1. Misure dell’angolo a del Triangolo Unitario
Fabrizio Bianchi
University of Torino and INFN-Torino

2. Outline Introduction to the measurement of a
Results from the B-factories:
B p+ p-, p± p0, p0 p0
B r+ r-, r± r0, r0 r0
B (r p)0
Summary and outlook

3. CKM Matrix I
SM accounts for flavor changing quark transition through the
coupling of the V-A charged current operator to a W boson:
where:
Vij are the elements of the CKM matrix
i, j run on the three quark generations

4. Wolfenstein Parameterization
CKM Matrix II
CKM matrix can be regarded as a rotation from the quark mass eigenstates (d, s, b) to a set of new states (d’, s’, b’) with diagonal coupling to u, c, t
Complex matrix described by 4 independent real parameters (including one phase)
l~ 0.22
sinθC
Cabibbo angle
Wolfenstein Parameterization
2 ® 1 ~l
3 ® 2 ~l2
3 ® 1 ~l3
h changes
sign under CP

5. Product of 1st and 3rd columns
Unitarity Triangle
Product of 1st and 3rd columns
(1 of 6 relations)
Can be represented as a triangle in the complex plane
a = f2
g = f3
b = f1
Dividing all sides by

6. Normalized Unitarity Triangleh
Apex at
r, h a g b r

7. Inc. penguin contribution
Measuring a
Access to a from the interference of a b→u decay (g) with B0B0 mixing (b)
Inc. penguin contribution

8. From aeff to a: Isospin Analysis
Gronau and London, Phys. Rev. Lett. 65, 3381 (1990)
Assume SU(2) symmetry among amplitudes
Neglecting EW Penguins:
is a pure tree mode.
The triangles share a common side.

9. PEP-II

10. Luminosity

11. BABAR Detector

12. Time Dependent Analysis Outline
Fully reconstruct the B decaying to a CP eigenstate.
Tag the flavor of the other B.
Mis-tag probability measured in Bflav sample.
Measure Dt.
Extract S and C with a ML fit on a signal enriched sample.
Signal PDF from MC.
Background PDF from MC or sidebands

13. Variables used in the ML fit
Event Topology
Combine variables in F or N
signal
signal
PID info:
DIRC + dE/dX (BaBar)
Aerogel + dE/dX (Belle) Dt
background
background

14. :results (preliminary)
347 million BB
hep-ex/
:results (preliminary)
Background Signal
B0tag
mES
B0tag
mES DE DE
Npp = 675±42
sPlot

15. :results (preliminary)
535 million BB
hep-ex/
:results (preliminary)
Npp = 1464±65

16. :results (preliminary)
C =−A
:results (preliminary)
347 million BB
Cpp = ± 0.11 ± 0.03
Spp = ± 0.14 ± 0.02
BaBar
(Spp, Cpp) = (0.0, 0.0) excluded at 3.6 s
Average
535 million BB
Belle
Cpp = ± 0.08 ± 0.05
Spp = ± 0.10 ± 0.04
2.3 s discrepancy
Observation of Direct CPV at 5.5 s
Observation of mixing-induced CPV
at 5.6 s

17. (preliminary) Np±p0 = 572 ± 53 Np0p0 = 140 ± 25 347 million BB
hep-ex/
Np±p0 = 572 ± 53
Np0p0 = 140 ± 25

18. a constraint from Da = a - aeff Da a a 1- C.L.
|Da| < 41o at 90% C.L. a a
1- C.L.
Frequentist interpretation: use only the B→pp
branching fractions and isospin-triangle relations.
No stringent constraint
from pp system alone
 need rr and rp

19. The analysis Worse than pp at first sight: However:
V V final state. Mixture of CP = +1 and -1: need to know each fraction
However:
~100% longitudinally polarized (~pure CP-even state)
no need for elaborate angular analysis
Branching fraction for B0 g r+r- is larger than p+p-
Branching fraction for B0 g r0r0 is small (~1.1x10-6)
small penguin pollution

20. results (preliminary)
347 million BB
results (preliminary)
hep-ex/

21. 275 million BB
results
PRL 96, (2006)
Nrr = 194±32

22. results (preliminary)

23. results (preliminary)
232 million BB
results (preliminary)
hep-ex/
Nr+r0 =390 ± 49

24. results (preliminary)
347 million BB
results (preliminary)
hep-ex/
Nr0r0 = 98 ± 32 ± 22
3.0 s evidence

25. a constraint from a hep-ex/0607098 PRL 96, 171801 (2006)
at 68.3% C.L.
Use BR(B->r0r0)<1.1 X 10-6 a
Frequentist interpretation: use only the B→ρρ
branching fractions, polarization fractions and
isospin-triangle relations.
First evidence of B→r0r0
Constraint on a is less stringent

