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

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

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…

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

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).

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], …

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?

Sources of DS: Three basic sources of DS: Other sources? 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?

Corrections on DS Since VcbV*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

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

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)

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

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)

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]

(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

Dominant Penguin Contributions (PP,PV) V=(V-A)/2+(V+A)/2 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)

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

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

hKS, h’KS Contructive interference in P(h’KS) both in a4,6 and 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

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

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)].

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

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

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

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

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

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.

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

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

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)

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).

Back up

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

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).

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

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.

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)

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

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)

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

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.

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).

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 …

K anomaly: A(0K-)  A(+ K-), while experimentally they differ BR SD (10-6) with FSI Expt DCPV B--K0 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+K- 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-0K- 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0K0 6.0 9.0+2.3-1.5 11.51.0 -0.04 0.022+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(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.

B   B  ﹣ _ _ _ B0+- B0-+ B000 B--0 B-0- BR SD (10-6) with FSI Expt DCPV B0+- 8.3 8.7+0.4-0.2 10.12.0 -0.01 -0.430.11 -0.47+0.13-0.14 B0-+ 18.0 18.4+0.3-0.2 13.92.1 -0.02 -0.250.06 -0.150.09 B0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-0- 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 (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.

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

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

Factorized into transition and creation parts Tree Penguin