Systematic Analysis of B Ｋ πll decaysSystematic Analysis of B Ｋ πll decays

Tadashi Yoshikawa Nagoya U.

International Workshop “Towards the Precise Prediction of CP violation” Oct. 22 – 25, 2007 YITP, Kyoto University

To investigate CP phase is very important !

In SM and In New Physics !!

and

One of the most important aims

of B factories and super B factory. It is very important to investigate by using B meson decays (or τdecays ).

Kobayashi-Maskawa Theory ( CKM matrix) are almost confirmed !!

We are going to next stage to search for

New physics hiding well !

Unitarity Triangle :

Where are they hiding ?

Where can we find them in ?

direct search

VS Indirect search

tree loop

High energy exp. High luminosity Exp.

Both approach are important to understand (find) new Physics .

Physics are going to indirect search of New Physics .They will give us some useful hints and strong constraints for new

Physics.

B factory

→super B

factory 　

→ 　 super-super B …

Main Targets are in Penguin processes .

ｂ su

ud d

Bd

b – s(d) gluon penguin

b – s(d) electro weak penguin

……

..

They will give us some useful hints and strong constraints for new Physics.

A few years ago, We had several excitingly large discrepancies between the experimental data and theoretical expectations.

As you know.

1) In CP asymmetries in b-sqq penguin decays, ex) B ’K ….

2) In BK decays, which are called “K puzzle”. ( = 0 in SM)

Direct CP

Time-dependent CP

= 0

= 0

= 0

Time-dependent CP Asymmetry : Bigi and SandaBigi and Sanda

cc mode S penguin

No CP phase in diagrams No CP phase in diagrams

b

BB

c

B

b

c

s

J/

K

K

J/

B

b

s

Discrepancy of Scp between CC modes and b-s modes

in the SM

The EX. Data are moving to the SM direction !!

Present status of the Puzzle Lipkin, Atwood-Soni

Yoshikawa( 03)., Gronau - Rosner, Buras-Fleischer et al ,

Li, Mishima and Yoshikawa(04) ……. Many works.

What was the Puzzle ?

. Discrepancies from expectations by Sum ruleSum rule among the branching ratios.

(Theory)

(After LP07)

Still remaining this Problem ??

History of Rc - Rn

Rc – Rn Rc

Rn

The EX. Data are moving to the SM direction !!

0 or not

A few years ago, We had several excitingly large discrepancies between the experimental data and theoretical expectations.

As you know.

1) In CP asymmetries in b-sqq penguin decays, ex) B ’K ….

2) In BK decays, which are called “K puzzle”.

= 0.14 ±0.10

( = 0 )

OK ?

Still remaining

small windows.

How do you think about this situation ?

Still remaining deviation.

There were many many works to explain these deviations,

SUSY, extra D model ………

It will give us several useful hints or constraint to build new model !!

New Physics is hiding in them !!

　

The several relations comes from main contribution, which is QCD penguin.The new contribution to explain these situations may be in EW penguin,

because it is the sub-leading contribution.

A possibility is new physics with new CP phase in EW Penguin!!

Where ?

B decays ： topological diagram topological diagram decompositiondecomposition

ＴＴｒｒｅｅｅｅ

QCDQCD ＰＰｅｎｇｅｎｇｕｉｎｕｉｎ

CColor olor suppressed suppressed

treetree

EElectrolectroWWeakeak

PPenguin (enguin (PPEWEW))

AAnnihilatinnihilationon SSinglet QCD inglet QCD

PenguinPenguin

CColor suppressed olor suppressed

EWEW PPenguinenguin

((PPCCEWEW ))

Gronau, Hernandez,London, Rosner

b

B

B

B

BB

B

B

bb

b

b

bb

What can we learn from the K pi puzzle ?

We should be investigate pure EW penguin processes

to find some evidences of New Physics (new CP phase ). (Direct or indirect ) CP asymmetries of EW processes ( b->s gamma, b->s ll )

BUT

Tiny strong phase difference

・ Including both CP odd and even states ・ Small interference term 　 and X2 ∝ 1/q

Slightly difficult to investigate the CP asymmetries !!

CP Asymmetries

Direct CPA

Strong phase difference CP phase

Need strong phase difference !!

Ceff9 Has imaginary part

C9 is including strong phase comes from CC resonances

However no phase in low q^2 region !!

Z 　＝ k^2

Im[C

9]

If EW Penguin : ( Z penguin ) : should include new phase,

the effect will appear in semi-leptonic decays .

But to investigate the effects in C10 process is slightly difficult !!

