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1 SM expectations on sin2 from b → s penguins Chun-Khiang Chua Academia Sinica FPCP 2006 9 April 2006, Vancouver

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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

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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…

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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

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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).

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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], …

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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 ?

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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?

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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

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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

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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 )

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12 S<0.22 An example |r ’Ks |≡

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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)

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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]

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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)

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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

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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…

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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

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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 ).

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

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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

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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

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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.

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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

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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.

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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

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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

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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

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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.

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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 .

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31 Back up

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

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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.

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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 ).

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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)

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36 BR SD (10 -6 ) BR with FSI (10 -6 ) BR Expt (10 -6 ) DCPV SD DCPV with FSI DCPV Expt BB 16.6 22.9 +4.9 -3.1 24.1 1.3 0.01 0.026 +0.00 -0.002 -0.02 0.03 B0B0 13.7 19.7 +4.6 -2.9 18.2 0.8 0.03-0.15 +0.03 -0.01 -0.11 0.02 B0B0 9.3 12.1 +2.4 -1.5 12.1 0.8 0.17-0.09 +0.06 -0.04 0.04 0.04 B0B0 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. _ _ _ _

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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 _

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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

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

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40 Factorized into transition and creation parts Tree Penguin

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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

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