Monte Carlo samples are used. These samples and the signal MonteCarlo are processed with the EKP full reconstruction in a first step. Only thetag side B mesons with the highest rank are permitted, meaning the mesonswith the highest network output from the full reconstruction. On the signalside, viable candidates for the decay products of the B meson are lookedfor. These are all gammas recorded in the ECL and for the lepton chargedtracks with loose cuts on the impact parameters, i.e. multiple candidatesper event are allowed initially. Subsequently, skimming cuts are applied to

45

the samples to reduce the data volume, especially for the generic MonteCarlo that contains 5 × 772 × 106 BB events. After this primary selection,successive precuts are applied to the samples. These cuts are determined”by eye“, since they have very large signal efficiencies. These precuts areidentical for the two decay modes, with the exception of a lepton PID cut.The aim is to remove easily distinguishable background events, which is apreparation for a network training. After this, a neural network is trainedfor each channel in a relevant signal region with the NeuroBayes software[5]. The variables for these networks are chosen with great care and they aresimilar for the two decay channels. The network cut is determined with afigure of merit variable defined by Punzi [11]. The final sample selected bythe network cut is fitted in the square missing mass, which is the strongestvariable. For each sample a separate function is used and its parameters arecomputed on Monte Carlo. After the parameters are determined, they areare fixed except for the yields of the functions. With this setup a toy studyis carried out, in which toy Monte Carlo samples are generated with theshapes determined in the analysis. These generated Monte Carlos are fittedwith the parameterized functions and the yields are determined, which givesa measure for the stability of the fit. Furthermore, sidebands are defined inthe samples to check for the consistency of the background shape betweendata and Monte Carlo.

46

5.2 Monte Carlo samples

The Monte Carlo samples are divided into background and signal parts. Thebackground samples are provided by the Belle Collaboration and contain allrelevant decay channels simulating the event. The signal Monte Carlo isgenerated separately with an event generator in its exclusive decay mode.

5.2.1 Background Monte Carlo

The background estimation is done with different sorts of Monte Carlo sam-ples. It is essential to utilize background samples that are as big and diverseas possible, due to the rarity of the signal decay. This helps to diminish sta-tistical uncertainty, by reaching a good statistical representation for unlikelyevents, resulting in smooth signal and background distributions. Taken intoaccount are generic, rare and ulnu Monte Carlo samples; each of these areconstructed to encompass specific background compositions.The generic sample is the most versatile and it contains decays of the Y(4S)resonance into bb quark pairs and also continuum events, where (u,d,s,c)quark pairs are generated. The resonant Y(4S) decays divide into equalamounts of charged B+B− and mixed B0B0, and smaller non-BB contribu-tions. The exact relations for these contributions were determined on earlyBelle data. The generic sample contains only b and b decays into charmquarks which are the most common bottom quark decays. Continuum eventscontaining up, down and strange quark pairs are included in equal amountsand the charmed mode, having the largest cross-section, is added separately.The charm cross-section relative to the uds sample is determined to be 62.2%;this value is taken from the BaBar experiment. Because the continuum eventscreate less massive quarks, they display a jet-like structure, due to an excessof energy available for particle momenta. The sample consists of severalstreams, where one of these corresponds to the whole data sample recordedby the Belle experiment. Each stream consists of several experiments, whichindicate a streak of data taken under stable circumstances with specific de-tector and software calibrations. Due to the earthquake in Japan, instead ofthe original generic samples, already skimmed ones were used. This was anecessary measure to save computing time due to a power shortage at thattime. Five streams of generic Monte Carlo are used in this analysis.The rare Monte Carlo consists of less likely B meson decays with for examplebottom quark transitions into strange quarks, without the common bottom-

47

charm quark transitions that are contained in the generic Monte Carlo. Therare sample contains both signal decay channels with branching fractions of5× 10−6. These are generated with the same module that is used for signalMonte Carlo creation. The rare Monte Carlo contains fifty times the amountof the data sample.The third sample used is the ulnu, which contains charged B mesons decay-ing into semileptonic channels like B+ → X0

uℓ+ν. These events consist of a

lepton neutrino pair and a meson containing an up quark. Especially the π0

and η modes are of interest in this sample, because of their similarity to thesignal decay. The ulnu sample contains twenty streams of data.

5.2.2 Signal Monte Carlo

The Monte Carlo generation works in two steps. In a first step the events aregenerated by the specified decay model obtained from a theoretical prediction(LNUGAMMA in this case). Afterwards this output is fed into a detectorsimulation specifically designed for the pertaining experiment, containing thedetector layout and simulating the particle interaction with its components.As mentioned in chapter 1.2.1 and 1.2.2 the decay model used the LNUGAMMAmodule, contained in the EvtGen Monte Carlo generator, refers to an olderpaper [3]. It includes a mistake in a higher order term of the form factors andalso differs in its precision from latest calculation given in [2]. The impactof these disparities is studied in the following. To check on these differencesthe theoretical prediction is compared to the output of the LNUGAMMAmodule. This comparison is performed on generator level without running adetector simulation on the events.The signal Monte Carlo is produced with the following form factors

FA = FV =1

Eγ

(

Qu ∗R− Qb

mb

)

=1

Eγ

(2

3∗ 3− (−1

3· 15))

,

where R is equivalent to 1λb, Qu and Qb are the constituent quark charges

of the B meson and mb the bottom quark mass. The values chosen for theparameters are R=3 and mb=5 GeV. Constant factors are omitted, since onlythe shape and not the normalization of the decay model are of interest.

48

The form factors for the new model are

FV =QumBfB2EγλB(µ)

R(Eγ, µ) +[


+QumBfB(2Eγ)2

]

FA =QumBfB2EγλB(µ)

R(Eγ, µ) +[


− QumBfB(2Eγ)2

+QlfBEγ

]

,

where the values for all parameters are taken from table 1 in [2]. Since thereis no difference between muon and electron channel (models assume masslessleptons), only the muon channel will be shown. The characteristics of thesetwo models can be seen in figure 5.2, together with events generated with theLNUGAMMA module. The histogram shows the photon energy spectrum in

Photon Energy [GeV]0.5 1.0 1.5 2.0 2.5

Arb

itrar

y U

nits

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

-1810×

MC simulation, 50069 entries

New Decay Model

Old Decay Model

Figure 5.1: Comparison between old decay model (red), new decay model(black) and photon energy spectrum in B meson rest frame from MC simu-lation on generator level (blue)

the B meson rest frame of the generated events above the threshold energyof 350 MeV. The two functions depict the shape of the old and new model.All elements in the plot are normalized to each other. It can be seen that

49

the two theoretical predictions exhibit only minor differences in the shape forthe photon energy distribution. The differences evoked by the higher ordercorrections are thus quite small, as is the effect of the sign error incurred inthe LNUGAMMA module. Although the impact on the shape is quite small,the overall branching fraction decreases with the correction by at least 25%.The signal Monte Carlo is generated with two million events for each chan-nel. In the analysis the signal yield is scaled to the upper limit measured byBaBar, therefore the resulting number should be considered an optimistic es-timate. The scaling factor for the signal Monte Carlo to align the expectationto data is determined as follows

w =NBB × BR(B+ → ℓ+νγ)

Number of generated events

=768× 106 · 16× 10−6

2× 106= 0.006144.

NBB denotes the number of B meson pairs in the full Belle data sample. Itcontains half neutral and half charged B mesons. Only the charged mesonsdecay into the analyzed decay channels, however in an event the signal decaycan occur in both charged mesons, therefore factor of one half cancels withthe doubled probability.

50

5.3 Missing mass variable

After running through the detector simulation, the samples’ squared missingmass distributions (m2

miss) are calculated with

m2miss = (pBsig − plepton − pγ)

2

where the four-momenta of the children of the signal B meson are subtractedfrom the signal B meson four-momentum. The square of this difference givesa value which corresponds to the mass of the unreconstructed particles inthe signal decay. For correct signal decays this particle is a neutrino thatproduces a peak around zero in the m2

miss distribution. Generally the dis-tribution can be interpreted as a parameter indicating the quality of thereconstruction. The more particles are missed, the farther off zero m2

miss willbe.The resulting m2

miss distribution for the electron and muon channel is given

]2 [GeVmiss2m

-5 0 5 10 15 20

Num

ber

of E

ntrie

s

0

1000

2000

3000

4000

5000

6000 , 53468 entriesγ µν +µ →+signal MC B

, 51401 entriesγ eν + e→+signal MC B

Figure 5.2: m2miss distribution for electron (black) and muon (red) Monte

Carlo after skimming cuts

in figure 5.2. The samples shown have undergone rough skimming cuts. The

51

]2 [GeVmiss2m

-2 0 2 4

Num

ber

of E

ntrie

s

0

200

400

600

800

1000

1200

1400

1600SignalMCinfo>0

, 13811 entriesγ µν +µ →+signal MC B


Figure 5.3: m2miss distribution for electron (black) and muon Monte Carlo

(red) with correct signal particle hypotheses

distributions have large tails towards positive masses, which corresponds toevents where parts of the decay products have been missed. This can beascribed to wrong particle hypotheses, where the signal decay particles arewrongly chosen, and/or unused particles either from signal or tag side arepresent in the event. The latter effect is dominated by missed photons re-maining in the calorimeter. On the other hand, negative masses are caseswhere too much energy has been detected, which is caused by detector noiseand energy resolution effects. Thus the deviation to negative masses is farless likely. As already mentioned the electron and muon channel are identicalon the generator level, therefore the differences seen in the m2

miss distribu-tions are caused by the detector simulation. The masses constitute the onlydifference between the two particle sorts, where the muon is roughly 2000times heavier than the electron. The electron’s small mass makes it easierfor external forces to accelerate it, and because accelerated charges emit pho-tons the particle radiates bremsstrahlung. This effect is completely negligiblefor the muon. Therefore the electron has the tendency to lose some amount

