Mid-Term at the B Factories : the New Picture of CP Violationseminar/extern/HoeckerLausanne05.pdf · Seminar at Lausanne - Feb 14, 2005 A. Höcker – Mid-Term at the B Factories

Seminar at Lausanne - Feb 14, 2005 A. Höcker – Mid-Term at the B Factories : the New Picture of CP Violation 1

Mid-Term at the B Factories : the New Picture of CP Violation

Andreas HöckerLaboratoire de l’Accélérateur Linéaire, Orsay

Seminar

E.P.F. Lausanne, February 14, 2005

[email protected]


1. The Universe is empty* !

2. The Universe is almost empty* ! ( )baryon baryon baryon 10

~ 10n nn

On nγ γ

−−∆

=

Sakharov rules (1967) to explain Baryogenesis1. Baryon number violation 2. CP violation3. No thermic equilibrium (non-stationary system)

Why CP Violation?

Bigi, Sanda, « CP Violation » (2000)Initial condition ?

Dynamically generated ?


CP Violation is flavor physics

Discovery of CP violation (1964)

The smallness of KL → µ+µ– predicts charm quark (GIM)

KM theory (to describe CP violation) predicts third quark generation

∆mK = m(KL) – m(KS) predicts mass of charm quark

Frequency of B0B0 mixing (∆mB) predicts heavy top quark

What’s next ???

V.L. Fitch R. Turlay J.W. Cronin J.H. Christenson

PRL 13, 138 (1964) [cited: 1007 times]

Moments of glory in flavor physics :


(parenthesis)

Evolution of working conditions (example BABAR) :

PRL 87, 091801 (2001) [cited: 280 times]

… we are 593 physicists !


The Search for New Physics in the B System

see, e.g., the instructive talk by Yuval Grossman at LP’03: hep-ph/0310229

6

4NP

(10 ) for , ~ ~

(10 ) for , Qq tQ tq

W

V V O Q s q dm O Q b q d

δ ∗ −

−

⎧ = =⎪⎨Λ = =⎪⎩

Since the successful and precise measurement of sin2β in decays (in perfect agreement with the SM), there is considerable effort at B Factories towards the search for specific signs of New Physics (NP)…. WHY ?

b ccs→

The gauge hierarchy Problem (Higgs sector, scale ~ 1 TeV)

Baryogenesis (CKM CPV too small)

The strong CP Problem (why is θ ~ 0 ?)

Grand Unification of the gauge couplings

... many more

Conflict between limits from flavor physics ? 1 TeV (e.g., K0, D0, B0 mixing), and NP scale (1 TeV) NP cannot have a generic flavor structure


New Physics: some possibilities

MFV models (minimal flavor violation) : CP violation is completely governed by CKM

precision tests in rare processes

Q : why ?

The NP is essentially flavor blind up to large scales

test of CP violation in flavor conserving processes (EDM, …)

Q : and what about the leptons ?

Intermediate solutions (example : only b→s is affected by low energy NP), …

Q : why would these two families by special ?

… and other still unknown alternatives, which certainly will give the correct answer


The CKM Matrix and the Unitarity Triangle

αβγ

( )3 3 3

0ud ub cd cb td tbV V V V V V

A A Aλ λ λ

∗ ∗ ∗+ + =

∝ ∝ − ∝

d s b

u

c

t

CKMV =

Re

Im

td tbV V ∗

cd cbV V ∗

ud ubV V ∗

Re

Im

1 0ud ub td tb

cd cb cd cb

V V V VV V V V

∗ ∗

∗ ∗+ + =

iρ η+

( , )ρ η

(1,0)

phase invariant :

ud us ub

cd cs cb

td ts tb

V V VV V VV V V

W –

QqVqQ

Q → q

Bob

Cah

n

J/2

Jarlskog invariant J = 0 ⇔ no VCP Jarlskog, PRL 55, 1039 (1985)

CP Violation(Im[...] ≠ 0)

arg(...) γ≈

arg(...) β≈


The Bd System (e+e– →ϒ(4S) factories)

( )0 0, ( )1,0

( )ρ,η

Re

Im

α

βγ

uR tR0 0

0 0

0 ( ) ( )( )

0 0

/ , ...

/

, ...

S

s

S

B J K

B JB D D

B K

ψ

ψπ

φ

∗ + ∗ −

→

→

→

→

0

( ) ( )

( )

0 0

0

, ...

( )

SK

S

B D KB D K

B DK

B D

π π

π ρ

+ −

∗ ∗

∗

∗

→

→

→

→

b ub c

νν

→→

l

l

0 , ,B ππ ρπ ρρ→

( )( ) /B B Kρ ω γ γ∗→ →

0 0 : dB B m↔ ∆

0ud ub cd cb td tbV V V V V V∗ ∗ ∗+ + =

the Bd is also accessible by the hadron machines !

b ccs→

b ccd→

b sss→


The Bs SystemATLASATLASATLAS CM

S

CCMM

SS

( )0 0, ( )1,0

( )ρ,η

Re

Im

γ ′

uR% tR%

0

0

/ , ...

