Diapositive 1

1
B Physics, CP Violation and the CKM Fit
Andreas Höcker (LAL, Orsay)
FNAL Colloquium, May 18, 2005
hoecker_at_lal.in2p3.fr
2
Outline
Themes

• Introduction
• CKM phase invariance and unitarity
• Statistical issues
• CKM metrology
• the traditional inputs
• deep B physics ?, ?, ?
• a new star B ? ??
• the global CKM fit
• Related topics (radiative B decays and the B ?
  K? system)
• Preparing the future

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To start with

1. The Universe is empty !
2. The Universe is almost empty !

Bigi, Sanda, CP Violation (2000)

• Initial condition ?
• Dynamically generated ?

• Sakharov rules (1967) to explain Baryogenesis
• Baryon number violation
• CP violation
• No thermic equilibrium (non-stationary system)

• So, if we believe to have understood CPV in the
  quark sector, what does it signify ?
• A sheer accident of nature ?
• What would it do to us if we set the CKM phase
  to zero ?

see in this respect B. Cahn, The eighteen
arbitrary parameters of the Standard Model in
your everyday life, RMP 68, 951 (1996)
4
CP Violation is flavor physics

• Discovery of CP violation (1964)
• The smallness of KL ? ? ? predicts charm
  quark (GIM)
• KM theory (to describe CP violation) predicts
  third quark generation
• ?mK m(KL) m(KS) predicts mass of charm
  quark
• Frequency of B0B0 mixing (?mB) predicts heavy
  top quark
• Prove of KM theory (sin2?)
• ?

Moments of glory in flavor physics
PRL 13, 138 (1964) cited 1067 times
5
(parenthesis)
Evolution of working conditions (example BABAR)
BABAR PRL 87, 091801 (2001) cited 308
times Belle PRL 87, 091802 (2001) cited
319 times
593 physicists (in early 2005).
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The Search for New Physics in the B System

• Since the precise measurement of sin2ß in
  decays (in perfect agreement with the SM),
  there is considerable effort at B Factories
  towards the search for specific signs of New
  Physics (NP). WHY ?
• Conflict between limits from flavor physics ? 1
  TeV (e.g., K0, D0, B0 mixing), and NP scale (1
  TeV) ? NP cannot have a generic flavor
  structure

• The gauge hierarchy Problem (Higgs sector,
  scale 1 TeV)
• Baryogenesis (CKM CPV too small)
• The strong CP Problem (why is ? 0 ?)
• Grand Unification of the gauge couplings
• ... many more

see, e.g., the instructive talk by Yuval Grossman
at LP03 hep-ph/0310229
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New Physics some possibilities

• Minimal flavor violation (MFV) models CP
  violation is completely governed by CKM
• ? precision tests in rare processes
• Q why ?
• The NP is essentially flavor blind up to
  large scales
• ? test of CP violation in flavor conserving
  processes (EDM, )
• Q and what about the leptons ?
• Intermediate solutions (example only b ? s
  transitions are affected by low energy NP),
• Q why would these two families by special ?
• and other still unknown alternatives, which
  certainly will give the correct answer

8
The CKM Matrix and the Unitarity Triangle
d
s
b
u
c
t
?
?
?
9
digression The Unitary Wolfenstein
Parameterization

• The standard parameterization uses Euler angles
  and one CPV phase ? unitary !

• Now, define

• And insert into V ? V is still unitary ! With
  this one finds (to all orders in ?)

where
Buras et al., PRD 50, 3433 (1994)
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Flavor Physics and CP Violation
P940
E787/949
BTEV
ATLAS
KEK / J-PARC
Super-B ?
NA48
CLEO-c
Super-BABAR ?
(?)
EDM experiments at several places in the world
Present and future - Worldwide Program on
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The Bd System (ee ? ?(4S)
factories)
the Bd is also produced by the hadron machines
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The Bs System
(hadron machines)
the Bs is not produced by the ?(4S) B factories
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Asymmetric-Energy B Factories (ex. PEP II)
e
e
3 km
Quantum coherence at ?t 0, the system is a
superposition of
9 GeV e against 3.1 GeV e

• coherent production of neutral B pair
• boost of ?(4S) in the laboratory ?? 0.56

Einstein-Podolsky-Rosen phenomenon measurement
of flavor of one meson determines flavor of other
meson at same proper time this property is
exploited for the flavor tagging
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The Global CKM Fit
Inspired by the global electroweak fits
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Fitting Approach
Constraints on theoretical parameters
Measurement
xexp
ytheo
(A,?,?,?,mt,?, )
Theoretical predictions
(BK,fB,BBd, )
Xtheo(ymodel
, yQCD)
ytheo
yQCD
Define ? 2 2 lnL(ymodel) L(ymodel) Lexp
xtheo(ymodel) ? Ltheo(yQCD)
ytheo free parameters (DONT USE
PDFs !)
xexp
 guesstimates 
statistical quantities
Frequentist Rfit
Bayesian