52

of its energy before reaching the detector. Furthermore the lepton-matterinteractions in the detector differ widely for the two leptons, causing dif-ferences in detection characteristics. Consequently the electron distributionis prone to higher m2

miss values, what can be attributed mainly to emit-ted bremsstrahlung photons that are not added to the electron energy, thuscausing m2

miss to deviate from zero more often than for muons. This becomesespecially apparent in figure 5.3, where MC matched correct signal eventsare plotted. The muon channel has also about 4% greater efficiency, whichcan be ascribed to the cleaner signal the muon produces in the detector. Itis captured in the KLM and there it can very efficiently be distinguishedfrom kaons. The electron on the other hand is measured in the ECL, wherethe density of detected particles is much higher and thus errors in particledetection are more likely.To clean the signal Monte Carlo from wrong reconstructed events, a MonteCarlo matching variable provided by the EKP full reconstruction is used.This variable can assume integer values codifying several matching constella-tions. Simply put, it assumes negative values if the signal particle candidatesor their relations to mother particles have fundamental flaws. The most im-portant checks are, whether all children are the correct particles for the as-sumed decay, if the particles originate from the designated mother (chargedB meson), if two children are identical and if Monte Carlo information issaved for the decay. The variable mostly becomes positive in cases in whichonly photons are missed not including the signal photon. The matching isnot perfect but it leaves very few wrong events in the signal sample after de-manding a value above zero for the MC matching variable (SignalMCinfo>0).The cleaned distribution is shown in figure 5.3. After the cut on the MonteCarlo matching variable, i.e. for correct particle hypotheses, the tails ofm2

miss

decrease considerably and the distribution contracts to a asymmetric peakaround zero, with a difference still present between the two signal channels.The range is now reduced to a window around -2 and 4 GeV2. This is therelevant region which will be considered in the remainder of the analysis.It turns out that this variable is the strongest available and the goal of theanalysis is to fit the m2

miss to determine the absolute branching fraction ofthe two signal decay channels. The three background Monte Carlo samplesare shown normalized together with the signal sample for the muon mode infigure 5.4. The background shapes look similar, where the ulnu sample ex-hibits a step-like structure at zero. This can be attributed to a larger amountof signal-like decays in the ulnu that produce peaking background. As men-

53

]2 [GeVmiss2m

-2 0 2 4

Num

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of E

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0.00

0.02

0.04

0.06

0.08

0.10




rare MC (no signal decay) , 1.33912e+06 entries

, 1564 entriesγ µν +µ →+rare MC B

Figure 5.4: m2miss distribution for signal (blue), rare signal part (teal), rare

(black), ulnu (green) and generic (red), normalized for the muon channel

tioned above the rare sample contains the signal decay, therefore it is split upinto a signal and a background contribution, with the full reconstruction MCmatching variable which is augmented by a custom stricter MC matching.The rare Monte Carlo contains about one tenth of the events of the signalsample and the shapes of the signal sample and the rare Monte Carlo arein good agreement. For the further analysis the signal portion of the raresample will be filtered out.

54

5.4 Precuts

After the reconstruction, skimming cuts are applied on the samples. It isdemanded that lepton and B meson charges match and that the remainingenergy in the electromagnetic calorimeter (ECL) is below 1.2 GeV. The lattervariable is explained below. The signal lepton selection has weak cuts on theimpact parameters, i.e. the distance perpendicular to the beam, dr, shouldbe below 2 cm and the distance in beam direction, dz, should be shorter than4 cm. No cut is performed on the photon candidates, these are taken directlyfrom the gamma particle lists.For the determination of the precuts, the pertaining variables are plottednormalized with all three background samples and the correct signal MonteCarlo satisfying the MC matching condition (SignalMCinfo>0). The misre-constructed signal decays (SignalMCinfo<0) constitute a negligible amountafter the final selection and will not be shown in the plots. Due to the sim-ilarity of the decay modes the cuts are chosen identically for electron andmuon channel. In this section the n-1 plots of the precuts are given for themuon mode only, the plots for the electron mode are given in section 6.1 inthe appendix. A complete summary of the event numbers in the four samplesafter each precut and the efficiencies for each cut is given in table 5.1. Theefficiencies for signal events for the single precuts are mostly above 95%. Theoverall efficiency for the signal Monte Carlo sample is 71.9% for the muonand 73.7% for the electron channel. In the following the single precuts andthe pertaining variables are discussed.The first cut performed is a best candidate selection for the photon. Eventsin which the signal photon is the highest energetic one are chosen, sinceevents with lower ranked photons are highly populated with background.The missing mass distribution after the cut is seen in figures 5.5 and 6.1.The shape of the distribution does not change discernibly from figure 5.4.This cut gets rid of 32%− 48% of the background in all samples.The second cut is a condition for the remaining charged tracks. In principlethere should be no track left, because no such process could possibly originatefrom a viable candidate. If the track stems from the signal side the eventis definitely wrong. A constellation in which the charged track originatesfrom the tag side with a correct signal side is given for roughly five percentof the signal events. If a particle is sufficiently low energetic it can producea curling track. That track will be detected twice, leading to a remainingtrack even though all charged particles have been reconstructed. Therefore

55

]2 [GeVmiss2m

-2 0 2 4

Num

ber

of E

ntrie

s

0.00

0.02

0.04

0.06

0.08

0.10




rare MC (no signal decay) , 917865 entries

Figure 5.5: m2miss after photon selection

a variable is defined that matches the remaining tracks with the signal sidetracks and counts the number of hits. It is defined as follows

• All charged tracks are compared to signal side tracks

• The tracks should be parallel, i.e. the cosine of the angle between twotracks should be above 0.999

• The transverse momentum difference should be below 30 MeV

• If only one of the tracks has hits in r-phi-plane it is kept (plane per-pendicular to the beam axis)

• Else the track with lower error defined by ( drσdr

)2 + ( dzσdz

)2 is kept

The tag side tracks are not matched among each other, because if a chargedparticle is used twice for the tag side, this case should be handled in thefull reconstruction. Figures 5.6 and 6.2 show the remaining tracks minus thecurling tracks. This variable is required to be zero. This condition givesabout a one percent higher signal and background efficiency, than directlysetting the remaining charged tracks to zero. This is desirable, because the

56

relative reduction of the background should clearly exceed the signal portion.For the third precut the electron Id (muon Id) is required to be below 0.5

No. of Tracks0 2 4 6

Num

ber

of E

ntrie

s

0.0

0.2

0.4

0.6

0.8





Figure 5.6: Remaining charged tracks minus curling tracks (cut == 0)

for the muon (electron) mode. These cuts serve as vetoes for cross-feedsfrom the other signal channel. The Ids comprise gathered information frommany parts of the detector. These variables are standardly provided by theBelle experiment and due to the versatility of the Belle detector, they makepowerful discriminators for leptons. A check of the Monte Carlo truth beforeand after the cut shows that the cut has an effect exclusively on the leptoncomposition of the background samples. The cut impacts mainly ulnu andgeneric backgrounds with a reduction of 32% and 40%. These backgroundstend to have events with good electrons and muons. The rare background isnot affected because it has bad values for both the electron and the muon idvariable. The distribution can be seen in figures 5.7 and 6.3 for electron andmuon channel respectively.

57

Electron Id Value0.0 0.5 1.0

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of E

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0.0

0.2

0.4

0.6

0.8





Figure 5.7: Electron Id (cut < 0.5)

Muon Id Value0.0 0.5 1.0

Num

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of E

ntrie

s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9rare MC (no signal decay) , 153835 entries




Figure 5.8: Muon Id (cut > 0.5)

58

The next cut is performed on the muon Id (electron Id) which should begreater than 0.5 for the muon (electron) channel. This serves as a qualitycut for the signal lepton. The distributions for both channels are given infigures 5.8 and 6.4. Nearly all of the rare Monte Carlo is sorted out withthis condition. The efficiencies for the other samples are comparable to theprevious cut.After the quality cuts for the lepton, quality cuts for the signal photon areapplied. The first one is a minimum energy cut on the photon in the restframe of the B meson. This cut serves two purposes. Firstly, events withlow energetic signal photon candidates are highly polluted with background,since photons with a low energy stemming directly from a three body decayof a B meson are rare. Secondly, because the signal Monte Carlo is producedwith photon energies above 350 MeV, it makes sense to consider only thisrange. The cut is performed above an energy of 400 MeV.

Photon Energy [GeV]1 2

Num

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of E

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s

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16





Figure 5.9: Signal photon energy in B meson rest frame (cut > 0.4 GeV)

The distribution is given in figure 5.9 and 6.5. The step in the signal shapeoriginates from the just mentioned production threshold. Events below 350MeV are populated by the detector simulation in which the original energyis altered to lower values. The cut on the signal photon energy is especially

59

effective on the ulnu sample, which is in general more resistant to the cuttingprocedure. This is due to the fact that all signal photons candidates in theulnu originate from mesonic decays, namely π0 and η particles, which tendto be lower energetic.Another quality cut for the signal photon is preformed on a network out-put, which is provided by the EKP full reconstruction. There it serves as adiscriminator for true photons on the first level of the tag side reconstruc-tion. The network is not decay specific, but a general measure for photonquality and it has been trained with the NeuroBayes software [5]. The mostimportant variables included are:

• ECL energy in the seed cell, which is the cell with the highest energydeposit for the energy cluster

• ECL RMS of the shower width

•E9

E25, this is the relation of the energy deposit in 3 × 3 to a 5 × 5 tile

array in the ECL

• ECL AUX ID of the seed cell,

• number of crystals in the cluster

• ECL energy in the cluster

• transverse momentum

• Ks finder variables for converted photon categorization

The network captures the signature of a photon in the electromagnetic calorime-ter through shower shapes and general kinematic variables. The output isshown in figures 5.10 and 6.6 and the cut is made above 0.4. Nearly nosignal is lost with this cut and especially the generic and rare background isreduced, since most of the ulnu events have true photon candidates. A MonteCarlo matching reveals that the network cut filters most of the false photonsand also beam related background. The number of events with correct signalphoton candidates nearly does not change at all. This illustrates that thiscut focuses just like the lepton Id cuts, only on candidate quality and not ondecay specific dynamics. The two photon quality cuts remove about half ofthe events in all background samples.

