Vivek Sharma

University of California at San Diego

CP Violation in B DecaysCP Violation in B Decays

Ringberg Workshop 2006

2

Task: Over Constrain The Unitarity Triangle

CPVB-DK-

B0 D0K0

CPV

BK0 (bccs)BK0 (bsss

CPV B0+- , , +-

b u

l

B-

b c l

b dB 0B 0

By Measurement of UT Sides By Measurement of UT Angles

Is CKM Matrix the (only) Source of CP Violation?

3

CP Violation

• CP violation can be observed by comparing decay rates of particles and antiparticles

• The difference in decay rates arises from a different interference term for the matter Vs. antimatter process.

1A

2A

1A

2A

CP Viola io( t) n) ( a f a f

4

CP Violation Due to Quantum Interference

Weak phase wk changes sign under CP, strong phase st does not

stwkCP Violation

( ) ( )f or 0 and 0B f B f

2

1 2( ) wk sti iB f A A e e

st 1A

2A

wk

(B

f ) wk

2

1 2( ) wk sti iB f A A e e(B f

)

1AB f

2

wk sti iAe e

5

Direct CP Violation in B0 K

2 iSM amplitude e T P

sinKA

TP

•Loop diagrams from New Physics (e.g. SUSY) can modify

SM asymmetry contributing to the Penguin (P) amplitude

• Measurement is a simple “Counting Experiment”

Classic example of Quantum Interference

6

Direct CP Violation in B0K+

0

0

9

696

10

n B K

n B K

Bkgd symmetric!

696 9100.133

696 910A

0.133 0.030 0.009KA

4.2, syst. includedBaBar

LARGE CP Violation !unlike Kaon system

7

CPV In Interference Between Mixing and Decay

0 0

CP asymm. can be very large and can be clean

Neutral B Decays into CP final state acces

ly related to CKM angles

when only a single

ible by both & de

dominant decay amplitud

ca s

e

yCPf B B

0B

fiCPA e

CPf

0B2iq

ep

fi

CPA e

8

Peculiarities at (4S)BB (4S)

Ebeam= 5.29 GeV

e+ e-

Ebeam= 5.29 GeV

e

e

b

b

(4 )S

0B0B

Under symmetric energy collisions, B mesons are slow (0.07) travel only ~30m, not enough to measure their decay time

9

• B0 B0 are in coherent l=1 state

• Since production, each of the two particles evolve in time, may mix

• BUT they evolve coherently (Bose statistics |> = |> flavor |>space is

symmetric ) so that at any time, until one particle decays, there is exactly one B0

and one B0 present but never a B0 B0 or B0 B0 (quantum coherence)

• However when one of the particles decays, the other continues to evolve

• Now possible to have (4S) final state with 2 B0 or 2 B0,

• probability is governed by the difference in time between the two B decays

0 0Quantum Entanglement (EPR) in Y(4S) B B

(4S) B0 B0

Spin = 1 0 0

With l = 1

10

When One B decay tags b flavor, Other decays to fCP

(4S)B0 B0

ttag ttagtfcp

K0t

0 0B B

Tag

fCP

0

0

1.When one B decays to

2.It identifies the other B particle as B at THAT time

3.Ultimate

state which t

ly the de

ags its flavor at time t (as a B

cays at tim

t= t

e into some CP final state B

)

CP

tag

g

f

ta

t CPf

11

B Decays to CP Eigenstates

CP CP

0 0f CP f

CP tag

tag CP

tag

1

1

C

2

P

2

Pr obability of observing a final state |f | f depends on :

1. decay time t and t

2. decay amplitude

3. Oscillation paramete

A f | H | B ;A

r

4. Flavor of B , wheth

q | M |

p

e

f

M

| H | B

r

C

C

P

P CP

CP

CP C

C

P

P CP CP

CP

f f f

f C0

CP

f ff

f

0 0tag g

f

f

a

P

t

A f |

B B or B B

Using property

Define a useful CP parameter

A A

where CP eigenva

AAq q=

p

lue of f &

A

| B

H

p A

12

Time dependent CP Asymmetry in “Interference”

0 0

0 0

2

2 2

Time dependent CP asymmetry in time

( ) ( )

( ) ( )

12 sin cos

1 1

= sinS

t =

CPCP

CP CP

phys CP phys CP

phys CP phys CP

ff

B B

f f

B

CPtagf

B t f B t f

f B t f B t fCP

m t m t

m

t t

a

Im

cosC Bt m t

CP

CP CP

CP

When is dominated by a single decay amplitude:

1 0

Asymme str iy n

f

f f

B f

C

m tB

a

Im

13

Decay Rates and CP Asymmetries at (4S)

At (4S): integrated asymmetry is zero must do a time-dependent analysis !