• experimental likelihood
• if not available Gaussian errors
• asymmetric errors
• correlations between xexps

Uniform likelihoods allowed ranges CKMfitter
Group and others
Probabilities UTfit Collaboration
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Three-Step CKM Analysis using Rfit
Test New Physics
Metrology
Probing the SM

• If CL(SM) good
• Obtain limits on New Physics parameters
• If CL(SM) bad
• Try some other model

• Define
• ymod a µ
• ?, ?, A,?,yQCD,...
• Set Confidence Levels in
• a space, irrespective of
• the µ values
• Fit with respect to µ
• ?²min µ (a) minµ ?²(a, µ)
• ??²(a)?²min µ(a)?²minymod
• CL(a) 1 Prob(??²(a), Ndof)
• (or toy MC)

• Test of Goodness-of-fit
• Evaluate global minimum
• ?²minymod(ymod-opt)
• Create perfect data set
• xexp-opt xtheo(ymod-opt)
• generate xexp using Lexp
• Perform many toy fits ?²min-toy(ymod-opt)
  ? F(?²min-toy)

AH-Lacker-Laplace-Le Diberder EPJ C21 (2001) 225,
hep-ph/0104062
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m e t r o l o g y
Inputs to the Global CKM Fit

• Vud and Vus not discussed here
• Vub and Vcb
• CPV in K0 mixing
• Bd and Bs mixing
• sin 2?
• ?
• B ? ? ?
• B ? ? ?
• B ? ? ?
• ?
• ADS, GLW
• Dalitz
• B ? ??

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Vcb and Vub

• For Vcb and Vub exist exclusive and inclusive
  semileptonic approaches

d
s
b
exclusive
inclusive
B ? Xu l?
B ? ? l?
b ? u
u
c
b ? c
B ? D l?
B ? Xc l?
dominant uncertainties
t
Form factor
OPE (Vcb,ub) and shape function
(Vub)

• Vub (? ?2 ?2) is crucial for the SM
  prediction of sin(2? )
• Vcb (? A) is important in the kaon system
  (?K, BR(K???? ), )

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Vcb and Vub

• Inclusive approaches most appealing at present

nonperturbative corrections
free quark decay

• Vcb moments analyses have 1.52 precision !

CKM-05

• Vub reduced conflict between excl. and incl.
• SF params. from b?cl? , OPE from Bosch et al.
• reduction of central value 4.6 ? 4.1 ?103
• ?l? result goes up with Lattice FF (unquenched)

CKMfitter average
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CPV in Neutral Kaon Mixing

• Neutral kaon mixing (FCNC) mediated by box
  diagrams

effective matrix element

• Most precise results from amplitude ratio of KL
  to KS decays to ?? and ?0?0

• ?ij from perturbative QCD
• improvement on BK from Lattice QCD (quenched)
  reported at CKM-05 BK 0.79 0.04 0.09
  (now also Nf2heavy calc. available)

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B0 Mixing

• Effective FCNC Processes (CP conserving top
  loop dominates in box diagram)

Perturbative QCD
CKM Matrix Elements
Non-perturbative Lattice (eff. 4 fermion
operator)
Loop integral (top loop dominates)

• Dominant theoretical uncertainties

consider in fit that Lattice results are
correlated !

• Improved error indirect via ?ms

SU(3) breaking correction
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B0 Mixing

• ?md (0.510 0.005) ps1

CKM constraint dominated by theory error
CKM fit predicts ?md 0.47 ps1
HFAG Winter 2005
0.23 0.12
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sin(2?) the first UT input that is not theory
limited
Principal modes
?
Tree dominant
Penguin dominant
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CP-Violation Primer

• Condition for CP invariance

• Definition of CP parameter 

decay amplitude ratio
CP eigenvalue

• CP invariance requires

• Classification of CP violation

CP violation in mixing (indirect)
CP-violating phenomena
CP violation in the decay (direct)
CP violation in interference between mixing and
decay
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Direct CP Violation

• First seen by NA48 and KTeV in kaon system (?)

• Large asymmetry observed by BABAR and
  Belle in B0 ? K? decays

BABAR
none.

• Direct CPV requires interference of amplitudes of
  similar size and with different weak and strong
  phases cannot be reliably predicted (at
  present) for use in CKM fit

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Mixing-Induced CP Violation

• CP Violation due to the interference of decays
  
• with and without mixing

• Time-dependent asymmetry observable

CP observables
0
sin(2? )
for b ? ccs, sss
and
with
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sin 2? first UT input that is not theory
limited !