60

Network Ouput0.2 0.4 0.6 0.8

Num

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of E

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0.10

0.15

0.20





Figure 5.10: Signal photon full reconstruction network output (cut > 0.4)

Another cut is performed on the extra energy in the electromagneticcalorimeter (ECL) additionally to the skimming cut, to filter events with toohigh background levels. This variable counts the energy of remaining energyclusters in the ECL above certain energy thresholds after event reconstruc-tion. The thresholds differ for the forward and backward cap, and barrelregion of the detector. The specific values are a standard definition which iswidely used in the Belle collaboration. They are optimized to enhance thephysical content of the variable by avoiding polluting fluctuations and beamrelated background. The ECL variable counts the following clusters

• Θ > 0.216 and Θ < 0.548 and E>100 MeV forward end-cap

• Θ > 0.562 and Θ < 2.246 and E>50 MeV barrel

• Θ > 2.281 and Θ < 2.707 and E>150 MeV backward end-cap

The plot of this variable is shown in figures 5.11 and 6.7. The remainingenergy is selected to be below 0.9 GeV, which removes 22% − 36% of thebackground. For the entries exactly at zero no cluster above the thresholdcuts is measured in the event. The gap is due to the minimal energy thresholdof 50 MeV which has to be satisfied. The background and signal separates

61

nicely in this distribution and it would be conceivable to fit this variableinstead of m2

miss. However this distribution has the drawback, that it reliesvery much on background shapes which are less predictable.

Energy [GeV]0.0 0.5 1.0

Num

ber

of E

ntrie

s

0.000.020.040.060.080.100.120.140.160.180.200.22





Figure 5.11: Extra energy in the electromagnetic calorimeter (cut < 0.9 GeV)

The next cut is performed on the angle between the signal lepton andphoton in the rest frame of the signal B meson. Although this analysisshould not rely too much on kinematic distributions among the child parti-cles, it is evident due to the helicity that the lepton and the photon shouldfly in different directions. The cut applied demands the cosine of the angleto be below 0.6. The plot is shown in figures 5.12 and 6.8. The cut has asignal efficiency near one and sorts out 4% − 8% of the background. Thebackground samples in the electron channel have significantly more events inwhich lepton and photon are in parallel. That is because of bremsstrahlungthat is emitted by the electron along its trajectory and which in some casesis identified as a signal photon candidate.The last cut is a quality cut for the B meson on the tag side. Its mass

is required to lie above 5.27 GeV, removing most of the combinatoric back-ground of the tag side B meson reconstruction. This background consists of

62

Muon channel

Cuts Event numbers Efficiencies Puritysignal generic ulnu rare signal generic ulnu rare

Initial 13811 268424 600178 1339120 - - - - 0.006Best. Photon 13137 166170 380464 917865 0.951 0.619 0.634 0.685 0.009Tracks 12543 123180 92527 158439 0.955 0.741 0.243 0.173 0.034eid 12543 83695 55142 153835 1.000 0.679 0.596 0.971 0.043muid 11476 58062 43308 7524 0.915 0.694 0.785 0.049 0.105Photon En. 11005 43128 20902 4716 0.959 0.743 0.483 0.627 0.160Photon net 10981 30868 19005 4034 0.998 0.716 0.909 0.855 0.204Energy Ecl 10633 19801 14801 2674 0.968 0.641 0.779 0.663 0.285Angle lep gam 10596 18171 14344 2575 0.997 0.918 0.969 0.963 0.302Tag side mass 9930 6550 8923 1328 0.937 0.360 0.622 0.516 0.591

Overall efficiencies: 0.719 0.024 0.015 0.00099

Electron channel

Cuts Event numbers Efficiencies Puritysignal generic ulnu rare signal generic ulnu rare

Initial 12520 265361 594117 1329670 - - - - 0.006Best. Photon 11857 164204 376829 910682 0.947 0.619 0.634 0.685 0.008Tracks 11260 121674 91844 157846 0.950 0.741 0.244 0.173 0.030muid 11257 64180 48803 149108 1.000 0.527 0.531 0.945 0.043eid 10781 38882 37099 3419 0.958 0.606 0.760 0.023 0.136Photon En. 10342 30348 18690 2311 0.959 0.781 0.504 0.676 0.201Photon net 10318 20123 16957 1823 0.998 0.663 0.907 0.789 0.265Energy Ecl 9943 13163 13226 1240 0.964 0.654 0.780 0.680 0.360Angle lep gam 9882 12056 12665 1142 0.994 0.916 0.958 0.921 0.382Tag side mass 9233 4843 8001 441 0.934 0.402 0.632 0.386 0.695

Overall efficiencies: 0.737 0.018 0.013 0.00033

Table 5.1: Event numbers, efficiencies and purities for every precut stage forthe electron and muon channel

63

cos(angle)-1.0 -0.5 0.0 0.5 1.0

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0.15

0.20

0.25 rare MC (no signal decay) , 2674 entries




Figure 5.12: Cosine of the angle between signal lepton and gamma (cut <0.6)

B mesons which have been reconstructed with cross-fed particles from thesignal side. The mass region below 5.27 GeV will be retained as a sidebandfor consistency checks on data. The plot is seen in figures 5.13 and 6.9.37%− 62% of the background is rejected by this condition.The overall background efficiencies are in the percent range for generic andulnu and even lower for the rare Monte Carlo in both channels. The impor-tant contributions are the ulnu and generic sample, the rare contribution issmaller. The m2

miss distribution for muons after all precuts with the expectedturnout on data is shown in figure 5.14 in this section and for the electronchannel in figure 6.10 in section 6.1. To obtain the expectation on data, thegeneric MC is weighted by 1

5, the ulnu MC by 1

20, the rare MC by 1

50and the

signal MC by 0.006144 as computed in section 5.2.2.

64

]2B-Tag Mass [GeV/c5.22 5.24 5.26 5.28

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0.02

0.03

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0.07

0.08





Figure 5.13: B meson mass of the tag side (cut > 5.27 GeV)

]2 [GeVmiss2m

-2 0 2 4

Num

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xpec

ted

Eve

nts

0

10

20

30

40





Figure 5.14: m2miss distribution for the muon channel after precuts with the

expected data yields

65

5.5 Network training

After the samples are cleaned of easily separable backgrounds with the pre-cuts, a neural network is trained. The training is performed in the m2

miss

region below 1 GeV2 in which most of the signal events are contained ina peaking shape. In this chapter the procedure is outlined for the muonchannel, all plots and specific information for the electron channel is givenin chapter 6.2 in the appendix. The most numerous backgrounds are thegeneric and the ulnu sample, the rare Monte Carlo gives a smaller contri-bution. To check which variables are sensible for a discrimination, a MonteCarlo matching is carried out in the relevant region for the muon channel. Ta-ble 5.2 shows the most important contributions. Shown are the percentagesof gamma candidates which are real photons and the mothers of these candi-dates, additionally the lepton candidates are listed. The differences betweenpositive and negative lepton charges are due to statistical fluctuations. Onthe photonic side, the two important backgrounds exhibit a common struc-ture. Most of the candidates are real photons and most of them originatefrom π0 and η decays. The leptonic side is more diverse, but at least forthe ulnu sample nearly all events contain muons which have a charged Bmeson as their mother. Thus the ulnu sample’s leptonic part of the signalside is identical to correct signal events, making the ulnu background muchmore problematic. This is especially true if the child photon of the mesonicdecay mimics the signal photon. These consideration apply identically to theelectron channel.The important π0 and η distributions of the ulnu background are shown infigure 5.15. The distributions are obtained through Monte Carlo matching,where the following criteria have to be met: the correct photon is comingfrom a π0 or an η, which in turn originates from a charged B, the lepton iscorrect and comes from a charged B meson. It can be seen that only theulnu backgrounds survive this cut, exhibiting a distinct class of events thatprevail. The π0 events are a little closer to zero than the η events, due totheir lower meson mass. The generic background is of a mixed nature and,as it turns out, poses less of a problem for a network discrimination.These results show that a good way to tackle the background is to find

an effective π0 and η veto. For both signal channels, variables used for thenetwork training are the π0 and η masses that are calculated through thecombination of the signal photon candidate with one of the remaining pho-tons in the event. Combinations with all background photons are calculated

66

Gamma CandidateRare Generic Ulnu93.8% γ 82% γ 98.8% γ− > 26.5% π0 − > 90.6% π0 − > 73.3% π0

− > 28.6% B+ − > 5% η − > 23% η− > 22% B− - -

Lepton CandidateRare Generic Ulnu26.5% π+ 23.5% π− 51.8% µ+

25.3% K+ 20% K+ − > 96.2%B+

23.3% π− 17.3% π+ 48.1% µ−

16% K− 15.5% µ− − > 94.7%B−

- 10.8% K− -- 10.8% µ+ -

No. expected eventsRare Generic Ulnu5.14 64.6 115.55

Table 5.2: Signal particle composition obtained from MC matching of thethree background samples for the signal selection with MissingMass < 1 GeV2

for the muon channel

and the π0 (η) candidate with a mass closest to the nominal energy of 135MeV (550 MeV) is kept. This procedure has the risk that artificial peakscan be produced through mere combinatorics, because if the number of back-ground photons in the event is large, the probability grows that a candidateclose to the nominal mass can be constructed. Therefore variables with en-ergy thresholds for the background photons are also computed, reducing thenumber of combinations in an event. These energy thresholds are chosen in10 MeV steps starting at zero and their performance is tested in several net-work trainings. The ones with the best results, according to NeuroBayes, arekept. The cuts on the background photons are chosen higher in the η-casedue to higher energetic daughters. Two examples for this set of variables areshown in figure 5.16 normalized for the pion case. The first one is without

