Branching Fractions and Direct CP Violation in Hadronic 3-body B decays Hai-Yang Cheng Academia Sinica, Taipei in collaboration with Chun-Khiang Chua ICHEP, Valencia, July 4, 2014

Introduction Many charmless three-body B decays have been studied at B factories and LHCb (with Dalitz-plot analyses for many of Bu,d decay modes). Most with BFs ~ 10-5 (BFs ~ 10-6 for B KK & Bs KKK) useful for extracting CKM angles & CP violation A(B→P1P2P3) = resonant + nonresonant (NR) All the quasi-2-body B decays, B→VP, SP (except 00, ) are extracted from Dalitz plot analysis of 3-body decays NR signal is less than 10% in D decays. Is this also true in B decays ? (LHCb)

Direct CP asymmetries (3-body) LHCb (’13) found evidence of inclusive CP asymmetry in B- +--, K+K-K-, K+K-- BaBar(%) Belle(%) LHCb(%) Average + - - 3.24.4+4.0-3.7 11.72.11.1 10.52.2 K+ K- K- -1.7+1.9-1.41.4 -4.30.90.8 -3.71.0 K- + - 2.82.02.3 4.92.62.0 3.20.80.8 3.31.0 K+ K- - 0103 -14.14.01.9 -11.94.1 Large asymmetries observed in localized regions of p.s. ACP(KK) = -0.6480.0700.0130.007 for mKK2 <1.5 GeV2 ACP(KKK) = -0.2260.0200.0040.007 for 1.2< mKK, low2 <2.0 GeV2, mKK, high2 <15 GeV2 ACP() = 0.5840.0820.0270.007 for m, low2 <0.4 GeV2, m, high2 > 15 GeV2 ACP(K) = 0.6780.0780.0320.007 for 0.08< m, low2 <0.66 GeV2, mK2 <15 GeV2

B-  K-+- ACP(K) = 0.0320.0080.0040.007 inclusive ACP(K) = 0.6780.0780.0320.007 for 0.08< m, low2 <0.66 GeV2, mK2 <15 GeV2

Three-body B decays KKK:  70-90% K:  35-40% by Belle, 20% by BaBar Two striking features: 1. Large NR fractions in penguin-dominated modes Nonresonant fraction (%) BaBar Belle B-→K+K-K- 6824 78±10 B0→K+K-K0 ~ 130 B0→K-KSKS ~ 196 B0→K0+- 22.1+3.6-3.0 41.9+5.3-5.7 B-→K-+- 17.1+12.5-2.5 34.0+3.0-2.8 B0→K-+0 19.73.6 15.67.7 B-→+-- 34.9+9.0-6.2 KKK:  70-90% K:  35-40% by Belle, 20% by BaBar K0: 15-20% :  35% NR contributions are essential in penguin-dominated B decays One of our goals is to identify the origin of NR signals HYC, Chua, Soni (’07)

2. A new broad scalar resonance fX(1500) ? A broad scalar resonance fX(1500) [or X(1550) by BaBar] has been seen in K+K+K-, K+K-KS, K+K-- at energies ~1.5 GeV. It cannot be identified with f0(1500). So what is its nature ? Production puzzle: The fraction of fX(1500) in K+K+K- is ~120% by BaBar and 63% by Belle, whereas it is  4% in K+K-KS by BaBar BaBar(’06) Belle(’04) B+→K+K+K- B0→K+K-K0 New angular momentum analysis by BaBar (’12) fX(1500) is a sum of f0(1500), f0(1710) & f’2(1525) and no more production puzzle 6

Most of theory studies focus only on either resonant or NR effects We take the factorization approximation as a working hypothesis to discuss resonant & NR contributions Three factorizable amplitudes for B0→K+K-K0 current-induced process: <B0→K0><0→K+K-> transition process: <B0 → K-K0><0→K+> annihilation process: <B0→0><0→K+K-K0> b→s b→u

+,r r +,-,r r NR contribution of Early attempt: Apply heavy meson chiral perturbation theory (HMChPT) to evaluate form factors r and  Bajc, Fajfer, Oakes, Pham; Deandrea et al. (’99) Yan et al.; Donoghue et al.; Wise (’92) K- K0 K- B0 +,r B0 B- r K0 K0 K0 K- B0 B*0s +,-,r B0 K- B*0s B- r 8

NR rates for tree-dominated B→KK,  will become too large For example, Br(B-→K+K--)NR = 3310-6 larger than total BF, 510-6 ⇒ HMChPT is applicable only to soft mesons ! Ways of improving the use of HMChPT have been suggested before We write tree-induced NR amplitude as Fajfer et al; Yang, HYC,… p2 p1 -- HMChPT is recovered in soft meson limit, p1, p2→0 -- The parameter NR » 1/(2mB) is constrained from B-→+--

V=, , …, S=f0(980), f0(1370), f0(1500), f(1710),… b→s V=, , …, S=f0(980), f0(1370), f0(1500), f(1710),… Decay constants for scalar mesons have been evaluated in various approaches Chua,Yang, HYC; L.D. Lu et al. How about the NR contributions ? 10