This is achieved by producing boosted (4S)BB

CPfa d t 0 !!

sin Δm ΔtBS

14

Asymmetric Energy Collider To Measure B Decay Time

Electron Beam Positron Beam

(4S)

Boost (4S) in lab frame by colliding beams of unequal energy but with same E2

CM = 4.Elow Ehigh=M2

Daughter B mesons are boosted and the decay separation is large Z ~ 200, distance scale measurable with Silicon detectors

15

CP Violation Studies at Asymmetric Energy Colliders

Probing The CKM Angle

17

CPV In B0 J/K0 (Platinum Mode)

1λ

β)sin(2)Im(λ

S

S

ψK

ψK

L SψK ψKλ λ

CP = -1 (+1)

for J/K0S(L)

0 /,/ 1 sin 2 sin( )t

S L CPB J K e mt

0 /,/ 1 sin 2 sin( )t

S L CPB J K e mt

0B

fiCPA e

CPf

0B

12

2i

M

ie

fiCPA e

Same is true for a variety of B (cc) s final states

S

S

S

*cb cs*cb cs

*cs cd*cs

*t

* *ψKB tb cbb td td

* *cd

ψK *B ψK tb cb cdtb td tdcd

Vq A V V Vλ =

V VV V

V V

V V

V=- = -

p A V VV V VV V

2ie

dominatedby a single

decay amplitude

18

Time-Dependent CP Asymmetry with a Perfect Detector

sin2( ) sin(ΔmΔβ )CPA t t sin2( ) sin(ΔmΔβ )CPA t t

• Perfect measurement of time interval t=t• Perfect tagging of B0 and B0 meson flavors•For a B decay mode such as B0Ks with |f|=1

sin 2

B0B0

Asy

mm

etry

AC

P

CP

V

Vivek Sharma , UCSD 19

+e-e

B0 J/ KsB0 J/ Ks

z

Δ zΔ tβγ c

Brec

Btag 4s

(4S) = 0.55

z-π

0sK

+π

+μ-μ

Coherent BB pair

B0

B0

distinguish

B0 Vs B0

distinguish

B0 Vs B0

Steps in Time-Dependent CPV Measurement

20

Effect of Mis-measurements On t Distribution

00tag BB 00

tag BB 00tag BB 00

tag BB

CP PDF

perfect flavor tagging & time

resolution

realistic mis-tagging & finite time

resolution

| |/

, ( ) 1 sin2 (1 2 )sin4

t

CP CPef t tw m

~ 1 ps 170 m

~ 6 ps 1000 m2

t

mixt

21

B Charmonium Data Samples (348M ) BB(348M ) BB

6028 signal

4323

965 11000 non-CP

22

Sin(2 Result From B Charmonium K0 Modes (2006)

(cc) KSmodes

(CP = 1)

J/ψ KL mode

(CP = +1)

sin2β = 0.7220.040 (stat) 0.023 (syst)

BaBar 348M BB

sin2β = 0.6420.031 (stat) 0.017 (syst)

Belle 535M BB

sin2β = 0.6740.026Average

23

Breaking Ambiguities In Measurement of

24

T

Angle From B0 +-

* *

-* *

sin(2 - 2 - 2 ) sin 2Imtb td ud ub

tb td ud ub

V V V VB

V V V V

Neglecting Penguin diagram (P)

2ie 2 ie

P

eff

*Weak Phase in Penguin term is arg( ) different from Tree, so modifies

and depending on its relative strength w.r.t Tree

td tb

peng

V V

Im

25

Estimating Penguin Pollution in B0 +-, + -

A2

1

A2

1

00 AA

00A

00A

peng2 00 0 0 0

00 0 0 0

0

0

0 0

0 0

( )