67

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, 187 events0π µν +µ →+ulnu MC B

, 77.65 eventsη µν +µ →+ulnu MC B

Figure 5.15: m2miss distribution of signal (blue), MC matched π0 contribution

from ulnu (green) and generic (red), and η contribution from ulnu (black)with expected yields on data for the muon channel

any cuts on the background photons, the second one has a cut at 90 MeV.The background samples peak nicely at the nominal pion mass of 135 MeV.The signal Monte Carlo distribution should not exhibit a peak at the pionmass, however a bulging shape in the signal can be seen in figure 5.16a forthe variable without any cut. A clear decrease in combinatorics can be seenin figure 5.16b for a cut on the background photon energy, where the shape ofthe signal Monte Carlo becomes very flat over the whole range. Furthermoreat the higher energetic cut, a peak for the η mass at 550 MeV shows up, forwhich this variable does not optimize. This is an additional sign that thisvariable is not a pure result of combinatorics but that real physical infor-mation is contained in it. Monte Carlo matching of the ulnu sample for etaand pion decays confirm that the peaks consist mostly of events containingthe searched mesons. Also added into the network training is a pion massreconstruction with a combination of just two background photons above anenergy of 75 MeV. A disadvantage of these variables could be that these

68

pion vetoes carry information about background photon shapes, which couldexhibit differences when compared to data.Besides the mass variables for the mesons, the angular information between

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Figure 5.16: Pion mass with and without energy cut on background photonnormalized for the muon channel; signal (blue), ulnu (green), generic (red),rare (black)

the two daughter candidate photons of the pion is utilized. A decay angle isdefined as the angle between the two daughter photons of the π0, where oneof the daughters is boosted into the rest frame of the π0 before computingthe angle. This angle is a measure for the energy asymmetry between thedaughter photons and it tends to be lower for true π0 processes. The angleis only used in the muon channel, due to low significance for the electronmode. Several other angular constellations in various reference frames weretested, but none was found to deliver a good discriminator. The remainingvariables used in the training are already used for the precuts. The completelist of variables sorted by the importance for the muon case is:

• m(π0) reconstructed with the signal photon and a background photonabove 60 MeV

• Extra energy in the electromagnetic calorimeter as defined above

69

• Signal photon energy in the B meson rest frame

• m(π0) reconstructed with the signal photon and any background photon

• m(η) reconstructed with the signal photon and a background photonabove 200 MeV


• Muon Id

• m(π0) reconstructed from two background photons above 75 MeV

• m(π0) reconstructed with signal photon and background photon above90 MeV

• Decay angle of the daughter photons of a π0 candidate reconstructedwith the signal photon and any background photon

• Network output for the signal photon from the full reconstruction

All variables used in the network training must be more or less uncorrelatedto the fitting variable which is m2

miss, to avoid a distortion of this distributionby aligning the background and signal shapes. Without any differences inthe shapes the distribution becomes unfittable and moreover the distortioncan differ unpredictably on data, making the fit unreliable. However, thedistinction between what kind of correlation is permissible, is not clear cutand has to be decided in a more qualitative way. A check on the correlationof the network to m2

miss can be done by training the signal region of m2miss

against its sideband. The network output for the sideband versus signalregion training for the variables listed above is shown in figure 5.17, wherethe signal region is below 1 GeV2 and the sideband is between 1 GeV2 and2 GeV2 in the m2

miss distribution. Despite the diligence in picking variablesnot too strongly correlated to m2

miss, the network is still able to separate thetwo regions. However, the distortion of the distribution after the final cuton the network is completely admissible. No variable regarding the leptonmomentum or its energy is used, although performing well in the training,due to the strong correlation tom2

miss. This is because the lepton carries mostof the momentum in the event and thus contributes most to m2

miss. This isto a lesser extent also true for the signal photon energy, however the effect

70

Figure 5.17: Network output for sideband vs. signal region training for themuon channel

on the shape of m2miss after a cut on the network is acceptable.

The training and the analysis are performed on separate samples, to avoidthe network learning specific sample fluctuations. Therefore each sample issplit into two samples of equal size by dividing the events in a changing orderto a training and an analysis sample. The network outputs stemming froma training carried out on the training sample are shown in figure 5.18, wherethe analysis sample is depicted in the stacked histogram and the trainingsample is shown with the black dots. The network outputs are in goodagreement between these samples, showing that the training is independentof fluctuations and stable.The training is performed with all background samples at once, where eachsample receives a weight. The weights are chosen to be 2 for the ulnu and1 for the remaining two background samples and the signal sample. Thischoice is made by maximizing the network’s ability to produce a good valuefor the figure of merit. The weighting of the backgrounds to their appropriatenumbers on data, i.e. 1

5for generic, 1

20for ulnu and 1

50for the rare, delivers

a worse result. The ulnu sample has the most difficult background and itsover-representation helps the network to concentrate on this part, since themore easily separable background will be discriminated anyway.

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Network Output0.0 0.2 0.4 0.6 0.8 1.0

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ulnu MC , 451 events


Figure 5.18: Network output for the analysis sample stacked histogram withsignal (blue), ulnu (green), generic (red), rare (black) and the stacked trainingsample (data pionts) weighted to expectation on data for the muon channel

The cut on the network output is optimized with a figure of merit defined byPunzi in [11]. The definition reads

FOM =εsigl

12nσ +

√

N bkgl

,

where εsigl denotes the signal efficiency, nσ the desired sigma value for the

significance, which is chosen to be 3σ in our case, and N bkgl the number of

background events in the signal region. The value for the figure of merit isplotted against the network cut in figure 5.19. The figure of merit is computedon the analysis samples with the appropriate weighting of the Monte Carlosamples that reproduces the data sample. The peaking region is relativelybroad and the maximum lies at 0.69, which will be rounded to 0.7.The m2

miss distribution of the analysis sample with this optimized cut isshown in figure 5.20 and the efficiencies are given in table 5.3. In this final

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network cut0.0 0.5 1.0

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Figure 5.19: Figure of merit value vs. network cut for the muon channel

selection only the ulnu and generic background samples are left in largeramounts. The overall signal efficiency from generation to the final selectionis about 0.4% for both signal Monte Carlo samplesAs discussed in section 4 there is a difference in the yields on Monte Carloand data for the full reconstruction. This discrepancy is alleviated with afunction provided by [10]. This function depends on the decay channel of thetag side and the network output for the B meson candidate. The weightingdoes only apply to decays at the Y(4S) resonance, thus the non-resonantlyproduced background will be kept unaltered. The weighting factor for thetraining sample is plotted in figure 5.21. On average the weighting reducesthe yield by a factor of 0.7. The m2

miss distribution, which can be seenin figure 5.22, does not change considerably in shape after the correctiveweighting is applied.

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rare MC (no signal decay) , 4 events

Figure 5.20: m2miss distribution after figure of merit cut weighted to expecta-

tion on data for the muon channel

Events numberssignal generic ulnu rare

After precuts 9930 6550 8923 1328Fom network cut 7846 1598 2206 200Efficiencies 0.790 0.244 0.247 0.151

Table 5.3: Parameters of the network cut for the muon channel

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Figure 5.22: m2miss distribution after tag side correction for the muon channel

weighted to expectancy on data

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5.6 Fitting

The fitting is done with RooFit, a software extension for Root. At first thesamples are fitted separately and the parameters for the fit functions aredetermined. Afterwards all parameters except for the yields are fixed andthe bias of the fit functions is checked in toy Monte Carlo studies. Since thereis no underlying basic physical process to the shape of the m2

miss distribution,but rather a host of effects that are not quantifiable, the functions for thedistributions are chosen to approximate the different contributions. Thecombination of the function set used has no deeper physical meaning. Thefitting results in this section will be given for the muon channel, the fits forthe electron channel are given in section 6.3.The generic Monte Carlo displays a polynomial shape growing large to higherm2

miss values, while the ulnu has a more intricate shape showing a bumpslightly above zero with a maximum at 0.5 and a slowly declining tail. Thisconcentration around zero is due to the similarity of the π0/η ℓ+ν decays tothe signal decay. The decay products are identical apart from an additionalphoton, therefore the ulnu Monte Carlo delivers good m2

miss values which isshown in figure 5.15 for the separate pion and eta components. The signalMonte Carlo has an asymmetric Gaussian shape with a larger tail to highermasses, caused by events in which a number of decay products have beenmissed and a small extension to negative values. A more detailed descriptionfor this shape is given in section 5.3. The rare Monte Carlo is of similarshape as the generic sample, but it is scarce enough to be disregarded in thefinal fit.The signal shape is fitted with a crystal ball function, which is often used

for lossy processes. It is akin to a Gaussian distribution with an asymmetrictail. It has the form

f(x;α, n, x, σ) = N ·

exp(− (x−x)2

2σ2 ), for x−xσ

> −α

A · (B − x−xσ)−n, for x−x

σ≤ −α

where

A =

(

n

|α|

)n

· exp(

−|α|22

)

,

B =n

|α| − |α| .

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Figure 5.23: Signal fit for the muon with crystal ball function (black), Gaus-sian contribution (green), sum distribution (blue) and muon signal sample(black data points)

The crystal ball function alone does not suffice to fit the signal, therefore aGaussian function is added to it. This function accounts for the small tailat negative masses. The result can be seen in figures 5.23 and 6.14. The fitreproduces the shape well, apart from a slight deviation at the left footingof the distribution.The ulnu Monte Carlo is fitted with a Novosibirsk function, that is a functionof the form

f(x; peak,width, tail) =

e−0.5( x−peakwidth

)2·tail, for tail < 10−7

e−0.5(ln(qy)

tail)2+tail2 , for tail > 10−7

qy = 1 + tail · x− peak

width· sinh(tail ·

√

ln(4))

tail ·√

ln(4).