, ...s

s

B J

B

ψφ

φφ

→

→

0

0

0 0

0

/

, ...

s s

s

s S

s s s

B D K

B K K

B J K

B D D

ψ

+ −

+ −

→

→

→

→

0 0 : /s s s dB B m m↔ ∆ ∆

0td ud ts us tb ubV V V V V V∗ ∗ ∗+ + =

δγ ~ 1°

the Bs is not accessible by the ϒ(4S) B factories!

0( )sB µ µ+ −→ 0 10(BR for ~ 2 10 )dB −×

0 9(BR for ~ 4 10 )sB −×

(hadron machines)

b ccs→

b sss→


Flavor Physics and the Search for CP Violation

Flavor Physics and the Search for CP Violation

ATLAS

Present and future - Worldwide Program :

BTEV

NA48CLEO-c

E787/949

???

KEK / J-PARC

0 0LK

Kπ νν

π νν+ +

→

→

+ neutron EDM experiments: ILL (Grenoble), PSI (Zürich), Los Alamos, ...

Super-BABAR ?Super-B ?


After the B physics pioneers : Argus, CLEO and the LEP experiments ...The B Factories : PEP-2 (SLAC) and KEK-B (KEK, Japan)

SLD (& MARK II)

BABAR

Fixed target experiments

Linac


coherent production of neutral B pair

boost of ϒ(4S) in the laboratory : βγ = 0.56

e–

e+

+ − → ϒ →(4 )e e S BB

Asymmetric-Energy B Factory : PEP-II

Quantum coherence : at ∆t = 0, the system is a superposition of :

one and one0B 0Bone and oneHB LB

one and one1CPB =+ 1CPB =−

Einstein-Podolsky-Rosen phenomenon : measurement of flavor of one meson determines flavor of other meson at same proper time; this property is exploited for the “flavor tagging”

9 GeV e– against 3.1 GeV e+ :

3 km


July 31, 2004

3 × design

PEP-II Luminosity

Peak luminosity 0.92×1034 cm–2s–1

Best shift 246.3 pb–1

Best month 16.7 fb–1

Best 30 days 17.0 fb–1

BABAR logged 264.4 fb–1

710.5 pb–1

4.5 fb–1

Best day

Best 7 days

PEP-II records :

~245 million BB pairs recorded


PEP-II : ~5 Hz continuousKEKB : every ~5-10 min

Best shift, without trickle Inj.

Best shift, LER trickle Inj.

Best shift, LER + HER trickle Inj.

“Trickle Injection”

Nov 2003

Mar 2004

PEP-II LumiHER current LER current


e+ (3.1GeV)

e– (9 GeV)

The BABAR Detector

1.5 T solenoid EMC6580 CsI(Tl) crystals

Drift Chamber40 stereo layers

Instrumented Flux Returniron / RPCs (muon / neutral hadrons)

Silicon Vertex Tracker5 layers, double-sided strips

DIRC (PID)144 quartz bars

11000 PMTs

BABAR, NIM A479, 1 (2002 )


Particle Identification : the Čerenkov Detector (DIRC)

tracks penetrating the radiators

Simulated Čerenkov ring

Hits measured by PMTs


Summary of Summary of ICHEPICHEP 2004 Results2004 Results

Measurements of |Vub| and |Vcb| [ appendix ]β :

sin2β and cos2β with B0 → charmonium K0

sin2β with « penguin » modesDirect CP Violation (B0 → K+π –)α :

B0 → π +π –

B0 → ρ +ρ –

B0 → (ρ π)0

γ :methods/measurements with charged B’smethods/measurements with neutral B’s


β

Measurement of the angle Measurement of the angle ββ—— and the search for New Physicsand the search for New Physics ——

[∆B=2]

b

btt

W

W0B 0Bd

d

[∆B=2]

b

d b

dt

tWW0B 0B

( )2arg 2td tbV V β∗ ≈ −


The three CP-Violation phenomena

Condition for CP invariance :

CP invariance requires :

Classification of CP violation :

CP violation in mixing (”indirect”) :

CP violation in the decay (“direct”) :

CP violation in interference between mixing and decay :

220 0( ) ( ) , CP CPf H B t f H B t t= ∀

/ 1

/ 1

Im 0CP CP

CP

f f

f

q p

A A

λ

=

=

=1

CPfλ = ±

| / | 1q p ≠

phén

omèn

esde

VC

P

{ } { }1 1, ,L H CP CPB B B B=+ =−=

Definition of “CP parameter” :

2ie β−≈

CP

CP CP

CP

ff f

f

Aqp A

λ η= ⋅

CP eigenvalue

decay amplitude ratio

| | 1CPfλ ≠

Im 0CPfλ ≠


0 01 Prob( ( ) ) Prob( ( ) )CPf CP CPB t f B t fλ ≠ ± ⇔ → ≠ →

Time-dependent asymmetry observable

CP Violation due to the interference of decays with and without mixing

0 0

0 0

( ( ) ) ( ( ) )( )( ( ) ) ( ( ) )

sin( ) cos( )CP

P

C

C

P

CP CPf

CP P

d df

C

f

B t f B t fA tB t f B t f

m t C m tS

Γ → −Γ →=Γ → + Γ →

= ∆ − ∆

= 0= sin(2β ) for b → ccs, sssandwith :

