1. Measurements of the UT Angle a from BABAR
Carlos A. Chavez
University of Liverpool
On behalf of the BABAR collaboration
The 12th International Symposium on Particles Strings and Cosmology
PASCOS 2006
The Ohio State University. Wednesday, September 13, 2006
The University of Liverpool

2. Outline B → +−, ± 0 , 00 B → +−, ±0, 00 B0 → ()0
Introduction to the CKM angle 
Analysis techniques, BABAR results
and their implications for  :
B → +−, ± 0 , 00
B → +−, ±0, 00
B0 → ()0
Summary
All these are new results based on 347 million of BB pairs
(except ±0 uses 232 million)
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

3. How to measure a ?
Defined as :
Need to look for :
B mesons decaying to CP eigenstates through transitions
Tree
Need to measure :
ACP
Indirect CP
Direct CP
@ Tree level: ACP (t )  sin(2a) ; Direct ACP = 0
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

4. How to measure a ? (2)
Penguin
Tree +
Carries a different phase compared to tree level
Tree + Penguins: ACP (t )  sin(2aeff); aeff = a +D ; direct ACP ≠ 0
We measure
then need to bound
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

5. University of Liverpool
Isospin analysis in B →  , ρρ
M. Gronau, D. London, Phys. Rev. Lett. 65, 3381 (1990)
6 unknowns
 → 6 observables (there is no vertex to measure S00)
 → 5 observables (or 7, when both C00 and S00 are measured)
 → there are 3 such relations (one for each polarization state)
4-fold ambiguity in 2Δ : due to orientation of triangles
Neglecting EW penguins, A ± 0 is a pure tree mode, and so the two triangles share a common side:
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

6. University of Liverpool
Analysis Techniques
Signal selection
B candidate’s energy and mass
Particle identification
/K separation (Cherenkov light detector)
Signal
Background
K+K-
K+p-
p+p-
Background
12 σ  /K separation at 1.5 GeV/c, 2 σ at 4.5 GeV/c
Calibration sample: B− → −D0, D0 → +K−
From p+p- Monte-Carlo
Event Shape variables for background suppression p* h+ q* e- e+ e- e+ h-
Background events from light quark have jet-like topology
B signal
B events are spherical
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

7. University of Liverpool
BABAR results: B0 → +− (1)
hep-ex/
Simultaneous ML fit to B0 → +−, K+−, +K−, K+K− ( 347 Million of BB pairs )
Using DIRC Cherenkov angle to separate  / K, additional  / K / KK separation from ΔE
N+− = 675 ± 42
B0 tags
signal
background
mES Δt
B0 tags _
asymmetry
sPlot:
Builds a histogram of x excluding it from the Maximum-Likelihood fit, assigning a weight to each event, keeping all signal events, getting rid of all background events, and keeping track of the statistical errors in each x bin
M. Pivk and F. R. Le Diberder,
“sPlot: a statistical tool to unfold data distributions,” Nucl. Instrum. Meth. A 555, 356 (2005) [arXiv:physics/ ].
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

8. University of Liverpool
BABAR results: B0 → +− (2)
hep-ex/
3.6 σ evidence for CP violation is observed
S = −0.53 ± 0.14 ± 0.02
C = −0.16 ± 0.11 ± 0.03
The result
(S,C) = (0.0, 0.0)
is excluded at
a % C.L.
(3.6 σ)
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

9. BABAR results: B → ±0, 0 0
hep-ex/
(using 347 Million of BB pairs)
Simultaneous ML fit to B+ → +0, K+0, using DIRC Cherenkov angle to separate  / K
In B0 → 00 we measure branching fraction and time-integrated direct CP asymmetry
(In addition to 0 → , we use merged 0 and  → e+e− conversions)
N±0 = 572 ± 53
N00 = 140 ± 25
±0
mES
mES
00
sPlot - qq
background
signal
B± → ±0 background
Br±0 = (5.12 ± 0.47 ± 0.29)  10−6
Br00 = (1.48 ± 0.26 ± 0.12)  10−6
C00 = −0.33 ± 0.36 ± 0.08
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

