Theoretical review on sin2 b(f 1 ) from b → s penguins

1. Theoretical review on sin2b(f1) from b → s penguins Chun-Khiang Chua Chung Yuan Christian University

2. Mixing induced CP Asymmetry Bigi, Sanda 81 Quantum Interference • Both B0 and B0 can decay to f: CP eigenstate. • If no CP (weak) phase in A: Cf=0, Sf=hfsin2b Oscillation, eiDm t (Vtb*Vtd)2 =|Vtb*Vtd|2e-i 2b hf = 1 Direct CPA Mixing-induced CPA

3. The CKM phase is dominating • The CKM picture in the SM is essentially correct: • WA sin2b=0.681±0.025 Thanks to BaBar, Belle and others…

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 nB/ng~10-10 (SM 10-20) • It is unlikely that we have only one CP phase in Nature NASA/WMAP

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

6. The Basic Idea (more penguin modes) • In addition to fKS, {h’KS, p0KS, r0KS, wKS, hKS} were proposed by London, Soni [97](after the CLEO observation of the large h’K rate) • For penguin dominated CP mode with f=fCP=M0M’0, • cannot have color allowed tree (W± cannot produce M0 or M’0) • In general Fu should not be much larger than Fc or Ft • More modes are added to the list: f0KS, K+K-KS, KSKSKS Gershon, Hazumi [04], …

7. D sin2beff • To search for NP, it is important to measure the deviation of sin2beff in charmonium and penguin modes • Most data: DS<0 • Deviation  NP • How robust is the argument? • What is the expected correction?

8. Sources of DS: • Three basic sources of DS: • VtbV*ts = -VcbV*cs-VubV*us =-Al2 +A(1-r)l4-ihAl4+O(l6)(also applies to pure penguin modes) • u-penguin (radiative correction): VubV*us(also applies to pure penguin modes) • color-suppressed tree • Other sources? • LD u-penguin, LD CS tree, CA tree?

9. Corrections on DS • SinceVcbV*cs is real, a better expression is to use the unitary relation lt=-lu-lc(define Au≡Fu-Ft,Ac≡Fc-Ft;; Au,Ac: same order for a penguin dominated mode): • Corrections can now be expressed as (Gronau 89) • To know Cf and DSf, both rf and df are needed. ~0.4 l2

10. Several approaches for DS • SU(3) approach (Grossman, Ligeti, Nir, Quinn; Gronau, Rosner…) • Constraining |Au/Ac| through related modes in a model independent way • Factorization approach • SD (QCDF, pQCD, SCET) • FSI effects (Cheng, CKC, Soni) • Others

11. SU(3) approach for DS • Take Grossman, Ligeti, Nir, Quinn [03] as an example • Constrain |rf|=|luAu/lcAc| through SU(3) related modes b→s b→d intrinsic un.: O(l2)

12. An example |rh’Ks|≡ icA  ic|A|: conservative, less modes  better bound  DS<0.22

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. (fK- first considered by Grossman, Isidori, Worah [98] using fp-, K*0K-) • In the 3K mode U-spin sym. is applied. • Fit C/P in the topological amplitude approach ⇒DS Gronau, Grossman,Rosner (04) Engelhard, (Nir), Raz (05,05) |DSf|<1.26 |rf| |Cf|<1.73 |rf| Gronau, Rosner (Chiang, Luo, Suprun)

14. DS from factorization approaches • There are three QCD-based factorization approaches: • QCDF: Beneke, Buchalla, Neurbert, Sachrajda [see talk by Martin Beneke] • pQCD: Keum, Li, Sanda[see talk by Cai-Dai Lu] • SCET: Bauer, Fleming, Pirjol, Rothstein, Stewart [see talk by Ira Z. Rothstein]

15. (DS)SD calculated from QCDF,pQCD,SCET • Most |DS| are of order l2, except wKS, r0KS (opposite sign) • Most theoretical predictions on DS are similar, but signs are opposite to data in most cases • Signs and sizes of DS? • QCDF: Beneke[results consistent with Cheng-CKC-Soni] • pQCD: Mishima-Li • SCET: Williamson-Zupan (two solutions) Some “hints” of deviations, e.g. p0KS

16. Dominant Penguin Contributions (PP,PV) • Dominant contributions: (similar sizes, common origin) (V-A)(V-A): a4, (S+P)(S-P): rM2 a6 (: M1=V) • Constructive Interference: a4+rM2a6 M2M1=PP,VP Destructive Interference: a4rPa6, M2M1=PV • Interferences between q=s and q=d amp. (in KSh’, KSh) V=(V-A)/2+(V+A)/2

17. fKS • No CS tree, unsuppressed P  DS small (~0.03) and positive Beneke, 05

18. w(r0)KS, p0KS • w(r0)KS: C(a2) + suppressed P  DS large • Opposite signs come from signs in wave functions. • p0KS: C(a2) + unsuppressed P  DS small, • signs different from (rKS), due to a6 terms Ratio of F.F. fM not shown

19. hKS, h’KS • Contructive interference in P(h’KS) both in a4,6and in q=d,s  DS>0 and small • Destructive interference in P(hKS) in q=d,s  DS>0, large (unstable) Ps>PdP flip sign

20. FSI effects on sin2beff(Cheng, CKC, Soni 05) • FSI can bring in additional weak phase • B→K*p, Kr contain tree Vub Vus*=|Vub Vus|e-ig • Long distance u-penguin and color suppressed tree

21. FSI effect on DS • Small DS for h’Ks, fKs. • Tree pollutions are diluted for non pure penguin modes: wKS, r0KS FSIs enhance rates through rescattering of charmful intermediate states [expt. rates are used to fix cutoffs (L=m + r LQCD, r~1)].