2

/~ i

q pe β−

CP

mixing

decay

0t =

t0B

0B

CPfA

CPfA

CPf

avec:

Mixing-Induced CP Violation (3rd type)

[ ]

2

2

2

1

1

2Im

1

f

f

f

f

f

fS

Cλ

λ

λ

λ

+

=+

−=

CP

obse

rvab

les


Single weak phase:clean extraction of CP phase

no direct CPV:

The Golden Channel:

0 0, ,/ /( ) sin(2 ) sin( )

dS L S LBJ K J K

A t m tψ ψ

η β= − ⋅ ⋅ ∆

0,/

| | 1S LJ Kψ

λ =

2e

tb td cb cs

tb td cb cs Ki

V V V Vq A qp A V V V V p

β

∗ ∗

∗ ∗

−

⎛ ⎞= − ⎜ ⎟

⎝ ⎠= −

⊕*tbV

*cbV

csVcbV

*csVW

tdV*tbV

tdV

Wb

d

c

d

cs

ccsdb

d

0 0 0, /B B J Kψ→

2*cscb λAVV ⋅∝

top-quark dominates

bcs

d d

ct,c,ug

4

real

real

( )

cb cs

tb ts

ub us

V V

V V

V V Aγ λ

∗

∗

∗ → ∝ ⋅

Tree Diagram

“Penguins”

So that time-dependent asymmetry simplifies to a pure sinusoidal function:


∆z

0tagB

e+e−

−l

K −

0recB

Fully reconstructed

µ+

π −0SK

/J ψ π +

µ−

0 0rec flavB B= (flavor eigenstates) mixing, lifetime, ...0 0rec CPB B= (CP eigenstates) CP analysis

ϒ(4S)

∆t ≈ ∆z/⟨βγ ⟩c⟨∆z⟩ ≈ 250µm Flavor tagging

Quality : Q = 30.5 %

Coherent B0B0 production :

Experimental Technique

0recB


sin(2β ) with B0 to charmonium

stat syst

stat syst

sin2 0.722 0.040 0.023

| | 0.950 0.031 0.013

β

λ

= ± ±

= ± ±

1205fb 227M BB− ⇔

BABAR, hep-ex/0408127 (2004)

compatible with Belle (see later) and the Standard Model (indirect) :

CP-odd (J/ψ KS …) CP-even (J/ψ KL)

BABARBBAABBARARBABARBBAABBARAR

β = ±[CKM]sin2 0.73 0.13


Metrology of the CKM Matrix

β +−⎡ ⎤= °⎣ ⎦

1.6 1.523.3

Precision measurement :

Excellent agreement. But: ρ,η don’t tell us everything !

CKMfitter, hep-ph/0406184 (2004) UTfit, hep-ph/0408079 (2004)

Measurement of the sign of cos2β is a direct test of the SM : if SM ⇒ cos2β > 0

cos2β accessible through time-dependent angular correlations in

But :

with one ambiguity on sign …

induced by ambiguity on strong phase

Ambiguity can be lifted with analysis of interference pattern between S and P wave in (Kπ) system.

( )000*0*0 / πψ SKKKJB →→

β >cos(2 ) 0

β <cos(2 ) 0

cos(2 ) 0 at 89% C.L.β >


Both decays dominated by single weak phaseBoth decays dominated by single weak phase

b s

, ,u c t, ,g Z γ

tb tsV V∗

Penguin :

s

dd

s

Tree :

b

dd

W +cbV ∗

csV

φ

0K

c /J ψ

s0K

New Physics? 3×

0 0 0, , ,

2/ / /S L S L S L

icb csJ K J K J K

cb csB K

V Vq q ep V V p

βψ ψ ψ

λ η η∗

−∗

⎛ ⎞⎛ ⎞ ⎛ ⎞= ⋅ ⋅ =⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎝ ⎠

c

0 0 0, , ,

2~S L S L S L

itb tsK K K

tb tsB K

V Vq q ep V V p

βφ φ φλ η η

∗−

∗

⎛ ⎞⎛ ⎞ ⎛ ⎞= ⋅ ⋅⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎝ ⎠

b ccs→

b sss→

?β β=sin2 si[ n2 charmonium] [ -pingouin]s

Confronting Loop and Tree Decays

0B

0B

High virtual mass scales involved: believed to be sensitive to New Physics

decays are tree and penguin diagrams, with equal dominant weak phases

decays are pure “internal” and “flavor-singlet” penguin diagrams

b ccs→

b sss→

(7000 tagged events) (1500 tagged events)


why the hell do you call these Penguin diagrams?

They don’t look like penguins!