26. The Dalitz analysis r+p- r-p+ B0 r0p0 p+p-p0 B0 Monte Carlo
A. Snyder and H. Quinn, Phys. Rev. D, 48, 2139 (1993)
r+p-
r-p+
r0p0 B0
p+p-p0 B0
Monte Carlo
Time-dependent Dalitz-plot analysis assuming
isospin simmetry.
26 coefficients of the bilinear form factor
terms occurring in the decay rate are
measured with a UML fit.
Physically relevant quantities are derived
from subsequent fits to these coefficients.
Interference provides information on strong phase difference
r(1450) and r(1700) are included

27. analysis (preliminary)
347 million BB
hep-ex/
m’ and q’ are the
transformed Dalitz variables

28. analysis (preliminary)
449 million BB
hep-ex/
Dalitz + Isospin (pentagon) analysis
26(Dalitz) + 5(Br(rp), Br(r+p0), Br(r0p+), A(r+p0), and A(r0p+))
r+p r-p r0p0
Signal
SCF
BB bkg
continuum
mass
helicity

29. a constraint from (preliminary)
[0,8]o U [60,95]o U[129,180]o
at 68.3% C.L.
1- C.L.
1- C.L.
a (deg)
a (deg)

30. a constraints Belle rp result is not included.
It will weakens the suppression
of solutions around 0o and 180o.
CKMfitter
UTfit
a constraints
Global Fit
B-Factories
aB-Factories = [ ] º
+11 -9
aB-Factories = [92 ± 7]o (SM Solution)
aGlobal Fit = [93 ± 6]o
Nice agreement
aGlobal Fit = [ ] º +5
-19

31. Pending Issues Cpp = - 0.16 ± 0.11 ± 0.03 Discrepancy on Cpp
Solutions at 0o and 180o should be (more) suppressed.
Using rp: nice suppression from BaBar, not from Belle.
Background modeling.
Interference with other resonances or non-resonant component in rp, rr modes.
Subtleties on statistical analysis with small statistics.
Cpp = ± 0.11 ± 0.03
Cpp = ± 0.08 ± 0.05

32. Uncertainties on a extraction
Possible contribution of EW penguin and isospin breaking effect.
EW penguin effect seems to be small (~2°).
Other isospin breaking effect ~ O(1°).
[M.Gronau and J.Zupan PRD 71, (2005)]
I=1 contribution due to finite width of r mass (rr mode).
[A.Falk et al. PRD 69, (R)]
Too small to be an issue at B-factories

33. Summary and Outlook The three modes are complementary.
Need to study them all.
Good agreement between the CKM fit (a determined by others) and direct measurements.
Still a lot to do.
Refine previous analysis and exploit new ideas:
a from B->a1p ?
Constraint on a from B0->r+r- and B+->K*0r+
[M. Beneke et al., Phys. Lett. B638, 68(2006)]
Doubling of statistics at the B-factories is much needed.
Looking forward to LHC and to a Super B-Factory.

34. Backup Slides

35. Trickle injection at the B Factories
Best shift, no trickle
Best shift, LER only trickle
Nov 2003
Best shift, double trickle
Mar 2004
PEP-II: ~5 Hz continuous
KEKB: at ~5-10 min intervals
PEP-II Lumi
HER current
LER current

36. Detection of Internally Reflected Cherenkov light
The high optical quality of the quartz preserves the angle of the
emitted Cherenkov light. The measurement of this angle, in
conjunction with knowing the track angle and momentum from
the drift chamber, allows a determination of the particle mass.
qc = arcos (1/nb)

37. DIRC: Control samples for p and K
Projection for
2.5 < p < 3 GeV/c

39. Time Dependent CP Asymmetry
mixing
decay
Amplitude
ratio
CP eigenvalue

40. :results (preliminary)
Cpp = ± 0.11 ± 0.03
Spp = ± 0.14 ± 0.02
(Spp, Cpp) = (0.0, 0.0) excluded at 3.6 s

41. :results (preliminary)
App = ± 0.08 ± 0.05
Spp = ± 0.10 ± 0.04
Observation of Direct CPV at 5.5 s
Observation of mixing-induced
CPV at 5.6 s

42. a constraint from

43. a constraint from

44. formalism Direct CP Violation
CP violation in the interference with and without B mixing.

45. parameters (prelim)

46. Direct CP violation in Significance for non-zero DCPV:
BaBar: 3.0 s Belle: 2.4 s

47. Differences in peak height
Courtesy of Marcella Bona
Differences in peak height