Flavor Diagram Approach to Hadronic B Decays

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Flavor Diagram Approach toHadronic B Decays
November 30, 2004 NTHU/NCTS Seminar

• Cheng-Wei Chiang
• National Central University

2
Outline
-

• Beauty in B physics
• CPV in SM
• unitarity triangle
• Charm in B physics
• charmed decays for some B meson properties
• charmed decays for indirect CPV
• charmless decays for direct CPV
• global c2 fits and weak phase g
• Strangeness in B physics
• accumulating hints of new physics in charmless B
  decays
• FCNC Z0 as an example
• Perspective and Summary

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Beauty in B Physics
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4
Motivations for Studying B Decays
-

• We have observed in K meson system
• indirect CPV 1964 in KL ? p p
• direct CPV 1999 in CERN-NA48 and FNAL-KTeV
  expts
• B factories have produced a lot of interesting
  results, particularly in measuring indirect CPV
  in the B system
• sin2b0.725 ?0.037 from y KS data
  (ICHEP) indicating that B physics is entering a
  precision era
• Finally, we have recently observed direct CPV in
  B system (ACP(Bd ? pK) 0.113 0.019).
• Most branching ratios of charmless B ? P P and P
  V are currently measured with errors about
  1020 (mostly based upon 100M B anti-B pairs)
• 510 errors on amplitudes
• One hopes to have most modes
• more precise information on a and g (

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Beauty in the B Meson
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• The beauty of B mesons lies in its large mass or
  the mass hierarchy
• mq
• In the heavy quark limit, mQ ? 1, we discover
• Flavor symmetry dynamics unchanged under heavy
  flavor exchange (b ? c), corrections incorporated
  in powers of 1/mb1/mc
• Spin symmetry dynamics unchanged under heavy
  quark spin flips, corrections incorporated in
  powers of 1/mb.
• B mesons provide an ideal system for studying
  heavy-to-heavy transitions.
• Much progress has been made in understanding
  heavy-to-light transitions in recent years
• Perturbative approach naïve factorization,
  generalized factorization, QCD-improved
  factorization, pQCD, and SCET
• Nonperturbative approach flavor SU(3) symmetry.

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The Matrix
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Within SM, CPV in the quark sector is explained
using the CKM matrix, which is unitary and
complex
(Kobayashi and Maskawa, 1973)
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The Matrix Reloaded
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The CKM matrix written in terms of Wolfenstein
parameters (l, A, r, and h) becomes to
O(l3) Wolfenstein, PRL 51, 1945 (1983)
l ' 0.2264 A ' 0.801

• The ultimate goal of studying B physics is not
  only to achieve precision measurements of the
  above parameters, but also to discover evidences
  of new physics and possibly its type (e.g. GUT,
  SUSY, XD).
• One way to detect new physics is to perform
  consistency checks for the sizes and phases of
  the CKM elements.
• Even if no deviation is seen from SM in these
  studies, we can still obtain useful and stringent
  bounds on new physics scales.

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Unitarity Triangle
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• Vub and Vtd can be related to each other through
  the unitarity relation
• VudVub VcdVcb VtdVtb 0
• A triangle can be formed on a complex plane as a
  geometrical representation of the above relation,
  where a nonzero area signifies CPV.
• This triangle has three sizeable angles.

decay side
oscillation side
ACPpp,ph,rp
a (f2)
DMBd and DMBs
BR(B?Xc,uln)
g (f3)
b (f1)
(1,0)
(0,0)
ACP(t)J/Y KS, h KS, f KS(?),
ACPDCPK, Kp,
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Charm in B Physics
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Charmed Decays
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• B mesons decay dominantly into charmed final
  states used to determine many properties 20
  04 PDG
• Bd DMd 0.502 0.007 ps-1 Gd 1.542
  0.076 ps.
• Bs DMs 14.5 ps-1 Gs 1.461 0.057 ps.
• Vcb determined mainly from semileptonic B ?
  D() transitions important for normalization in
  the UT.
• Bd ? J/y Ks involves a tree-level, dominant
  subprocess b ? c anti-c s with no CPV phase
  Bd-anti-Bd mixing involves a factor e 2 i b.
• Time-dependent CPA gives Sy Ks sin2b
  0.7250.037 (WA), consistent with constraints
  from other processes.
• The result is clean without much ambiguity or new
  physics pollution (unless contrived cancellation
  between mixing and decay).