10. a from B →  results |Δ |   = 0 excluded at
Only the B → branching fractions and isospin-triangle relations are used in arriving at these constraints on Δ = | − eff| and on  itself
 near 0 is disfavored by other experimental information (rp)
|Δ | 
 = 0 excluded at
1−C.L. = 4.4  10−1
|Δ | < 41º at 90% C.L.
BaBar-CONF-06/039 or hep-ex/
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

11. B →  angular analysis fL(B0 → +−)WA= 0.967+0.023
 is a vector-vector final state
An angular analysis is required to separate the CP content
“helicity frame”
pure CP = +1
transverse
is not a CP
eigenstate
Fortunately, the helicity-zero state in B →  decays is dominant (fL close to 1):
fL(B0 → +−)WA=
−0.028
fL(B± → ±0)WA= 0.96 ± 0.06
Heavy Flavor Averaging Group, April 2006,
We have the same situation as in B →pp decays
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

12. BABAR results: B0 → +− N+− = 615 ± 57 B0 tags ΔΕ mES B0 tags
hep-ex/
N+− = 615 ± 57
(using 347 Million of BB pairs)
B0 tags ΔΕ
B0 tags _
mES
sum of backgrounds
BABAR
preliminary
 helicity
m±0
asymmetry
distributions for the highest-purity tagged events
Δt (ps)
Br +− = (23.5 ± 2.2 ± 4.1)  10−6
Slong = −0.19 ±
−0.07
fL(B0 → +−) = ±
−0.013
Clong= −0.07 ± 0.15 ± 0.06
Important to reduce systematics:
hep-ex/ ,
accepted by PRD
Br (B0 → a± )  Br (a± →  +  − ± ) < 30  10−6 (90% C.L.) 1
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

13. University of Liverpool
BABAR results: B0 → 00
hep-ex/
N00 = ± 22
−31
3.0  significance
(using 347 Million of BB pairs) ΔΕ
mES
0f0
00
Results are statistically consistent with the previous analyses
Br00 = ( ± 0.27)  10−6
−0.36
fL(B0 → 00)= ± 0.05
−0.13
The main systematic errors are dominated by interference with B0 → a± (1260)  (where a± (1260) →    ±  ±) and by PDF parameter uncertainties 1 1
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

14. University of Liverpool
BABAR results: B± → ±0
hep-ex/
(Based on 232 million BB pairs)
N±0 = 390 ± 49
BABAR
preliminary
BABAR
preliminary
mES
continuum + BB
backgrounds ΔΕ
Br±0 = (16.8 ± 2.2 ± 2.3)  10−6
fL(B± → ±0) = ±
−0.027
The systematic error is dominated by modeling of backgrounds, signal misreconstruction, and by statistical PDF uncertainties
The latest BABAR measurement in B± → ±0 allows the  isospin triangle to close
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

15. University of Liverpool
a from B →  results
Only the B → branching fractions, polarization fractions and isospin-triangle relations are used in arriving at these constraints on Δ =  − eff and  itself Δ
BABAR
preliminary 
BABAR
preliminary
|Δ | < 21º at 90% C.L.
[74, 117]º
at 68.3% C.L.
|Δ | < 18º at 68% C.L.
Improvement in the precision of the the  isospin analysis will be possible with the determination of both C and S from B0 →00 (need more data)
BaBar-CONF-06/27, BaBar-CONF-06/016
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

16. B0 → ()0 Dalitz-plot analysis
rp is not a CP eigenstate
In principle we can use an isospin-pentagon analysis method, but is not suitable with current statistics
A. Snyder and H. Quinn,
Phys. Rev. D, 48, 2139 (1993)
Time-dependent Dalitz-plot analysis assuming isospin symmetry
Monte Carlo
Interference in the corners of the Dalitz plot provides information on strong phases between resonances
allowing the extraction of the angle a with no ambiguity
r0p0
Measures the time-dependent decay rate B0 (B0 ) using:
r+p−
r−p+
Fitting for 27 coefficients of the bilinear form factors in the
time-dependent decay rate.
The resonances  (770) ,  (1450) and  (1700)
are all included in this analysis
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