( )

( )

(

)

)

( )

(

A A B

A A

A A B

A A B

A A B

A

B

A B

0 0 0 +- +0 00

0

B states can have I=0 or

B , and related by SU(

2; Gluonic Penguins co

2) Isospin relation between amplitudes A ,

ntribute only to I=0 ( I=1/2 rule)

A and A

B has only tree ampli

+0 -0tude | A | = | A |

00 00penguin

+0 00

To constrain by isospin analysis requires A and A to be very small or

very large ! Measure and constrain A ,A by rate and asymmetry

measurements

26

B0 + - System As Probe of

0 6

0

Br(B ) (23.5 2.2 4.1) 10 !!

Five times larger than Br(B )

“Large” rate

615 ± 57

openg ef

0 0 0 6

0 6

f

0Substantially smaller (x25) than B !

Much more amenabl

Br(B ) 1.16 0.37 10 (3 )

Br(B ) 1

constraint on | | 18 @ 6

e to Isospin analysis

6.8 3.1 10

8% CL

“Smaller” Penguin Pollution

mES 0f0

00

98 ± 22

2A00

A+0

/ 2A

27

B0 + - System As Probe of

• Longitudinally polarized0

L

Angular analysis shows that B

is almost 100% longitudinally polarized !

Pure CP-even final state

This simpli

f 0.9

fies

77 0.

CPV analysis

024

Helicity angle

28

TD CPV Measurement in B0 + -

0.050.070.19 0.21

0.07 0.15 0.06

Long

Long

S

C

615 57 signal events

CPV not yet observed herebut measurement constrains

CP sin mA S Ccos tt m

29

Discerning : Not Very Precise Yet

119

Combining

B , , (93 )

Precise measurement

needs much more data

o

CPV

[74 117]

Dominant uncertainty

is the Penguin pollution

o

B

Probing The CKM Angle

31

CP Asymmetry In B DK Decay

0K

Look for B decays with 2 amplitudes with relative weak phase

iV eub

000~ DreDD i

Relative phase: (B– DK–), (B+ DK+)

includes weak (γ) and strong (δ) phase.

Relative strength of the two B decay amplitudes matters for interference

A(b u)r 0.1 0.3 , larger r larger CPV precise

A(b )c

32

from B±D0 K±: D0 KS + - Dalitz Analysis

2 2 2 ( ) 2 2 2 For : | | | ( , ) ( , )| i

bB A f m m r e f m m

2 2 2 ( ) 2 2 2 For : | | | ( , ) ( , )| ibB A f m m r e f m m

2 0 2 2 0 2 Defining ( ) ; ( ) S Sm M K m M K

2

( )ibr e

2

sKm

2

sKm

2

SKm

2

sKm

0 D 0 D

2A

Schematic view of the interference

0S

+ -B

Simultaneous fit to D K Dalitz distribution of

info on rB and , B data and strong phase gives

33

B Samples From Belle ( 357 fb-1)

Clean signals but poor statisticsfor a Dalitz analysis !

331±17 evnt

BDK

81±8 events

54±8 evnt

BD*K

BDK*

34

The B->D0 K Dalitz Distributions: Belle

B- B+B-DK- B+DK+

Direct CP Violation lies in in the dissimilarity betweenthe two Dalitz distributions: See any ?

35

Measurement Of CKM Angle /3

Belle ( 357 fb-1)

W.A. combining all measurementsγ = (82 ± 19)o [63,101] @ 95% CL γ = (-98 ± 19)0 [-118,-79] @ 95% CL

36

The Unitarity Triangle Defined By CPV Measurements

11993 , , 82 19 degrees

First time that all angles

22.2 1.0

measured + +

Precise Portrait of UT Triangle

from CPV Measurements

37

UT With CPV & CP Conserving Measurements

ub

cb

V

V

Inputs:

dm

sm

B

K

sin2

Incredible consistency between measurements Paradigm shift ! CKM Picture well describes observed CPV