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Overall UT Fit Results(2004 Winter)
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CKM Fitter Group http//ckmfitter.in2p3.fr/
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Overall UT Fit Results(2004 Summer, ICHEP)
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CKM Fitter Group http//ckmfitter.in2p3.fr/
Everything simply fits together nicely!
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Charmless is Charmful !
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• Although rare in comparison with charmed decays
  (suppressed by CKM factors), charmless decays are
  actually very charmful and important processes.
• Include strangeness-conserving (DS0) and
  strangeness-changing (DS1) transitions some
  processes in the latter category already give us
  hints about new physics.
• Offers opportunities to discover direct CPV
  because many of them involve more than one
  significant subprocesses with different weak and
  strong phases.
• B ? p p, p h(0), r p provide info on a, as a
  result of the interference between mixing and
  decay
• B ? K p provides info on g.
• B ? Xu l n provides info on Vub (theoretically
  hard though because of the large charm
  background), thus one side of the UT.

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Importance of Strong Phases
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• Strong interaction matters because what we
  observe are hadrons but not the fundamental
  degrees of freedom in the theory.
• Consider rate CP asymmetry of modes with the
  amplitudes

• Such an asymmetry requires at least two
  amplitudes characterized by distinct weak phases
  and strong phases.
• It is of great importance to understand the
  patterns of FSI phases in as wide as possible a
  set of decays, although what we really care about
  are weak phases (signals), not really strong
  phases (noises).

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Getting Strong Phases
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• The Bander-Silverman-Soni (BSS) type strong phase
  calculation only accounts for the perturbative
  strong phases in penguin diagrams with
  intermediate q anti-q pair being on shell.
• BSS, PRL 43, 242 (1979)
• No first-principle method for computing FSI
  strong phases exists because they involve
  nonperturbative long-distance physics.
• see a recent try by Cheng, Chua, Soni,
  hep-ph/0409317
• One conventional and efficient method of
  obtaining strong phase information is to directly
  extract from data using isospin analysis.
• Flavor diagram approach offers a way to extract
  strong phases associated with individual
  topological amps and to relate them using flavor
  SU(3) symmetry.

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Flavor Diagram Approach
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• This approach is intended to rely, to the
  greatest extent, on model independent flavor
  SU(3) symmetry arguments, rather than on specific
  model calculations of amplitudes.
• Zeppenfeld, ZPC 8, 77 (1981) Chau Cheng, PRL
  56, 1655 (1986) PRD 36, 137 (1987) PRD 43, 2176
  (1991) SavageWise, PRD 39, 2246 (1989)
  Grinstein Lebed, PRD 53, 6344 (1996) Gronau
  et. al., PRD 50, 4529 (1994) 52, 6356 (1995)
  52, 6374 (1995)
• The flavor diagram approach
• is diagrammatic (can be formulated in a formal
  way)
• only concerns the flavor flow (arbitrary gluon
  exchange among quarks)
• has a clearer weak phase structure (unlike
  isospin analysis where different weak phases
  usually mix).
• Very recent works in this direction includeChua
  PRD 68, 074001 (2003) and Luo Rosner PRD 67,
  094017 (2003) for baryons Charng Li PLB 594,
  185 (2004) and hep-ph/0410005 for weak phase
  extraction and He McKellar hep-ph/0410098
  for analyzing recent data.

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Tree-Level Diagrams
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• All these tree-level diagrams involve the same
  CKM factor.

q u,d,s q d,s
tree (external W emission)
color-suppressed (internal W emission)
1/mb suppresseddue to fB.
annihilation (charged mesons only)
exchange (neutral mesons only)
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Loop-Level (Penguin) Diagrams
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NLO Flavor Diagrams in Weak Interactions
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• Nothing forbids you from drawing one of the
  following diagrams whenever you see T, C, or P
  in your amplitude list. They involve two weak
  boson propagators.

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Physical Flavor Diagrams
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• Treat T, C, P, E, A, S as leading-order
  amplitudes (note that only S is of loop nature)
  and PEW and PCEW as higher-order contributions
  (in the sense of weak interactions).
• Physical amplitudes contain flavor diagrams both
  leading order and next-to-leading order in
  weak interactions
• t T PCEW, c C PEW, p P PCEW / 3,
  s S PEW / 3, a A.
• Moreover, P contains t-, c-, and u-quark mediated
  penguins, Pt,c,u. One may use the unitarity to
  rewrite Pt as the sum of two parts, one having
  the same weak phase as Pc and the other having
  the same weak phase as Pt. This amounts to
  separating P into Ptc Ptu.
• Ptu involves the same CKM factor as the
  tree-level amplitudes. One may thus sweep this
  amplitude to the tree-level amplitude category.
  Note that this amplitude may be sizeable,
  particularly for DS 0 decays.
• For example, what many people call T or C
  extracted from p p decays are actually T Ptu
  and C Ptu. Thus, C / T 1 is possible.