17. Time & flavor integrated A = −0.142 ± 0.041 ± 0.015
BABAR results: B0 → ()0 (1)
BaBar-CONF-06/037 ΔΕ
minimum of the three di-pion invariant masses
mES
data
projection of the fit result
signal misreconstruction
expected B background
continuum background
NN output
Δt/(Δt) m'
 '
S = 0.01 ± 0.12 ± 0.028
C = ± ± 0.037
Time & flavor integrated A = −0.142 ± ± 0.015
A & C are transformed into more physically Intuitive quantities
A = 0.03 ± 0.07 ± 0.03 +−
quasi-two-body approach
(ignoring interference):
ΔS = 0.06 ± 0.13 ± 0.029
A = − ± 0.07
−0.16 −+
ΔC = ± ± 0.021
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

18. University of Liverpool
BABAR results: B0 → ()0 (2)
+ − = arg(A+*A−) :
The constraint on  from B0 → ()0
is relatively weak but has no ambiguity
Relative phase between the amplitudes of
B0 → −+ and B0 → +−
+ −
[5, 63]º
at 68.3% C.L.
[75, 152]º
at 68.3% C.L. 
BaBar-CONF-06/037
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

19. Global constraint on    [86, 114]º
Frequentist interpretation of constraints on  using B → , ,  measurements:
97.5°
  [86, 114]º
at 68.3% C.L.
CKMfitter Group (J. Charles et al.),
Eur. Phys. J. C41, (2005),
[hep-ph/ ],
Belle excludes  in the range [9, 81]º at 95.4% C.L. from their latest B →  measurements
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

20. University of Liverpool
Summary
The BaBar experiment has improved the precision in several measurements related to the extraction of  , and has observed evidence of
CP violation in B0 → +−
The decay process B0 → 00
The branching fractions and CP parameters in B0 → 00 and B0 → 00 decays are crucial to make a precision measurement of  at the B-Factories
When extracting  from all BaBar measurements, the frequentist approach (CKMfitter) differs from the Bayesian one (UTfit) significantly. The larger of the 68.3% C.L. intervals is   [86, 114]º (CKMfitter), and gives a solution at 97.5°
Improved measurements of  from BaBar are expected in the future, more data and improvements to the analysis techniques are underway
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

21. University of Liverpool
Backup Slides
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

22. University of Liverpool
The CKM Matrix & CP Violation
3x3 unitary matrix:
3 real parameters,
1 phase: only source
of CPV in SM
CKM matrix describes mixing between flavor and weak eigenstates in the Standard Model.
Unitarity implies
Wolfenstein parameterization
This talk
(1,0)
(0,0)
(,)
CP violating phases
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

23. University of Liverpool
How to measure a ?
Decays sensitive to a
B0-B0 mixing
Tree level
Time dependent cp asymmetry:
Can be written as:
Indirect CP
relevant to a
Direct CP
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

24. University of Liverpool
B tagging & vertexing
BCP
(4S)
Btag
Accurate measurement of Dt requires accurate measurement of the decay vertices.
Resolution in Dt is dominated by the tagging side.
Determine resolution parameters from a large sample of fully reconstructed B events.
For time-dependent analyses we must know the flavor of BCP when Btag decays (t=0).
This is done by looking at the decay products of Btag. For instance, leptons and kaons.
The ”mistag” rate dilutes the measured asymmetry.
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU

25. Global constraint on    [164, 176]º at 68.3% C.L. 169.7°
Constraint on  from Bayesian interpretation using B → , ,  measurements
CKM fit
no  in fit
169.7°
  [164, 176]º at 68.3% C.L.
UTfit group (M. Ciuchini et al),
JHEP 0107 (2001) 013,
[hep-ph/ ],
University of Liverpool
Carlos A. Chavez
PASCOS 2006, OSU