gf3

1
The CKM Angles a and b
Introduction Theory overview Experiments at
B-factories Measuring b/f1 Measuring a/f2 Summary
a/f2
b/f1
g/f3
2
The Cabibbo-Kobayashi-Maskawa Matrix

• The weak interaction can change the favor of
  quarks and lepton
• Quarks couple across generation boundaries
• Mass eigenstates are not the weak eigenstates
• The CKM Matrix rotates the quarks from one
  basis to the other

Vcb
Vub
3
Visualizing CKM information from Bd decays The
Unitarity Triangle
d
b
s

• The CKM matrix Vij is unitary with 4
• independent fundamental parameters
• Unitarity constraint from 1st and 3rd columns
• ?i Vi3Vi10
• Testing the Standard Model
• Measure angles, sides in as many ways possible
• Area of triangle proportional to amount of CP
  violation

u
Vud Vus Vub Vcd Vcs Vcb Vtd
Vts Vtb
c
t
CKM phases (in Wolfenstein convention)
4
Three Types of CP Violation
In this talk we will be discussing type III) CP
violation
5
CP Violation at the Y(4S)
CP violation from the interference between two
paths, decay with and without mixing
Direct CP Violation C¹ 0
Af/Af?1? direct CP violation
q/p?1? CP violation in mixing
Sf and Cf depend on CKM angles
6
Getting the Data Sample
BB Threshold

• The Y(4S) - a copious, clean source of B meson
  pairs
• 1 of every 4 hadronic events is a BB pair
• No other particles produced in Y(4S) decay
• Equal amounts of matter and anti-matter

7
B Factories
To get the large data set necessary to measure
CP-violation with Bs use B-factories SLAC
and KEK Both factories have attained
unprecedented high luminosities gt1034/cm/s2
BaBar has 352 fb-1 and Belle has 610fb-1 of data
Note 1fb-1 1.1 million BB pairs
8
Asymmetric ee- Colliders
PEPII
KEKII

• KEK/SLAC are asymmetric ee- colliders
• KEK 8 GeV (e-)/3.5 GeV (e)
• SLAC 9 GeV (e-)/3.1 GeV (e)
• B travels a measurable distance before decay
• SLAC bg0.56 ? bgct260mm
• KEK bg0.42 ? bgct193mm

9
Detectors at Asymmetric ee- Colliders
Both detectors feature Charged particle
tracking (silicondrift chambers 1.5T B-field)
Electromagnetic calorimetry (CsI) g and
electron ID p/K/p separation up to the
kinematic limit BABAR dE/dxDIRC
Belle dE/dxaerogelToF Muon/KL
identification
10
Key Analysis Techniques
Threshold kinematics we know the initial energy
of the Y(4S) system Therefore we know the
energy and magnitude of momentum of each B

Event topology
Signal
Signal
(spherical)
Background
Background
(jet-structure)
Most analyses use an unbinned maximum likelihood
fit to extract parameters of interest
11
How to Measure Time Dependent Decay Rates

• We need to know the flavour of the B at a
  reference t0.

At t0 we know this meson is B0
B 0
rec
B 0
B 0
tag
12
The Many Ways to Measure sin2b
Can use 3 different categories of B0 decays to
measure b
golden mode
13
Precise Measurement of sin2b from B0charmonium
K0
Theoretically very clean
ACP(t)Sfsin(DmDt)-Cfcos(DmDt) The dominant
penguin amplitude (suppressed by l2Cab) has same
phase as tree SM prediction Cf0 Þ
ACP(t)Sfsin(DmDt) confirmed by recent
model-independent analyses e.g. PRL 95 221804
(2005) DS0.0000.012 Experimentally very
clean Many accessible decay modes with
(relatively) large BFs B??K08.5x10-4
B??(2S)K06.2x10-4 B??c1K04x10-4
B??cK01.2x10-3
CP odd
CP even
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Precise Measurement of sin2b from B0charmonium
K0
15
Brief history of sin2b from B0?charmonium K0
World Average sin2bWA0.6870.032 From
external constraints sin2bUTFit 0.7930.033
(sides) sin2bUTFit0.7340.
024 (all)
Great success for Standard Model Great success
for all of us theorists, experimentalists,
accelerator physicists
16
Resolving the sin(2b) Ambiguity
sin(2b) is the same for b, p/2-b, pb, 3p/2-b

