1. 1 SM expectations on sin2    from b → s penguins Chun-Khiang Chua Academia Sinica FPCP 2006 9 April 2006, Vancouver

2. 2 Mixing induced CP Asymmetry Both B 0 and B 0 can decay to f: CP eigenstate. If no CP (weak) phase in A: A=±A C f =0, S f =±sin2  Oscillation, e i  m t (V tb * V td ) 2 =|V tb * V td | 2 e -i 2  Bigi, Sanda 81 Quantum Interference Direct CPAMixing-induced CPA

3. 3 The CKM phase is dominating The CKM picture in the SM is essentially correct: WA sin2  =0.687±0.032 Thanks to BaBar, Belle and others…

4. 4 New CP-odd phase is expected … New Physics is expected  Neutrino Oscillations are observed  Present particles only consist few % of the universe density What is Dark matter? Dark energy?  Baryogenesis n B /n  ~10 -10 (SM 10 -20 ) It is unlikely that we have only one CP phase in Nature NASA/WMAP

5. 5 The Basic Idea A generic b→sqq decay amplitude: For pure penguin modes, such as  K S, the penguin amplitude does not have weak phase [similar to the J/  K S amp.] Proposed by Grossman, Worah [97] A good way to search for new CP phase (sensitive to NP).

6. 6 The Basic Idea (more penguin modes) In addition to  K S, (  ’K S,  0 K S,  0 K S,  K S,  K S ) were proposed by London, Soni [97] (after the CLEO observation of the large  ’K rate) For penguin dominated CP mode with f=f CP =M 0 M’ 0,  cannot have color allowed tree (W ± cannot produce M 0 or M’ 0 )  In general F u should not be much larger than F c or F t More modes are added to the list: f 0 K S, K + K - K S, K S K S K S Gershon, Hazumi [04], …

7. 7  sin2  eff To search for NP, it is important to measure the deviation of sin2  eff in charmonium and penguin modes Deviation  NP How robust is the argument? What is the expected correction ?

8. 8 Sources of  S: Three basic sources of  S:  V tb V* ts = -V cb V* cs -V ub V* us =-A 2 +A(1-  ) 4 -i  A 4 +O( 6 ) (also applies to pure penguin modes)  u-penguin (radiative correction): V ub V* us (also applies to pure penguin modes)  color-suppressed tree Other sources?  LD u-penguin, CA tree?

9. 9 Corrections on  S Since V cb V* cs is real, a better expression is to use the unitary relation t =- u - c (define A u ≡F u -F t, A c ≡F c -F t; ; A u,A c : same order for a penguin dominated mode): Corrections can now be expressed as ( Gronau 89 ) To know C f and  S f, both r f and  f are needed. ~0.4 2

10. 10 Several approaches for  S SU(3) approach (Grossman, Ligeti, Nir, Quinn; Gronau, Rosner…)  Constraining |A u /A c | through related modes in a model independent way Factorization approach  SD (QCDF, pQCD, SCET) FSI approach (Cheng, CKC, Soni) Others

11. 11 SU(3) approach for  S Take Grossman, Ligeti, Nir, Quinn [03] as an example  Constrain |r f |=| u A u / c A c | through SU(3) related modes b→s b→d O( 2 )

12. 12  S<0.22 An example |r  ’Ks |≡

13. 13 More SU(3) bounds (Grossman, Ligeti, Nir, Quinn; Gronau, Grossman, Rosner) Usually if charged modes are used (with |C/P|<|T/P|), better bounds can be obtained. (  K - first considered by Grossman, Isidori, Worah [98] using  -, K* 0 K - ) In the 3K mode U-spin sym. is applied. Fit C/P in the topological amplitude approach ⇒  S Gronau, Grossman, Rosner (04) |  S f |<1.26 |r f | |C f |<1.73 |r f | Gronau, Rosner (Chiang, Luo, Suprun)

14. 14  S from factorization approaches There are three QCD-based factorization approaches:  QCDF: Beneke, Buchalla, Neurbert, Sachrajda [see talk by Alex Williamson]  pQCD: Keum, Li, Sanda [see talk by Satoshi Mishima]  SCET: Bauer, Fleming, Pirjol, Rothstein, Stewart [see talk by Christian Bauer]

15. 15  S) SD calculated from QCDF,pQCD,SCET Most |  S| are of order 2, except  K S,  0 K S (opposite sign) Most theoretical predictions on  S are similar, but signs are opposite to data in most cases Perturbative phase is small   S>0 QCDF: Beneke [results consistent with Cheng-CKC- Soni] pQCD: Mishima-Li SCET: Williamson-Zupan (two solutions)