77

To this function an additional small constant contribution is added, whichaccounts for a few events on the negative side of the m2

miss distribution, help-ing the Novosibirsk function to converge. The fit reflects the shape of theulnu background well, as it is illustrated in figure 5.24 and 6.15.The generic Monte Carlo is fitted with a custom made third order polyno-

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Figure 5.24: Ulnu fit with Novosibirsk function (blue), constant contribution(green), sum distribution (blue) and muon ulnu sample (black points)

mial, which works like a usual polynomial except that negative values are setto zero. This is necessary because there are few to no events on the negativeend of the m2

miss distribution, causing a Chebycheff polynomial to assumenegative values in that region. The fit is depicted in figure 5.25 and 6.16.With the three fitted functions a Monte Carlo study is performed. This

technique generates many toy Monte Carlo samples according to the shapesprovided by the functions. These generated samples are fitted with the orig-inal functions, with the yield as the only free parameter. Ideally, the fittingshould on average reproduce the input yields for the signal and each back-

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Figure 5.25: Generic fit with third order polynomial (blue) and muon genericsample (black data points)

ground component. If unbiased, the pull distribution should be fittable bya Gaussian distribution with a mean of zero and an error of one σ. Thevalues of the pull are computed by subtracting the yields by their mean andthen dividing them by their error. The bias is checked for several possiblescenarios in different toy studies. The number of signal decays is varied to:the expected BaBar limit to which the network cut has been optimized, onethird of the BaBar limit which is closer to the favored theoretical value andto no signal at all. Overall 1000 toy Monte Carlos are generated and fittedfor each toy study.For the background components the fitting works well for all signal decaynumbers and for both decay channels. This is shown for the muon channelin figures 5.27, 5.29, 5.31 and for the electron channel in figures 5.33, 5.35,5.37. All fit results are summarized in table 5.5 for the ulnu sample and intable 5.6 for the generic sample.

79

The summary of the fit results for the signal Monte Carlo can be found in ta-ble 5.4. Generally the fitting works better for the muon channel than it doesfor the electron channel and it deteriorates for both channels with decliningnumber of signal events. At the BaBar limit, the fits deliver good results,where the pull distributions look unbiased for muon (figure 5.26) and electronmode (5.32). At one third of that limit the fitting of the muon channel stilldelivers good values (figure 5.28), whereas for the electron channel the pulldistribution becomes a little bit biased (figure 6.29). However, the means ofthe yields are in very good agreement for both signal channels. For zero sig-nal events the pull distributions are not Gaussian anymore in both channels,which is shown in figure 6.23 and (figure 6.32) for muon and electron channelrespectively. The fits are biased towards smaller values, but the means of theyields are within two sigma of the true value. The biases will be consideredas systematic errors. All in all the fits perform well for both channels.The complete results for the toy studies of each fitted component are shownfor the muon mode in section 6.4 and for the electron mode in section 6.5.The figures consist of four panels, where the upper left panel shows the resultsfor the yields from the fitting procedure, the upper right panel the accord-ing error to the fitting results, the lower left panel the pull distribution andthe lower right panel the input yield parameter for the toy generation, thecomponent name and the cuts applied.

Muon channel

No. of signal events 37.67 12.43 0Yields mean 37.6± 0.31 12.64± 0.23 −0.50± 0.21Error mean 10.03± 0.03 7.74± 0.03 5.39± 0.03Pull mean −0.076± 0.03 −0.08± 0.03 −0.22± 0.04Pull sigma 1.01± 0.03 1.05± 0.02 1.20± 0.03

Electron channel

No. of signal events 35.41 11.68 0Yields mean 35.43± 0.26 11.65± 0.29 −0.56± 0.23Error mean 11.47± 0.03 8.61± 0.04 6.56± 0.04Pull mean −0.077± 0.03 −0.13± 0.04 −0.22± 0.04Pull sigma 1.03± 0.02 1.1± 0.03 1.14± 0.03

Table 5.4: Fit results for the signal Monte Carlo

80

Muon channel

No. of signal events: 87.37 Complete signal Signal at one third No signalYields mean 86.94± 0.61 86.78± 0.8 88.43± 0.82Error mean 27.32± 0.04 25.29± 0.04 23.98± 0.05Pull mean −0.04± 0.03 −0.055± 0.03 −0.001± 0.034Pull sigma 1.01± 0.02 1.00± 0.02 1.07± 0.02

Electron channel

No. of signal events: 77.81 Complete signal Signal at one third No signalYields mean 80.21± 0.87 78.46± 0.84 79.29± 0.56Error mean 28.07± 0.04 25.52± 0.04 23.89± 0.05Pull mean 0.06± 0.03 −0.003± 0.033 0.02± 0.03Pull sigma 0.99± 0.02 1.05± 0.02 1.05± 0.02

Table 5.5: Fit results for the ulnu sample

Muon channel

No. of generic events: 276.28 Complete signal Signal at one third No signalYields mean 275.6± 0.57 277.34± 0.82 276.13± 0.82Error mean 26.16± 0.02 25.52± 0.03 25.01± 0.03Pull mean −0.04± 0.03 0.02± 0.03 −0.03± 0.03Pull sigma 0.98± 0.02 1.01± 0.02 1.04± 0.02

Electron channel

No. of signal events: 187.34 Complete signal Signal at one third No signalYields mean 187.9± 0.55 188.06± 0.74 186.6± 0.72Error mean 23.8± 0.03 23.02± 0.03 22.44± 0.03Pull mean 0.002± 0.032 0.01± 0.03 −0.05± 0.03Pull sigma 1.03± 0.02 1.02± 0.02 1.02± 0.02

Table 5.6: Fit results for the generic sample

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-4 -2 0 2 40

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60 0.032±pullMean = -0.0764

0.023±pullSigma = 1.009

Figure 5.26: Signal sample pull distribution for the muon channel with signalnumbers at BaBar limit

-4 -2 0 2 40

10

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30

40

50

0.032±pullMean = -0.0442

0.023±pullSigma = 1.009

-4 -3 -2 -1 0 1 2 30

10

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30

40

50

0.031±pullMean = -0.0444

0.022±pullSigma = 0.981

Figure 5.27: Pull distributions for the muon channel ulnu MC (left) andgeneric MC (right) with signal numbers at BaBar limit

82

-4 -2 0 2 40

10

20

30

40

50

60

70 0.033±pullMean = -0.0830

0.023±pullSigma = 1.050

Figure 5.28: Signal sample pull distribution for the muon channel with signalnumbers at one third of the BaBar limit

-3 -2 -1 0 1 2 30

5

10

15

20

25

30

35

40

45

0.032±pullMean = -0.0548

0.022±pullSigma = 1.000

-3 -2 -1 0 1 2 30

10

20

30

40

50

0.032±pullMean = 0.022

0.023±pullSigma = 1.014

Figure 5.29: Pull distributions for the muon channel ulnu MC (left) andgeneric MC (right) with signal numbers at one third of the BaBar limit

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-5 0 50

20

40

60

80

100

0.038±pullMean = -0.2173

0.027±pullSigma = 1.203

Figure 5.30: Signal sample pull distribution for the muon channel with nosignal

-6 -4 -2 0 2 4 60

10

20

30

40

50

60

70

0.034±pullMean = -0.0014

0.024±pullSigma = 1.066

-4 -2 0 2 40

10

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30

40

50

60 0.033±pullMean = -0.0245

0.023±pullSigma = 1.038

Figure 5.31: Pull distributions for the muon channel ulnu MC (left) andgeneric MC (right) with no signal

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-4 -2 0 2 40

10

20

30

40

50

60

0.032±pullMean = -0.0770

0.023±pullSigma = 1.027

Figure 5.32: Signal sample pull distribution for the electron channel withsignal numbers at BaBar limit

-3 -2 -1 0 1 2 30

10

20

30

40

50

0.031±pullMean = 0.060

0.022±pullSigma = 0.987

-4 -3 -2 -1 0 1 2 3 40

10

20

30

40

50

0.032±pullMean = 0.002

0.023±pullSigma = 1.025

Figure 5.33: Pull distributions for the electron channel ulnu MC (left) andgeneric MC (right) with signal numbers at BaBar limit

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-4 -2 0 2 40

10

20

30

40

50

60

0.035±pullMean = -0.1255

0.025±pullSigma = 1.102

Figure 5.34: Signal sample pull distribution for the electron channel withsignal numbers at one third of the BaBar limit

-4 -2 0 2 40

10

20

30

40

50

0.033±pullMean = -0.0032

0.023±pullSigma = 1.046

-4 -2 0 2 40

10

20

30

40

50

0.032±pullMean = 0.009

0.023±pullSigma = 1.016

Figure 5.35: Pull distributions for the electron channel ulnu MC (left) andgeneric MC (right) with signal numbers at one third of the BaBar limit

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-6 -4 -2 0 2 40

10

20

30

40

50

60

70 0.036±pullMean = -0.2160

0.026±pullSigma = 1.141

Figure 5.36: Signal sample pull distribution for the electron channel with nosignal

-4 -3 -2 -1 0 1 2 3 40

10

20

30

40

50

0.033±pullMean = 0.024

0.023±pullSigma = 1.048

-4 -2 0 2 40

10

20

30

40

50

60

0.032±pullMean = -0.0529

0.023±pullSigma = 1.023

Figure 5.37: Pull distributions for the electron channel ulnu MC (left) andgeneric MC (right) with no signal

87

5.7 Sideband consistency check

After the procedure is worked out, the sideband shapes are compared betweenthe Monte Carlo and data sample. The sidebands are checked for threevariables: the network output, m2

miss and the B meson mass of the tag side.All possible combinations of the cuts

• m2miss ≶ 1 GeV2

• Network output ≶ 0.7

• Tag side B meson mass ≶ 5.27 GeV

are checked on these variables which do not include the signal region, withthe signal region being defined as: m2

miss < 1 GeV2, network output > 0.7and B meson mass > 5.27 GeV.The overall efficiency is larger on data than on Monte Carlo. This can be seen

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Figure 5.38: m2miss distribution for the electron channel with network

output<0.7 weighted to expected yields (left) and normalized (right), withsignal (blue), ulnu (green), generic (red), rare, (black) and data (dots)

examplarily in figure 5.38 for one sideband of the m2miss distribution of the

electron channel, where the left panel shows the unnormalized and the rightpanel the normalized distributions. All sideband plots show the correctlyweighted Monte Carlo samples stacked together, with the data sample drawn

88

as black data points with Poisson errors. If normalized, data and Monte Carloseem in good agreement. In the following only the shapes of the distributionsare checked and therefore all further results are shown normalized.For the electron channel the remaining results are shown in section 6.6 inthe appendix, where all possible sidebands for m2

miss and one sideband forthe B-tag mass and the network output are shown. The electron mode hasa good agreement between data and Monte Carlo shapes for all sidebands.In the muon channel the m2

miss distribution has an unexpected feature in thedata sample. It shows up as a peak in a very narrow range near zero fordistributions containing the whole B meson mass sideband below 5.27 GeV,as seen in figure 5.39a.

