Guillaume Therin 1

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Measurements of sin(2b g) / sin(2f1 f3)
Guillaume Therin LPNHE Paris XLème rencontres
de Moriond
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CP violation in standard model
Unitarity triangle
CKM matrix
a/f2
g/f3
b/f1
sin (2b) 0.725 0.037
HFAG ICHEP04

• Experimental constraints on a
• Need direct measurements of g

• Talk on time dependent analysis to constraint
  sin(2bg)
• Experimental results on B0 ? D() p/r
• Partial reconstruction
• Full reconstruction
• B0 ? D()0K()0 branching ratio

See P.Krokovnys talk for a review of g
measurements.
http//ckmfitter.in2p3.fr
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CP violation in B0?D()p/r
g
2b
Favored b ? c decay
Suppressed b ? u decay
Strong phase difference
CKM angle
Determines the sensitivityof the method

• Large branching fraction for favoured decay (3?x
  10-3)
• Small BR for suppressed decay (10-6)
• Small CP violating amplitude

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Time-dependent decay rate distributions
?-
K
?-s
Tag B
K
U(4s)
Reco B
z
?
Dt _at_ Dz/gbc
Dz
Mixing-Decay interference
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P(B0 ? D() p ,Dt) 1 C cos(Dmd Dt)
S sin(Dmd Dt)



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P(B0 ? D() p ,Dt) 1 C cos(Dmd Dt)
- S sin(Dmd Dt)


neglecting terms in o(r2)

• Measurements of S and S- determine 2bg and d
  if r is an external input
• Experiment tag the flavour of the B with
  lepton and kaon categories

lepton tag
kaon tag
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Possible CP violation on the tag side
Long, Baak, Cahn, Kirkby, PRD68, 034010

• Potential competing CP violating effects in B
  decays used for flavour tagging

Kaon tag expect CP violation comparable to
signal ? Modified time distributions
signal side
tag side
P(B0 ? D() - p ,Dt) 1 C cos(Dmd Dt)
sin(Dmd Dt) 2r sin(2bgd) 2r sin(2bgd)
Kaon and other flavour tags
Lepton tags
Observables S, S-
Observables a, b, c
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Determination of r
I. Dunietz, Phys. Lett. B 427, 179 (1998)

• Simultaneous determination of sin(2??) and r
  from time-evolution is not possible with current
  statistics ? Need r as external inputs
• Estimate amplitude ratios from B0?Ds()?- using
  SU(3) symmetry

• Assuming several hypotheses
• Assuming factorisation in SU(3) symmetry
• W-exchange and annihilation diagrams neglected

without any theoritical errors
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B0?D-p partial reconstruction
Babar
BaBar Collaboration,hep-ex/0408038 (previous
reference)
227MBB
Lepton Tags
Find events with two pions and examine the
missing mass mmiss
Preliminary
All available statistics
Preliminary
kaon Tags
Preliminary
Lepton Tags
Mean value

• 18710 270 lepton tags

• 70580 660 kaon tags

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B0?D-p partial reconstruction (interpretation)
Babar
BaBar Collaboration,hep-ex/0408038 (previous
reference)
227MBB

• Adding 30 theoretical error on r(Dp) for
  different hypotheses
• Using the Feldman Cousins method

r-h plane whith experimental constraints on
sin(2ß?) and ß (from BaBar).
r 0.015 0.005 0.005
Preliminary
1 - CL
68
90
Preliminary
sin(2ß?)gt0.62 (0.35) _at_ 68 (90)CL
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B0?D-p partial reconstruction (lepton tag)
Belle Collaboration,hep-ex/0408106
154MBB
SF Sign(pfast) Sign(l)
OF Sign(pfast) - Sign(l)
Preliminary
Preliminary
Preliminary
Preliminary
Preliminary
Preliminary
helicity angle calculated with psoft
Fit Signal Background

• 2823 Same Flavour (SF)

• 10078 Opposite Flavour (OF)

S 0.035 0.041 0.018 S- 0.025 0.041
0.018
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B0?D()-p/r full reconstruction
BaBar Collaboration,hep-ex/0408106
D p-
D- p


