Direct CP violation in 3-body B decays Hai-Yang Cheng Academia Sinica in collaboration with Chun-Khiang Chua XS2014, Hefei May 06, 2014

 Direct CP asymmetries (2-body) AK  ACP(K-0) – ACP(K-+) Bu/Bd K-+ +- K- K*0 K*-+ K- f2(1270) K-0  ACP(%) -8.20.6 295 -378 195 -236 -68+20-18 3711 -134 S 13.7 5.8 4.6 3.8 3.6 3.4 3.3 Bu/Bd - K- 0K*- K-0 + +K- 00 -+ K*0 ACP(%) -145 104 3113 4.02.1 -209 2011 4324 116 4525 S 2.8 2.5 2.4 1.9 1.8  Bs K+- ACP(%) 264 S 7.2 B- K- ACP(%) 2.22.3 No CP asymmetry observed by LHCb in B- K- AK 12.22.2 5.5 AK  ACP(K-0) – ACP(K-+) K puzzle: AK is naively expected to vanish 2 2 2

Direct CP asymmetries (3-body) LHCb 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

K-+- K+K+K- ++- K+K+-

Wen-Fei Wang’s talk on May 8th Cheng, Chua, Soni [0704.1049] Zhang, Guo, Yang [1303.3676] Bhattacharya, Gronau, Rosner [1306.2625] Xu, Li, He [1307.7186] Bediaga, Frederico, Lourenco [1307.8164] Gronau [1308.3448] Cheng, Chua [1308.5139] Zhang, Guo, Yang [1308.5242] Lesniak, Zenczykowski [1309.1689] Di Salvo [1309.7448] Xu, Li, He [1311.3714] Cheng, Chua [1401.5514] Ying Li [1401.5948] Bhattacharya, Gronau, Imbeault, London, Rosner [1402.2909] Wang, Hu, Li, Lu [1402.5280] Ying Li [1402.6052] Wen-Fei Wang’s talk on May 8th

Many three-body B decays have been observed 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. Many argued that 3-body B decays are also dominated by resonant contributions (LHCb) 6 6

Three-body B decays KKK:  70-90% K:  35-40% by Belle, 20% by BaBar A striking feature: 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 three-body B decays One of our goals is to identify the origin of NR signals 7 HYC, Chua, Soni (’07)

P2 b P1 P3 P2 P1 P3 P3 P2 P1 P3 P2 P1 All three mesons energetic (a) All three mesons energetic, but two of them nearly parallel P1 P3 (b) P3 All three energetic & two of them nearly parallel. The spectator quark is kicked by a hard gluon to become hard P2 P1 (c) (b) & (c) mimic 2-body decays P3 P2 P1 Two energetic (P1, P2) & one soft (P3) (d)

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 HMChPT to evaluate form factors r and  (CLY)2; Wise; Burdman, Donoghue Bajc, Fajfer, Oakes, Pham; Deandrea et al. (’99) K- K0 K- B0 +,r B0 B- r K0 K0 K0 K- B0 B*0s +,-,r B0 K- B*0s B- r 10

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 propose to write NR amplitude as Fajfer et al; Yang, HYC,… -- HMChPT is recovered in soft meson limit, p1, p2→0 -- The parameter NR » 1/(2mB) is constrained from B-→+--

Resonant contribution of - Resonant contribution of + B- - V=, , …, S=f0(980), f0(1370), f0(1500), f(1710),… 12 12

How about the NR contributions ? b→s Decay constants for scalar mesons have been evaluated in various approaches Chua,Yang, HYC; C.D. Lu et al How about the NR contributions ? 13

<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 x strong coupling) NR NR  exp[i/4](3.39+0.18-0.21) GeV from K+K- spectrum of K+K-KS from KSKSKS rate 14

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): Br(B0 K+ K- 0) = (2.170.65)10-6 is a surprise ! Recall that Br(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  0.510-6

Inclusive direct CP asymmetries Expt (%) Theory(%) 2007 + - - 11.72.4 8.7+2.0-2.2 4.4+0.4-0.4 K+ K- K- -4.31.2 -7.1+2.5-1.6 -10.4+2.1-1.8 K- + - 3.21.1  -3.7 -3.3+0.9-0.6 K+ K- - -14.14.4  13.1 17.5+2.9-5.1 U-spin symmetry (s  d)  Xu, Li, He; Bhattacharya, Gronau, Rosner Relative signs between K-K+K- & -+- and between K-+- & -K+K- agree with experiment & U-spin symmetry predictions However, relative signs between -K+K- & -+- and between K-+- & K-K+K- disagree with the data

Naïve U-spin symmetry relations Xu, Li, He (I, ’13) However, momentum dependence of decay amplitudes should be taken into account Xu, Li, He (II, ’13) 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 11.72.4 (+ - -)region 22.5+2.9-3.3 58.48.7 K+ K- K- -7.1+4.8-4.1 -4.31.2 (K+ K-K-)region -17.7+4.9-2.9 -22.62.2 K- + - 2.7+0.7-0.8 3.21.1 (K- + -)region 14.1+13.9-11.7 67.88.5 K+ K- - -10.0+2.1-2.7 -14.14.4 (K+K- -)region -18.2+1.8-1.8 -64.87.2 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 predictions

K-+- K+K+K- ++- K+K+- 22

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 Zhang, Guo, Yang advocated that local CP violation in +-- arises from interference of 0 with f0(500)

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+-)

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 CP asymmetries are the ideal places to discriminate between different models. 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.