I’ve never seen a Feynman diagram

that looks like you ☺

a controversy …

mirror image of Richard Feynman

courtesy : G. Hamel de Monchenault (École de Gif, 2003)

Why « penguins » ?


Bro

nze

Silv

erG

old b

dgu

0B

d

ss

φ

W −

digression : Classification of the penguins One may identify golden, silver and bronze-plated s-penguin modes:

γλ∗ −∝ 4~ iub us uV V R e

b

dgt

0B

d

ss

s

W −γλ∗ −∝ 4~ i

ub us uV V R e 2~tb tsV V λ∗∝

W −bd

0B

d

uu

0', fη

s 0K

0K 0K

0', fη

0K

arbre suppr. de couleur

s

b

dgt

d

ss

s

W −

0B

2~tb tsV V λ∗∝

b

dgt

0B

d

ds

d

W −γλ∗ −∝ 4~ i

ub us uV V R e 2~tb tsV V λ∗∝

W −bd

0B

d

uu 0 0, ,π ρ ω

s 0K0 0, ,π ρ ω

0K

Naive (dimensional) uncertainties on sin2β

2( )~ 5%λΟ

~ 10%

2( / )~ 20%λ λΟ

Note that within QCD Factorization/SU(3) these uncertainties can be much smaller !

λ λΟ +2( (1 / ))qqf

arbre suppr. de couleur

φ


B0 → K+K–K0 bronze and B0 → KS KS KS new golden mode !!!

Note that:

if NP contributes significantly to CPV in loop decays, we naturally expect it to be different among the modes

averaging only meaningful in case of SM

digression : KKK0 modes

What about B0 → K+K–K0 and B0 → KS KS KS ?

b

d

0B K +

g

t

s

us

u

W − 2~tb tsV V λ∗∝

0Kds

K − b

d

0BK +

s

us

u

W −

0Kds

K −

γλ∗ −∝ 4~ iub us uV V R e

0( )K

:u d↔0( )K

0( )K

:u d↔0( )K

but : « popup » ss-bar dynamically disvafored with respect to popup uu-bar

is B 0 → K+K–K0 silver ?


s-penguin : comparison BABAR vs. Belle (I)

BABAR : s-penguin average at 2.9σ from sin2β [cc] (WA)

Belle : s-penguin average at 2.9σ from sin2β [cc] (WA)

ICHEP 2004


s-penguin : comparison BABAR vs. Belle (II)

New result

pre- Moriond2005

Moriond EW

BABAR,hep-ex/0502013

Averages:

BABAR : CL = 0.62

Belle : CL = 0.05

both : CL = 0.15


Compilation of s-penguin Modes

sin2 [ ] 0.726 0.037sin2 [ -peng] 0.41 0.07

ccsβ

β= ±= ±

sin(2β) : disagreement of 3.8σbetween charmonium and s-penguin (neglecting theor. errors) :

New Physics in b → s transitions? (δ23)RR ?

b s

s

dd

s φ

0K0B

23( )RRδ%×b% s%g%

HFAG: http://www.slac.stanford.edu/xorg/hfag/

A difference of about 0.05-0.25 (depending on the mode) is expected in the SM : 3.8σ ~3.0σ.

Theoretical errors

ICHEP 2004


Direct Direct CPCP ViolationViolation—— and the and the ““KKππ puzzlepuzzle”” ——

Bob

Cah

n


... CP invariance implies :CP-conjugated amplitudes :

define2 2

2 2

| | | |( ) ( )| | | |( ) ( )

f fCP

f f

A AB f B fAA AB f B f

−Γ → −Γ →≡ =

+Γ → + Γ →

( )

( )f

f

A A B f

A A B f

= →

= →| | | |f fA A=

2 ( )

j j

j jB f

i if j

j

i iijf

j

A a e e

A e a e e

θ φ

θ φξ ξ −− −

= ⋅

= ⋅

∑

∑CP

alters sign under CP(weak phase)

CP invariant (strong phase)jθ

jφ

( ) ( )( ) ( )co

sin s n

os

i

s c

i jij

CPi j i j i j

ij

i j i ja aA

a a

θ θ φ φ

θ θ φ φ

⋅=

⋅

− ⋅ −

− −

⋅

∑∑

Direct CP violation requiresat least two amplitudes withdifferent weak and strong phases

CP Violation in the Decay

“don’t expect direct CP violation in copious decays; rather look into rare modes”

Direct CP violation theorem :


bd d

W −

us K −

0B

Tree : Cabibbo-suppressed

u π +

b

d

W −

g, ,t c u

Penguin : dominant ?

0B

d

us

K −

u π +

4ub usV V

λ

∗∝

∝ 2tb tsV V

λ

∗∝

∝

Direct CP Violation : B0 →K+π –

b uus→

0

0

B KB K

π

π

− +

+ −

→

→

Flavor eigenstate :

sPlotB0→K−π+

B0→K+π−

Discovery of direct CP violation by BABARand Belle in 2004 :

0( ) 0.109 0.019CPA B K π+ −→ = − ±BABARBBAABBARAR


Do we Understand the B →ππ , Kπ System?