B ? D p
D- p
D p-

• 7611 97 B ? Dp
• 7068 89 B ? Dp
• 4400 79 B ? Dr

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B0?D()-p full reconstruction
Belle Collaboration, PRL 93 (2004) 031802
Dp
Dp
Use kaon and lepton tags
Estimation of CP violation on the tag side with
B?Dl n
D p-
D- p
Assuming d 0 or p (factorisation)
D p-
D- p
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Summary of sin(2bg) results with B0 ? D()p/r
227 MBB
110 MBB
152 MBB
152 MBB
Partially rec.
Fully rec.
Partially rec.
Fully rec.
0.060 0.040 0.019
a(Dp)
0.049 0.031 0.020
-0.034 0.014 0.009
0.031 0.028 0.018
c(Dp)
0.004 0.028 0.018
-0.019 0.022 0.013
0.044 0.054 0.033
0.049 0.040 0.019
a(Dp)
0.032 0.031 0.020
0.062 0.037 0.018
c(Dp)
0.025 0.037 0.018
0.059 0.055 0.033
a(Dr)
0.005 0.044 0.021
c(Dr)
0.147 0.074 0.035
a 2 r sin(2bg) cos (di)
c 2 r cos(2bg) sin (di)
without any errors coming from theoretical
hypotheses
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Interpretation of sin(2bg) assuming SU(3)
Assign 30 theoretical error on r(Dp), r(Dp)
and r(Dr)
Bayesian approach
www.utfit.org
h
68
90
68
90
r
2bg
sin(2bg)gt0.74 _at_68 CL
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Constraining sin(2bg) with B0?D()0Ks
b?c amplitude
b?u amplitude

• Small branching fraction for favoured decay (3?x
  10-5)
• Large asymmetry
• B0?D()0Ks with any D0 measures sin2bg with time
  dependent analysis
• B0?D()0K0 with D0?CP eigenstate measures g
  (self-tagging mode ,not this talk)

For r00.4, an error of 0.5 on sin(2bg) is
expected with 550 MBB .
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Branching ratios of B0?D()0Ks
Preliminary
mes (GeV)
Belle Collaboration,hep-ex/0408108
BaBar Collaboration,hep-ex/0408052
Average of B0 and B0
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Conclusions

• Many different approaches to measure g have been
  investigated with similar sensitivity.
• Limits on sin(2bg) with time dependent
  analysis were updated
• Measurements on sin(2bg) still statistics
  limited.
• Some analyses need to be updated with all
  available statistics
• Need to estimate CP violation on the tag side to
  use completely kaon tag
• Results on g can be combined with other DK
  measurements (also no penguin contribution)
• With higher statistics, methods to constraint
  sin(2bg) with B0 ? D()0 Ks will play a role as
  well ( r 0.4 )

sin(2bg)gt0.74 _at_68 CL
Assuming SU(3) symmetry
www.utfit.org
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SU(3) breaking and Dsp0

• SU(3) has been proven to hold at a few level
  for factorizable processes, but here the heavy
  meson is emitted and factorization does not hold
• Note that the use of the form-factors
  automatically assumes factorization
• In the future BR(Dp0) will be measured
• expected to be 10-6
• SU(2) partner of Dp-
• SU(3) partner of Dsp0 ? will be able to test
  SU(3)
• First search of B?Dsp0
• Consistent with SU(2) prediction from Br(Dsp )
• Br(B?Dsp0) 1.6 10-5

Small statistics Annihilations around
Br(B?Dsp0)lt2.8 10-5_at_90 C.L.
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W-exchange diagrams

• B0?D()p- has contributions also from W exchange

Constrained by smallness of Br(B0?Ds-K)/Br(B0?D-p
)(1.40.5)10-2
c
D()-, Ds()-
p,K
u
Unfortunately this sets a limit only on the
annihilation on the cabibbo allowed process.
Assuming it is the same is controversial
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D()Ks probing annihilations
SU(2) partner of D0K Expected to be 10-7 but
could get large contributions from rescattering
Br(B? DKs) lt xxx 10-6 Br(B? DKs) lt 7 10-6
Note Br(B? D0K) (3.70.6)10-4 Br(B?
D0K)(3.61.0)10-4
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Avoiding colour suppression B0?DKSp (88 MBB)
b?c amplitude
b?u amplitude

• Method has two advantages
• Avoids colour suppression in b?u
• Integrating over Dalitz plane removes ambiguities
  in eventual g extraction
• First experimental step complete
• Branching fraction measurement
• Currently, Too few events for TD analysis
• ?1/3 of events are NOT in the K region

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Data samples collected with Belle and BaBar
BELLE _at_ KEK-B Accelerator
BaBar _at_ PEP-II Accelerator
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sin(2bg) in Pictures
No Interference ? CP Violation
CP Violation only in fully reconstructed B0 r ?
0
CP Violation in both tag and fully reconstructed
B0s r ? 0 and r ? 0

• r exaggerated (x5 expectation) to enhance visual
  effect
• Small values of r significantly reduce
  sensitivity of the method