CP asymmetry of B ll or B s gamma, B Xs ll

tiny Br

final states are both CP odd and even .

Need angular analysis of B K pi ll .

Let’s consider semi-leptonic decays

Small strong phase.

In this talk, I am going to introduce the following works:

1.New measurements using External Photon Conversion at a High Luminosity B Factory

2.Systematic analysis of BKπ ｌｌ　 decays

Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039

C.S. Kim and T.Y, preparing now

Low invariant mass region, z = (p+ + p-)^2 ~ 0

Using Photon Conversion

Using photon conversions in detector, we may measure

Using photon conversions in detector, we may measure

1. Time –dependent CP asymmetry of B

2. Vphoton polarization

3.

4.

At Super B factoryAt Super B factory

Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039

Using Photon

Conversion 1. Time –dependent CP asymmetry of

BS

To find S we need know the vertex position.

But it is difficult to find Bdecay vertex because the final states are neutral pions which go to 2 photons.

Tag sideBB

BB

t

Can not trace to a vertex from 4 photons !

Using Photon

Conversion 1. Time –dependent CP asymmetry of

BS

Tag side

BB

BB

t

Photon change to 2 leptons by conversion with some material inside so that can trace to vertex!!

Detector etal, e

e

Conversion : X ｌ + ｌ -

SS

Can get one more information to understand Bsystem !

Br(B), Br(B), Br(B)Acp, S, Acp, Acp, SS

6 measurements + 1 + 1 8 measurements

For Tree, Penguin, Color-suppressed tree , EW-Penguin,

strong phase differences (2 + 1), weak phase 2

After neglecting EW-penguin contribution,

6 measurements + 1 more vs 6 parameters 6 measurements + 1 more vs 6 parameters

NewNew

?? We have several Questions. Is the isospin relation (triangle) exact one ? Is the isospin relation (triangle) exact one ?

Is Isospin triangle closed ? Is Isospin triangle closed ? or 0 ?

or

1)1)

2) How is EW Penguin dependence ? 2) How is EW Penguin dependence ?

3) Can we remove the discrete ambiguity for the solution ? 3) Can we remove the discrete ambiguity for the solution ?

which depend on how to use the 2 triangles which depend on how to use the 2 triangles

X = orX = or

PPEWEW

B decay

A

B decay

A

V V using photon using photon conversionconversion

By photon conversion : B B (K* (K*KK + ( + (ll++ l l--Semi-leptonic decay through Real photonthrough Real photon,

z

l+

l -

K

π

K* γB

θl

φ

We can do angular analysis

by .

Can get information of Photon Polarization !!

Using Photon

Conversion 2. BV gamma photon polarization

Tag side

BB

BB

t

Real Photon change to 2 leptons by conversion with some material inside so that can trace to vertex!!

Detector etal, e

e

Conversion : X ｌ + ｌ -

The angular distribution : definition of the angles

z

l+

l -

K

π

K* γB

θl

φ

θl ：　 angle between l+ momentum direction and z axis

at CM system of (l+ l- )

：　 angle between π direction and - z axis at CM of (K pi )

φ ：　 angle between ２　 decay planes

FB asymmetry

There are 3 angles. 　　　　　 Can not we use them ?

ｑ＾２

Q^2 ～０

b-s Tiny contribution in SM ∝ ms/mb

Points:Using small-q^2 region, ( q^2 ~ 0 )

One can investigate 　 B 　　 Vγ 　 by using polarization analysis or angular distribution

We can neglect 1) local interactions with O9, O10

2) longitudinal modes, A0

NEGLIGIBLE

Grossman and Pirjol, JHEP0006: 029 (2000)

Kim, Kim, Lu and Morozumi, PRD62: 034013 (2000) Grinstein and Pirjol, PRD73 014013 (2006)

After integrating angles and q^2 at small region, approximately,

From the distribution for angle φ + 　 B->V γ 、 one can extract

which may be including new physics info.

Angler analysis

C7 C7’

whereSmall contribution in SM

Combining with time dependent CP asymmetry :

Where is a phase of decay amplitude

C7 or C7’

We can extract NEW CP Phase of EM penguins !!

After finding R and

We should investigate the phase of C10 or C9 as Z penguin .

Atwood, Gershon, Hazumi and Soni, PRD71:076003 (2005)

2. Systematic Analysis of BKπll 　 decays

Kim and T.Y. To be appear soon.

investigate the contributions of the new CP phase by using

angular analysis and the CP asymmetries for

B Kπll 4 body decays .

We defined several partial angle integration asymmetries,

like Forward-Backward asymmetry (FB).