• The raison dêtre of the B factories

Theory uncertainty ?
HFAG Winter 2005
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? next UT input that is not theory limited
?
Tree dominant
Penguin competitive ?
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Charmless b ? u Decays

• Tree T amplitude dominates

No direct CP violation

• Time-dependent CP observable

ideal scenario
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Isospin Analysis for B ? ? ? , ??
Account
Constraints
Observables
Unknowns
13 unknowns 7 observ. 5 constraints 1 glob.
phase 0 ?
2 isospin triangles and one common side
B, S?? , C?? B0, ACP B00, (S00), C00
?, T, P, T0, P0, T00, P00

• Assumptions
• neglect EW penguins (shifts ? by 2o)
  penguins
• neglect SU(2) breaking
• in ?? Q2B approx. (neglect interference)

? can be resolved up to an 8-fold ambiguity
within 0,?
Refs. for SU(2) analyses Gronau-London, PRL,
65, 3381 (1990), Lipkin et al., PRD 44, 1454
(1991), a.o.
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CP Results for B 0? ? ?

• Results for the time-dependent analysis

BABAR (227m) Belle (275m) Average
S?? 0.30 0.17 0.03 0.67 0.16 0.06 0.50 0.12
C?? 0.09 0.15 0.04 0.56 0.12 0.06 0.37 0.10
BABAR, hep-ex/0501071 Belle, hep-ex/0502035
Mediocre (but improved) agreement ?2 7.9 (CL
0.019 ? 2.3s)
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B ? ? ? Isospin Analysis

• ?2 fit of isospin relations to observables

BABAR
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A surprise the B ? ? ? Isospin Analysis

• Natures great present longitudinal
  polarization dominates ? almost no CP dilution

• Rates for the B ? ?? system

? small penguins !
BABAR, hep-ex/0412067

• Results from CP fit

BABAR, hep-ex/0503049
BABAR (232m)
S??,L
C??,L 0.03 0.18 0.09

• Isospin analysis

penguin / tree
As expected much smaller
than in B ? ??
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The B ? ?? System

• Dominant mode ? ? is not a CP eigenstate

Aleksan et al, NP B361, 141 (1991)

• Isospin analysis requires to constrain pentagon

Lipkin et al., PRD 44, 1454 (1991)

• 13 observables vs 12 unknowns ?
• needs statistics of Super-B ? systematics?

• Better exploit amplitude interference in Dalitz
  plot

Snyder-Quinn, PRD 48, 2139 (1993)

• simultaneous fit of ? and strong phases
• BABAR determines 16 (27) FF coefficients
• correlated ?2 fit to determine physics
  quantities

BABAR
?0?0
??
??
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Results of B 0? (?? )0 ? ? ? ? 0 Dalitz
analysis

• From the 16 FF coefficients one determines the
  physical parameters

• Parameters ?, T,T,T00,P,P

• Direct CP violation ?

Average BABAR (213m) Belle (152m)
Scan in ? using the bilinears
A 0.47
A 0.15 0.09
??2(no direct CPV) 14.5 (CL 0.00070 ? 3.4s)
A
no direct CPV
BABAR
A
BABAR, hep-ex/0408099
36
Combination of ??, ??, ?? first measurement of ?

• Combining the three analyses (B ? ?? best single
  measurement)

• mirror solution disfavored
• for the SM solution we find

37
digression Color-Suppressed Amplitudes
Famous modes

• The color of the quarks emitted by the virtual W
  must correspond to the external quark lines to
  produce color-singlets ? suppression by 1/Nc
  (naïve!)

Suppression ? verified in B(B0 ? D0?0)/B(B0 ? D
?) (1/10.4)exp ? (1/Nc)2
important non-factorizable contributions when
large penguins ? Large u-penguins ?
38
? next UT input that is not theory limited

• GLW D 0 decays into CP eigenstate
• ADS D 0 decays to K ? (favored) and K ?
  (suppressed)
• GGSZ D 0 decays to KS? ? (interference in
  Dalitz plot)
• All methods fit simultaneously ?, rB and ?

the million dollar Q
Gronau-London, PL B253, 483 (1991) Gronau-Wyler,
PL B265, 172 (1991)
Atwood-Dunietz-Soni, PRL 78, 3257 (1997)
Giri et al, PRD 68, 054018 (2003)
No Penguins ?
relative CKM phase ?
Tree dominant
Tree color-suppressed
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ADSGLW Constraint on ?

• BABAR and Belle have measured the observables for
  GLW and ADS in the modes B ? D0K, D0K, D0K

not yes used

• No significant measurement of suppressed
  amplitude yet ? limit rB() ? 0.2

BABAR, hep-ex/0408082, 0408060, 0408069, 0408028
Belle, Belle-CONF-0443, hep-ex/0307074, 0408129

• for the SM solution

• not yet competitive with CKM fit

40
GGSZ Constraint on ?

• Promising Increase B decay interference through
  D decay Dalitz plot with D 0? KS? ?
• huge number of resonances to model K (892),
  ? (770), ? (782), f0(980,1370), K0 (1430), ... ?
• amplitudes of Dalitz plot measured in charm
  control sample ?