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0.035 Stacked Plot --- Tagside-Corrected --- BTagMbc<5.27&&net1<0.7






(b) netout < 0.7 and B meson mass < 5.27 GeV

Figure 5.39: m2miss distribution for the muon channel weighted to expected

yields, with signal (blue), ulnu (green), generic (red), rare, (black) and data(dots)

The peak prevails if additionally a cut on the network below 0.7 is applied(figure 5.39b), but it vanishes, wihtin the margin error, for network selectedevents with outputs above 0.7 (figure 5.40a). Similarly, the reversed casewith good B meson masses above 5.27 GeV and a network cut below 0.7shows a good agreement between Data and Monte Carlo (figure 5.40b). Itseems that a class of events in the combinatoric background of the B me-son reconstruction deliver a good m2

miss. This behavior can be suppressed

89

by requiring correct B meson masses above 5.27 GeV and by the networkselection which reduces this peak, too.

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mal

ized

to U

nity

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035 Stacked Plot --- Tagside-Corrected --- BTagMbc>5.27&&net1<0.7






(b) netout < 0.7 and B meson mass > 5.27 GeV

Figure 5.40: m2miss distribution for the muon channel weighted to expected

yields, with signal (blue), ulnu (green), generic (red), rare, (black) and data(dots)

The remaining distributions for the muon mode are given in section 6.7.These agree well between data and Monte Carlo and they include the m2

miss

distribution above 1 GeV2 with the signal selection for B meson masses above5.27 GeV and a network cut above 0.7 (figure 6.44); the B-tag mass distri-bution for network cuts below 0.7 (figure 6.45) and the network output withm2

miss above 1 GeV2 (figure 6.46). Like in the electron mode, the overall yieldis higher on data than on Monte Carlo as can be seen in figure 6.42.

90

5.8 Comparison between the BaBar analysis and thisdiploma thesis

This diploma thesis uses a similar approach to the analysis as BaBar but itdiffers in many aspects. Both analyses employ the full reconstruction whichenables a clean signal reconstruction and the computation of am2

miss variable.However the full reconstruction techniques differ significantly, as describedin sections 3 and 4.Another big difference between the signal side analyses is that BaBar makesa purely cut-based approach, be it for signal candidate selection or for themeson vetoes (pion, eta and omega) that reject peaking background. Thisanalysis does also a cut-based pre-selection, rejecting easily separable back-ground and applying quality cuts for the signal candidates, however, its finalselection is performed with a neural net predominantly serving as a pion andeta veto. The meson veto variables are computed similarly in both analyses,but additionally to that, this diploma thesis uses several of these variableswith different background photon energy cuts to be used in the network train-ing. Moreover, the quality cut for the photon selection also employs a neuralnetwork. Both analyses use the same figure of merit variable to optimize thecut values, where this analysis only optimizes the final cut on the networkoutput.This thesis has the goal to fit the m2

miss variable and it validates the stabil-ity of the fit results with several Monte Carlo studies with different signalyields. The BaBar analysis on the other hand is setup as a counting ex-periment, cutting on the m2

miss distribution and validating its approach bylooking at the m2

miss shape of the very similar B+ → π0ℓ+ν decay and de-termining its branching fraction with the presented procedure (meson vetoesexcluded). For this analysis such a validation would be difficult, since theneural network contains the meson vetoes and other variables, therefore thevetoes are not easily removalbe without impacting the remaining selection.BaBar tries to gain model-independence through multiple measures. It usestwo different decay models, though latest theoretical predictions favor one ofthese models strongly, making the second one obsolete. It further does notuse angles between the signal particles for its model-independent branchingfraction. This is also implemented in this analysis, except for one precut ona helicity suppressed kinematic, that favors the photon and the lepton tobe emitted in opposite directions. Particularly no angles between the signalchildren are used for the network training in this analysis.

91

Both analyses use the sideband shapes of m2miss and the tag side B meson

mass to check the agreement between data and Monte Carlo, additionally,this analysis uses the NeuroBayes network output.The number of expected events for the final selection differ strongly, whereBaBar expects 3.4 (2.7) background events and observes 7 (4) events on datafor muons (electrons), this analysis has much higher efficiency with expected57.3 (40.8) background events and 45.6 (38.1) signal events for the muon(electron) channel in the signal region, assuming BaBar’s upper limit for thesignal branching fraction.

92

6 Appendix

6.1 Precuts electron channel

The sample coloring scheme for all precut plots is:signal MC = blue, generic MC = red, ulnu MC= green and rare MC = black(without signal admixture).The signal MC sample will always be shown with a cut on the MC matchingvariable (SignalMCinfo>0) for clean signal events.

]2 [GeVmiss2m

-2 0 2 4

Num

ber

of E

ntrie

s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 , 11857 entriesγ eν + e→+signal MC B





93


93

No. of Tracks0 2 4 6

Num

ber

of E

ntrie

s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8





Figure 6.2: Remaining charged tracks minus curling tracks (cut == 0)

Muon Id Value0.0 0.5 1.0

Num

ber

of E

ntrie

s

0.0

0.2

0.4

0.6

0.8





Figure 6.3: Muon Id (cut < 0.5)

94

Electron Id Value0.0 0.5 1.0

Num

ber

of E

ntrie

s

0.0

0.2

0.4

0.6

0.8

1.0rare MC (no signal decay) , 149108 entries




Figure 6.4: Electron Id (cut > 0.5)

Photon Energy [GeV]0 1 2 3

Num

ber

of E

ntrie

s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07





Figure 6.5: Signal photon energy in B meson rest frame (cut > 0.4 GeV)

95

Network Ouput0.2 0.4 0.6 0.8

Num

ber

of E

ntrie

s

0.00

0.05

0.10

0.15

0.20

0.25 generic MC , 30348 entries




Figure 6.6: Signal photon full reconstruction network output (cut > 0.4)

Energy [GeV]0.0 0.5 1.0

Num

ber

of E

ntrie

s

0.00

0.020.04

0.060.08

0.100.12

0.140.16

0.180.20





Figure 6.7: Extra energy in the electromagnetic calorimeter (cut < 0.9 GeV)

96

cos(angle)-1.0 -0.5 0.0 0.5 1.0

Num

ber

of E

ntrie

s

0.00

0.02

0.04

0.06

0.08

0.10

0.12generic MC , 13163 entries




Figure 6.8: Cosine of the angle between signal lepton and gamma (cut < 0.6)

]2B-Tag Mass [GeV/c5.22 5.24 5.26 5.28

Num

ber

of E

ntrie

s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08





Figure 6.9: B meson mass of the tag side (cut > 5.27 GeV)

97

]2 [GeVmiss2m

0 2 4

Num

ber

of e

xpec

ted

Eve

nts

0

5

10

15

20

25

30

35

40generic MC , 968.6 events




Figure 6.10: m2miss distribution for the electron channel after precuts with

the expected data yields

98

6.2 Network training results for the electron channel

The network is trained with similar variables as in the muon case. The listof variables sorted by their importance is


• Extra energy in the electron calorimeter as defined above


• Electron Id


• Signal photon energy in the B meson rest frame

• m(π0) reconstructed with the signal photon and any background photon

• m(π0) reconstructed with two background photons above 75 MeV


The training is performed just as for muons with all samples at once. Theweights are 2 for ulnu sample and 1 for the rest of the samples. The networkoutput for the split training and analysis samples is shown in figure 6.11. Thefigure of merit is plotted against the network cut in figure 6.12. The absolutemaximum is at 0.7175 which is rounded to 0.7, since the maximum regionextends from below 0.7 to 0.75. The m2

miss distribution after the optimizednetwork cut with the applied corrective weighting for the tag side is shownin figure 6.13. The efficiency of the network cut for all samples is given intable 6.1.

