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

Tadashi Yoshikawa Nagoya U.

３ｒｄ　 International Workshop on “B factories and New Measurements” Jan. 24 – 26, 2008 Atami, Japan

This talk is based on :

C.S. Kim and T. Yoshikawa arXiv:0711.3880[hep-ph]

In Penguin processes as the loop effects.

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.

New Physics is hiding very well in B decays!!

Important modes to find NP

New Physics is hiding very well in B decays!!

　

The new physics may be hiding in EW Penguin!!

Where ?

Why ?

If you can think K puzzle is still remaining,

One of the solutions is the contribution as an EW penguin with the new CP phase which may be induced by new physics.

“K puzzle” in B K decays.

= 0

= 0

= 0

( should be 0 within the SM)

POINT!!POINT!!

What can we learn from the K pi puzzle ?

We should 　 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/k

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 k^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.

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, arXiv:0711.3880[hep-ph]

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

investigate CP phase in b->s ll ]

2 methods

At large invariant mass region,

Investigate the CP asymmetries or FB asymmetry in BKll.

2. Systematic Analysis of BKπll 　 decays

C.S.Kim and T.Y. arXiv:0711.3880[hep-ph]

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) and the CP asymmetries.

Points:

1. There are 3 angles so that we can have many observables by angular decompositions.

2. Tiny CPV is enhanced by strong phases from cc resonance effects.

3. We may use the strong phase from K^*, K-scalar … resonances.

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.

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

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

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

Proportional Im(CProportional Im(C1010* * CC77))

An asymmetry for

Triple FB asymmetry

Proportional Im(CProportional Im(C99* * CC77))

Im(CIm(C77** C C77’ )’ )

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^+

FB2

FB2

C10 i |C10|

Acp

C7 = C7SM, C7’ = 0/2

FB4

FB4

C9 i |C9|

C7 = C7SM, C7’ = 0 ＝ /2

FB5

Triple FB asymmetry

FB5

C7 = C7SM, C7’ = 0 ＝ /2

C10 i |C10|FB6

Double FB asymmetry for and

FB6

Sensitive to the phase of

C10 and C7 　

FB7

C10 i |C10|

An Example FB2 　

The CP phase of C_9 are

０π/４π/2

FB2

　－ Sin2φ１

2FBcpS

2FBcpA

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

KK*(l+

l- )

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

π/８０

π/４

π/2

CP Phase of C9　

4FBcpSA

UP-Down asymmetry for angle FB ４＾ｓ

2FBcpSA

FB ２＾ｓ

K meson FB asymmetry

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