Interpreting CP asymmetries in

1
Interpreting CP asymmetries in
2
B ? ?? CP asymmetries
Tree diagram
Penguin diagram
Rt /Rc
?
Ru /Rc
g
b
need P/T and ?arg(P/T)
3
Theoretical frameworks

• strong isospin symmetry SU(2) (GL)
• CP-averaged Br(B???) only (?0?0 not seen yet)
• EW penguins neglected
• 1 SU(3) flavour symmetry (BF,Ch)
• OZI-suppressed annihilation penguins neglected
• No correction of SU(3) breaking

• 1 P?? from K0?- (GR,BBNS)
• Rth from QCD factorisation
• Neglect annihilation diagram in K0?-
• ? remains unconstrained
• QCD factorisation (BBNS)
• Use the prediction of both P/T and ?
• Non-factorisable 1/mb contributions fixed to
  default value

use Br(B0?K?-) and P?? PK?
GL Gronau, London, Phys.Rev.LettD653381,1990
BF Buras,Fleisher, Phys.Lett.B360138,1995 Ch
Charles, Phys.Rev.D59054007,1999
GR Gronau, Rosner, Phys.Rev.D65013004,2002 BBNS
Beneke et al., Nucl.Phys.B606245-321,2001
4
Experimental inputs
Global CKM fit using standard constraints
(referred as standard CKM fit in this talk)
ICHEP02 Aspen03
BaBar Belle
S?? 0.02 ? 0.34 1.23 ? 0.42
C?? 0.30 ? 0.25 0.77 ? 0.28
? -0.10 0.024
sign convention changed!
ICHEP02 Branching fractions (x10-6) WA BaBar
Belle CLEO
not seen
?32? CL range
CKMFitter Hoecker et al., Eur.Phys.J.C21,225,2001
and http//ckmfitter.in2p3.fr
5
Constraints in the (r,h) plane from isospin
analysis
BABAR
Belle
BABAR
Belle
no significant constraints
Grossman-Quinn 98 Charles 99 Gronau-London-Sinha
-Sinha 01
Gronau,London,Sinha,Sinha bound
6
Constraints in the (r,h) plane SU(3)
BABAR
Belle
no significant constraints
Charles 99
7
Constraints in the (r,h) plane P?? from K0?-
BABAR
Belle
8
Constraints in the (r,h) planeQCD Factorisation
BABAR
Belle
BABAR
Belle
Negative C?? and small positive ? negative ?
9
What about ? ?
BABAR
Belle
At present, significant theoretical input needed
to extract ?
10
QCD Factorisation uncertainty from hard
spectator interaction and annihilation diagram
BABAR
Belle
no zoom
Non-factorisable power-suppressed contribution
parameters free
11
Constraints/predictions on P/T and ?
(C??,S?? ) and (? ,?) from standard CKM fit
non-factorisable contributions fixed

• non-factorisable contributions free
• theoretical parameters varied within a given
  range
• uncertainty from (? ,?)

12
Predicting C?? and S?? using ? ,? from standard
CKM fit
Only predictive approach QCD Factorisation. poor
knowledge of sin2? ? large uncertainty in S??
13
Constraint on Br(B ? ?0?0)
Inputs C??, Br(B ? ??-), Br(B ? ??0)
Moriond02 Belle measurements !
!
S??
C??
Gronau-London-Sinha-Sinha 01
14
How about More Statistics?
Isospin analysis for present central values, but
500 fb1 (BaBar C??,,S?? and WA branching
fractions)
and even more...
The only hope for BaBar and Belle is not to
observe B0 ? ?0?0
15
Conclusion

• Various strategies to interpret time-dependent
  asymmetry measurements C??, S?? studied
• Significant constraints on ? from QCD
  Factorisation but still need validation from data
• Qualitative information when constraining the
  penguin amplitude using Br(B-?K0?-)
• Mild assumption frameworks based on SU(2) and
  SU(3) do not lead to significant constraints
• If central value of BR(?0?0) stays large, isospin
  analysis probably cannot be performed by first
  generation B factories