99

Network Output0.0 0.2 0.4 0.6 0.8 1.0

Num

ber

of E

ntrie

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0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 ulnu MC , 4048 entries




(a) Training sample

Network Output0.0 0.2 0.4 0.6 0.8 1.0

Num

ber

of E

ntrie

s

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08





(b) Analysis sample

Figure 6.11: Network outputs of the split samples normalized for the muonchannel; signal (blue), ulnu (green), generic (red), rare (black)

network cut0.0 0.5 1.0

Fig

ure

of M

erit

0

1

2

3

4

5

Figure 6.12: Figure of merit value vs. network cut for the electron channel

100

Events numberssignal generic ulnu rare

After precuts 9233 4843 8001 441Fom network cut 7382 1104 1878 96Efficiencies 0.800 0.228 0.235 0.218

Table 6.1: Parameters of the network cut for the electron channel

]2 [GeVmiss2m

-2 0 2 4

Num

ber

of e

xpec

ted

Eve

nts

0

1

2

3

4

5

6

7

8Tagside-Corrected





Figure 6.13: m2miss distribution after tag side correction for the electron chan-

nel weighted to expectancy on data

101

6.3 Fitting results electron channel

]2 [GeVmiss2m

-1 0 1 2 3Num

ber

of E

xpec

ted

Eve

nts

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-1 0 1 2 3

-5

0

Figure 6.14: Signal fit for the electron with crystal ball function (black),Gaussian contribution (Green), sum distribution (blue) and electron signalsample (black data points)

102

Figure 6.14: Signal fit for the electron with crystal ball function (black),Gaussian contribution (Green), sum distribution (blue) and electron signalsample (black data points)

102

]2 [GeVmiss2m

0 1 2 3Num

ber

of E

xpec

ted

Eve

nts

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3

-5

0

Figure 6.15: Ulnu Fit with Novosibirsk function (blue), constant contribution(Green), sum distribution (blue) and electron ulnu sample (black data points)

]2 [GeVmiss2m

-0.5 0 0.5 1 1.5 2 2.5 3 3.5Num

ber

of E

xpec

ted

Eve

nts

0

1

2

3

4

5

6

7

8

-0.5 0 0.5 1 1.5 2 2.5 3 3.5-6

-4

-2

0

2

Figure 6.16: Generic Fit with Third Order Polynomial (blue) and electrongeneric sample (black data points)

103

6.4 Monte Carlo study muon channel

0 10 20 30 40 50 60 70 80

Eve

nts

/ ( 0

.857

428

)

0

5

10

15

20

25

30

35

40

45

A RooPlot of "" 0.22±RMS = 9.96

0.31±Mean = 37.60

Entries = 1000

A RooPlot of ""

Error6 7 8 9 10 11 12 13

Eve

nts

/ ( 0

.076

8489

)

0

10

20

30

40

50

A RooPlot of " Error" 0.018±RMS = 0.804

0.025±Mean = 10.029

Entries = 1000

A RooPlot of " Error"

Pull-4 -3 -2 -1 0 1 2 3 4

Eve

nts

/ ( 0

.093

4535

)

0

10

20

30

40

50

A RooPlot of " Pull" 0.032±pullMean = -0.0764

0.023±pullSigma = 1.009

A RooPlot of " Pull"

signal

net1>0.7&&BTagMbc>5.27

Mpar: 37.6683

Figure 6.17: MC study signal fit (signal numbers at expected BaBar limit),muon channel

104

Figure 6.17: MC study signal fit (signal numbers at expected BaBar limit),muon channel

104

0 50 100 150 200

Eve

nts

/ ( 2

.551

63 )

0

10

20

30

40

50


0.87±Mean = 86.94

Entries = 1000

A RooPlot of ""

Error22 24 26 28 30 32

Eve

nts

/ ( 0

.121

246

)

0

10

20

30

40

50

60


0.038±Mean = 27.322

Entries = 1000


Pull-4 -3 -2 -1 0 1 2 3 4

Eve

nts

/ ( 0

.092

0992

)

0

10

20

30

40

50


0.023±pullSigma = 1.009


ulnu


Mpar: 87.3691

Figure 6.18: MC study ulnu fit (signal numbers at expected BaBar limit),muon channel

200 250 300 350 400

Eve

nts

/ ( 2

.463

5 )

0

10

20

30

40

50


0.81±Mean = 275.60

Entries = 1000

A RooPlot of ""

Error24 25 26 27 28 29

Eve

nts

/ ( 0

.060

452

)

0

5

10

15

20

25

30

35

40

45


0.024±Mean = 26.162

Entries = 1000


Pull-4 -3 -2 -1 0 1 2 3

Eve

nts

/ ( 0

.080

5833

)

0

5

10

15

20

25

30

35

40

45


0.022±pullSigma = 0.981


generic


Mpar: 276.282

Figure 6.19: MC study generic fit (signal numbers at expected BaBar limit),muon channel

105

-10 0 10 20 30 40

Eve

nts

/ ( 0

.635

671

)

0

10

20

30

40

50


0.23±Mean = 12.64

Entries = 1000

A RooPlot of ""

Error3 4 5 6 7 8 9 10 11

Eve

nts

/ ( 0

.085

5016

)

0

10

20

30

40

50


0.030±Mean = 7.373

Entries = 1000


Pull-4 -2 0 2 4

Eve

nts

/ ( 0

.108

472

)

0

10

20

30

40

50

60


0.023±pullSigma = 1.050


signal


Mpar: 12.4305

Figure 6.20: MC study signal fit (signal numbers weighted by one third),muon channel

0 50 100 150 200

Eve

nts

/ ( 2

.179

08 )

0

10

20

30

40

50


0.80±Mean = 86.78

Entries = 1000

A RooPlot of ""

Error20 22 24 26 28 30

Eve

nts

/ ( 0

.113

291

)

0

10

20

30

40

50

60


0.041±Mean = 25.293

Entries = 1000


Pull-3 -2 -1 0 1 2 3

Eve

nts

/ ( 0

.075

7486

)

0

5

10

15

20

25

30

35

40


0.022±pullSigma = 1.000


ulnu


Mpar: 87.3691

Figure 6.21: MC study ulnu fit (signal numbers weighted by one third), muonchannel

106

180 200 220 240 260 280 300 320 340 360 380

Eve

nts

/ ( 2

.208

73 )

0

10

20

30

40

50


0.82±Mean = 277.34

Entries = 1000

A RooPlot of ""

Error23 24 25 26 27 28

Eve

nts

/ ( 0

.066

9436

)

0

10

20

30

40

50


0.025±Mean = 25.524

Entries = 1000


Pull-3 -2 -1 0 1 2 3

Eve

nts

/ ( 0

.074

9342

)

0

10

20

30

40

50

A RooPlot of " Pull" 0.032±pullMean = 0.022

0.023±pullSigma = 1.014


generic


Mpar: 276.282

Figure 6.22: MC study generic fit (signal numbers weighted by one third),muon channel

-80 -60 -40 -20 0 20

Eve

nts

/ ( 1

.225

15 )

0

20

40

60

80

100


0.21±Mean = -0.503

Entries = 1000

A RooPlot of ""

Error1 2 3 4 5 6 7 8 9

Eve

nts

/ ( 0

.094

3496

)

0

10

20

30

40

50


0.033±Mean = 5.389

Entries = 1000


Pull-8 -6 -4 -2 0 2 4 6 8

Eve

nts

/ ( 0

.190

264

)

0

20

40

60

80

100


0.027±pullSigma = 1.203


signal


Mpar: 0

Figure 6.23: MC study signal fit (signal number at zero), muon channel

107

0 50 100 150 200 250

Eve

nts

/ ( 3

.298

75 )

0

10

20

30

40

50

60


0.82±Mean = 88.43

Entries = 1000

A RooPlot of ""

Error18 20 22 24 26 28 30 32 34

Eve

nts

/ ( 0

.170

459

)

0

10

20

30

40

50

60


0.048±Mean = 23.981

Entries = 1000


Pull-6 -4 -2 0 2 4 6

Eve

nts

/ ( 0

.124

229

)

0

10

20

30

40

50

60


0.024±pullSigma = 1.066


ulnu


Mpar: 87.3691

Figure 6.24: MC study ulnu fit (signal number at zero), muon channel

150 200 250 300 350 400

Eve

nts

/ ( 2

.743

68 )

0

10

20

30

40

50

60


0.82±Mean = 276.13

Entries = 1000

A RooPlot of ""

Error22 23 24 25 26 27 28

Eve

nts

/ ( 0

.070

2009

)

0

10

20

30

40

50


0.025±Mean = 25.055

Entries = 1000


Pull-4 -3 -2 -1 0 1 2 3 4

Eve

nts

/ ( 0

.092

5066

)

0

10

20

30

40

50


0.023±pullSigma = 1.038


generic


Mpar: 276.282

Figure 6.25: MC study generic fit (signal number at zero), muon channel

108

6.5 Monte Carlo study electron channel

0 20 40 60 80

Eve

nts

/ ( 1

.048

63 )

0

10

20

30

40

50


0.37±Mean = 35.43

Entries = 1000

A RooPlot of ""

Error8 9 10 11 12 13 14 15 16

Eve

nts

/ ( 0

.088

5226

)

0

10

20

30

40

50


0.033±Mean = 11.473

Entries = 1000


-4 -2 0 2 40

10

20

30

40

50

60

0.032±pullMean = -0.0770

0.023±pullSigma = 1.027 signal


Mpar: 35.4081

Figure 6.26: MC study signal fit (signal numbers at expected BaBar limit),electron channel

109

Figure 6.26: MC study signal fit (signal numbers at expected BaBar limit),electron channel

109

0 50 100 150 200

Eve

nts

/ ( 2

.469

74 )

0

10

20

30

40

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0.87±Mean = 80.21

Entries = 1000

A RooPlot of ""

Error22 24 26 28 30 32 34

Eve

nts

/ ( 0

.124

382

)

0

10

20

30

40

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0.042±Mean = 28.071

Entries = 1000


-3 -2 -1 0 1 2 30

10

20

30

40

50

0.031±pullMean = 0.060

0.022±pullSigma = 0.987 ulnu


Mpar: 77.809

Figure 6.27: MC study ulnu fit (signal numbers at expected BaBar limit),electron channel

100 150 200 250 300

Eve

nts

/ ( 2

.397

13 )

0

10

20

30

40

50


0.77±Mean = 187.90

Entries = 1000

A RooPlot of ""

Error20 21 22 23 24 25 26 27

Eve

nts

/ ( 0

.079

1339

)

0

5

10

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20

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30

35

40

45


0.027±Mean = 23.790

Entries = 1000


-4 -3 -2 -1 0 1 2 3 40

10

20

30

40

50

0.032±pullMean = 0.002

0.023±pullSigma = 1.025 generic


Mpar: 187.341

Figure 6.28: MC study generic fit (signal numbers at expected BaBar limit),electron channel

