OUTLINE

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OUTLINE
PART I 1. Introduction a) CKM-matrix
b) Unitarity Triangle 2. Determination of the
CKM-matrix a) Constraints on the CKM-matrix
b) Theoretical uncertainties c)
Statistical approaches 3. The Standard CKM fit
a) Determination of Vud Vus gt ? b)
Determination of Vcb gt A c)
Determination of Vub d) ?md ?ms e)
eK ( f) sin2ß) g) The global CKM fit
PART II 4) Constraints on a B?pp 5)
Constraints on ? sin(2ß?) 8) New Physics
in B mixing? 9) Conclusion Outlook
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Determination of Vub Inclusive Decays
Kinematic limit B?Xc l ?
Exercise What would you do to pin them down?
Strategies 1) El Shape Function from
B?Xs? 2) MX (Shape Function vary ?, ?1) 3) If
possible, reject low q2 values However
Annihilation diagrams (Reduce shape function
might
become important! dependence)


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Determination of Vub Inclusive Decays
Enormous statistics available at the
B-factories New experimental methods can be
realised!
e.g. BaBar Full reconstruction of one B small
efficiency but quite clean
Lepton plgt1.0 GeV/c S/B 2.5
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Determination of Vub Inclusive Decays
Enriched sample charm BG in signal region
(mXlt1.5 GeV) fixed using mXgt1.5 GeV
Belle Alternative method using D l ? tags
CLEO Hermeticity of the detector !
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Determination of Vub Inclusive Decays
My Average (4.12 ? 0.13 ? 0.42) ? 103 Does
not take into account subleading shape function
effects and annihilation diagrams Error
inflated (4.12 ? 0.13 ? 0.60) ? 103
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Determination of Vub Summary
Error not inflated
68 CL region
Input for the CKM fit LL(Incl.)
L(Excl.) if Incl. Excl. independent In other
words log L log L(Incl.) log L(Excl.) ?2
?2(Incl.) ?2(Excl.)
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Time evolution of B0-B0 System
with mass eigenstates
Defining
Expected not measured
Exercise Derive the relations above!
Exercise Why
? What about ?
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The ?md constraint
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The ?md constraint
SM prediction (top-loop dominates)
Hadronic matrix element
Exercise Why does the top dominate ?
Loop integral (Inami-Lim-function) including
radiative corr.
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The ?md constraint
This leads to a circle, at least to a good
approximation !
(D0 CDF)
Taken from Lattice QCD Dominant theoretical
error gt A. Kronfeld's lecture
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The ?ms constraint
How to obtain a Confidence Level ? We use the
following recipe 1) Calculate for each ?ms the
expected PDF 2) From the prefered ?ms value
calculate CL 3) Translate the CL in an equivalent
?2
gt Bs-Oscillations much more rapid than
Bd-Oscillations
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The ?ms constraint
What do we learn from this measurement?
Very weak dependence on ? and ?
However
For illustrative purpose
gt Measurement can constrain since is
much better known from Lattice QCD (with
some caveats)
Additional Motivation Search for New Physics !
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The eK constraint
CP violation in decay
1) CP violation in mixing 2) CP violation in the
interference between mixing and decay
Standard Model prediction for eK
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The eK constraint
BK Taken from theory fK Can be measured.
How?
gt Two Hyperbolae in the ?-? plane (Sign
of Bag parameter essential!)
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The eK constraint
All together
Rfit Linear addition of theoretical errors
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Putting all together The Global Fit
1) SM passes a highly non-trivial test The
KM mechanism describes all observables in a
consistent way ! The B-mixing phase (at
least one solution for ß) is compatible with
the SM prediction using 1)
Vub/Vcb 2) ?md ?ms 3) eK 2)
Does this rule out New Physics? Not at all!
Will see later an example.
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The Global Fit
1) sin2ß the most precise constraint on ? and
? ! 2) To test the KM mechanism of CP
violation in more detail One needs to
improve the (mainly theoretical) errors on
Vub/Vcb, ?md ?ms , eK 3) Additional
constraints needed (e.g. a and ? rare kaon
decays) 4) Which of the four solutions for
ß is the correct one? 5) Are other channels
measuring the same angle ß (in the SM)
consistent ?
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(?) Without using a priori information
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Constraints on a (f2)
Fundamental problem in all cases Two
amplitudes with different weak phases Tree
Penguin Will treat in the following only
(1) Measurement of (2) also already performed
(BaBar) Interpretation in terms of CKM
parameter very difficult
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Exercise Where is the u- and the top-penguin?
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P/T from Flavor-Symmetries SU(2) ( PEW0)
Gronau-London Isospin-Analysis
Grossmann-Quinn-Bound
(Charles, Gronau-London-Sinha-Sinha)
SU(3) ( dynamical Assumptions)
Fleischer-Buras, Charles (P??
PK?) P from
BR(B ? ????0) (Charles, Gronau Rosner)
Theoretical Predictions for P/T P/T and Phase
from QCD Factorization (Beneke et al.)
pQCD (Li et al.) (A wide field discussions
on control over
theoretical uncertainties see M. Neubert's talk)
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Assumption Pure Gluonic Penguin
Exercise Why don't we have I1 in the final
state?
Key observation Penguins ?I 1/2
Tree ?I 3/2 ?I 1/2
gt Tree can be isolated
As a consequence is a pure
tree!
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Depend only on
gt Both triangles have a common base !
FT CKM tree phase
Superimpose both triangles by
Problems 1) Four solutions for ?pp Two
solutions for sin(2a?pp) gt 8
solutions 2) Need to measure BR small (What
if too small?)
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If BR(?0?0) is very small Bound(s) on ?pp
using SU(2) symmetry.
Most effective bound.
Before LP 2003
After LP 2003 Evidence for
BABAR Belle
gt Bound useless gt Full Isospin analysis
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Similar in line to Grossman-Quinn bound
Dynamical Assumption Neglect OZI-suppressed
Penguin Annihilation diagrams
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1) SU(2) No EW-Penguins gt PK0p
PKp 2) No VusVub-Contribution 3) No
rescattering gt PK0p A(B?K0p) 4)
SU(3)-Breaking Factorisation uncertainty 5)
Strong phases are free to vary
2) VusVub-Contribution
Annihilation-diagrams
3) Rescattering
Exercise Can you draw the quark-level diagram
for this process?
4) SU(3)-Breaking
K or p
If the two currents do not talk to each
other fK or fp
Rth correction to naïve Factorisation
Choose here Rth 0.91 0.10
B?p
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Prediction for Spp und Cpp , if CKM phase
constrained by the standard CKM-fit
Predictions for P/T argP/Td , if CKM
phase constrained by the standard CKM-fit
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Constraints on ? (f3)
1) 2ß ? from Bd?D()p 2) ? - 2d?
from Bs?DsK 3) ? from B?DK 4)
? from B?Kp 5) ß ? from
Bd?pp Bs?KK ..... Will discuss here only
1)
Experimentally, ? is very difficult.
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sin(2ß?)
CP-violation in interference between two
amplitudes 1) Final States no
CP-eigenstates 2) No Penguin Pollution 3)
Extraction of ? even in the presence of
New Physics in B mixing 4) Phase
convention as for the UT B-mixing phase
2ß Relative Phase
between amplitudes with w/o mixing
? 5) Strong phase difference between both
amplitudes d
CP Violation
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Sin(2ß?)
Experimental approaches 1) Fully Reconstructed
Decays Small BG Small Statistics
(5000 Evts per channel with current
statistics) 2) Partially Reconstructed Decays B
?D p (fast pion slow pion) Higher BG
Large Statistics (6000 Leptons tags, 25000
kaon tags)
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sin(2ß?)
Problem 1
Problem 2 The interference on the signal side
can also appear on the tag side! Kaon
tags affected (How ?) Lepton tags no
problem
Extraction of r from time-dependent rates huge
amount of data
f(D()-p, ?t) N e-G?t 1cos(?md?t)
sin(?md?t)
2r sin(2ß?-d)
2r'
sin(2ß?d')
I. Dunietz
Lepton tags
BaBar
Assign additional 30 error 1) Uncertainty on
SU(3)-breaking 2) Missing W-exchange diagrams
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Constraints on from sin(2ß?) on ? and ?
BaBar

