Lectures on Flavor Physics

224 Pages·2004·2.975 MB·English

by  Jürg Gasser (auth.), Ulf-G. Meissner, Willibald Plessas (eds.)

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U.-G. Meißner W. Plessas (Eds.)
Lectures on Flavor Physics
123
Editors
Ulf-G.Meißner WillibaldPlessas
Universita¨tBonn Universita¨tGraz
Helmholtz-Institut Institutfu¨rTheoretischePhysik
fu¨rStrahlen-undKernphysik Universita¨tsplatz5
Nussallee14-16 8010Graz,Austria
53115Bonn,Germany
SupportedbytheO¨sterreichischeBundesministeriumfu¨rBildung,Wissenschaft
undKultur,Vienna,Austria
U.-G.Meißner W.Plessas(Eds.),LecturesonFlavorPhysics,Lect.NotesPhys.629(Springer,
BerlinHeidelberg2004),DOI10.1007/b98411
LibraryofCongressControlNumber:2004107013
ISSN0075-8450
ISBN3-540-22255-3Springer-VerlagBerlinHeidelbergNewYork
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HeavyQuarkPhysics
Preface
This volume contains the written versions of some selected lectures delivered
at the “41. Internationale Universita¨tswochen fu¨r Theoretische Physik” in
Schladming,Austria.The41st“SchladmingWinterSchool”tookplaceduring
the period February 22nd–28th, 2003. The theme of the School was “Flavor
Physics”.
Flavor physics is one of the hot topics in contemporary elementary par-
ticle physics, because it relates to fundamental questions like the origin of
masses, the size and strength of CP violation, or the oscillations between
various neutrino species. One thus explores the Standard Model as well as
its possible extensions and related phenomena in astrophysics and cosmo-
logy. The lectures collected in this volume deal with important (theoretical)
developments at various length scales. At low energies and for light quarks,
one is able to analyze the strong interactions in terms of an effective field
theory, as described in Ju¨rg Gasser’s lectures on light-quark dynamics. The
interrelationbetweenpreciselycalculableelectroweakandthemuchmoredif-
ficult strong interactions comes into play in precision QED observables, like
the anomalous magnetic moment of the muon as discussed in the lectures by
Marc Knecht. In fact, the presently available precision data might already
give a glimpse at physics beyond the Standard Model.
The issue of CP violation in kaon and B-meson systems is addressed in
the lectures by Andrzej Buras. Only with the advent of the B-factories, CP
violationintheStandardModelcouldbemeasuredbeyondthekaonsystem,
and one is now testing the unitarity of the CKM matrix and tries to under-
stand the fundamental mechanism underlying CP violation. The richness of
this field is underlined by the lectures of Matthias Neubert, who presents a
new scheme to systematically calculate strong-interaction effects in certain
B-decays and also dwells on the unitarity triangle. Last but not least, with
therecentmeasurementsofneutrinooscillationsatSuper-Kamiokande,SNO,
and Kamland, the review on the foundations of the various forms of flavor
transitions in vacuum and in media by Walter Grimus is very timely.
At the School, we had further lectures on the experimental status of B-
decays (by D. Hitlin) as well as neutrino physics (by G. Drexlin), on lattice
calculations of flavor-physics matrix elements (by G. Martinelli), and an in-
VI Preface
troduction to supersymmetry (by H. Dreiner). They are not included here,
but their essential content can be found from other sources in the literature.
Here, we should like to express our sincere gratitude to the lecturers for
all their efforts in preparing and presenting their lectures. We are especially
grateful to those colleagues who managed to find time to write up their lec-
tures. We thank also the main sponsors of the School, the Austrian Federal
Ministry for Education, Science, and Culture as well as the Government of
Styria, for providing financial support. In addition, we acknowledge the con-
tributions from the University of Graz and the valuable organisational and
technical assistance by the town of Schladming, Ricoh Austria, and Hornig
Graz. Furthermore, we are grateful to our secretaries, S. Fuchs and E. Mon-
schein, a number of graduate students from our institute, and, last but not
least, our colleagues from the organizing committee for their valuable assi-
stance in preparing and running the school.
Bonn and Graz, Ulf-G. Meißner
December 2003 Willibald Plessas
Contents
Light-Quark Dynamics
Ju¨rg Gasser .................................................... 1
1 Introduction ................................................ 1
2 QCD with Two Flavours ..................................... 3
2.1 Symmetry of the Lagrangian ............................. 3
2.2 Symmetry of the Ground State ........................... 4
2.3 A Remark on Isospin Symmetry .......................... 5
3 Goldstone Bosons ........................................... 6
3.1 The Goldstone Theorem ................................. 6
3.2 The Free Scalar Field ................................... 7
3.3 The Linear Sigma Model ................................ 7
3.4 QCD with Two Flavors.................................. 11
4 Effective Field Theories ..................................... 12
4.1 Linear Sigma Model at Low Energy ....................... 13
4.2 QCD at Low Energy .................................... 15
5 Calculations with L ........................................ 16
eff
5.1 Leading Terms ......................................... 17
5.2 Higher Order Trees ..................................... 18
5.3 Loops ................................................. 19
5.4 Renormalization Made Systematic ........................ 21
6 Pion-Pion Scattering......................................... 22
6.1 Chiral Expansion of the ππ Amplitude .................... 23
6.2 Type A,B LECs ........................................ 26
7 Roy Equations and Threshold Parameters ...................... 26
7.1 ππ →ππ: Roy I ........................................ 26
7.2 ππ →ππ: Roy II ....................................... 28
7.3 The Coupling ¯l ........................................ 29