Look for NP as correction to the CKM picture

38

Searching For New Physics by Comparing pattern of CP asymmetry in bs Penguin

decays With goldplated b ccs (Tree)

39

Tree

b

dd

W cbV

csV

c /J

s0K

c

Penguin

b s

, ,u c t, ,g Z

tb tsV V

s

dd

s

0K

3

New Physics

Comparing CP Asymmetries : Penguins Vs Tree

In SM both decays dominated by a single amplitude with no

additional weak phase

New physics coupling to Penguin decays can add additional amplitudes withdifferent CPV phases

S

Asymmetry must be same

[B K ] [penguin]sin2 sin2

Measured CPV

S

Asymmetries can be very differe

sinsi 2n2

nt

[B K ] [pengu in]eff

CPV

40

New Physics ?

Standard Model

S

experimentally observe

[B K ] [pesin2 nguisin2 n]

then ...

eff

If

41

Naïve Ranking Of Penguin Modes by SM “pollution”B

ron

zeG

old

Su

pe

rgo

ld

b

dg

t0B

d

ss

s

W 2~tb tsV V

0K

0', f

0K

b

dg

t

d

ss

s

W

0B

2~tb tsV V

b

dg

t0B

d

ds

d

W

2~tb tsV V 0 0, ,

0K

2( )

~ 5%

~ 5%

2( / )

~ 20%

2( (1 / ))qqf

b

dg

u0B

d

ss

W 4~ i

ub us uV V R e

4~ iub us uV V R e

W b

d

0B

d

uu 's 0K

0Ks

4~ iub us uV V R e

W b

d

0B

d

uu 0 0, ,

s 0K

Decay amplitude of interest SM PollutionNaive (dimensional) uncertainties on sin2

Note that within QCD Factorization these uncertainties turn out to be much smaller !

42

First Observation of TD CPV in B0 ’K0

• Large statistics mode

1252 signal events

(Ks +KL mode)

0 0 6BR( ) ~ 65.2 10B K 0 0 6

recBR( ) ~ 14.9 10SB K

0

0

0.58 0.03

0.16

0.10

0.07 0.03

K

K

S

C

5.5 measurement

BaBar 384M

’KS

similar result from Belle

43

Golden Penguin Mode : B0 K0

0K

b

dg

t

d

ss

s

W

[ ],

CPK K Belle: 535M BB

307 21 KS signal114 17 KL signal

307 21 KS signal114 17 KL signal S K0 = 0.50 0.21(stat) 0.06(syst)

C K0 = 0.07 0.15(stat) 0.05(syst) S K0 = 0.50 0.21(stat) 0.06(syst)

C K0 = 0.07 0.15(stat) 0.05(syst)

44

Golden Penguin Mode : B0 K0 K0 K0

Belle 535M BB

SKsKsKs= 0.30 0.32(stat) 0.08(syst)CKsKsKs= 0.31 0.20(stat) 0.07(syst)

SKsKsKs= 0.30 0.32(stat) 0.08(syst)CKsKsKs= 0.31 0.20(stat) 0.07(syst)

185 17 KSKSKS signal

185 17 KSKSKS signal

background 　　 subtracted good tags

45

Summary of sin2eff In b s Penguins

But smaller than bccs in all 9 modes !

But smaller than bccs in all 9 modes !

Interesting ! Measurements statistically limited !

Naïve b s penguin average sin2eff = 0.52 0.05Compared to Tree:sin2eff = 0.68 0.03 2.6 difference

Theoretical models predict SM pollution to increase sin2eff !!

Individually, each decay mode in reasonable agreement with SM

46

Theory Predictions, Accounting For subdominant SM Amplitudes

2-body:Beneke, PLB 620 (2005) 143

sin2 sin2 eff

3-body:Cheng, Chua & Soni,

hep-ph/0506268

Calculations within framework

of QCD factorization

greblu

y =e = 1

full s

ig ae

mrang

sin2eff > 0.68 points to an even larger discrepancy !

47

What Are s-Penguins Telling Us ?