QCD FA

pQCD

SCETincluding the treatment of charming penguins by Ciuchini et al.

With conservative error treatment, only a data-driven fit is predictive

Is there a Kπ puzzle ?

“Color Transparency”

Several theoretical tools existent to describe non-leptonic B decays. All are based on the concept of Factorization.

Beneke et al, PRL 83, 1914 (1999); NP B675, 333 (03)

Keum et al, PLB 504, 6 (2001); PRD 67, 054009 (03)

Bauer et al, PRD 63, 114020 (2001); hep-ph/0401188

Buras et al, EPJ C32, 45 (2003)


α

Measurement of the angle Measurement of the angle αα—— using using charmlesscharmless B B decaysdecays ——

Interference of b → u decay amplitudes with B0B0 mixing


“Charmless” b → u Decays

If penguin is negligible

b uud→

bd d

W −

ud π −

0B u π +

b

d

W −

g, ,t c u

0B

d

ud π −

u π +

Principal modes :0

0

0

BBB

π π

ρ π

ρ ρ

+ −

±

+ −

→

→

→

m

2 2 2i i iub udh h h h h h h h

ub udB

V Vq e e ep V V

β γ αλ η η η+ − + − + − + −

∗− −

∗

⎛ ⎞⎛ ⎞= ⋅ = =⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠

Time-dependent CP observable

( ) sin( ) cos( )

sin( ) sin( )sin(2 )d dh h

d d

h h h h

h h

S CA t m t m

tS

t

m t mα+ − + − + −

+ −

= ∆

⋅

− ∆

= ∆ = ∆

2

2

| | 1

1 | |0

1 | |CP

h h

h hf

h h

C

λ

λλ

+ −

+ −

+ −

=

−= =

+!

1 for h h

hη π+ − = =

idea

lsc

enar

io

3ub udV V

λ

∗∝

∝ 3tb tdV V

λ

∗∝

∝ Not a CP eigenstate

Tree : dominant Penguin : competitive ?


eff

( )2

( )

2

1 | / ||1 | /

i i

i ih h h hB

ii

ih h

ih h

T PT P

P TP T

q e ep e e

eee

e

δ

γ β

γ β

αα

δ

α

α

λ η

η

λ

+ − + −

+ −

+ −

+−

+−

+− +−

+− +−

+− +−

+−

− +

+ −

++

−

+−

−

⎛ ⎞⎛ ⎞ += ⎜ ⎟⎜ ⎟ +⎝ ⎠ ⎝ ⎠

⎛ ⎞−= ⎜ ⎟−⎝ ⎠

≡ where

is the relative strong phaseP T

δ θ θ+− +−+− ≡ −

“Charmless” b → u Decays : realistic case

If “T” and “P” are of the same order of magnitude :[Note that T and P are complex amplitudes !]

2eff1 sin

( ) sin( ) cos( )

sin( ) cos(2 ) ( )

d dh h h h h h

h dh h dh

S C

C

A t m t

C

m t

m t m tα

+ + − + −

+ − + −

−

−

= ∆ − ∆

= ∆ − ∆⋅

2

2

| | 1

1 | |0

1 | |CP

h h

h hf

h h

C

λ

λλ

+ −

+ −

+ −

≠

−= ≠

+

!

Direct CP violation can occur :

real

istic

scen

ario

Time-dependent CP observable


α can be resolved up to an 8-fold ambiguity within [0,π]

Isospin Analysis for B →ππ , ρρ

Réfs. for SU(2) analyses : Gronau-London, PRL, 65, 3381 (1990), Lipkin et al., PRD 44, 1454 (1991), a.o.

13 unknowns– 7 observ.– 5 constraints– 1 glob. phase = 0 ☺

2 isospintriangles and one common side

B+–, Sππ , Cππ

B+0, ACP

B00, (S00), C00

α, T+–, P+–, T+0, P+0, T00, P00

AccountConstraintsObservablesUnknowns


π 0

BBAABBARARA B0 → π 0π 0 candidate

SU(2) – Crucial Ingredient : B →π 0π 0 (color-suppressed)

π 0π 0

π 0

0 0 0 6( ) (1.51 0.28) 10B π π −→ = ± ×B 0 0 0( ) 0.28 0.39CPA B π π→ = ± BABAR, hep-ex/0412037 Belle, hep-ex/0408100


BABAR, hep-ex/0501071

Results for B0→π +π –

Results for the time-dependent analysis :

BABAR (227m) Belle (152m) Average

–1.00 ± 0.21 ± 0.07

–0.58 ± 0.15 ± 0.07

Sππ –0.30 ± 0.17 ± 0.03 –0.61 ± 0.14

Cππ –0.09 ± 0.15 ± 0.04 –0.37 ± 0.11

BABAR, hep-ex/0501071 Belle, PRL 93 021601 (2004)

Bad agreement :

χ2 = 13.1 (CL = 0.0014 ⇒ 3.2σ)

Isospin analysis : eff 37α α− < ° (90% CL)

