Misure dell

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Misure dellangolo a del Triangolo Unitario

• Fabrizio Bianchi
• University of Torino and INFN-Torino

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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
• B0 (r p)0
• Summary and outlook

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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
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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
• sin?C
• Cabibbo angle

Wolfenstein Parameterization
2 1 l 3 2 l2 3 1 l3
h changes sign under CP
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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
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Normalized Unitarity Triangle
h
Apex at r, h
a
g
b
r
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Measuring a
Access to a from the interference of a b?u decay
(g) with B0B0 mixing (b)
Inc. penguin contribution
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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.
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PEP-II
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Luminosity
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BABAR Detector
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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

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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
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results (preliminary)
347 million BB
hep-ex/0607106
Background Signal
B0tag
mES
B0tag
mES
DE
DE
Npp 67542
sPlot
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results (preliminary)
535 million BB
hep-ex/0608035

Npp 146465
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results (preliminary)
C -A
347 million BB

Cpp - 0.16 0.11 0.03 Spp - 0.53 0.14
0.02
BaBar
(Spp, Cpp) (0.0, 0.0) excluded at 3.6 s
Average
535 million BB
Belle
Cpp - 0.55 0.08 0.05 Spp - 0.61 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
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(preliminary)
347 million BB
hep-ex/0607106
Np0p0 140 25
Npp0 572 53
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a constraint from
Da a - aeff
Da
1- C.L.
Da lt 41o at 90 C.L.
a
a
Frequentist interpretation use only the
B?pp branching fractions and isospin-triangle
relations.
1- C.L.
No stringent constraint from pp system alone ?
need rr and rp
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The analysis

• Worse than pp at first sight
• 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 rr- is larger than
  pp-
• Branching fraction for B0 g r0r0 is small
  (1.1x10-6)
• small penguin pollution

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results (preliminary)
347 million BB
hep-ex/0607098
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results
275 million BB
PRL 96, 171801 (2006)
Nrr 19432
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results (preliminary)
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results (preliminary)
232 million BB
hep-ex/0607092
Nrr0 390 49
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results (preliminary)
347 million BB
hep-ex/0607097
Nr0r0 98 32 22
3.0 s evidence
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a constraint from
PRL 96, 171801 (2006)
hep-ex/0607098
71, 105o at 68.3 C.L.
Use BR(B-gtr0r0)lt1.1 X 10-6
a
Frequentist interpretation use only the
B??? branching fractions, polarization fractions
and isospin-triangle relations. First evidence
of B?r0r0 Constraint on a is less stringent
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The Dalitz analysis
A. Snyder and H. Quinn, Phys. Rev. D, 48, 2139
(1993)
rp- r-p r0p0
B0
pp-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
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analysis (preliminary)
hep-ex/0608002
347 million BB
m and q are the transformed Dalitz variables
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analysis (preliminary)
hep-ex/0609003
449 million BB

• Dalitz Isospin (pentagon) analysis
• 26(Dalitz) 5(Br(r?p?), Br(rp0), Br(r0p),
  A(rp0), and A(r0p))

rp- r-p
r0p0
Signal SCF BB bkg continuum
mass
helicity
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a constraint from
(preliminary)
0,8o U 60,95o U129,180o at 68.3 C.L.


1- C.L.
1- C.L.
a (deg)
a (deg)
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a constraints
Belle rp result is not included. It will weakens
the suppression of solutions around 0o and 180o.
CKMfitter http//ckmfitter.in2p3.fr/ UTf
it http//utfit.dreamhosters.com/
Global Fit
B-Factories
aB-Factories 92 7o (SM Solution) aGlobal
Fit 93 6o
Nice agreement
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Pending Issues

• 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 - 0.16 0.11 0.03 Cpp - 0.55 0.08
0.05
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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, 074017(2005)
• I1 contribution due to finite width of r mass
  (rr mode).
• A.Falk et al. PRD 69, 011502(R)

Too small to be an issue at B-factories
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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-gta1p ?
• Constraint on a from B0-gtrr- and B-gtK0r
• 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.

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Backup Slides
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Trickle injection at the B Factories
PEP-II 5 Hz continuous KEKB at 5-10 min
intervals
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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)
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DIRC Control samples for p and K
p
K
Projection for 2.5 lt p lt 3 GeV/c
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(No Transcript)
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Time Dependent CP Asymmetry
mixing
decay
Amplitude ratio
CP eigenvalue
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results (preliminary)
Cpp - 0.16 0.11 0.03 Spp - 0.53 0.14
0.02
(Spp, Cpp) (0.0, 0.0) excluded at 3.6 s
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results (preliminary)
App 0.55 0.08 0.05 Spp - 0.61 0.10
0.04
Observation of Direct CPV at 5.5 s Observation
of mixing-induced CPV at 5.6 s
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a constraint from
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a constraint from
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formalism
Direct CP Violation
CP violation in the interference with and without
B mixing.
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parameters (prelim)
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Direct CP violation in
Significance for non-zero DCPV BaBar 3.0 s
Belle 2.4 s
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Differences in peak height
Courtesy of Marcella Bona