16. 16 A closer look on  S signs and sizes constructive (destructive) Interference in P of  ’ Ks (  Ks) small large small (  ’Ks) large (  Ks) small large Beneke, 05 B→V

17. 17 Expt(%) QCDF PQCD Direct CP Violations in Charmless modes With FSI ⇒ strong phases ⇒ sizable DCPV FSI is important in B decays  What is the impact on  S Cheng, CKC, Soni, 04 Different , FF…

18. 18 FSI effects on sin2  eff (Cheng, CKC, Soni 05) FSI can bring in additional weak phase  B→K * , K  contain tree V ub V us *=|V ub V us |e -i   Long distance u-penguin and color suppressed tree

19. 19 FSI effects in rates FSIs enhance rates through rescattering of charmful intermediate states [expt. rates are used to fix cutoffs (  =m + r  QCD, r~1)]. Constructive (destructive) interference in  ’K 0 (  K 0 ).

20. 20 FSI effects on direct CP violation Large CP violation in the  K,  K mode.

21. 21 FSI effect on  S Theoretically and experimentally cleanest modes:  ’K s (  K s ) Tree pollutions are diluted for non pure penguin modes:  K S,  0 K S

22. 22 FSI effects in mixing induced CP violation of penguin modes are small The reason for the smallness of the deviations:  The dominant FSI contributions are of charming penguin like. Do not bring in any additional weak phase.  The source amplitudes (K * ,K  ) are small (Br~10 -6 ) compare with Ds*D (Br~10 -2,-3 )  The sources with the additional weak phase are even smaller (tree small, penguin dominate) If we somehow enhance K * ,K  contributions ⇒ large direct CP violation (A  Ks ). Not supported by data

23. 23 Results in  S for scalar modes (QCDF) (Cheng-CKC-Yang, 05)  S are tiny (0.02 or less): LD effects have not been considered. Do not expect large deviation.

24. 24 K + K - K S(L) and K S K S K S(L) modes Penguin-dominated K S K S K S : CP-even eigenstate. K + K - K S : CP-even dominated, CP-even fraction: f + =0.91±0.07 Three body modes Most theoretical works are based on flavor symmetry. (Gronau et al, …) We (Cheng-CKC-Soni) use a factorization approach

25. 25 K + K - K S and K S K S K S decay rates K S K S K S (total) rate is used as an input to fix a NR amp. (sensitive). Rates (SD) agree with data within errors.  Central values slightly smaller.  Still have room for LD contribution.

26. 26 It has a color-allowed b→u amp, but… The first diagram (b→s transition) prefers small m(K + K - ) The second diagram (b→u transition) prefers small m(K + K 0 ) [large m(K + K - )], not a CP eigenstate  Interference between b→u and b→s is suppressed. b→sb→u

27. 27 CP-odd K + K - K S decay spectrum Low m KK :  K S +NR (Non-Resonance).. High m KK : (NR) transition contribution.. b→sb→u

28. 28 CP-even K + K - K S decay spectrum Low m KK : f 0 (980)K S +NR (Non-Resonance). High m KK : (NR) transition contribution. b→s b→u

29. 29 K + K - K S and K S K S K S CP asymmetries Could have O(0.1) deviation of sin2  in K + K - K S  It originates from color-allowed tree contribution.  Its contributions should be reduced. BaBar 05  S, A CP are small  In K+K-Ks: b→u prefers large m(K + K - ) b→s prefers small m(K + K - ), interference reduced  small asymmetries  In KsKsKs: no b→u transition.

30. 30 Conclusion The CKM picture is established. However, NP is expected (  m, DM, n B /n  ). The deviations of sin2  eff from sin2  = 0.687  0.032 are at most O(0.1) in B 0  K S,  K S,  0 K S,  ’K S,  0 K S, f 0 K S, a 0 K S, K* 0  0, K S K S K S. The O(0.1)  S in B 0 →KKK S due to the color-allowed tree contribution should be reduced. A Dalitz plot analysis will be very useful. The B 0 →  ’K S,  K S and B 0 →K S K S K S modes are very clean. The pattern of  S is also a SM prediction. A global analysis is helpful. Measurements of sin2  eff in penguin modes are still good places to look for new phase(s)  SuperB  →0.1 .