0.37 0.17r +− = ±

( )101236δ +− +−= − °

penguin / tree


A “surprise” : B0→ρ +ρ –

Isospin analysis :

Branching fractions for the B → ρρ system (WA) :

B+– = (30 ± 6)×10–6 , B+0 = (26.4 )×10–6 , B00 < 1.1×10–6 à 90% CL

Note that : a small B00/B+0 ratio requires small penguins ! [ But: P+– = 0 would mean that : B+-/B+0 = 2 ]

Experimental complication :

B → VV can have LVV=0,1,2, with CP(LVV=0,2) = +1 and CP(LVV =1) = –1

Nature’s great present : longitudinal polarization dominates almost no CP dilution

6.16.4+−

BABAR (123m)

Sρρ –0.19 ± 0.33 ± 0.11

Cρρ –0.23 ± 0.24 ± 0.14

eff 15α α− < ° (90% CL) 0.110.100.10r +− +−=

(...)δ +− = °

penguin / tree

BABAR, hep-ex/0407051,0412067

BBAABBARAR


Dalitz analysis of B0→ (ρπ )0 →π +π –π 0

Exploit interference between amplitudes contributing to B0 → π +π –π 0

to simultaneously determine α and the strong phases

ρ–π+

ρ+π–

ρ0π0

003 0

003 0

A f A f A f A

A f A f A f Aπ

π

+− −++ −

+− −++ −

= + +

= + +

Form factor for ρresonance (Breit-Wigner )

( / )

ab i ab ab

ab i ba ba

A e T Pq p A e T P

α

α

−= +

= +

with :

All contributions to A3π must be modeled !

( )

( ) ( )

2

3

23 3

3 3

223 3

sin

cos

2Im d

d

f m t

A A

A A

A mA t

π π

π π

π

π

π

∗

⎛ ⎞⎜ ⎟⎜ ⎟

∝ − ∆⎜ ⎟⎜ ⎟⎜ ⎟+ ∆⎜ ⎟⎝ ⎠

+

⎡ ⎤⎣ ⎦

−

Time dependence

Simultaneous fit of 16 bilinears (Ui , Ii )(27 in total, 9 parameters are insignificant, 1 unphysical phase)

Snyder-Quinn, PRD 48, 2139 (1993)

Decay amplitudes


∆χ2(no direct CPV) = 14.5 (CL = 0.00070 ⇒ 3.4σ)

From the 16 bilinears (Ui, Ii), we determine the physical parameters :

Results of the B0→ (ρπ )0 →π +π –π 0 Dalitz analysis


Average : BABAR (213m) & Belle (152m)

A–+ –0.47 0.130.14+−

Parameters : α, |T+–|,T–+,T00,P+–,P–+Direct CP violation ?

A+– –0.15 ± 0.09

Scan in α using the bilinears :

BBAABBARAR

A+–

A–+

no direct CPV


Combination of ππ, ρπ, ρρ : first measurement of α

mirror solution disfavored

for the SM solution we find :

Combining the three analyses (dominated by ρρ and ρπ) :

α +−⎡ ⎤= °⎣ ⎦

9meas. 10100

better precision than CKM fit :

[ ]α = ± °CKM 98 16


digression : “Color-Suppressed” Amplitudes

Famous modes :0 0 0

0 0 0

0 0 0

BBB

π π

ρ π

ρ ρ

→

→

→

important non-factorizable contributions when large penguins !

[ Suppression ≈ verified in B(B0 → D0π0)/B(B0 → D–π+) = (1/10.4)exp ≈ (1/Nc)2 ]

The color of the quarks emitted by the virtual W must correspond to the external quark lines to produce color-singlets suppression by ~1/Nc (naïve!)

bd d

W −

ud π −

0B u π +

bd

0B

d

ud

0πu

0π

W −

Example : b uud→

0.130.10[ ]| / | 0.10P T ρρ

+− +− +−= [ ]| / | 0.37 0.17P T ππ

+− +− = ± [ ]7.52.1| / | 5.0KP T π

+− +− +−=


Measurement of the angle Measurement of the angle γγ—— the most difficult taskthe most difficult task ——

Interference of b → c and (suppressed) b → u amplitudes

γ


The Measurement of γ : Methods

bu u

W −

us

( )K ∗ −

B−

Tree: dominant

c ( )0D ∗

Tree: color-suppressed3cb usV V

λ

∗∝

∝ 3 2 2

ub csV V

λ ρ η

∗∝

∝ +

bu

u

W −

cu ( )0D ∗B−

s ( )K ∗ −

relative CKM phase : γ

No Penguins ☺No Penguins ☺

,b cus ucs→

Measurement of γ through direct CP violation in B decays to charm

Several variants :

D0 decays into CP eigenstate (interference between amplitudes) « GLW »

D0 decays to K –π + (favored) and K +π – (suppressed) « ADS »

D0 decays to KSπ +π – (interference in Dalitz plot) « GGSZ »

Gronau-London, PL B253, 483 (1991); Gronau-Wyler, PL B265, 172 (1991)