This could be one of the greatest discoveries of the century, depending, of course, on how far down it goes…

2.6

discrepancy

48

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40Ja

n-03

Jul-

03

Jan-

04

Jul-

04

Jan-

05

Jul-

05

Jan-

06

Jul-

06

Jan-

07

Jul-

07

Jan-

08

Jul-

08

Jan-

09

Jul-

09

Err

or

on

sin

e am

pli

tud

eNeed More Data To Understand The Puzzle

K*

4 discovery region if non-SM physics is 0.19 effect

2004=240 fb-1

2008=1.0 ab-1

Individual modes reach

4-5 sigma level

Projections are statistical errors only; but systematic errors at few percent

level

Luminosity expectation

s:

20082004

( ) 0.19S

f0KS

KS0

KS

’KS

KKKS

49

0

200

400

600

800

1000

1200

Ju

l-9

9

Ju

l-0

0

Ju

l-0

1

Ju

l-0

2

Ju

l-0

3

Ju

l-0

4

Ju

l-0

5

Ju

l-0

6

Ju

l-0

7

Ju

l-0

8

Projected Data Sample GrowthIn

teg

rate

d L

um

inosit

y [

fb-1]

12

17

20

Lpeak = 9x1033

o PEP-II: IR-2 vacuum, 2xrf stations, BPM work, feedback systems

o BABAR: LST installation

4-month down for LCLS, PEP-II &

BABAR

Double from 2004 to 2006

ICHEP06

Double again from 2006 to

2008 ICHEP08

Expect each experiment to accumulate 1000 fb-1 by 2008

50

Summary & Prospects

• CP Violation in B decays systematically studied at BaBar & Belle. A Comprehensive picture emerging

• Standard Model picture (3 generation CKM matrix) of CP Violation consistent will all observations

• New Physics (in loops) can still contribute to observed CPV but is unlikely to be the dominant source

• CPV violation in the clean bs Penguin Decays appears lower than SM predictions (> 2.6)– more data needed to reveal true nature of discrepancy– B-factories expect to triple data sets by 2008

• LHC-B will probe the Bs sector…Super B-factories ?

51

Suggested Reading: A Partial List

• Reviews of |Vub| & |Vcb|, CKM Matrix, B Mixing & CP Violation in the Particle Data Book

– http://pdg.lbl.gov/

• CP violation and the CKM matrix : A. Hocker & Z. Ligeti

– hep-ph/0605217

• BaBar Physics Book available online at

– http://www.slac.stanford.edu/pubs/slacreports/slac-r-504.html

• Discovery Potential of a Super B factory:

– http://www.slac.stanford.edu/pubs/slacreports/slac-r-709.html

• B Physics at the Tevatron: Run II and Beyond :

– hep-ph/0201071

• Textbooks:

– Heavy Quark Physics: Manohar & Wise; Published by Cambridge

– CP Violation: Branco,Lavoura,Silva; Published by Clarendon Press

– CP Violation by Bigi & Sanda; Published by Cambridge Press

Backup Slides

53

*c

*ub u

b cs

-2

s*

cb cs

(V V )

Aexpect -1

V V 1Since

V V 50

=10 A

T is the dominant amplitude

Hence "Platinum" mode !

0B K : The "Platinum" Final State Penguin:: u,c,t loops

* * *P tb ts cb cs ubt usc u A =V V +V V VP V + PP

Tree

*T cb cs ccsA V V T

T P c

* * *t

*cb cs

b ts

*cb

*u

cb

c

c

s c t u tb us

*ub

cs u s

us

b

s

u

V V

Use Unitarity

A A (T P P ) (P P )

relation V V V V V V

= (V

to rearrange terms

V V

(V VV

A

) +

T ) P

54

The Unitarity Triangle For B System

2

1

3

*arg

*

*arg

*

*arg

*

V Vtd tb

V Vud ub

V Vcd cb

V Vtd tb

V Vud ub

V Vcd cb

Angles of Unitarity Triangle† * *1 0 ud cd cb tbV V V V V VtdV *ubV

Specific forms of CP Violation in B decay provide clean information about the angles of the UT triangle

Same triangle also defined by length of its sides (from CP conservingB decay processes such as b u l nu ) Overconstrained triangle

2 6J A

55

Rules out Superweak model

Establishes CPV not just due

to phase of B Mixing

But hadronic uncertaintiespreclude determination ofCKM angle challenge to theory

Combined significance >> 6

Direct CP Violation in B0 K : Belle (386M BB)

Belle

56

57

The Unitarity Triangle Defined By CPV Measurements

159105 , , 59 19 degrees

First time that all angles

21.7 1.3

measured + +

New B Factory milestone: Comparable UT precision

from CPV in B decays alone

58

Belle and Babar Detectors: Optimized For CP Studies

e

e

b

b

(4 )S

0B0B

Enough energy to barely produce 2 B mesons, nothing else!