3
7.4 Note Added: On the Precision of the Theoretical Predictions
for ππ Scattering ....................................... 30
8 Outlook.................................................... 31
The Anomalous Magnetic Moment of the Muon:
A Theoretical Introduction
Marc Knecht ................................................... 37
1 Introduction ................................................ 37
VIII Contents
2 General Considerations....................................... 39
3 Brief Overview of the Experimental Situation ................... 45
3.1 Measurements of the Magnetic Moment of the Electron...... 45
3.2 Measurements of the Magnetic Moment of the Muon ........ 45
3.3 Experimental Bounds on the Anomalous Magnetic Moment
of the τ Lepton......................................... 48
4 The Anomalous Magnetic Moment of the Electron............... 48
4.1 The Lowest Order Contribution .......................... 49
4.2 Higher Order Mass Independent Corrections ............... 50
4.3 Mass Dependent QED Corrections ........................ 53
4.4 Other Contributions to a ............................... 56
e
4.5 Comparison with Experiment and Determination of α ....... 56
5 The Anomalous Magnetic Moment of the Muon ................. 58
5.1 QED Contributions to a ................................ 59
µ
5.2 Hadronic Contributions to a ............................ 61
µ
5.3 Electroweak Contributions to a .......................... 73
µ
5.4 Comparison with Experiment ............................ 77
6 Concluding Remarks......................................... 78
CP Violation in B and K Decays: 2003
Andrzej J. Buras................................................ 85
1 Introduction ................................................ 85
1.1 Preface................................................ 85
1.2 CKM Matrix and the Unitarity Triangle ................... 86
1.3 The Special Role of |V |, |V | and |V |................... 88
us ub cb
1.4 Grand Picture.......................................... 90
1.5 Theoretical Framework .................................. 90
2 Particle-Antiparticle Mixing and Various Types
of CP Violation ............................................. 93
2.1 Preliminaries........................................... 93
2.2 Express Review of K0−K¯0 Mixing ....................... 94
2.3 The First Look at ε and ε(cid:1) ............................... 96
2.4 Basic Formula for ε ..................................... 98
2.5 Express Review of B0 -B¯0 Mixing....................... 99
d,s d,s
2.6 Basic Formulae for ∆M ............................... 101
d,s
2.7 Classification of CP Violation ............................ 101
3 Standard Analysis of the Unitarity Triangle (UT) ............... 106
3.1 General Procedure ...................................... 106
3.2 The Angle β from B →ψK ............................ 107
d S
3.3 Unitarity Triangle 2003.................................. 108
4 ε(cid:1)/ε in the Standard Model ................................... 110
4.1 Preliminaries........................................... 110
4.2 Basic Formulae ......................................... 110
4.3 Numerical Results ...................................... 111
4.4 Conclusions ............................................ 112
Contents IX
5 The Angles α, β and γ from B Decays ......................... 114
5.1 Preliminaries........................................... 114
5.2 Classification of Elementary Processes..................... 114
5.3 Neutral B Decays into CP Eigenstates..................... 115
5.4 Decays to CP Non-eigenstates ............................ 118
5.5 U–Spin Strategies....................................... 121
5.6 Constraints for γ from B →πK .......................... 121
6 K+ →π+νν¯ and K →π0νν¯ ................................ 124
L
6.1 Branching Ratios ....................................... 124
6.2 Unitarity Triangle and sin2β from K →πνν¯ ............... 126
6.3 Concluding Remarks .................................... 126
7 Minimal Flavour Violation Models............................. 127
7.1 Preliminaries........................................... 127
7.2 Universal Unitarity Triangle.............................. 128
7.3 Models with Universal Extra Dimensions .................. 128
8 Outlook.................................................... 128
8.1 Phase 1 (2003-2007)..................................... 128
8.2 Phase 2 (2007-2009)..................................... 129
8.3 Phase 3 (2009-2013)..................................... 130
Heavy-Quark Physics
Matthias Neubert ............................................... 137
1 Introduction ................................................ 137
2 Statement of the Factorization Formula ........................ 140
2.1 The Idea of Factorization ................................ 140
2.2 The Factorization Formula............................... 141
3 Arguments in Favor of Factorization ........................... 142
3.1 Preliminaries and Power Counting ........................ 142
3.2 Non-leptonic Decay Amplitudes .......................... 145
3.3 Remarks on Final-State Interactions ...................... 147
4 Power-Suppressed Contributions .............................. 149
4.1 Interactions with the Spectator Quark..................... 149
4.2 Annihilation Topologies ................................. 150
4.3 Non-leading Fock States ................................. 151
5 Limitations of the Factorization Approach...................... 153
5.1 Several Small Parameters ................................ 153
5.2 Power Corrections Enhanced by Small Quark Masses........ 154
6 QCD Factorization for Charmless Decays....................... 155
7 Testing Factorization in B →πK,ππ Decays.................... 157
8 Establishing CP Violation in the Bottom Sector................. 158
9 Mixing-Independent Construction
of the Unitarity Triangle ..................................... 162
10 Outlook.................................................... 165