22. FSI effects in mixing induced CP violation of penguin modes are small • The reason for the smallness of the deviations: • Use rates to fix FSI parameters: F.F.  FSI contributions dominated by DsDbar final states • The dominant FSI contributions are of charming penguin like. Do not bring in any additional weak phase. • Other sources of LD contributions? • DA(Kp) and p0p0 rate may hint at larger and complex CS tree… SU(3): Chiang, Gronau, Rosner, Luo, Suprun Zhou; Charng, Li, … • Implications on DS? See Cheng Wei’s talk

23. DS from RGI parametrizations A(K-p0) • aaa DS are still small: at UL=0.5 Ciuchini et al.; taken from 0801.1833

24. DA(Kp)DS? • C from exchange-type rescattering of T (enhance DA, B(p0p0)) • Similar results for DS: QE FSI:TC CKC,Hou,Yang 2003; CKC 2007

25. Results in DS for scalar modes (QCDF) (Cheng-CKC-Yang, 05) • DS are tiny (0.02 or less): • LD effects have not been considered.

26. K+K-KS(L) and KSKSKS(L) modes • Penguin-dominated • KSKSKS: CP-even eigenstate. • K+K-KS: CP-even dominated, CP-even fraction: f+0.9 • Three body modes • Most theoretical works are based on flavor symmetry. (Gronau et al, …) • We (Cheng-CKC-Soni) use a factorization approach • See Hai-Yang’s talk for more details

27. It has a color-allowed b→u amp, but… b→s b→u • The first diagram (b→s transition) prefers small m(K+K-) • The second diagram (b→u transition) prefers small m(K+K0) [large m(K+K-)], not a CP eigenstate • Interference between b→u and b→s is suppressed.

28. CP-odd K+K-KS decay spectrum • Low mKK: fKS+NR (Non-Resonance).. • High mKK: bu transition contribution. • Experimental data: fKS only  bu is highly constrained. b→s b→u See Hai-Yang’s talk

29. CP-even K+K-KS decay spectrum • Low mKK: f0(980)KS+NR (Non-Resonance). • High mKK: bu transition contribution. • b s and bu do not interfere b→s b→u peak at mKK  1.5 GeV due to X0(1550) See Hai-Yang’s talk

30. DS for K+K-KS, KSKSKS and others • DS are small. • For KsKsKs: - no b→u transition. • For K+K-KS: - b→u prefers large m(K+K-), not seen - b→s prefers small m(K+K-), - interference reduced  small DS • theory expt • S(K+K-KS) =0.040+0.028-0.033 0.05±0.11 • S(KSKSKS) =0.038+0.027-0.032 -0.10±0.20 • S(KS00) =0.048+0.027-0.032 -1.200.41 • S(KS+-) =0.037+0.031-0.032 Stheory < O(0.1) Cheng,CKC,Soni, 2007 See Hai-Yang’s talk sin2=0.6810.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

31. Conclusion • The CKM picture is established. However, NP is expected (Dmn, DM, nB/ng). • In most calculations: the deviations of sin2beff from sin2 = 0.6810.025 are • At most O(0.1) in B0KS, ’KS, 0KS, f0KS, a0KS, K*0p0, KSKSKS… • Larger |DS|: B0 KS, r0KS, hKS… • The color-allowed tree contribution to DS in B0→KKKS is constrained by data to be small. • In existing theoretical claculations: • DS in B0→h’KS, KS and B0→KSKSKS modes are tiny. Not affected by LD effects explored so far. • Need more works to handle hadronic effects. More measurements [SU(3)]. • The pattern of DS is also a SM prediction. Most DS>0. A global analysis is helpful. • Measurements of sin2beff in penguin modes are still good places to look for new phase(s) SuperB (d→0.1d).

32. Back up

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

34. FSI effects in rates • FSIs enhance rates through rescattering of charmful intermediate states [expt. rates are used to fix cutoffs (L=m + r LQCD, r~1)]. • Constructive (destructive) interference in h’K0 (hK0).

35. FSI effects on direct CP violation • Large CP violation in the rK, wK mode.

36. K+K-KS and KSKSKS decay rates • KS KS KS (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.

37. K+K-KS and KSKSKS CP asymmetries • Could have O(0.1) deviation of sin2b in K+K-KS • It originates from color-allowed tree contribution. • Its contributions should be reduced. BaBar 05 • DS, ACP 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. sin2=0.6800.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

38. b→sqq tCPV measurements Sf= ± sin2eff from b→ccs 2-body: HYC,Chua,Soni;Beneke 3-body: CCS Naïve b→s penguin average: 0.68±0.04, 0.56±0.05 (if f0K0 excluded), 0.0.1, 2.2, 2.6 deviation from b→ccs average

39. A closer look on DS signs and sizes Beneke, 05 small large B→V large small small (h’Ks) large (hKs) constructive (destructive) Interference in P of h’Ks (hKs)

40. A closer look on DS signs (in QCDF) M1M2: (B→M1)(0→M2)

41. 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.

42. 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).

43. FSI as rescattering of intermediate two-body state (Cheng, CKC, Soni 04) • 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 …

44. _ _ _ _ • For simplicity only LD uncertainties are shown here • FSI yields correct sign and magnitude for A(+K-) ! • K anomaly: A(0K-)  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.

45. B   B  ﹣ _ _ _ • Sign and magnitude for A(+-) are nicely predicted ! • DCPVs are sensitive to FSIs, but BRs are not (rD=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.

46. 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-allowed Color-suppressed

47. K+K-KS and KSKSKS (pure-penguin) decay amplitudes Tree Penguin

48. Factorized into transition and creation parts Tree Penguin