CP Violation in B meson and Belle

2009/03/09 Sack Lunch Talk @ UIUC 1

CP-violation in B mesons and Belle

Pinghan Chu

University of Illinois at Urbana-Champaign

Sack Lunch Talk @ UIUC

• CP-violation and B decays

• The Belle experiment and analysis

• Recent results of CP-violation in B decays


Matter and Antimatter Asymmetry

•Baryon asymmetry of universe

•The Sakharov conditions: three necessary

conditions that a baryon-generating interaction must satisfy to produce matter and antimatter at different rates.(JETP Lett. 5, 24-27, 1967)

•Baryon number B violation -> No experimental evidence

•Interactions out of thermal equilibrium -> The rate of a

reaction which generates baryon-asymmetry must be less than the

rate of expansion of the universe. The particles and antiparticles do

not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation.

••CPCP-- symmetry violationsymmetry violation -> Discovered in 1964


CP-Violation in K meson

•Discovery in neutral

Kaon decays by Cronin and Fitch (PRL 13, 138 ,1967)

•The observation of BR(KL��pp) ~ 2e-3

• KL and KS are the mass eigenstates.

•KL normally decays to ppp, with CP=-1. But pp is CP=+1

•Mass eigenstatesCP eigenstates.


CP-Violation in Standard Model - KM model

•Kobayashi and

Maskawa proposed three generations of quarks to produce one irreducible phase accounting for the CP

violation(Prog. Theor. Phys.

49, 652 ,1973)

•CKM matrix uses three mixing angles (q12, q23, q13) and one CP-violating phase

(d13)


CKM Matrix

13

13 13

13 13

-iδ

ud us ub 12 13 12 13 13

-iδ -iδ

CKM cd cs cb 12 13 12 23 13 12 23 12 23 13 23 13

iδ iδ

td ts tb 12 23 12 23 13 12 23 12 23 13 23 13

23

22

V V V c c s c s e

V V V V -s c -c s c e c c -s s c e s c

V V V s c -c c s e -c c -s c s e c c

λ1- λ Aλ (ρ-iη)

2

λ-λ 1- Aλ

2

≡ =

≈ , CKM

3 2

d' d

where s' =V s

b' bAλ (1-ρ-iη) -Aλ 1

Wolfenstein parameterization (PRL 51, 1945, 1983)

Cabibbo angle

•S12=sinq12

•c12=cosq12

•CP symmetry is broken by the complex phase appearing in the quark mixing matrix.

13

2

12 C

23

iδ 3

13

s =λ=sinθ 0.22

s Aλ

s e =Aλ (ρ iη)

≈

=

+

o o

12

o o

13

o o

23

13

θ =13.04 ±0.05

θ =0.201 ±0.011

θ =2.38 ±0.06

δ =68.8 ±4.6� ��


The Unitary Triangle

, ,ππ ρπ ρρ→

⇓

B

2 ( )φ α

*

ij iki

* * *

ud ub cd cb td tb

The unitarity of the CKM matrix leads to:

We can have six relations.

The interesting relation

for B

V V =0, (j k)

V V +V V +V

decays i

V =0

s

≠∑

V udV

* ub V

td V*tb

VcdV*cb

→ ⇒0B D K ⇐ → sB J/ψK1( )φ β3( )φ γ

*

1 *

*

2 2*

* 2

3 *

1arg( ) arg( ) 22.0

1

1arg( ) arg( ) 89.2

(1 )( )2

arg( ) arg(( )(1 )) 68.92

cd cb

td tb

td tb

ud ub

ud ub

cd cb

V V

V V i

V V i

V Vi

V Vi

V V

φρ η

ρ ηφ

λρ η

λφ ρ η

= − = =− −

− −= − = − =

− +

= − = + − =

��

��

��

See later!

0.0009

0.0010

0.021

0.022

0.031

0.016

0.015

0.017

0.2257

0.814

0.135

0.349

A

λ

ρ

η

+

−

+

−

+

−

+

−

=

=

=

=


1. Direct CP-Violation

Bf

•CP violation arises from the difference between the magnitudes of a decay amplitude and its CP conjugate amplitude.

•The measurement is to compare the decay rate of B meson and its CP conjugate.

•Only possible source of CP asymmetry in charged meson

decays (for example B+zK+p0, discussed later).