• Belle Use b?cud B 0?DCP(Kspp-) h0 decays
• A.Bondar, T.Gershon, P.Krokovny, PL B624 1
  (2005)
• Theoretically clean (no penguins), Neglect DCS
  B0?DCPh0 decay
• Interference of Dalitz amplitudes sensitive to
  cos2b
• Dalitz model fitted in D-tagged D0 decays
• f1(162112)o rules out f168o _at_ 97 CL
• Belle. hep-ex/0507065
• BABAR B0?J/yK0(K0?Ksp0)
• Extract cos2b from interference of CP-even and
  CP-odd
• states (L0,1,2) in time-dependent transversity
  analysis
• cos2blt0 excluded at 86 C.L.
• BABAR, PRD 71, 032005 (2005)

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These decays suffer from potential
penguin-pollution
bd penguin amplitude has different weak
strong phases with respect to tree.
BABAR B0 J/yp0 updated measurements
hep-ex/0603012, submitted PRD-RC Br(B0
J/yp0)(1.940.220.17)x10-5
SJ/yp0-0.680.300.04 CJ/yp0-0.210.260.09
Consistent with previous Belle results
PRL93, 261801 (2004) SJ/yp0-0.720.420.09
CJ/yp0-0.010.290.03
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DD- PRL 95, 151804 (2005) VV decay both
CP-odd and CP-even components. CP-odd fraction
extracted with transversity analysis fodd0.125
0.0440.070 S-0.750.250.03
C0.060.170.03 D()D- PRL 95, 131802
(2005) SDD -0.290.630.06 CDD
0.110.350.06 SDD--0.540.350.07
CDD-0.090.250.06 SD-D-0.290.330.07
CD-D0.170.240.04
D-D
DD-
DD-
19

• All results consistent with SM expectation of
  tree dominance
• DSDDSDD-sin2b0.02-0.05 Z-Z. Xing, PR D61
  014010 (2000)
• Still below current experimental sensitivity

20
Sin2beff in b ? s Penguins
Decays dominated by gluonic penguin diagrams
Golden example B0?fKS No tree level
contributions theoretically clean SM predicts
ACP(t) sin2bsin(Dmt)
Impact of New Physics could be significant New
particles could participate in the loop ? new CPV
phases Measure ACP in as many b?sqq penguins
as possible! fK0, K K- KS, ?' KS, KS p0, KS
KS KS, ? KS, f0(980) KS BUT there are
complications Low branching fractions (10-5)
non-penguin processes can pollute
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All sin2b Results Compared
Will be discussed in O. Longs talk Rare decays
and new physics studies
22
The Unitarity Triangle

• b

21.7 1.3o
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The CKM angle a
B0?Kp- large Br2x10-5 Pure Penguin
But we do not live in the ideal world.
There are penguins...
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sin(2a) Overcoming Penguin Pollution
Access to a from the interference of a b?u decay
(g) with B0B0 mixing (b) complicated by Penguin
diagram
g
Inc. penguin contribution
How can we obtain a from aeff ?
T "tree" amplitude P "penguin" amplitude
dstrong phase
Time-dep. asymmetry
25
How to estimate a-aeff Isospin analysis

• Use SU(2) to relate decay rates of different pp
  final states
• pp-, pp0, p0p0
• Important point is that pp can have I0 or 2 but
  gluonic penguins only contribute to I0 (by
  DI1/2 rule) EW penguins are negligible
• Need to measure several B.F.s