110

-30 -20 -10 0 10 20 30 40 50

Eve

nts

/ ( 0

.893

989

)

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0.29±Mean = 11.65

Entries = 1000

A RooPlot of ""

Error4 6 8 10 12

Eve

nts

/ ( 0

.101

219

)

0

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0.036±Mean = 8.607

Entries = 1000


Pull-4 -2 0 2 4

Eve

nts

/ ( 0

.112

59 )

0

10

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30

40

50


0.025±pullSigma = 1.102


signal


Mpar: 11.6847

Figure 6.29: MC study signal fit (signal numbers weighted by one third),electron channel

0 50 100 150 200

Eve

nts

/ ( 2

.394

57 )

0

10

20

30

40

50


0.84±Mean = 78.46

Entries = 1000

A RooPlot of ""

Error20 22 24 26 28 30 32

Eve

nts

/ ( 0

.135

505

)

0

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40

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0.044±Mean = 25.516

Entries = 1000


Pull-4 -3 -2 -1 0 1 2 3 4

Eve

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/ ( 0

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2467

)

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20

30

40

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0.023±pullSigma = 1.046


ulnu


Mpar: 77.809

Figure 6.30: MC study ulnu fit (signal numbers weighted by one third),electron channel

111

100 150 200 250 300

Eve

nts

/ ( 2

.284

79 )

0

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30

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0.74±Mean = 188.06

Entries = 1000

A RooPlot of ""

Error20 21 22 23 24 25 26

Eve

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/ ( 0

.070

5604

)

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0.027±Mean = 23.022

Entries = 1000


Pull-4 -3 -2 -1 0 1 2 3 4

Eve

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.090

8487

)

0

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20

30

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0.023±pullSigma = 1.016


generic


Mpar: 187.341

Figure 6.31: MC study generic fit (signal numbers weighted by one third),electron channel

-50 -40 -30 -20 -10 0 10 20 30

Eve

nts

/ ( 0

.917

511

)

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40

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0.23±Mean = -0.561

Entries = 1000

A RooPlot of ""

Error3 4 5 6 7 8 9 10

Eve

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.088

9653

)

0

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0.037±Mean = 6.560

Entries = 1000


Pull-6 -4 -2 0 2 4

Eve

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/ ( 0

.116

51 )

0

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60


0.026±pullSigma = 1.141


signal


Mpar: 0

Figure 6.32: MC study signal fit (signal number at zero), electron channel

112

-20 0 20 40 60 80 100 120 140 160 180

Eve

nts

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.157

57 )

0

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0.79±Mean = 79.29

Entries = 1000

A RooPlot of ""

Error18 20 22 24 26 28 30 32

Eve

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.159

778

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0.047±Mean = 23.888

Entries = 1000


Pull-4 -3 -2 -1 0 1 2 3 4

Eve

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.087

7942

)

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0.023±pullSigma = 1.048


ulnu


Mpar: 77.809

Figure 6.33: MC study ulnu fit (signal number at zero), electron channel

80 100 120 140 160 180 200 220 240 260 280

Eve

nts

/ ( 2

.220

72 )

0

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20

30

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0.72±Mean = 186.60

Entries = 1000

A RooPlot of ""

Error20 21 22 23 24 25

Eve

nts

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9348

)

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0.025±Mean = 22.435

Entries = 1000


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Eve

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.091

6052

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0.023±pullSigma = 1.023


generic


Mpar: 187.341

Figure 6.34: MC study generic fit (signal number at zero), electron channel

113

6.6 Sidebands Monte Carlo vs. data plots for the elec-tron channel

The sample coloring scheme for all plots is:signal = blue, generic = red, ulnu = green, rare = black (without signaladmixture) and data (black dots)

]2 [GeV

miss

2m-2 0 2 4

Ent

ries

Nor

mal

ized

to U

nity

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

]2 [GeVmiss2m

-2 0 2 4

Ent

ries

Nor

mal

ized

to U

nity

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040Stacked Plot --- Tagside-Corrected --- BTagMbc<5.27&&net1<0.7






Figure 6.35: m2miss sideband for netout < 0.7 and B meson mass < 5.27 GeV

for the electron channel

114

Figure 6.35: m2miss sideband for netout < 0.7 and B meson mass < 5.27 GeV


114

]2 [GeVmiss2m

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0.040Stacked Plot --- Tagside-Corrected --- BTagMbc>5.27&&net1<0.7






Figure 6.36: m2miss sideband for netout < 0.7 and B meson mass > 5.27 GeV


]2 [GeVmiss2m

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0.040 Stacked Plot --- Tagside-Corrected --- BTagMbc<5.27






Figure 6.37: m2miss sideband for B meson mass < 5.27 GeV for the electron

channel

115

]2 [GeVmiss2m

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Figure 6.38: m2miss sideband for netout > 0.7 and B meson mass < 5.27 GeV


]2 [GeVmiss2m

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Stacked Plot --- Tagside-Corrected --- BTagMbc>5.27&&net1>0.7&&MissingMass>1






Figure 6.39: m2miss sideband for netout > 0.7, B meson mass > 5.27 GeVand

m2miss > 1 GeV 2 for the electron channel

116

]2B-Tag Mass [GeV/c5.22 5.24 5.26 5.28

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Figure 6.40: B-tag mass sideband for netout < 0.7 for the electron channel

Network Output0.0 0.2 0.4 0.6 0.8 1.0

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Figure 6.41: Network output sideband for m2miss > 1 GeV 2 for the electron

channel

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6.7 Sidebands Monte Carlo vs. data plots for the muonchannel

The sample coloring scheme for all plots is:signal = blue, generic = red, ulnu = green, rare = black (without signaladmixture) and data (black dots)

]2

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Figure 6.42: m2miss sideband not normalized for netout < 0.7 for the muon

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Figure 6.42: m2miss sideband not normalized for netout < 0.7 for the muon

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]2 [GeVmiss2m

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Figure 6.43: m2miss sideband for netout < 0.7 for the muon channel

]2 [GeVmiss2m

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Stacked Plot --- Tagside-Corrected --- BTagMbc>5.27&&net1>0.7&&MissingMass>1






Figure 6.44: m2miss sideband for netout > 0.7, B meson mass > 5.27 GeV

and m2miss > 1 GeV 2 for the muon channel

119

]2B-Tag Mass [GeV/c5.22 5.24 5.26 5.28

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Figure 6.45: B-tag mass sideband for netout < 0.7 for the muon channel

Network Output0.0 0.2 0.4 0.6 0.8 1.0

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Figure 6.46: Network output sideband for m2miss > 1 GeV 2 for the muon

channel

120

References

[1] B. Aubert et al.Search for the radiative leptonic decay B+ → γℓ+νarXiv:0704.1478 (2007)

[2] M. Beneke, J. RohrwildB meson distribution amplitude from B+ → γℓνarXiv:1110.3228v1 (2011)

[3] G. P. Korchemsky, D. Pirjol and T.-M. YanRadiative leptonic decays of B mesons in QCDarXiv:hep-ph/9911427 (2000)

[4] M. Feindt,F. Keller, M. Kreps, T. Kuhr, S. Neubauer, D. Zander, A.ZupancA Hierarchical NeuroBayes-based Algorithm for Full Reconstruction ofB Mesons at B FactoriesarXiv:1102.3876 (2011)

[5] M. FeindtA Neural Bayesian Estimator for Conditional Probability DensitiesarXiv:physics/0402093 (2004)

[6] www.wikipedia.org

[7] A. Ryd, D. Lange, N. Kuznetsova, S. Versille, M. Rotondo, D. Kirkby,F. Wuerthwein, A. IshikawaEvtGen: A Monte Carlo generator for B-Physics

[8] The Belle collaborationThe Belle DetectorNuclear Instruments and Methods in Physics Research A 479 (2002)

[9] F. KellerImprovement of the full reconstruction of B mesons at the Belle exper-imentDiploma Thesis, Institut fuer experimentelle Kernphysik, KIT (2011)

[10] A. Sibidanov and K. VarvellExclusive B+ → Xuℓν decays using new full reconstruction tagging (7.

121

Tag effieciency evaluation)Belle Note 1206 v1.0 (2011)

[11] G. PunziSensitivity of searches for new signals and its optimizationarXiv:physics/0308063v2 (2003)

[12] G. J. Feldman and R. D. CousinsUnified approach to the classical statistical analysis of small signalsPhys. Rev. D 57, 38733889 (1998)

122

Danksagung

Ich mochte mich bei Prof. Dr. Michael Feindt, fur die Moglichkeit dieseDiplomarbeit am EKP zu erstellen, sowie fur seine ausgezeichnete Betreuungbedanken. Auch danke ich Prof. Dr. Ulrich Husemann fur die Ubernahmedes Korreferats fur diese Arbeit.

I would like to offer my special thanks to Dr. Anze Zupanc for his profoundsupport and his great diligence in advising me.Gleichzeitig mochte ich mich bei Dr. Thomas Kuhr und Dr. Martin Heckfur ihre intensive Betreuung und viele Problemlosungen bedanken.

Im weiteren mochte ich mich bei dem Admin Team des EKP und der gesamtenB-Gruppe bedanken, speziell bei Dr. Sebastian Neubauer, Daniel Zanderund Markus Roehrken, die ihre Zeit investiert haben, um mir bei Fragen undProblemen behilflich zu sein. Zudem mochte ich mich bei Michael Prim undBastian Kronenbitter fur das Korrekturlesen von Teilen meiner Diplomarbeitdanken.

Mein Dank gilt auch Colin Bartel, der ein guter Freund und stets unterhalt-samer und hilfsbereiter Zimmerkollege ist.

Mein besonderer Dank gilt meiner Familie, welche mir das Studium ermoglichthat und die mir immer eine zentrale moralische Stutze und Hilfe ist.

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