<K+K-|qq|0> can be related to the kaon’s e.m. form factors ch, x1, x2 fitted from kaon e.m. data Chua,Hou,Shiau,Tsai (’03) motivated by asymptotic constraint from QCD counting rules Brodsky, Farrar (’75) The fitted ch agrees with the model (~ decay constant  strong coupling) NR  exp[i/4](3.39+0.18-0.21) GeV NR from K+K- spectrum of K+K-KS from KSKSKS rate 11

Weak phase: CKM matrix elements The decay amplitude of B0  K+K-K0 consists of two pieces: Nonresonant: <B0 K+K-><0 K0> <B0 K0><0 K+K-> (<B0 K0><0 K+K->)penguin Resonant: B0 f0K0 K+K-K0 , f0 = f0(980), f0(1500), f0(1710),… B0 VK0 K+K-K0, V = , , ,… Weak phase: CKM matrix elements Strong phases: (i) effective Wilson coefficients (ii) propagator (s - m2 + im)-1 (iii) matrix element <M1M2|qq|0> for NR contribution in the penguin sector

B-→K+K-K- NR rates: mostly from b→s (via <KK|ss|0>) BF(10-6) theory errors: (NR) , (ms, NR, form factors), () calculable for the first time Large NR rate is penguin-dominated and governed by <K+K-|ss|0>NR NR rates: mostly from b→s (via <KK|ss|0>) and a few percentages from b→u transitions

We predict a larger rate of +-0 than +-- as the former receives  and 0 resonant contributions with BF of order 2010-6, while only 0 to the latter. Belle (’13): BF(B0 K+ K- 0) = (2.170.65)10-6 is a surprise ! Recall BF(B- K+K--) = (5.00.7)10-6 At short-distance level, we obtain BF ~ 510-8 Long-distance contribution due to B0 +-0 followed by +- K+K- rescattering  BF  510-7

Inclusive direct CP asymmetries Expt (%) Theory (%) Predictions in 2007 + - - 10.32.5 8.7+2.0-2.2 4.4+0.4-0.4 K+ K- K- -3.71.0 -7.1+2.5-1.6 -10.4+2.1-1.8 K- + - 3.31.0  -3.7 -3.3+0.9-0.6 K+ K- - -12.44.5  13.1 17.5+2.9-5.1 HYC,Chua,Soni (`’07) Relative signs between K-K+K- & -+- and between K-+- & -K+K- agree with experiment & U-spin symmetry (s  d) predictions: Xu, Li, He; Bhattacharya, Gronau, Rosner However, relative signs between -K+K- & -+- and between K-+- & K-K+K- disagree with the data

Correlation seen by LHCb: ACP(K-K+K-)  – ACP(K-+-), ACP(-K+K-)  – ACP(-+-) It has been conjectured that CPT theorem & final-state rescattering of +-  K+K- may play important roles Bediaga et al FSI Fit to B- K-+-  U-spin symmetry  U-spin symmetry which relates <K|sd|0> to <KK|ss|0> is badly broken

Direct CP violation in 3-body Bu,d decays Theory (%) Expt (%) + - - 8.7+1.7-1.9 10.32.5 K+ K- K- -7.1+4.8-4.1 -3.71.0 K- + - 2.7+0.7-0.8 3.31.0 K+ K- - -10.0+2.1-2.7 -12.44.5 K- K+ 0 -9.2+0.0-0.0 K-K+KS -5.5+1.5-1.1 K-KSKS 3.5+0.3-0.2 45 KS+0 0.64+0.07-0.07 7534 (+ - -)region 22.5+2.9-3.3 58.48.7 (K+ K-K-)region -17.7+4.9-2.9 -22.62.2 (K- + -)region 14.1+13.9-11.7 67.88.5 (K+K- -)region -18.2+1.8-1.8 -64.87.2 Inclusive CP asymmetries predictions BaBar Predicted local CP asymmetries seem to be too small except K+K-K-

Regional CP asymmetries due to NR contributions (ACPregion)NR+RES 22.5+2.9-3.3 14.1+13.9-11.7 -18.2+1.8-1.8 -17.7+4.9-2.9 Except K+K-K- the magnitude of local CP asymmetries is substantially reduced by nearby resonances Wang et al. 51.9+16.7-23.9 (pQCD) Zhang, Guo, Yang advocated that local CP violation in +-- arises from interference of 0 with f0(500) It is important to pin down the underlying mechanism responsible for large local CP violation in 3-body charged B decays

BFs & CP violation in 3-body Bs decays LHCb made first observation of three charmless 3-body Bs decays Penguin-dominated (10-6) (10-6) Tree-dominated Penguin-dominated modes K0K-+, K0K+- have largest rates, dominated by K*0(1430) resonances Tree-dominated mode K+K-K0 is predicted to have BF ~ 1.410-6 ACP(K0K+K-)  - 2ACP(K0+-) 19

U-spin symmetry relations They cannot be tested by the present available data, but can be checked by dynamical calculations. U-spin relations are generally not well respected as U-spin symmetry is sometimes badly broken

Conclusions Three-body B decays receive sizable NR contributions governed by the matrix elements of scalar densities. Three sources of strong phases responsible for direct CP violation in 3-body B decays. It is important to pin down the mechanism responsible for large local CP asymmetries.