Belle Partially Rec.
Fully Rec. Fully
Rec. CL a
-0.063 0.024 0.017 -0.068 0.038 0.021
0.063 0.041 0.016 0.013 0.04 c
-0.004 0.037 0.020 0.031 0.070 0.035
0.030 0.041 0.016 0.030 0.87 a
-0.022
0.038 0.021 0.058 0.038 0.013
0.83 c
0.025 0.068 0.035 0.036
0.038 0.013 0.036 0.99
Constraints for BaBar
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New Physics in B mixing ?
There are many possible extensions of the
SM! Instead of discussing specific models
here In a large class of models the only
significant NP effects in CP asymmetries in
B?J/?Ks, B?pp is in B mixing Using
one can perform 1)
Model-Independent Reconstruction of the UT 2)
SM and NP contributions to the mixing can be
disentangled Assumptions (for further details
See Gino Isidori's lecture) (I) NP
contributions can not compete with tree-level
diagrams (II) NP in ?b1 transitions can not
compete with NP in ?b2 transitions
(important to interprete Spp)
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New Physics in B mixing ?
NP contribution in B mixing can be described as
follows
SM rd2 1, 2?d 0 rd lt 1 Destructive
Interference rd gt 1 Constructive Interference
Assuming no Penguin Pollution in B?pp
SM
NP
In this NP scenario What would be the constraint
in ?-? look like if we used only
?
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New Physics in B mixing An exercise
However, we have Penguin Pollution in
B?pp! Isospin analysis at this stage gt
Another strategy needed does not provide
stringent (with more theoretical
assumptions) constraints on a I
choose here
Crucial assumption beyond that No NP in
B?K0p Other model-independent Reconstructions
of the UT e.g. Fleischer, Isidori Matias
Neubert Some complications can be avoided in
the future by using e.g. 1) B?pp Isospin
analysis (even with NP in ?I1/2 Penguins) 2)
Bs?KK- assuming U-spin symmetry s?d (R.
Fleischer) 3) Measurement of ? from tree-level
processes
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New Physics in B mixing ?
16 solutions for ?
Overlapping ambiguities 16 ?12 allowed regions
1) ?0 can not be excluded yet! 2) There is still
much room for new NP !
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New Physics in B mixing ?
Future scenario Retain average values
and Reduce all uncertainties by factor of 2
(except Rth) (Improvement in statistics and
theoretical errors required! )
One would also like to reduce the number of
solutions for 2ß2?d ! e.g. Signcos(2ß2?d)
from B ??K0

1) Parameter space significantly reduced but NP
still be possible 2) ?0 excluded (CP-violation
in SM established even in presence of NP)
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The Standard Model has passed the sin2ß-test! The
other constraints need to be improved or still be
measured.
Lattice QCD other theoretical
techniques CLEO-c
CKM-Matrix Goals and Prospects
in B-Physik in the next years
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Conclusion Outlook
Kaon Physics (see also F. Muheim, G. Isidori)
No big improvements for BK expected in the near
future e'/e far from being mature to be
interpreted in terms of CKM parameters
Very challenging but also very promising
CKM physics The next decade will become very
exciting!