( ) - ( )1,

( ) ( )

,

CP

A B

A B A B

B A =

A B B

f

f

f

f

f

fΓ → Γ →≠

Γ → + Γ

≡ ≡

→

H H

≠ Bf


02. B flavor sensitive mode(B )l Dν+ −→ →

•Apply to neutral B0

•Decays have to be flavor sensitive. For example,

•The CP violation is due to mixing of through box-diagrams

0Bl

l Dν− +→

0 0 0 0,

1

2

,

0 0

L H

0

L

L

HB =p B +q B B =p B -q

(

Considering the neutral meson B

If p=q= , B is CP odd and

and B ,

two mass eigenstates are B and B (Light and Heavy)

If the initial

B is CP even s

state i

ta

s B , th

te.)

B

e amp

H

0 0 0( ) ( ) ,

( ) , ( )

H LL H H L

Γ

0 0

Γ- t - t

-imt -imt2 2

m +

litude for B and B at

mqB (t) B B Γ Γ =Γ, m= and m=m -m

p 2

∆m ∆me e co

time t:

s( t) e e sin( t)2 2

g t g t

g t g t i

+ −

+ −

= − ≈ ∆

= =

0 0B -B


02. B flavor sensitive mode(B )l Dν+ −→ →0 0

0

0

0 0

0

,

( ) ( ) ( ) ,

( )

( ) - (

2 2

CP

2 2 -Γt

A B B B

q q B p BB A B λ and µ

p p A q A

1+ λ 1- λB (t) B (t) A e + cos(∆mt)-Im(λ)sin(∆

The decay ratio should

B

b

(t) B (A

mt)2

=

2

e

l l

l

l l

l

l D H l D H

l D H t g t g t

l D l D

l D

ν ν

ν

ν ν

ν

+ − + −

+ −

+ −

+ − + −

− +

≡ ≡

= − ≡ ≡

→ = =

Γ → Γ

Γ H

0 0

)( )

( ) ( )

2 2t) 1--(

B (t) B (

cos(∆mt)µ λ Im(µ)-Im(λ))sin(∆mt

t)

) 2l

l l

l D

l D l D

ν

ν ν

+ −

− + + −

→∝ −

Γ → + Γ →

However, since B<<A, the Acp is much suppressed by the second order box diagram

Decay through box diagram

Flavor sensitive

b b c→ →

b c→


0 0 0 0

.

, , ,

(

, 0 0

L H cp cp

CP violation comes from the interference between a decay B and another

decay with mixing B B The fin

qAB =p B +q B B =p B -q B

al st

A

ate must be a CP

qA

B

eigenstate.

Im

A BpA

CP

CP CP

f

f

f

f

f λ

λ

≡ ≡

→

→ →

≡

=

H H

( ) - ( )) 0,

( ) ( )

CP CP

CP CP

CP CPCP

CP CP

2

2 2

B(t) B(t) A =

pA B(t) B(t)

λ -1 2Im(λ )cos(∆mt)+ sin(

( and denote the parameters for direct and mixing-induced CP vio

∆mt)= cos(∆mt) sin(∆mt)λ +1 λ +1

lation.)