Atwood-Dunietz-Soni, PRL 78, 3257 (1997)

Giri-Grossman-Soffer-Zupan, PRD 68, 054018 (2003)


The “GLW“ and “ADS“ Analyses

GLW : measure branching fraction of B– → D0(CP)K–

4 observables sensitive to γ :

D0CP± reconstructed in ±CP (for ex., D0

CP+→K–K+, D0CP–→KSπ 0) b → c and b → u interfere

0 0 2

0 0

( ) ( ) 1 2 cos cos

( ) ( ) 2 sin sin /CP CP CP B B B

CP CP CP B B CP

R B D K B D K r r

A B D K B D K r R

δ

δ

γ

γ

− − + +± ± ±

− − + +± ± ± ±

∝ Γ → + Γ → ∝ + ±

∝ Γ → −Γ → ∝ ±

( ) / ( )Br A b ucs A b cus≡ → →

strong phase in decay of B

~ 0.1 - 0.3 ??

( )( )

2 2ADS

ADS ADS

(...) 2 cos cos

(...) 2 sin sin /D B B D B D

B D B D

R r r r r

A r r R

γ δ δ

γ δ δ

≡ = + + +

≡ = +strong phase

in decay of D

ADS : disfavor favored amplitude and favor disfavored amplitude

0( )B D K Kπ− + − −→ → 0( )B D K Kπ− + − −→ →

( ) / ( )Dr A c dus A b sud≡ → →

2×Cabibbo-suppressed

= 0.060 ± 0.003

Problem of GLW : requires interference of amplitudes with very different sizes


“ADS+GLW” : Constraint on γ

BABAR and Belle have measured the observables for GLW et ADS in the modes B– → D0K–, D*0K–, D0K*–

BABAR, hep-ex/0408082, hep-ex/0408060hep-ex/0408069, hep-ex/0408028

Belle, Belle-CONF-0443, hep-ex/0307074hep-ex/0408129

No significant measurement of suppressed amplitude yet ⇒ limit : rB(*) 0.2

γ +−⎡ ⎤= °⎣ ⎦

20meas 3451

γ +−⎡ ⎤= °⎣ ⎦

8CKM 758

for the SM solution :

not yet competitive with CKM fit (indirect determination of γ)


GGSZ : B– → D0(→ KSπ +π – )K– : interference between amplitudes in Dalitz plot

( ) ( ) ( )

( ) ( ) ( )

2 2 0

02 2

, e

, e

iB

iB

A m m A B D K f r f

A m m A B D K f r f

δ γ

δ γ

−− −− − + −+ +−

++ ++ − + +− −+

⎡ ⎤= → +⎣ ⎦

⎡ ⎤= → +⎣ ⎦

Sum of amplitudes contributing toD0→ KSπ +π –

( )2 2

0

,

( )S

f f m m

m m K π

+− + −

±±

≡

≡

Decay amplitudes :

CP

2

2A− = ( ) iBr e δ γ−+ ×

2m+

2m−2m−

2m+

0D 0D

Simultaneous measurement of rB , δ and γ

K π∗− +

The “GGSZ” Dalitz Analysis



“GGSZ” : Constraint on γ

Amplitudes of Dalitz plot measured in control sample : D0→ KSπ +π –

large number of resonances contribute : K*(892), ρ (770), ω (782), f0(980,1370), K0*(1430), ...

0B D K− −→

0B D K− ∗ −→

B+ B−

B+ B−

BABAR 211m 0.18 , 0.24B Br r ∗< <stat syst model88 44 19 10γ ⎡ ⎤= ± ± ± °⎣ ⎦1415 stat syst model68 13 11γ +−⎡ ⎤= ± ± °⎣ ⎦ 0.21 0.09 , 0.39B Br r ∗= ± <

(90% CL)

Belle 274m (FPCP’04)

Future : reduce model-dependence by exploiting CP-tagged results from CLEO-c running at theψ(3770) → DD to measure arg[f+–] and arg[f–+] ?


digression : Measurement of sin(2β + γ)

bd d

W −

ud π −

0B

Tree: dominant

c D+

Tree: doubly CKM-suppressed 2cb udV V

λ

∗∝

∝ 4ub cdV V

λ

∗∝

∝

bd d

W −

cd D−

0B u π +

relative weak phase :

Exploit interference

BABAR and Belle have performed this analysis for D π, D*π and Dρ, using fully and partially reconstructed B decays.

Similarly:

golden mode to measure γ at LHCb/BTeV

0 ( )B D π∗ − +→ 0 0 ( )B B D π∗ − +→ →

2β γ+

Time-dependent CP analysis similar to : B0 → ρ +π –

0 0( )s s sB B D K− +→

,b cud ucd→

γ dependence of the order of O(10–4) !