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A Simple Example
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• Quark contents
• When vector mesons are involved, one further
  labels the amplitude by which meson the spectator
  quark goes into.
• Therefore,
• A(pp) (T P)
• A(pr) (TV PV).
• Minus sign comes from the wave functions of p
  and r.

pp-
pr-
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Hierarchy in Flavor Diagrams
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• In our definition, the amplitudes contains CKM
  factors and may involve an arbitrary number of
  gluon exchanges.
• An educated guess tells us that the magnitudes of
  the amplitudes should roughly satisfy the
  following hierarchical structure.
• It should be emphasized that l appearing in the
  hierarchy is not an expansion parameter but
  merely an order parameter. It simply reflects
  our naïve expectation in the magnitudes of flavor
  amplitudes.

when going from 1st row to 2nd row - tree-type
amps suppressed because Vud?Vus - loop-type amps
favored because Vtd?Vts
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Global Fits to Charmless Decays
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• Goals for the global fits
• Check if the SM offers a consistent picture for
  all available data
• Check the working assumption of SU(3)F
• Extract weak phase g (thus a by unitarity)
• Extract strong phases check Lipkin conjecture in
  V P decays
• Make predictions of unseen modes based upon
  current data.
• Parameters involved in the fits include
• Amplitude sizes
• Weak phases
• Strong phases.
• Data points used in the c2 fits include
• Branching ratios
• CP asymmetries (time-dependent and -independent).

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Some Basic Formulas
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• The invariant matrix element M for a decay
  process B ? M1 M2 and the corresponding decay
  width are
• where p is the 3-momentum of the final state
  particle in the rest frame of B. Note that M may
  contain polarization vector summation and average
  as is the case for final states containing vector
  mesons.
• We also assume the following SU(3)F relations
  (with l 0.224)

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B ? V P Decays
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CWC, M. Gronau, Z. Luo, J. Rosner, D. Suprun, PRD
69, 034001 (2004) hep-ph/0307395.
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Fitting Parameters for VP Modes
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Fitting Parameters for VP Modes
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• We thus have the following parameters
• amp sizes tP , tV , CP , CV , p0
  P , p0 V , P0 EWP , P0 EWV
• strong phases dP, dV, f
• weak phase g only (no b dependence).
• symmetric under simultaneous changes g ? p
  g, dP,V ? p d P,V and f ? f.

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List of Modes
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In our fit, there are totally 34 observables
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List of Modes
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finally, include time-dependent CP asymmetries
Sf Ks-0.1470.697 (S2.11), Af Ks0.0460.256
(S1.08) (contribute constant to c2) Browder,
talk at LP03 Srp-0.130.180.04,
DSrp0.330.180.03 (provide b dependence)
BaBar, talk by Jawahery at LP03
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c2-g Plots (34 data points)
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• major changes in c2 at g'65 and 165 from step
  1 to step 2
• positions of minima almost unaffected
• g(5315-33) if Srp is left out, c.f. g(636)
  here

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Fit Results
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Predictions for VP Modes(DS0, complex pV/pP)
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Predictions for VP Modes(DS1, complex pV/pP)
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Some Discussions
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• Overall, fits are satisfactory (at 38 and 55 CL
  for 10- and 12-parameter fits) and have solutions
  g (656) and (636) consistent with
  constraints from other processes.
• Data of r p play the roles of breaking the g ? p
  g symmetry and stabilizing the fit results.
• Note that the c2 fits allow us to extract
  preferred values of fitting parameters along with
  their 1 s errors. Moreover, we have an idea
  about how good our fits are from the CL.
• Global fits prefers the Lipkin conjecture p0
  p0 P.
• Only partial SU(3) breaking effect included for T
  amps can verify SU(3) for penguin amps when B ?
  K anti-K (pV) and anti-K K (pP) rates are
  measured.

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B ? P P Decays
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CWC, M. Gronau, J. Rosner, PRD 68, 074012 (2003)
hep-ph/0306021 CWC, M. Gronau, J. Rosner, D.
Suprun, PRD 70, 034020 (2004) hep-ph/0404073.
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List of Modes
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large CP asymmetries BR too small compared To
QCD fact. predictions
BR too large compared to QCD fact. predictions
purely p?
p K anomaly
need sS-PEW / 3
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c2-g Plot
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• From bottom to top, we use 8 and 6
• parameters to fit 14 data points (p p
• and K p) and 13 and 11 parameters to
• fit 24 data points (further including
• final states with h and h0).
• Find g ' 54 66, results still consistent
• with but less stable than the V P case.