31. 31 Back up

32. 32 A closer look on  S signs (in QCDF) M 1 M 2 : (B→M 1 )  (0→M 2 )

33. 33 Perturbative strong phases: penguin (BSS) vertex corrections (BBNS) annihilation (pQCD) Because of endpoint divergences,  QCD/mb power corrections in QCDF due to annihilation and twist-3 spectator interactions can only be modelled with unknown parameters  A,  H,  A,  H, can be determined (or constrained) from rates and Acp. Annihilation amp is calculable in pQCD, but cannot have b→uqq in the annihilation diagram in b→s penguin.

34. 34 Scalar Modes The calculation of SP is similar to VP in QCDF  All calculations in QCDF start from the following projection:  In particular  All existing ( Beneke-Neubert 2001 ) calculation for VP can be brought to SP with some simple replacements ( Cheng-CKC- Yang, 2005 ).

35. 35 FSI as rescattering of intermediate two-body state  FSIs via resonances are assumed to be suppressed in B decays due to the lack of resonances at energies close to B mass.  FSI is assumed to be dominated by rescattering of two-body intermediate states with one particle exchange in t-channel. Its absorptive part is computed via optical theorem: Strong coupling is fixed on shell. For intermediate heavy mesons, apply HQET+ChPT Form factor or cutoff must be introduced as exchanged particle is off-shell and final states are necessarily hard Alternative: Regge trajectory, Quasi-elastic rescattering … (Cheng, CKC, Soni 04)

36. 36 BR SD (10 -6 ) BR with FSI (10 -6 ) BR Expt (10 -6 ) DCPV SD DCPV with FSI DCPV Expt BB 16.6 22.9 +4.9 -3.1 24.1  1.3 0.01 0.026 +0.00 -0.002 -0.02  0.03 B0B0 13.7 19.7 +4.6 -2.9 18.2  0.8 0.03-0.15 +0.03 -0.01 -0.11  0.02 B0B0 9.3 12.1 +2.4 -1.5 12.1  0.8 0.17-0.09 +0.06 -0.04 0.04  0.04 B0B0 6.0 9.0 +2.3 -1.5 11.5  1.0 -0.040.022 +0.008 -0.012 -0.09  0.14 For simplicity only LD uncertainties are shown here FSI yields correct sign and magnitude for A(  + K - ) ! K  anomaly: A(  0 K - )  A(  + K - ), while experimentally they differ by 3.4  SD effects?   Fleischer et al, Nagashima Hou Soddu, H n Li et al.] Final state interaction is important. _ _ _ _

37. 37 BR SD (10 -6 ) BR with FSI (10 -6 ) BR Expt (10 -6 ) DCPV SD DCPV with FSI DCPV Expt B 0  +   8.3 8.7 +0.4 -0.2 10.1  2.0 -0.01 -0.43  0.11 -0.47 +0.13 -0.14 B 0    + 18.0 18.4 +0.3 -0.2 13.9  2.1 -0.02 -0.25  0.06-0.15  0.09 B 0  0  0 0.44 1.1 +0.4 -0.3 1.8  0.6 -0.005 0.53  0.01 -0.49 +0.70 -0.83 B     0 12.3 13.3 +0.7 -0.5 12.0  2.0 -0.04 0.37  0.10 0.01  0.11 B      6.9 7.6 +0.6 -0.4 9.1  1.3 0.06 -0.58  0.15 -0.07 +0.12 -0.13 Sign and magnitude for A(  +  - ) are nicely predicted ! DCPVs are sensitive to FSIs, but BRs are not (r D =1.6) For  0  0, 1.4  0.7 BaBar Br(10 -6 )= 3.1  1.1 Belle 1.6 +2.2 -1.6 CLEO Discrepancy between BaBar and Belle should be clarified. ﹣ _ _ B   _

38. 38 Factorization Approach SD contribution should be studied first. Cheng, CKC, Soni 05  Some LD effects are included (through BW). We use a factorization approach (FA) to study the KKK decays. FA seems to work in three-body (DKK) decays CKC-Hou-Shiau-Tsai, 03. Color-allowedColor-suppressed

39. 39 K + K - K S and K S K S K S (pure-penguin) decay amplitudes Tree Penguin

40. 40 Factorized into transition and creation parts Tree Penguin

41. 41 sin2  eff in a restricted phase space of the K + K - K S decay The corresponding s in2  eff, with m KK integrated up to m KK max. Could be useful for experiment. CP-even Full, excluding  K S