Huge statistics, but small CP asymmetry

Unknowns : rB0, γ and δ ⇒ needs external input


constraint on |sin(2β+γ)| constraint of sin(2β+γ) in ρ-η plane

Using SU(3) symmetry to estimate rB0(*) (assumed theoretical errors : 30%)

digression : Results for sin(2β + γ) BBAABBAR AR & Belle& Belle

BABAR, hep-ex/0408038, hep-ex/0408059 Belle, hep-ex/0408106, PRL 93 (2004) 031802; Erratum-ibid. 93 (2004) 059901


Summary :Summary : CPCP Violation in 2004Violation in 2004


First measurement of CPV : εK

Precise measurement of sin2β

First measurement of α

γ — the biggest challenge

Summary : CKM Metrology

Measurements of the CKM phase :

Significant progress on |Vcb,ub|

...but this is only the half time :4 × stat. (~ 2 ab–1) expected in 2009

First measurement of cos2β

β >cos(2 ) 0

β <cos(2 ) 0

Beyond CKM metrology :

Direct CP violation in B system

Quid the s-penguins ?


a p p e n d i x (i)t h e f u t u r e o f f l a v o r p h y s i c s

a p p e n d i x (i)t h e f u t u r e o f f l a v o r p h y s i c s


The Future Program for The Future Program for Flavor Physics and Flavor Physics and CPCP ViolationViolation

ATLASATLASATLAS CM

S

CCMM

SS

BTEVNA48


2000 2002 2004 2006 2008 2010

BABAR 100 / fb 500 / fb 1.x / ab ?

B and D Factories

NA48

K0PI0 (BNL)

Kaons (high intensity)

CDF & D0

ATLAS & CMS

Tevatron Run 2

LHC

SUNS at PSI

NA48/1 NA48/2

LHCb

BTeV ?

3-7 1035 ?

CLEO 10 / fb

E787 / E949

NA48/3

Belle 100 / fb 500 / fb 1.x / ab ? 2 1035 ?

CLEO-cscan

ILL, PNPIElectric dipole moment of neutron

@ J-PARC ?E391a (KEK) [~ 4×10–10]

ILL


a p p e n d i x (ii)t h e C K M e l e m e n t s |Vub| a n d |Vcb|

a p p e n d i x (ii)t h e C K M e l e m e n t s |Vub| a n d |Vcb|


( )

3 2 2 2et

circle in , planeub cbV A V Aλ ρ η λ

ρ η

= + =

⇒

The Elements |The Elements |VVubub| and || and |VVcbcb||—— semileptonicsemileptonic B B decays decays ——

/ub cbV V


The CKM Matrix elements : |Vub| and |Vcb|

The theoretical tools are HQET and HQE (OPE).

|Vub| (→ ρ2 +η2) is crucial for the SM prediction of sin(2β )

|Vcb| (→ A) is important in the kaon system (εK, BR(K→πνν ), …)

d s b

u

c

t ( taille ∝ |Vij | )

b → u

b → c

exclusive inclusive

B → ρ ℓν

B → D* ℓν

B → Xu ℓν

B → Xc ℓν

For |Vcb| and |Vub| exist exclusive and inclusive semileptonic methods

… concentration on the inclusive modes in the following


|Vub| (and |Vcb|) : Principle of Inclusive Measurements

( )QCD2

[ , ] ~ quark model (PS) b

n

u c b n mn

d V Cd

ΛΓ ⎛ ⎞× +⎜ ⎟⎝ ⎠

∑

free quark decay non-perturbativecorrections

☺ : relation between and |Vub| known to ~ 5%

: background from b → c dominant :

( )u

uX

B X νΓ →∑ l

( ) / ( ) ~ 100c uB X B Xν νΓ → Γ →l l

Hadronic mass spectrum in b u decays

kinematic limit of b → c

parton modelincluding the Fermimotion (model)

only b→u

1/ΛQCD

Compton wavelength

b

mb–1

Fermimotion

needs severe cuts to eliminate charm background

Fermi motion can be determined from γspectrum in b → s γ

Belle, hep-ex/0403004


|Vub| : Results

Electron momentum (GeV/c)

Num

ber o

f ele

ctro

ns

b ueν→b ceν→

( ) 3stat+sys SF HQE3.94 0.25 0.37 0.19 10ubV −= ± ± ± ×

… the electron endpoint … the invariant mass q2(e,ν)

b ueν→b ceν→

( ) +0.59 3stat syst 0.29 SF HQE4.57 0.47 0.22 10ubV −

+ −= ± ± ×

BABAR, hep-ex/0408045, hep-ex/0408075

b → ceν background rejection with cut on …

« electron endpoint »

« ν reco »

mD


|Vcb| - Moments Analysis

Hadronic mass moments

Lepton energy momentsRed line : HQE fitYellow band : uncertainty

( ) 3stat HQE theo41.1 0.4 0.4 0.6 10cbV −= ± ± ± ×

BABAR, PRL93, 11803, (2004)

2% precision !


Compilation of |Vub| and |Vcb| Results

Disagreement between exclusive and inclusive |Vub| determinations ?

Documents

Mid-Term at the B Factories : the New Picture of CP Violationseminar/extern/HoeckerLausanne05.pdf · Seminar at Lausanne - Feb 14, 2005 A. Höcker – Mid-Term at the B Factories