The angular distribution : definition of the angles

z

l+

l -

K

π

K* γB

θl

φ

θl ：　 angle between l+ momentum direction and z axis

at CM system of (l+ l- )

：　 angle between π direction and - z axis at CM of (K pi )

φ ：　 angle between ２　 decay planes

FB asymmetry

There are 3 angles. 　　　　　 Can not we use them ?

The branching ratios is

After integrating all angles, remains as the decay rate. The other terms shown the angular distribution.

B K l l mode

CP: odd

CP: even

CP: odd

CP: odd

CP: odd

CP: even

Kruger,Sehgal, Shinha, Shinha

Kruger, Matias

Kim,Kim,Lu,Morozumi

Kim, T.Y.

Angular decomposition

BK* l l decay matrix element

b-s Tiny contribution in SM

Z penguin

B (K* K ) + l l

l^-

l^+

l

K

Forward-Backward Asymmetry

l^+ l^+

For example

How to detect the evidence of New Phys. by B K* ll .

Using Forward-Backward asymmetry:

The zero of FB asymmetry is rather insensitive to hadron uncertainty .

We need to remove the hadronic uncertainty !!

We should use some asymmetries :

C7

-C7

AFB

z = (pl^+ + pl^-)^2 Dilepton invariant mass

AFB

V, Ti, Ai : B-K* Form Factors

B K* ll

How about BK pi l l decay ?

Depend on C7 and C9.

C7

-C7

If EW Penguin : ( Z penguin ) : should include new phase,

the effect will appear in semi-leptonic decays .

But to investigate the effects in C10 process is slightly difficult !!

CP asymmetry of B ll or B Xs ll

tiny Br

final states are both CP odd and even .

Need angular analysis of B K pi ll .

Let’s consider semi-leptonic decays

The branching ratios is

After integrating all angles, remains as the decay rate. The other terms shown the angular distribution.

B K l l mode

CP: odd

CP: even

CP: odd

CP: odd

CP: odd

CP: even

Decomposition by using 3 angle distribution

If Possible, we would like to extract these contributions by

using FB asymmetries.

FB asymmetry for l^+

Triple FB asymmetry

An asymmetry for

Triple FB asymmetry

Double FB asymmetry for and

CP: odd

CP: even

CP: odd

CP: odd

CP: odd

CP: even

Usual FB asymmetry

Double FB asymmetry for and

Proportional (CProportional (C99* * CC1010))

Double FB asymmetry for and

Appear Im ( C10 C7 ) Imaginary part of C10

Note: s = q^2 = (Pk + Pπ)^2

z = k^2 = (P+ + P- )^2

An asymmetry for

Triple FB asymmetry

CP Asymmetries

Direct CPA

Strong phase difference CP phase

Need strong phase difference !!

Ceff9has 　 imaginary part

C9 is including strong phase comes from CC resonances

Z 　＝ k^2

Im[C

9]

no phase in low q^2 region !!

And CP odd and even interference effect is also existing in the new FBs.

Important points to use new FBs

The definition of direct and time-dependent CP asymmetries:

s,s, 　　 z distributionsz distributions

),(),(

][),(

zsBzsB

FBzsA

iiiFBicp

][

*][2),(

12Im

iii

iiFBicp

FB

MMeFBzsS

＝ ＝ ＝＝＝ odd)

+1 (CP even)

direct CPV of FB asymmetry direct CPV of FB asymmetry 　　

time-dependent CPVtime-dependent CPV

),(),(

][),(

zsBzsB

FBzsA

iiiFBi

FB asymmetryFB asymmetry

FB asymmetry for l^+

C7

-C7

C10 i |C10|

AcpFB2

FB2

C9 i |C9|

FB4

If C7’ with CP phase exists, the effect will appear in FB4 and Acp .

C7’ not =0

If C7’ with CP phase exists, the effect will appear in FB4.

FB4

FB5

Triple FB asymmetry

C7’ not =0

If C7’ with CP phase exists, the effect will appear in FB5.

FB5

C10 i |C10|

FB6

Double FB asymmetry for and

C7’ not =0

C7

-C7

FB6

C10 i |C10|

Sensitive to the phase of

C10 and C7 　

FB7

An Example FB2 　

The CP phase of C_9 are

π/ ８０

π/ ４

π/2

FB2

2FBcpA

2FBcpS

　－ Sin2φ１

We need more strong phases .

How about interferences between K^* and scalar resonance as intermediated states ？

We may get many fruitful information from B K pi ll decay modes.