41
B ? ???

• A new star at the horizon helicity-suppressed
  annihilation decay sensitive to fB?Vub
• Powerful together with ?md removes fB
  dependence
• Sensitive to charged Higgs replacing the W
  propagator

• Best current limit from BABAR

M. Datta, SLAC seminar 2005

• Prediction from global CKM fit

42
Putting it all together
t h e
g l o b a l C K M f i t
Inputs
Perfect agreement if it werent for the
s-penguin decays
43
Putting it all together
the impact of the
unitarity triangle angles
?
The angle measurements dominate !
44
Consistent Predictions of all CKM-related
Observables
FOR UPTODATE RESULTS CHECK THE CKMFITTER WEB
numerical results at http//www.slac.stanford.edu
/xorg/ckmfitter/ and http//ckmfitter.in2p3.fr/
(mirror)
45
Theres much more in it

• Other CKM-related topics not discussed in this
  colloquium
• super rare kaon decays K ? ???
• charged decay already seen by E787, E949)
• radiative and leptonic B decays B ? ? ?, B ?
  K?, b ? s ?,
• model-independent analysis of new physics in
  mixing and decay

E787, PRL 88, 041803 (2002) E949, PRL 93, 031801
(2004)
next pages

• Dynamical analysis of B ? ??, K?, KK decays under
  different hypotheses
• Most simple charmless B decays theory
  understanding must start here
• SU(2) ? done for ??, not fruitful for K? at
  present
• SU(3)
• QCD Factorization

next pages
Puzzle ?
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Radiative Penguin Decays

• Radiative penguin decays B ? ?? (? Vtd2)
  and B ? K? (? Vts2) sensitive to New Physics

• Ratio of BRs predicted more cleanly than the
  individual rates SU(3) breaking correction

Ali, Parkhomenko, EPJ C23 (2002) 89 Bosch,
Buchalla, NP B621 (2002) 459 (and later
papers) errors from CKM 05
90 CL

• So far only upper limit for B ? ??

90 CL
BABAR, PRL 94, 011801 (2005) Belle,
hep-ex/0408137 (prelim.)
Charged modes larger limit
, but less
theoretically clean
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digression Puzzling B ? ? ? , K?, KK Decays
SU(3)

• About puzzles
• there is a ?? puzzle why are
  color-suppressed terms (or u-penguins) so large
  ?
• there is no K? puzzle using SU(2)
  quadrilateral system not constraining enough 9
  params vs. 9 obs
• there seems to be a K? puzzle using SU(3) when
  neglecting annihilation terms and PEW,C

Silva-Wolfenstein, 1993 Buras et al. (BFRS), EPJ
C32, 45 (2003) Chiang et al, PRD D70, 034020
(2004) Wu-Zhou, hep-ph/0503077 Charles et al.,
EPJ C21, 225 (2001) Charles-Malclès-Ocariz-AH, in
preparation apologies to the many other authors
on this problem

• Complete analysis in strict SU(3) limit

• Global analyses
• at present 13 parameters vs. 19 observables
• when everything is measured (incl. Bs)
  
• 15 parameters vs. 50 observables

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digression Puzzling B ? ? ? , K?, KK Decays
QCDF

• Several theoretical tools exist for nonleptonic B
  decays. All are based on the concept of
  Factorization

• QCD FA
• pQCD
• SCET
• including the treatment of charming
  penguins by Ciuchini et al.

Beneke et al, PRL 83, 1914 (1999) NP B675, 333
(03)
Keum et al, PLB 504, 6 (2001) PRD 67, 054009 (03)
Bauer et al, PRD 63, 114020 (2001)
Color Transparency
Is there a puzzle ?

• With conservative error treatment, only a
  data-driven fit is predictive

49
And the near Future ?
t h e g l o b a l C K M
f i t i n 2008
Inputs
?...?
50
and the far
F U T U R E
NA48
t h a n k y o u
51
a p p e n d i x none
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sin(2? ?)
Tree dominant
Tree doubly CKM-suppressed

• Relative weak phase 2? ?

but ? dependence of the order of O(104)
full toys

• Huge statistics, but small CP asymmetry
• Unknowns rB0, ? and ? ? needs external
  input
• Use SU(3) to estimate rB0() (theory error
  30)

therefore not used in global CKM fit
BABAR, hep-ex/0408038, hep-ex/0408059
Belle, hep-ex/0408106, PRL 93 (2004) 031802
Erratum-ibid. 93 (2004) 059901