Search for New Physics in B decays Tadashi Yoshikawa Nagoya U. KEKPH07 3/1 – 3/3

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.

Example:Ishidori and Paradisi (hep-ph/ )  TeV  u = -1.0 TeV Constraints for tan  and charged Higgs mass in the MFV within the MSSM. A Case: g-2 (Belle)

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.

Searching for New Physics in B decays Investigating Penguin effects. How to handle these penguin processes? How to play with penguin. ｂ d u u d d BdBd π＋π＋ π－π－

Plan of this talk: Introduction Status of several puzzle Scp of B   ’K K  puzzle Still remaining the window for NP ? B  V ll and B  Kp ll

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

Φ １＝ ２１．２ ± １． ０ °

Discrepancy of S cp between CC modes and b-s modes in the SM The EX. Data are moving to the SM direction !!

Comparison by CP asymmetry Time-dependent CP asymmetry: A f  direct CP violation S f  mixing CP violation :  M (phase of B-B mixing) ～  １  Ｄ (phase of A(B  f) ) Almost 0!!

New Physics window is still remaining ? 

 SM discrepancy

 SM

 SM

 SM

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 !! As the Next step, we should consider comparison among each decay modes even if the modes are b-s penguin. We have to investigate carefully the detail each contributions. New Physics is hiding them !! S K0  may have some hints of New Physics. S K0pi0 = 0.31  0.26 K  puzzle Kim, Kwon, Lee, TY

Present status of the  Puzzle Lipkin 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 ICHEP06) Still remaining this Problem ??

History of Rc - Rn Rc – Rn Rc Rn The EX. Data are moving to the SM direction !! 0 or not

2006 HFAG

What can we learn from the K pi puzzle ?

Diagram Decomposition Gronau, Hernandez,London, Rosner Relation among amplitudes : Isospin relation Several Sum rules for Br and Acp.

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

Hierarchy Assumption ＰＱＣ Ｄ in B  K  O(0.1) O(0.01) Naïve factorization method (Leading order)

Branching ratios under the assumption by neglecting r 2 terms including r C, r c EW, r A (smaller terms than O(0.01 ). )

＝０．２１ ± ０．１１ ≠ O （０．１＾２） （２００５） Rc - Rn The Origin of Sum rule breaking is Electro Weak Penguin ?? r EW : Electro Weak Penguin Contribution ＝０．１２ ± ０．１０ O （０．１＾２） （ ICHEP ０６） ＝０．１２ ± ０．１０ O （０．１＾２） （ ICHEP ０６） The difference comes from r^2 O(0.1^2) terms !!!

Rc – Rn   EW) Strong phase of EW penguin     r ew = 0.14, 0.2, 0.3, 0.4 Maximum of Rc – Rn for delta(EW) and r ew

Cos  T > 0 is favored.  T should be around 15 o. Fleischer-Mannel bound  as a function of  T with r T = 0.2.  T should be around 15 o or 155 o  T + Direct CP Violation of B  K+ 

What can we expect No strong phase difference between tree and EW(Z) penguin b b W z u s K K B B 1) 2) under SU(3) symmetry. Because the diagrams are topologically same. treeEW Penguin Neubert-Rosner, Buras and Fleischer

Rc – Rn   EW) Strong phase of EW penguin     r ew = 0.14, 0.2, 0.3, 0.4 If the strong phases of tree and EW penguin should be same, small discrepancy is still remaining !! If Rc – Rn keep the positive value, EW penguin should have extra (new) phase. New Physics window ?

Consider a case that EW Penguin including NP with New CP Phase. New Physics solution New Phase  EW ) Rc - Rn r ew = 0.14, 0.2, 0.3, 0.4       The maximum bound of Rc – Rn for  EW at  EW) =  and r T = 0.2 and under constraint Acp.  EW )  around 270 o is favored

= keeping r 2 C terms Relaxing the hierarchy assumption = keeping r 2 C terms in  Allowed prediction r EW rCrC rCrC Large r c solution in NLO PQCD --  Li, Mishima and Sanda PRD72: Need 3 times larger

2) Direct CP asymmetry : theoretically 、 1 > r_T ~ r_{EW} > r_C > r_A New Physics ? In r EW EW penguin ? expectation BUT different!! BUT different !! Experimental data, orLarge rc contribution ?

Direct CP asymmetries in B  K  Relation among the CP asymmetries : (SUM rules) Large EW Penguin ? Or Still early ? Consistent ? 

Direct CP asymmetries in B  K  Relation among the CP asymmetries : (SUM rules) Still depend on Acp00. Need more precise data!! 

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

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^+

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

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 ?

Using angle between decay planes: An Example: Grossman and Pirjol, JHEP0006: 029 hep-ph/ Kim, Kim, Lu and Morozumi, PRD62: hep-ph/ Points: Using small-q^2 region, ( q^2 ~ 0 ) We can neglect 1) local interactions with O 9, O 10 2) longitudinal modes, A 0 One can investigate B  Vγ by using polarization analysis or angular distribution A : CP-even A ⊥ : CP-odd = Time dependent CP From angular distribution analysis in B  K pi ll decay

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

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

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

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

C 10  i |C 10 |

We can also consider time-dependent CP of FBi. 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

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 Scp and K  puzzle Color suppressed tree ? Or Electro weak Penguin ? They are including fruitful information to build new physics model.