Angular analysis

CP asymmetries

l

l

S (scalar) K0*(800)

We can define new FB like asymmetries!!There is another strong phase source by the resonance effects.

We used

Im partsDescotes-Genon, Moussallam

EPJ C8, 553

Here we are using and start frommost general 4-fermi interaction

C9, C10, C7 : SM parameters

C9’, C10’, C7’ : L-R model et.al. 　　 R 　 current

Css, CAs, CsA, CAA : scalar type interactions

CT, CTE : tensor type interactions

Br

With scalar resonance We can define new type FBs.

K meson FB asymmetry

L-R asymmetry for angle

UP-Down asymmetry for angle

Triple asymmetry

L-R for phi, FB asymmetry for lepton

If there is such scalar resonance effects, these new FBs will appear!!

FB ２＾ｓ

FB ４＾ｓ

2FBcpSA

4FBcpSA

π/ ８０

π/ ４

π/2

C9 　の　 CP 位相　を

K meson FB asymmetry

UP-Down asymmetry for angle

Summary There are several discrepancies between Ex. and theory in B decays. But some ones seem to be moving to SM prediction.

Still remaining the region for New Physics in EW penguin as the new CP phases.

To understand and find the evidence of NP, we should investigate semi-leptonic rare decays.

At Low invariant mass k^2 ~ 0 region Using photon conversions technique C7’ and the CP phase

Angular analysis and the CP asym. C10 or C9 CP phase

With Scalar resonance effect New information

Buck up

＝ ＝

We are using ＝→＝ as a very strict constraints to new physics.

As you know well,

Nakao( ＝＝＝＝

Charged Higgs mass

)%95(295 CLGeVM

Constraint for ＳＵＳ Y

＝＝＝＝＝＝＝ et al (06)

HFAG06

For example

|A ＋－ ||A ＋ー｜

√ ２ |A+0 |= √ ２ |A － 0 |

Isospin analysis :Isospin analysis :

Relation:Relation:

Extract 2

By using 2 triangles, the angle between A and Ais extracted .

X

where

Isospin Triangles

Gronau and London

Where does new S appear in the triangles ? :

|A ＋－ ||A ＋＝｜

√ ２ |A+0 |= √ ２ |A － 0 |

X

Isospin Triangles

Y

As the same sense,

one can extract 2 .

As the same sense,

one can extract 2 .

then

2 = or not 22 = or not 2

New check item ! New check item !

3) Can we remove the discrete ambiguity ?

YX

X and Y have 4 fold ambiguity

1 2 3 4

2 ambiguity to find 22 – x from

22 - X, –22 + X

total 4 x 2 = 8 fold ambiguity

Using Using 22(() = ) = 22(() , one can reduce the ambiguity !) , one can reduce the ambiguity !

Z() + Xi

– z() - Xi----

Z() + Yi

– z() - Yii = 1 ~ 4

At each “ I ”, by comparing each solution, if they are same, then

it will remain as the solution.

An example:An example:

From the present data, one can predict some region of Sfor 2.

From recent HFAG data, S for 2 is shown in Figure.

Note that this is not 2 fitting

Within the 1 error for

all experimental data .

Within the 1 error for

all experimental data .

There are 8 regions

for each solution.

S

2

By using

Br() = 5.2 0.20, Br()= 1.31 0.21, Br) = 5.7 0.4

Acp(+-) = 0.39 0.07, Acp(00) = 0.36 0.32, Acp(+0) = 0.04 0.05

S = -0.59 0.09

22

S

If we find If we find SS, we can reduce, we can reduce

the ambiguity of the solutionsthe ambiguity of the solutions

for for 22..

Br() = 5.21 0.10, Br()= 1.31 0.10, Br) = 5.7 0.2

Acp(+-) = 0.39 0.04, Acp(00) = 0.36 0.16, Acp(+0) = 0.04 0.03

S = -0.59 0.005

After reduce the error (up to 1/2) :

Almost 2 hold ambiguity for SAlmost 2 hold ambiguity for S

One can reduce the ambiguity!!One can reduce the ambiguity!!22

S

Once we find S,

1) Is the isospin relation (triangle) exact one ? 1) Is the isospin relation (triangle) exact one ?

Is Isospin triangle closed ? Is Isospin triangle closed ? or 0 ?

What is the origin of “” ?

= 5/2 contribution no such diagram in the SM !!