B mesons are entangled Need for Asymm energy collisions

59

• B0 B0 are in coherent l=1 state

• Each of the two particles evolve in time (can mix till decay)

• BUT they evolve in tandem since Bose statistics requires overall symm. wavefn

• So that at any time, until one particle decays, there is exactly one B0 and one B0

present ( EPR !)

• However after one of the particles decays, the other continues to evolve

• Now possible to have a (4S) event final state with 2 B0 or 2 B0

• probability is governed by the time difference t between the two B decays

0 0Quantum Entanglement in Y(4S) B B

(4S) B0 B0

Spin = 1 0 0

With l = 1

60

Quantum Correlation at (4S)

• Decay of first B (B0) at time ttag ensures the other B is B0

– End of Quantum entanglement ! Defines a ref. time (clock)

• At t > ttag, B0 has some probability to oscillate into B0 before it decays at time tflav into a flavor specific state

• Two possibilities in the (4S) event depending on whether the 2nd B mixed/oscillated or not:

(4S)B0

ttag

B 0

ttag

in final state

in final state

0 0no oscillation/mixing B B 0 0 oscillation/mixing B B

tflavt

0 0B BX

Y

61

Time Dependent B0 Oscillation (Or Mixing)

62

B0 Decays to CP Eigenstates

0 0CP

0

CP

CP t g

CP

a

B Decay products can't tell Flavor of d

CP eigenstates f accessible to both B & B mesons

ecaying B (B or B)

This is why Quantum coherence i

Examples : B K or B ,

n B B is useful at

0

tag tag CP

0tag

If B is a B at decay time t then B must have been

a B at that time

( !

t

4S)

(4S)B0 B0

ttag ttagtfcp

K0t

0 0B B

Tag

fCP

63

B0 Decays to CP Eigenstates

CP CP

0 0f CP f

CP tag

tag CP

12

1

CP

2

tag

Pr obability of observing the final state |f | f depends on :

1. decay time t and t

2. decay amplitude

3. Oscillation parameq | M |

p Mter

4. Fl

A f | H | B ;A f | H |

av

B

or of B , wheth

CP CP

CP

CP

CP CP CP

CP CP

CP

0CPf

f ff

f

f f f

f CP

0 0t

f

ag tag

A A

where CP eigenvalue of f

er B B or B B

Using property

Define a usefuAA

A f | H |

q q=

p A

&

l CP parameter

B

p A

64

Rates and CP Asymmetries at (4S)

At (4S): integrated asymmetry is zero must do a time-dependent analysis !

This is impossible to do in a conventional symmetric energy collider producing (4S)BB !!

CPfa d t 0

sin Δm ΔtB

65

Summary of |Vub| From Inclusive Measurements

66

Unitarity Triangle From Measurement of Sides

ρ = 0.171 ± 0.041 η = ± 0.387 ± 0.031

Put all these measurementstogether

UT Definition from angles

67

When One B decay tags b flavor, Other decays to fCP

(4S)B0 B0

ttag ttagtfcp

K0t

0 0B B

Tag

fCP

0

0

1.When one B decays to

2.It identifies the other B particle as B at THAT time t= t

3.Ultimately

f

the decay

l

s

avor tagging state at ti

at time into some CP final s

me t (as

t

a

a e

t B

B)

CP

ta

P

ag

f

t

g

Ct f

2

f f2 2

f f

1 λ 2Im(λ )( ) exp( ) 1 cos( ) sin( )

1 λ 1 λ

F t t mt mt

0 0+ -Denoting rate of B by F (t) and B by F (t) CP CPf f