Systematic 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 treeloop 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 s u u d d BdBd 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 B  K  decays, which are called “K  puzzle”. ( = 0 in SM ) Direct CP Time-dependent CP = 0

Time-dependent CP Asymmetry : Bigi and Sanda cc modeS penguin No CP phase in diagrams b BB c B b c s J/  K K B b s

Discrepancy of S cp 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 ? Sum rule. Discrepancies from expectations by Sum 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 B  K  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 ?

topological diagram decomposition B decays ： topological diagram decomposition Ｔｒ ｅｅ QCD Ｐｅｎｇ ｕｉｎ Color suppressed tree ElectroWeak Penguin (P EW ) Annihilation Singlet QCD Penguin Color suppressed EW Penguin (P C EW ) Gronau, Hernandez,London, Rosner b B B B B B B B b b b b b b

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 X 2 ∝ 1/q Slightly difficult to investigate the CP asymmetries !!

CP Asymmetries Direct CPA Strong phase difference CP phase Need strong phase difference !! Has imaginary part C9 is including strong phase comes from CC resonances However no phase in low q^2 region !! Z ＝ k^2 Im[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  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 B  Kπ ｌｌ decays Ishino,Hazumi,Nakao, T.Y. hep-ex/ 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        V  photon polarization  At Super B factory Ishino,Hazumi,Nakao, T.Y. hep-ex/

Using Photon Conversion 1.Time –dependent CP asymmetry of B       S      To find S       we need know the vertex position. But it is difficult to find B       decay vertex because the final states are neutral pions which go to 2 photons. Tag side  B B  tt     Can not trace to a vertex from 4 photons !

Using Photon Conversion 1.Time –dependent CP asymmetry of B       S      Tag side  B B  t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 -

SSSS Can get one more information to understand B   system ! Br(B      ), Br(B      ), Br(B      ) S     A cp, S    , A cp, A cp, S      6 measurements  8 measurements For Tree, Penguin, Color-suppressed tree, EW-Penguin, strong phase differences (2 + 1), weak phase   After neglecting EW-penguin contribution, 6 measurements + 1 more vs 6 parameters New

?? We have several Questions. Is the isospin relation (triangle) exact one ? Is Isospin triangle closed ? or 0 ? or 1) 2) How is EW Penguin dependence ? 3) Can we remove the discrete ambiguity for the solution ? which depend on how to use the 2 triangles X =     or      P EW B decay A B decay A

   V  using photon conversion B  (K*  K  + (    l + l -  By photon conversion : B  (K*  K  + (    l + l -  through Real photon Semi-leptonic decay through Real photon, z l+l+ l -l - K π K*γ B θlθl φ  We can do angular analysis by  Can get information of Photon Polarization !!

Using Photon Conversion 2. B  V gamma photon polarization  Tag side  B B  t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+ l -l - K π K*γ B θlθl φ  θ l ： 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 O 9, O 10 2) longitudinal modes, A 0 NEGLIGIBLE Grossman and Pirjol, JHEP0006: 029 (2000) Kim, Kim, Lu and Morozumi, PRD62: (2000) Grinstein and Pirjol, PRD (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 C 7 C 7 ’ where Small 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: (2005)

2. Systematic Analysis of B  Kπll 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+ l -l - K π K*γ B θlθl φ  θ l ： 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: even Kruger,Sehgal, Shinha, Shinha Kruger, Matias Kim,Kim,Lu,Morozumi Kim, T.Y. Angular decomposition

B  K* l l decay matrix element b-s  Tiny contribution in SM Z penguin B  (K*  K  ) + l l l^- l^+ ll    KK Forward-Backward Asymmetry    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 : C7C7 -C 7 A FB z = (pl^+ + pl^-)^2 Dilepton invariant mass A FB  V, Ti, Ai : B-K* Form Factors B  K* ll How about B  K pi l l decay ? Depend on C7 and C9.

C7C7 -C 7

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: 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: even

Usual FB asymmetry Double FB asymmetry for  and  Proportional (C 9 * C 10 )

Double FB asymmetry for  and  Appear Im ( C 10 C 7 )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 !! has imaginary part C9 is including strong phase comes from CC resonances Z ＝ k^2 Im[C9] 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, z distributions  ＝ －  （ＣＰ odd) +1 (CP even) direct CPV of FB asymmetry direct CPV of FB asymmetry time-dependent CPV FB asymmetry

FB asymmetry for l^+ C7C7 -C 7 C 10  i |C 10 | Acp FB 2

C 9  i |C 9 | FB 4 If C 7 ’ with CP phase exists, the effect will appear in FB4 and Acp. C 7 ’ not =0 If C 7 ’ with CP phase exists, the effect will appear in FB4. FB 4