1. New Physics contribution ?

2. Final state interaction ?

3. ’ mixing ?

or

To use S is only method to check the situation about isospin triangle ! To use S is only method to check the situation about isospin triangle !

quite tiny contribution O(1/100)

Gronau and Zupan, PRD71,074017,(05)Gronau and Zupan, PRD71,074017,(05)

2 = 22 = 2

To extract a correct 2 and get some information about the discrepancy from the SM, we have to check the relation. To extract a correct 2 and get some information about the discrepancy from the SM, we have to check the relation.

Real situationfake situation

SummarySummaryIn (super) B factory, S will be measured !! -----> Ishino-san’s talk

You can be going to get one more information about B decays system . You can be going to get one more information about B decays system .

How to use the new measurement ?How to use the new measurement ?

1. To remove the discrete ambiguity.

2. To check the isospin triangle.

New Physics ? Final state int. ? ’mixing ?

The other effects we do not know ?

With BKpi gamma, we can extract New physics information in b-s gamma interaction by using polarization of gamma (=angular analysis of

We can find the magnitude of A_R coupling and the CP phase as a New physics evidence.

Application of PCApplication of PCBy using Photon Conversion Technique,

1. Can trace (find) to the decay vertex including et al.

at good accuracy.)

B

B

B

2.Can use angular analysis

B V

……

.

Please consider what we can do by using this new Please consider what we can do by using this new technique !!!technique !!!

New Physics search

The branching ratios is

After integrating all angles, remains as the decay rate. The other terms shown the angular distribution.

B K l l mode

CP: odd

CP: even

CP: odd

CP: odd

CP: odd

CP: even

Kruger,Sehgal, Shinha, Shinha

Kruger, Matias

If Possible, we would like to extract these contributions by

using FB asymmetries.

FB asymmetry for l^+

Triple FB asymmetry

An asymmetry for

Triple FB asymmetry

Double FB asymmetry for and

CP: odd

CP: even

CP: odd

CP: odd

CP: odd

CP: even

CP Asymmetries

Direct CPA

Strong phase difference CP phase

Need strong phase difference !!

Ceff9 の　 imaginary part (Buchalla 00)

C9 is including strong phase comes from CC resonances

However no phase in low q^2 region !!

FB asymmetry for l^+

C7

-C7

C10 i |C10|

Acp

FB2

CP: oddExample:

Buck up 2

system, decay amplitudes: T (tree), P (penguin), C (color suppressed )

6 measurements for 6 parameters = solve (can extract 2

Isospin analysis to remove penguin pollution.Isospin analysis to remove penguin pollution.

+ 1 measurement ( S

To check the SM, New Phys. And to solve discrete ambiguityTo check the SM, New Phys. And to solve discrete ambiguity

3 Br, 2 Acp, 1 Sfor T, rp, rc, 2 23 Br, 2 Acp, 1 Sfor T, rp, rc, 2 2

22 – X1

- 22 + X1

22 – X2

– 22 – X2

- 22 + X1

- 22 + X2

22 + X1

22 + X2

Z for each regionZ for each region

X1 = X2=

X3 = X1 , X4 = X2

2) How is EW Penguin dependence ? 2) How is EW Penguin dependence ?

Note that is not changed !!

We need a correction in the bottom line, which shows B.

|T+C||PEW|

22

rotate a triangle by angle to fit the botom linesrotate a triangle by angle to fit the botom lines

so that we cam use same isospin analysis to extract 2eff .

X

where

One can find “ 22“ by using isospin analysis

and can reduce the ambiguity as the same sense with no EWP case.

One can find “ 22“ by using isospin analysis

and can reduce the ambiguity as the same sense with no EWP case.

have to be determine by the other method !! have to be determine by the other method !!

In this case, there are 8 measurements

( Br+-, Br+0, Br00, Acp, Acp, Acp, S, S

for

( T, rp, rc, rEW, p, c, EW, 2 ) 8 parameters

may solve if we can get enough data.

ｂ

u, d

B0 decay

B+ decay

=？

New Physics?New Physics? usual case = b -- 3 light quarks vertex

spectator is free !! spectator is free !!

Not changed by the interactions

Isospin relaion

= 1/2 or 3/2 interactions

Usual type new physics can not break the isospin relation !!

ｂ

ｄ

ｄ

ｄ

ｄ

ｄ

？π ０

π ０

Bbresaking of isospin relation

New Physics?New Physics? an example of 5/2 interaction: b – 5 dquarks interaction

Which type seems to be quite exotic model.

New Physics ?

or

Final state interactions ?

PointPointTo extract a correct result as the weak phase 2, we have to remove all ambiguities.

To do so, the first

we have to check whether the isospin triangle is closed or not.

After that we can move to search for new physics including in the loop contributions as QCD, EW- Penguins.