f f

f f

A S

f f

f f

A S

Γ → Γ →≠

Γ → + Γ →

= +

Bf

Bf

B B

Bf

≠

Bf

+ +

A A and q p≈ ≠In contrast to B<<A

0 0/3. B CP eigenstate(B )SJ Kψ→ →


0 0/An example, CP violation in B SJ Kψ→

0

0

0

0

0 0

/

/

1

/

/

/

.2 2

The decay B is the golden mode used for extraction. The direct CP asymmetry

of this decay is expected to be very small. A A and q p

ANow consider calculating

AS

S S

S

S

J J

K

K

K

J

J

K

J K

q

p

ψ

ψ

ψ ψ

ψ φ

λ =

→

= ≃≃≃≃

0

*/* * *

/ / / / *, /

*

/

,

/

*

*

/

( ) ( ) ( ) ,

,d

A

A

For mixing in the B and K

A

-K mixing,

AA

S

J Kq cb csJ K cb cs J K qb qs J K cb cs J K

q u c t J K cb cs

J K

J KKJ

tb td cs cd

tb td K

K

V VV V T V V P V V T

V V

V V V Vq

q

q

p V

q

p

V

p

p

ψ

ψ ψ ψ ψ

ψ

ψ

ψψ

=

=

= + ≈ =

= =

∑

0 0

*

* * *

1 1* * */ 1/sexp( 2 ) Im in(2 )sin(( ) sin( ) )2 , A

S S

cs cd

tb td cs cd cb cs

J K J K

tb td cs cd cb cs

CP

V V

V V V V V Vi

V V V V Vmt

Vψ ψλ φφ λ φ

⇒ = = − − ⇒ =

= ∆

Box diagram

Amplitude ratio from Tree diagram

•Use similar argument to get other angles.Penguin diagram is very small here. No direct CP contribution!

0 0(involves K -K mixing)


B factories – Belle and BaBar


Analysis Technique (Belle)

•B candidates are identified by

•Beam-constrained mass

•Energy difference

•Dominated background:

•Other background from B decays are examined by Monte Carlo simulations.

2 * 2

bc beam BM = E -(P )

*

B beam∆E=E -E**

BE and P are the reconstructed B

energy and momentum in the CM frame.

B

+ -continuum e e qq processes,

and suppressed by event shapes.

→

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-0.2 -0.1 0 0.1 0.2

∆ E

0

0.2

0.4

0.6

0.8

1

1.2

1.4

5.2 5.25 5.3

Mbc

Argus

function 5.279

GeV/c2

Continuum background


Background Suppression

Spherical BB events

Jet-like qq events

+ -

The B decays signal events are

nearly at rest in the (4S)

frame. The daughter particles are

distribu

The dominant background

is from e e qq (q=u,d,s,c

The conti

ted sp

nuum e

)

v

herica

ents a

l

re

of i

l .

y

h

•

ϒ

→

•

•

gh momentum jet-like

and distributing near the

axis of the e e (beam

Event shape variables are used

to reject most of ba

pi

ckg

pe)

ro d.

.

un

+ −

•


Event Shape VariablesModified Fox-Wolfram moments•Event shape variables are

correlated with each other.

•Project these variables to 1-dimension by a Fisher Discriminator. (Ann. Eugen. 7

179, 1936)

so oo oo so oo

1 2 2 2 3 3 4 4 5 4

6 thrust 7

F=α R +α R +α R +α R +α R

+α cosθ +α S⊥

⋅ ⋅ ⋅ ⋅ ⋅

⋅ ⋅


Likelihood Ratio Fit

•Use a likelihood ratio to combine

all the information

•2-D likelihood fit for signal determination

+ =

sig

B

sig bkg

ff=Fisher×Cosθ , LR=

f +f

Apply a cut to suppress background

0

0.2

0.4

0.6

0.8

1

1.2

1.4

5.2 5.25 5.3

Mbc

0

0.2

0.4

0.6

0.8 1

1.2

1.4

-0.2

-0.1

0 0

.1 0

.2

∆ E

independent


(4 ) .B mesons are produced via the decay chain of e e BB

Only one B meson and one B meson at the same time.

One of the B mesons is tagged as a B by a semileptonic decay B X at

1.

time t ,

anoth

2.

3. l

S

l

+ −

+

→ ϒ →

→

22 2 2( )0 0 1 1[ [ ]( ) ( )] [ (1 ) (1 )cos(

2 2

CPer should be a B at time t and its final state is .

The time difference between these two B is t=t and the decay 4 rate.

l fP t t

l CP f SL f CP

l

l

CP

f

f

t

B B l X t f t e A A m tλ λ− ++Γ → ∝ + −

∆

− ∆ ∆

−

) Im( )sin( )]CP

m tλ+ ∆ ∆

Measurement of Time dependent CP asymmetry


Measurement of sin2f1 of J/yK0S

( ) - ( )

( ) ( )

CP CPCP

CP CP

B(t) B(t)A = = cos(∆mt) sin(∆mt)

B(t) B(t)

f fA S

f f

Γ → Γ →+

Γ → + Γ →

0/1 CP

indicates direct CP violation

=0, =sin2 i

,

f S

A

A S f J Kφ ψ=

Belle PRL 98, 031802 2007

•CP violation in B system is well

established within the Standard Model.

