Systematic Analysis of B  Ｋ πll decays

Systematic Analysis of B  Ｋπll decays Tadashi Yoshikawa Nagoya U. This talk is based on : C.S. Kim and T. Yoshikawa arXiv:0711.3880[hep-ph] ３ｒｄ　International Workshop on “B factories and New Measurements” Jan. 24 – 26, 2008 Atami, Japan

New Physics is hiding very well in B decays!! In Penguin processes as the loop effects. ｂ s u Bd u d d Important modesto find NP 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!! Where ? The new physics may be hiding in EW Penguin!! Why ? POINT!! If you can think Kp 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. “Kp puzzle” in B Kpdecays. = 0 = 0 ( should be 0 within the SM) = 0

What can we learn from the K pi puzzle ? We shouldinvestigate 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 strongphase difference ・Including both CP odd and even states ・Small interference termand X2 ∝ 1/k Slightly difficult to investigate the CP asymmetries !!

CP Asymmetries Direct CPA CP phase Strong phase difference Need strong phase difference !! Has imaginary part C9 is including strong phase comes from CC resonances Im[C9] However no phase in low k^2 region !! Z　＝k^2

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 Small strong phase. final states are both CP odd and even . tiny Br Need angular analysis of B  K pi ll . Let’s consider semi-leptonic decays

2 methods • New measurements using External Photon Conversion at a High Luminosity B Factory • Systematic analysis of BKπｌｌ　decays Ishino,Hazumi,Nakao, T.Y. hep-ex/0703039 At Low invariant mass region, z = (p+ + p-)^2 ~ 0 investigate CP phase in b->s g [ ->(Kp)ll ] C.S. Kim and T.Y, arXiv:0711.3880[hep-ph] At large invariant mass region, Investigate the CP asymmetries or FB asymmetry in BKpll.

2. Systematic Analysis of BKπlldecays 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 . • Points: • There are 3 angles so that we can have many observables by angular decompositions. • Tiny CPV is enhanced by strong phases from cc resonance effects. • We may use the strong phase from K^*, K-scalar … resonances. We defined several partial angle integration asymmetries, like Forward-Backward asymmetry (FB) and the CP asymmetries.

The angular distribution : definition of the angles φ K l+ qk θl K* γ z B π l- θl：　angle between l+ momentum direction and z axis at CM system of (l+ l- ) FB asymmetry q K：　angle between π direction and - z axis at CM of (K pi ) φ：　angle between ２　decay planes There are 3 angles. Can not we use them ?

Kruger,Sehgal, Shinha, Shinha B  K p l l mode Angular decomposition Kruger, Matias Kim,Kim,Lu,Morozumi Kim, T.Y. The branching ratios is After integrating all angles, G1 remains as the decay rate. The other terms shown the angular distribution. CP: odd CP: odd CP: even CP: odd CP: even CP: odd

Z penguin BK* l l decay matrix element b-s g Tiny contribution in SM l^- K qK B K* ql l^+ B (K* K p) + l l p For example Forward-Backward Asymmetry l^+ l^+ - B K* B K*

How to detect the evidence of New Phys. by B K* ll . We need to remove the hadronic uncertainty !! We should use some asymmetries : V, Ti, Ai : B-K* Form Factors Using Forward-Backward asymmetry: The zero of FB asymmetry is rather insensitive to hadron uncertainty . AFB AFB B K* ll C7 ~ + 4 Depend on C7 and C9. -C7 z = (pl^+ + pl^-)^2 How about BK pi l l decay ? Dilepton invariant mass

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 final states are both CP odd and even . tiny Br Need angular analysis of B  K pi ll . Let’s consider semi-leptonic decays

B  K p l l mode Decomposition by using 3 angle distribution The branching ratios is After integrating all angles, G1 remains as the decay rate. The other terms shown the angular distribution. CP: odd CP: odd CP: even CP: odd CP: even CP: odd

If Possible, we would like to extract these contributions by using FB asymmetries. FB asymmetry for l^+ CP: odd Triple FB asymmetry CP: even An asymmetry for f CP: odd Triple FB asymmetry CP: odd Double FB asymmetry for f and qk CP: odd CP: even

Here we are using and start from most general 4-fermi interaction C9, C10, C7 : SM parameters C9’, C10’, C7’ : L-R model et.al.Rcurrent Css, CAs, CsA, CAA : scalar type interactions CT, CTE : tensor type interactions

Proportional (C9* C10) Usual FB asymmetry Double FB asymmetry for f and qk

Proportional Im(C10* C7) Double FB asymmetry for f and qk Appear Im ( C10 C7 ) Imaginary part of C10 Note: s = q^2 = (Pk + Pπ)^2 z = k^2 = (P+ + P- )^2

Proportional Im(C9* C7) Im(C7* C7’ ) An asymmetry for f Triple FB asymmetry

CP Asymmetries Direct CPA CP phase Strong phase difference Need strong phase difference !! hasimaginary part Important points to use new FBs C9 is including strong phase comes from CC resonances Im[C9] no phase in low q^2 region !! Z　＝k^2 And CP odd and even interference effect is also existing in the new FBs.

The definition of direct and time-dependent CP asymmetries: s,z distributions FB asymmetry direct CPV of FB asymmetry time-dependent CPV η　＝　－1　　（ＣＰ　odd) +1 (CP even)

FB asymmetry for l^+ FB2 C7 = C7SM, C7’ = 0 F10 = p/2 p/4 0 FB2 Acp C10 i |C10|

FB4 C7 = C7SM, C7’ = 0 F９ = p/2 p/4 0 FB4 C9 i |C9|

Triple FB asymmetry C7 = C7SM, C7’ = 0 F９ = p/2 p/4 0 FB5 FB5

Double FB asymmetry for f and qk FB6 FB6 C10 i |C10|

FB7 Sensitive to the phase of C10 and C7 C10 i |C10|

An Example FB2 The CP phase of C_9 are ０ π/４ π/2 FB2 －Sin2φ１

We need more strong phases . How about interferences between K^* and scalar resonance as intermediated states？ K K* l B S (scalar) l K0*(800) π We used Im parts Descotes-Genon, Moussallam EPJ C8, 553 We may get many fruitful informationfrom B  K pi lldecay modes. Angular analysis CP asymmetries We can define new FB like asymmetries!! There is another strong phase source by the resonance effects.

Here we are using and start from most general 4-fermi interaction C9, C10, C7 : SM parameters C9’, C10’, C7’ : L-R model et.al.Rcurrent Css, CAs, CsA, CAA : scalar type interactions CT, CTE : tensor type interactions

With scalar resonance We can define new type FBs.

K meson FB asymmetry K (l+ l- ) K* qk L-R asymmetry for angle f UP-Down asymmetry for angle f Triple asymmetry L-R for phi, FB asymmetry for lepton

If there is such scalar resonance effects, these new FBs will appear!! K meson FB asymmetry FB２＾ｓ CP Phase of C9 ０ π/８ π/４ π/2 UP-Down asymmetry for angle f FB４＾ｓ

Summary • There are several discrepancies betweenEx.and theoryin B decays. But some ones seem to be moving to SM prediction. • Still remaining the region for New Physicsin 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

Systematic Analysis of B  Ｋ πll decays