Non-leptonic B meson decays as a probe of new physics [Elektronische Ressource] / vorgeelgt von Martin Jung

Martin Jung

Sujets

• Physik

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• Publié par: universitat_siegen
• Publié le: 01 janvier 2009
• Nombre de lectures: 31
• Langue: Deutsch
• Poids de l'ouvrage: 2 Mo

Extrait

Non-leptonic B Meson Decays
as a Probe of New Physics
Dissertation
zur Erlangung des Grades eines
Doktors der Naturwissenschaften
vorgelegt von
Dipl.-Phys. Martin Jung
geb. am 02.06.1978 in Siegen
eingereicht beim Fachbereich Physik
der Universität Siegen
Siegen 2009Gutachter der Dissertation
Prof. Dr. Thomas Mannel
Dr. habil. Alexander Khodjamirian
Datum der mündlichen Prüfung
17. Juli 2009
Gedruckt auf alterungsbeständigem holz- und säurefreiem Papier, nach ISO 9706.
iiAbstract Zusammenfassung
Trotz des enormen Erfolgs des Standard-Despite the tremendous success of the Stan-
modells ist die Notwendigkeit einer Erwei-dard Model, the arguments for the neces-
terung unbestritten. Es wird erwartet, dasssity of an extension are compelling. The
die zugehörige Energieskala im TeV-Bereichcorresponding energy scale is expected to
liegt. Dies sollte zu sichtbaren Effekten inbe𝒪eV);(T it should lead therefore to vis-
Hochpräzisions-Observablen in der Flavour-ible effects in high-precision flavour obser-
Physik führen. Während dort bis heutevables. While no conclusive effect is seen
kein eindeutiger Effekt beobachtet wurde,there up to now, the data reveal certain
gibt es doch zumindest gewisse Spannun-
puzzles when compared to Standard Model
gen, wenn man die Daten mit den Vorher-expectations based on a global fit of the
sagen des Standardmodells vergleicht, dieCKM unitarity triangle and general the-
aus dem globalen Fit an das Unitaritäts-oretical expectations. The discussion of
dreieck und allgemeinen theoretischen Er-these tensions in the channels 𝐵→ 𝐽/𝜓𝐾 ,
wägungen folgen. Die Diskussion dieser
𝐵 → 𝜙𝐾 ,and𝐵 → 𝜋𝐾 , and the de-
Spannungen in den Kanälen 𝐵 → 𝐽/𝜓𝐾 ,duced constraints for New Physics oper-
𝐵 → 𝜙𝐾 und 𝐵 → 𝜋𝐾 ,sowiedieda-ators of the class 𝑏 → 𝑠𝑞𝑞¯ form the first
raus abgeleiteten Einschränkungen an Op-project discussed in this thesis. On the
eratoren Neuer Physik der Form 𝑏→ 𝑠𝑞𝑞¯other hand, hadronic uncertainties within
bilden das erste Projekt, das in dieser Ar-the Standard Model are still not well un-
beit diskutiert wird. Auf der anderen Seitederstood. Therefore the opposite assump-
sind die hadronischen Unsicherheiten imtion of large hadronic Standard Model ef-
Standardmodell nach wie vor nicht gut ver-fects in 𝐵 → 𝐽/𝜓𝐾 is made in the sec-
standen. Daher wird im zweiten Projektond project, allowing in addition for a New
¯ die entgegengesetzte Annahme gemacht, dassPhysics phase in 𝐵−𝐵 mixing. Finally, the
große Standardmodellbeiträge in Kombina-necessity of reliable SM predictions is ad-
¯tion mit Neuer Physik in der 𝐵− 𝐵 Mis-dressed by developing a framework for the
chung für die Abweichungen verantwortlichmodel-independent inclusion of corrections
sind. Schließlich wird diskutiert, wie Ein-to 𝑈-spin symmetry predictions.
beziehung von Modell-unabhängigen Kor-
rekturen zu 𝑈-Spin-Relationen die Zuver-
lässigkeit einiger Standardmodell-Vorhersa-
gen erhöht werden kann.
iiiivContents
1 Introduction 1
2 Fundamentals 5
2.1 TheStandardModel......................... 5
2.2 CPViolation ............................. 10
2.2.1 CPViolationintheStandardModel............ 12
2.2.2 DifferentUnitarityTriangleFits............... 17
2.2.3 CP violating Observables in 𝐵MesonDecays ....... 20
2.2.4 BeyondtheSM........................ 23
2.3 ReparametrizationInvariance.................... 24
3 Methods 27
3.1 EffectiveFieldTheoryforWeakDecays............... 27
3.1.1 Operator Product Expansion in Weak Decays . . . . . . . 30
3.1.2 RGimprovedPerturbationTheory............. 34
3.1.3 The SM Weak Effective Hamiltonian . . . . . . . . . . . . 36
3.2 QCDFactorization.......................... 39
3.3 SymmetrybasedMethods...................... 45
3.3.1 TheWigner-EckartTheorem................. 46
3.3.2 Isospin............................. 47
3.3.3 𝑆𝑈 (3) 49
3.3.4 𝑈-spinanditsbreaking.................... 49
3.4 StatisticalApproach......................... 53
3.4.1 TheRFitApproach...................... 53
4 Applications 59
4.1 New Physics in 𝑏→𝑠TransitionAmplitudes............ 59
4.1.1 𝐵→𝐽/𝜓𝐾 .......................... 61
vCONTENTS CONTENTS
4.1.2 𝐵→𝜙𝐾 ............................ 69
4.1.3 𝐵→𝜋𝐾 73
4.1.4 Conclusions.......................... 82
4.2 NP in Mixing: the Golden Mode revisited . . . . . . . . . . . . . 83
4.3 𝑈-spinanditsbreaking........................ 93
4.3.1 Decays of charged 𝐵mesons................. 93