FB 5 Triple FB asymmetry C 7 ’ not =0 If C 7 ’ with CP phase exists, the effect will appear in FB5. FB 5

C 10  i |C 10 | FB 6 Double FB asymmetry for  and  C 7 ’ not =0 C7C7 -C 7 FB 6

C 10  i |C 10 | Sensitive to the phase of C10 and C7 FB 7

An Example FB2 The CP phase of C_9 are π/ ８ ０ π/ ４ π/2 FB2 － Sin2φ １

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) K 0 *(800)   We can define new FB like asymmetries!! There is another strong phase source by the resonance effects. We used Im parts Descotes-Genon, Moussallam EPJ C8, 553

Here we are using and start from most general 4-fermi interaction C 9, C 10, C 7 : SM parameters C 9 ’, C 10 ’, C 7 ’ : L-R model et.al. R current C ss, C As, C sA, C AA : scalar type interactions C T, C TE : 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 π/ ８ ０ 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 C 7 ’ and the CP phase Angular analysis and the CP asym. C10 or C9 CP phase With Scalar resonance effectNew information

Buck up

ＢＳ  We are using  ｂ → ｓ  as a very strict constraints to new physics. As you know well,  Nakao( ＬＰ０７  Charged Higgs mass Constraint for ＳＵＳ Y Ｉｓｉｄｏｒｉ et al (06) HFAG06 For example

|A ＋－ | |A ＋ー ｜ √ ２ |A +0 |= √ ２ |A － 0 | Isospin analysis : Relation: Extract   By using 2 triangles, the angle between A  and A  is extracted. X where Isospin Triangles Gronau and London

Where does new S     appear in the triangles ? : |A ＋－ | |A ＋ー ｜ √ ２ |A +0 |= √ ２ |A － 0 | X Isospin Triangles Y As the same sense, one can extract  2. then          = or not        New check item !

3) Can we remove the discrete ambiguity ? Y X X and Y have 4 fold ambiguity ambiguity to find 2  2 – x from   2 - X,  –2  2 + X total 4 x 2 = 8 fold ambiguity Using  2 (     ) =  2 (     ), one can reduce the ambiguity ! Z(     ) + X i  – z(     ) - X i ---- Z(     ) + Y i  – z(     ) - Y i i = 1 ~ 4 At each “ I ”, by comparing each solution, if they are same, then it will remain as the solution.

An example: From the present data, one can predict some region of S     for   From recent HFAG data, S      for   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S 2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  =  222 SS If we find S    , we can reduce the ambiguity of the solutions for . for .

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  =  After reduce the error (up to 1/2) : Almost 2 hold ambiguity for S  One can reduce the ambiguity!! 2222 SS Once we find S    ,

1) Is the isospin relation (triangle) exact one ? 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 ?    ’ mixing ? or 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)

         =        To extract a correct  2 and get some information about the discrepancy from the SM, we have to check the relation. Real situation fake situation

Summary In (super) B factory, S     will be measured !! -----> Ishino-san’s talk You can be going to get one more information about B   decays system. 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 B  Kpi 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 PC By 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 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: 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: even

CP Asymmetries Direct CPA Strong phase difference CP phase Need strong phase difference !! 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^+ C7C7 -C 7 C 10  i |C 10 | Acp FB 2 CP: odd Example:

Buck up 2

 system, decay amplitudes: T (tree), P (penguin), C (color suppressed ) 6 measurements for 6 parameters = solve (can extract    Isospin analysis to remove penguin pollution. + 1 measurement ( S      To check the SM, New Phys. And to solve discrete ambiguity 3 Br, 2 Acp, 1 S     for T, r p, r c, 2  

2  2 – X 1  - 2  2 + X 1 2  2 – X 2  – 2  2 – X 2  - 2  2 + X 1  - 2  2 + X 2 2  2 + X 1 2  2 + X 2 Z for each region X1 =  X2=  X3 =  X1, X4 =  X2

2) How is EW Penguin dependence ? Note thatis not changed !! We need a correction in the bottom line, which shows B       |T+C| |P EW | 2222  rotate a triangle by angle  to fit the botom lines so that we cam use same isospin analysis to extract   eff. X

where One can find “    “ by using isospin analysis and can reduce the ambiguity as the same sense with no EWP case. One can find “    “ 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 !! In this case, there are 8 measurements ( Br +-, Br +0, Br 00, A cp, A cp, A cp, S    , S       for ( T, r p, r c, r EW,  p,  c,  EW,  2 ) 8 parameters may solve if we can get enough data.

ｂ u, d B 0 decay B + decay = ？ New Physics? usual case = b -- 3 light quarks vertex 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 ？ π０π０ π０π０ B bresaking of isospin relation 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 ?

Point To extract a correct result as the weak phase  , 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.