CPA


Average of sin2f1 from all experiments

sin(2β) ≡ sin(2φ1)

-2 -1 0 1 2 3

BaBararXiv:0808.1903

0.69 ± 0.03 ± 0.01

Belle J/ψ K0

PRL 98 (2007) 0318020.64 ± 0.03 ± 0.02

Belle ψ(2S) KSPRD 77 (2008) 091103(R)

0.72 ± 0.09 ± 0.03

ALEPHPLB 492, 259 (2000)

0.84 +-01..8024 ± 0.16

OPALEPJ C5, 379 (1998)

3.20 +-12..8000 ± 0.50

CDFPRD 61, 072005 (2000)

0.79 +-00..4414

AverageHFAG

0.67 ± 0.02

H F A GH F A GICHEP 2008

PRELIMINARY

ccs

ccs

S =0.672 ±

HFA

0.024

A =0.005

G

±

(b ccs)

0.

:

019

→

Consists of direct CPV

oSin(44 )=0.69SM prediction:

consistent


Evident of direct CP:B Kπ Decays→

±

± 0

0 - + 0 + -

0 - + 0 + -K π

- - 0 + + 0

- - 0 + + 0K π

N(B K π )-N(B K π )A =

N(B K π )+N(B K π )

=-0.094±0.018±0.008



=0.07±0.03±0.01

→ →

→ →

→ →

→ →

∓∓∓∓

(Belle, Nature 452, 06827, 2008)

•A simple analysis. Just count the number of B mesons.

•The number difference shows the direct CP violation. The time dependent term (indirect CP-violation) will be time-integrated.

•Good agreement with other experiments. (BaBar, CDF. etc)

0B0B

-B +B


B Kπ Decays→

Penguin:suppressed

by the loop(2nd order)

b s→

ub

Tree:suppressed

by small V

b u→

•Sizeable direct CP asymmetry could be generated by the interference (next slide) between tree and penguin amplitudes.

•Sensitive to the f3 angle

0

0

Similar direct CP violation expected for B and

B decays.

K

K

π

π

± ±

±

→

→ ∓∓∓∓

iiii

3( )CPA T P sinδ sinB Kπ φ→ ∝

(since they have similar diagrams.)


Direct CP Violation•Direct CP violation may arise from the interference between two amplitudes, like tree diagram and penguin diagram.

•Assume A is tree diagram and B is penguin diagram.

iδ i

A= A

B= B e e φ iδ -i

A= A

B= B e e φ

CP transformation:

weak phase: -

strong phase:

φ φ

δ δ

→

→

CP

A=A

A+B

A+B

δ•Amplitude sum:

δ-φδ+φ

CP

A+B A+B

A A B sinδsinφ

≠

∝

•Two interfered amplitudes with similar order of magnitude.

•Non-vanished strong and weak phase

The difference phase between A+B and A+B induces direct CP violation.


± 0

±

± 0

±

0 - + 0 + -

0 - + 0 + -K π

- - 0 + + 0

- - 0 + + 0

K K π

π

π

K



=-0.094±0.018±0.008



=0.07±0.0

∆A=A -A =+0.164±0.03

3± 0

7

0. 1

→ →

→ →

→ →

→ →

∓∓∓∓

∓∓∓∓

•The large deviation in direct CP violation between charged and neutral B meson decays could be an indication of new sources of CP violation?

Hint of New Physics

0 + - + + 0

cp

Both B K and B K have similar diagrams,

but have different A sign and amplitude.

π π→ →iiii

Similar diagram


Summary

•The mechanism of CP violation is well established within the framework of Standard Model. But it is still too small to account for the matter-dominated universe.

•A large difference in direct CP violation for

is firmly established at Belle.

•The large deviation could be an indication of new sources of CP violation in b to s penguin loops.

•More data are needed in other modes (e.g. ). The precise measurement of mixing-induced and direct CP violation asymmetries is a promising approach to search for new physics.

0 0 0B K π→

0 + -B K π→

and B K π± ±→ ∓∓∓∓


CP-Violation in B meson

0 0 0 0,L H

L,H L,

0

L

H

0

H

B =p B +q B B =p B -q B

Considering the neutral meson B and B , two mass eigenstates are B and B (Light and Heavy)

The

p pi i( - )( )=(m - Γ )( )

±q ±

eigenvalue equation is

( is mass matrix and

q2 2

is deM Γ

M Γ

0 0 0

H LH,L H,L H,L L H H L

Γ- t

-imt2

H

L L H H

L

m +mA (t)=A (0)exp(-(Γ/2+im )t), where

cay matrix.)