4.3.2 Decays of neutral 𝐵mesons102
4.3.3 Conclusions107
5 Conclusions 109
6 Appendix 111
6.1 Diagrammatic Parametrization in 𝐵→𝜋𝐾 .............11
6.2 𝑈-spindecompositionsincharmlesdecays12
Literature 114
Acknowledgements 129
viChapter 1
Introduction
Particle Physics today is at a crossroad: on the one hand, the Standard Model
of Elementary Particle Physics (SM) is tremendously successful; there is still no
direct measurement in contradiction to it when neutrino masses are included. On
the other hand, there is the necessity of physics beyond the SM (New Physics
(NP)), preferably at the TeV-scale, associated for example with the hierarchy
problem, the question of dark matter and energy, as well as the baryon-antibaryon
asymmetry of the universe. In addition, some measurements performed lately,
prominently the so-called PAMELA anomaly and the ATIC data, showing both
2excesses in the cosmic fluxes of electrons and positrons in the𝒪(10GeV) regime,
pose questions, which could not be addressed in the SM so far. Finally the SM is
unsatisfactory from a theoretical point of view, as it leaves open several questions
about e.g. the family structure or the pattern of masses.
On the theory side one has constructed various models in order to address
these questions. Ideas include extending the Lorentz symmetry by a symmetry
between bosons and fermions (Supersymmetry), adding a fourth family to the
spectrum (SM4), embedding the SM gauge symmetry groups in a single one
(Grand Unified Theories (GUT)), or treating the four space-time dimensions as
arising effectively from a higher dimensional space (Extra Dimensions). Exploring
experementally what kind of NP is realized in nature will be a main task in the
coming years.
One big step forward in that direction will be the next generation experiments,
currently under planning and construction, of which the most prominent one is the
Large Hadron Collider (LHC) at CERN. As part of that program, a huge number
of new measurements regarding Flavour Physics will be carried out, including
11 Introduction
those at LHCb, especially dedicated to this field. Under the important topics in
that regime are the Flavour Problem, origin of the masses of and mixing between
the fermions, and a possible connection between the quark and lepton sector.
Flavour Physics has a tradition of identifying “NP” in various times: from
the postulate of the neutrino over the prediction of the charm quark (including
its mass) to the prediction of the third family and the mass of the top quark,
low-energy Flavour Physics has been an important complementary tool to the
high-energy particle accelerators in the last century.
In this regime lies the focus of this thesis. By now, an enormous amount of
data has been gathered regarding 𝐵 decays, dominated by the dedicated exper-
iments BaBar at SLAC and Belle and KEK, with important addition of several
measurements in the 𝐵 system in the D0 and CDF experiments at Tevatron.
𝑠
However, despite the high precision reached there, and in contrast to many situ-
ations in the past, there is no striking experimental result at the moment which
clearly contradicts theory. It is more the other way around: theory calls for
experimental results to contradict the SM, in order to gain more specific infor-
mation on the structure of a possible extension. This implies, that one has to
watch out for emerging discrepancies between the data and the SM, called puz-
zles. Being usually formed by deviations with an approximate significance of
around two standard deviations, their interpretation is usually difficult and not
conclusive. Another difficulty, which in light of the expected statistics in future
experiments will soon become the main issue, is the control of hadronic uncer-
tainties. While in the last decade huge progress has been made in understanding
hadronic matrix elements of 𝐵 decays, the methods developed so far still suffer
from relatively large non-factorizable contributions, which prevent in many cases
reliable SM predictions to which the data can be compared.
The three projects discussed mainly in this work try to address these issues
from different perspectives:
∙ The first project deals with NP in 𝑏 → 𝑠 transitions. Starting from the
observation of different puzzles in this class of decays, the data are fit-
ted under the assumption that one NP operator dominates the effect, and
that the SM contributions in these decays are understood reasonably well.
In discussing several effects in the same regime within a single, model-
independent framework tries to address the issue of the low significance of
the single effects.
21 Introduction
∙ In the second project, the oppos