BF(Bpp0)BF(B-p-p0) since pp0 is pure I2,
only tree amplitude
However, for this technique to work p0p0
amplitudes must be very small or very large!
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B0?pp-
227106 B pairs 46733 signal events
275106 B pairs 66643 signal events
Phys.Rev.Lett. 95 (2005) 151803
Phys.Rev.Lett. 95 (2005) 101801
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B0?pp-
S -0.670.160.06 C -0.560.120.06
S -0.300.170.03 C -0.090.150.04
So two comparable measurements of S sin(2aeff)
Measurements of direct CP asymmetry less
compatible
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B0?p0p0
PRL 94, 181803(2005)
PRL 94, 181802 (2005)
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Using isospin in pp system
PRL 94, 181802 (2005)
Precision measurement of a not possible with
current stats using pp
30
B ? rr to the Rescue
Pseudoscalar? Vector Vector 3 possible ang. mom.
states S wave (L0, CP even) P wave (L1, CP
odd) D wave (L2, CP even)
Nature is KIND! B0rr-100 longitudinally
polarized! Transverse component taken as 0 in
analysis, essentially all CP even Large
Branching Fraction! Br(B0rr-)(3045)x10-6
Br(B0rr-)6xBr(B0pp-)
PRL 93 (2004) 231801
r helicity angle
signal
bkg
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B0 ? rr-
PRL 96, 171801 (2006)
PRL 95, 041805 (2005)
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But How large is B0?r0r0 ?
Phys.Rev.Lett. 94 (2005) 131801

• In rr system the amount of neutral decays is
  small
• Measure B0?r0r0 events in 227 x 106 BB
  events
• Br lt 1.1 x 10-6 at 90 CL.

Isospin triangle for rr is flattened compared to
pp
Penguin Pollution Defeated!
33
B?rr0

• New result with 231 x 106 BB events
• Previous BaBar/Belle HFAG average
• hep-ex/0603003
• New result is better match to isospin model

Moriond QCD 2006
Smaller uncertainty on aeff-acompared to pp
mode
34
B0 ? (rp)0 Analysis

• B0 ? (rp)0 ?pp-p0 is not a CP eigenstate
• 6 decays to disentangle
• Tried by BaBar and Belle for just r phase space
• Did not set limits on a
• Can use a Dalitz plot analysis to get a from
  decays
• Snyder Quinn Phys. Rev. D48, 2139
  (1993)

Convert to a square Dalitz plot Mostly resonant
decaysMove signal away from edges Simplifies
analysis
MC
q0r helicty angle
m0invariant mass of charged tracks
35
B0 ? (rp)0 Dalitz plot analysis

• Dalitz plot analysis yields CP asymmetries and
  strong phases of decays
• Using 213 x 106 BB events hep-ex/0408099

Blue histos are different types of
backgrounds m and q are variables for a square
Daltiz plot
Analysis provides a weak determination of a
However, useful for resolving ambiguities..
36
Combined constraints on a
rr gives single best measurement rp resolves
2-fold ambiguity from rr
World Average
Global CKM Fit (w/o a)
Dms
37
The Unitarity Triangle
99 11o

• a

21.7 1.3o
38
Summary and Outlook

• BABAR Belle measure sin2b in ccK0 modes to 5
  precision
• sin2bcharmonium0.6870.032
• Comparison with sin2beff in b? s penguin modes
  could reveal new physics effects
• BUT need to carefully evaluate SM contributions
• sin2beff measurements are statistically limited,
  can add new modes, beat 1/vL scaling
• Extraction of a depends crucially on penguin
  contributions
• B?r0r0/rr0
• Theory Û experimental feedback is helpful

Expected precision Vs time
reference 1s
reference (current r0r0 Br)
reference -1s

• from rr

Luminosity (ab-1)
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Putting it all together

• As of today the complex phase in the CKM matrix
  correctly
• describes CP Violation in the B meson system!

More to come from BABAR/Belle, CDF/D0, and LHCb
Will they find CKM violation????
40
Extra Slides
41
Adding Theoretical Uncertainties

• size of possible discrepancies ?sin2ß have been
  evaluated for some modes
• estimates of deviations based on QCD-motivated
  specific models some have difficulties to
  reconcile with measured B.R.
• Beneke at al, NPB675
• Ciuchini at al, hep-ph/0407073
• Cheng et al, hep-ph/0502235
• Buras et al, NPB697
• Charles et al, hep-ph/0406184
• model independent upper limits based on SU(3)
  flavor symmetry and measured b? d,sqq B.R.
• Grossman et al, PRD58 Grossman et al, PRD68
  Gronau, Rosner, PLB564 Gronau et al, PLB579
  Gronau et al, PLB596 Chiang et al, PRD70

naive upper limit based on final state quark
content, CKM (?2) and loop/tree ( 0.2-0.3)
suppression factors Kirkby,Nir, PLB592 Hoecker,
hep-ex/0410069
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There is a problem
B0 ? pp-
B0 ? Kp-
Penguin/Tree 30