The

Γ Γ =Γ, m= and m=m -m2

∆m q ∆mB (t) (A (

amplitude for the states B and B

t) B +A (t) B )=e e cos( t) B i sin( t) B2 p

at time t

h

2

:

T

≈ ∆

= +

0 0

,

( )

0 0 0

cp cp c

2 22

Γ

p

2 - t

qAe decays of neutral B into a CP eigenstate and A B A B

1+ λ 1- λB (t) B (t) A e + cos(∆mt)-Im(λ)sin(∆mt

and p

2 2

A

)CP CP

f f f

f f

λ≡ ≡ ≡

→ = =

H

H H

Γ

It is related to sin2f1 and indirect CP-violation (showed later) due to CP phase.


Proposal of B factory

•A. I. Sanda proposed a specific experiments on

B mesons. (PRL 45, 952, 1980, Nucl. Phys. B 193, 85 1981)

•The idea, proposed by Pier Oddone, that these

experiments could be performed by colliding two beams of different energies, one of electrons and one of positrons.

•The construction of new accelerators at KEK and SLAC. In 2002, both Belle (PR D 66, 071102, 2002)

and BaBar (PRL 89, 201802, 2002) reported the first observation of a KM asymmetry in a B-meson

decay.


Appendix

•Argus function: ARGUS Collaboration, H. Albrecht et al., Phys. Lett. B 241,

278(1990). The ARGUS function is presented as

(a and b are constants that are determined from the data)• Thrust Angle CosqT (S. Brandt, Ch. Peyrou, R. Sosnowski and A. Wroblewski,

Phys. Lett. 12 (1964) 57 )

•Separate the particles tracks into two groups. One group is a B meson candidate and the other is the other B meson or jet background.•Angle between two groups is the thrust angle.•Random distribution for a real B•Close to +-1 for jet events.

2 2

beam beamax 1-(x/E ) exp(b(1-(x/E ) ))

1max

ii

ii

n P

T=P

n vector is the maximum of all vectors in the group.

n =

⋅∑

∑

��

��

��


Appendix

•Sphericity (J.D. Bjorken and S.J. Brodsky, PR . D1 (1970) 1416)•Define a specific direction of the signal particle’s daughter in the CM frame. •Sum over the transverse momentum with respect to the specified direction and divided it with overall momentum

•Fox-Wolfram moments (G.C. Fox and S. Wolfram, Nucl. Phys. B149 (1979) 413 )

,2,

(cos )

: Legendre polynomials functions

E is the total visible energy of the event.

i j

l l i j

i j tot

l

tot

p pH P

E

P

θ=∑� ��

ii

ii

Pt

S=P

∑

∑

��

��


Appendix

•Super Fox-Wolfram moments (R. Enomoto, Belle lectures 1999 )•Extension of Fox-Wolfram moments

SO

l i j l i,ji,j

OO

l j k l j,ki,j

SO OOSO OOl ll lSO OO

0

i

j

0

k

p : the momentum of candidate B daughters

p and p : the momentum of other

par

H = p p P(cosθ )

H = p p P(cosθ

ticles except the can

)

H HR =

dida

,R =

te B meson.

H H

∑

∑

� ��

� ��


Appendix

•Cos qB

•The angle between the B meson flight direction and beam direction in the rest frame.•Not correlated with previous parameters.•Due to quantum mechanics, the distribution for B is peak around zero. •The background is randomly distributed.


The three categories of CP violation:B-B mixing

Bf ≠ B

f

0 (*)

0 0

CP violation appear in neutral meson mixing.

An example is given in semileptonic neutral

meson decays, such as B decays.

The B B mixing is through the second order

box diagrams and its effec

ll Dν− +→

0 0

0

0 0 0

0

0

( ) - ( )1,

( )

,

( )

L H

CP

q B B

t is very sm

B =p B +q B B =

all.

A =

q

B

p

B

B - B

p

l X l X

l X l X

− +

− +

Γ → Γ →≠

Γ → + Γ →

B B

CP Violation in B meson and Belle

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Transcript of CP Violation in B meson and Belle