CKM fitter
38
Fit Results
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consistent with other constraints
large C/T ratio and non-trivial relative strong
phase unable to account for in perturbation
all strong phases relative to P
required to account for the large h 0 K BRs
satisfactory overall fit results
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Predictions for PP Modes
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no problem in p p modes
still problematic in p K modes
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Some discussions
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• see also Chua, Hou and Yang, Mod. Phys. Lett.
  A18, 1763 (2003)
• Buras et al, PRL 92, 101804 (2004)
  hep-ph/0402112
• Fits to p p p K data
• requires large C/T ratio ( 0.5)
• requires a nontrivial strong phase between C and
  T ( 100).
• Fits to all PP data
• one needs to introduce S (singlet penguin), Ptu
  (t,u-mediated penguin)
• one needs to introduce Stu (t,u-mediated singlet
  penguin) particularly for the ph mode.
• Robust results in our fits
• magnitude of QCD penguin P
• relative strong phase between T and P
• sizes of electroweak penguins (color-allowed and
  -suppressed), consistent with Neubert-Rosner
  relation
• obtain g ' 60 (48 with CKM fitter and earlier analysis for VP
  modes.
• We do not fully trust the stability of the
  shallow minima.

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Strangeness in B Physics
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V. Barger, CWC, P. Langacker, H.S. Lee, PLB 580,
186 (2004) hep-ph/0310073 V. Barger, CWC, J.
Jiang, P. Langacker, PLB 596, 229 (2004)
hep-ph/0405108 V. Barger, CWC, P. Langacker,
H.S. Lee, PLB 598, 218 (2004) hep-ph/0406126.
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p K Anomaly
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• Within the SM, the following ratios should be
  approximately equal
• but show a 2.4s ? 1.9s difference.
• Possible explanations
• underestimate of p 0 detection efficiency
  Gronau and Rosner, hep-ph/0402112
• new physics. Buras et al, PRL 92, 101804
  (2004) NPB 697133 (2004), hep-ph/0410407
• One minimal explanation is that the color-allowed
  electroweak penguins cause the problem ?
  isospin-violating new physics

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Z0 Model With FCNC
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• The B ? p K decay can be a tree-level process
  mediated by a Z' boson if there are FCNC
  couplings (possible for family non-universal
  charges).
• We simply a general Z' model by assuming
• (i) no right-handed flavor-changing couplings,
• (ii) no significant RG running effect between MZ'
  and MW scales,
• (iii) negligible Z' effect on the QCD penguins so
  that the new physics is manifestly
  isospin-violating.
• With these simplifications, we have 3 parameters
  left in the model.

carrying a new CP-violating source
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Parameter Extraction
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• Following the arguments in Buras et al, new
  physics is coded by the parameters
• Found solutions from p p and p K data
• Correspond to our parameters

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Simultaneous Solution to p K and f KS
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• Can the p K anomaly and f Ks asymmetries be
  accounted for by the same thing at the same time?
• According to Buras et al, their solution our
  solution (AL) to the p K anomaly leads to S(f
  Ks) greater than S(Y Ks)!
• However, due to different interference patterns
  between O7,8 and O9,10 operators in our model, it
  is possible all our other solutions (BL, ALR and
  BLR) to have S(f Ks) smaller than S(Y Ks).

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Perspective and Summary
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• Flavor diagram approach provides a simple and
  reliable picture for describing B decays. It is
  phenomenological (data driven), contains LO and
  NLO amps in weak interactions but all orders in
  strong interactions, includes final state
  interacting effects, and suffers from SU(3)F
  breaking effects.
• Flavor SU(3) generally fits data well, with some
  exceptions. Predictions are made based upon
  current measurements and provide tests of the
  formalism.
• All fits provide information on g that is
  consistent with other extractions.
• Results from ICHEP are being analyzed by D.
  Suprun for his thesis.
• We need to know more information about strong
  phases. In particular, one should understand
  better about final-state rescattering effects.
• We hope to see a proof of factorization in
  processes of interest to us, in particular, those
  involving penguin diagrams.
• We hope to see more affirmative evidence of new
  physics in B physics, e.g., Sf KS the p K
  anomaly, large Bs anti-Bs mixing, etc.

47
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• Thank You