Hadronic 3-body B decays Hai-Yang Cheng Academia Sinica, Taipei FPCP2008, Taipei, May 6, 2008

Introduction focus on charmless B→PPP Many three-body B decays have been observed with rates ~10-5 useful for extracting CKM angles, CP violation Most of quasi-2-body B decays (B→VP,SP) are extracted from Dalitz plot analysis of 3-body decays A(B→P1P2P3)= resonant + nonresonant (NR) NR signal is less than 10% in D decays. Is NR component also small in B decays ? There is no any theoretical study addressing both resonant and NR effects. Some works are based on flavor symmetry Chua, Soni, and I (2007) have applied the factorization approach to study the dynamics of 3-body decays Gronau, Rosner focus on charmless B→PPP

KKK:  90% K:  35-40% by Belle, 5% by BaBar K0: 12-15% Two striking features: Large NR fractions in penguin-dominated modes Nonresonant fraction (%) BaBar Belle B-→K+K-K- 14118 74.8±3.6 B0→K+K-K0 112±15 B0→K0+- 41.95.5 B-→K-+- 4.51.5 34.02.9 B0→K-+0 12.42.9 15.67.7 <25.7 B-→+-- 13.66.1 KKK:  90% K:  35-40% by Belle, 5% by BaBar K0: 12-15% :  14% NR contributions are essential in penguin-dominated B decays One of our goals is to identify the origin of NR signals

David Asner (Friday): DP in D decays NR amplitude in charm decays is usually treated as a constant over Dalitz plot. However, this is no longer true in B decays due to large energy release. Both BaBar & Belle employ the parametrization to study the NR component in B→KKK decay, but differ in the NR analysis in B→K: BaBar adopted the LASS parametrization which is an effective range NR component + Breit-Wigner form for K0*(1430) difficult to disentangle resonant & NR effects due to interference Recall that NR accounts for (95±7)% of D+→K-++ in old experiments. With + included by E791, NR fraction is reduced to (8.6±0.8)%, confirmed recently by CLEO. David Asner (Friday): DP in D decays

New broad scalar resonances fX(1550) & fX(1300) 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), otherwise it will decay to +- five times more frequently than to K+K- . Its nature is not clear. 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 Belle BaBar B+→K+K+K- B0→K+K-K0 Likewise, fX(1300) was seen in K++- and K0+-. Its mass & width are consistent with f0(1500)

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

b→u almost pure NR Early attempt: Apply HMChPT to evaluate form factors r and  Wise, Yan et al. Donoghue et al. (1992) 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

NR rates for B→KKK,K,  will become too large For example, Br(B0→K+K-K0)NR=7710-6 larger than total BR=2510-6 ⇒ HMChPT is applicable only to soft mesons ! Ways of improving the use of HMChPT have been suggested before We now propose to write NR amplitude as Fajfer et al. Yang, HYC,… -- HMChPT is recovered in soft meson limit, p2, p3→0 -- The parameter NR » 1/(2mB) is constrained from B-→+--

V=, , ,…, S=f0(980), f0(1370), f0(1500), fX(1500),… b→s V=, , ,…, S=f0(980), f0(1370), f0(1500), fX(1500),… Decay constants for scalar mesons have been evaluated using QCDSR Chua,Yang,HYC

<K+K-|qq|0> is related to the kaon’s e.m. form factors ch, x1, x2 fitted from kaon e.m. data Chua,Hou,Shiau,Tsai motivated by asymptotic constraint from QCD counting rules Brodsky, Farrar NR NR is constrained by KSKSKS rate and K+K- mass spectrum

B0→K+K-K0 BaBar: PRL, 99, 161802 (2007) Final state BRexpt (10-6) BRtheory K0 2.98±0.45 2.6+0.5-0.4 f0(980)K0 9.57±2.51 5.8+0.1-0.5 X0(1550)K0 0.98±0.44 0.93+0.16-0.15 NR 26.7±4.6 18.1+5.1-3.9 total 23.8±2.6 19.8+0.6-0.6 NR rates: 88% from b→s (via <KK|ss|0>) and 3% from b→u transitions

B-→K+K-K- BR(10-6) 1st theory error: NR BaBar: PRD, 74, 032003 (2006) Belle: PRD, 71, 092003 (2005) BR(10-6) B-→K+K-K- 1st theory error: NR 2nd theory error: ms, NR, form factors 3rd theory error:  The predicted NR rate agrees with Belle The large fraction of X0(1550), 121% by BaBar and 63% by Belle, is entirely unexpected, recalling that it is only 4% in K+K-K0

B-→K-+- BaBar Belle Evidence for direct CP violation in B→0K: ACP=(30±11+11-5)% by Belle, PRL 96, 251803 (2006) ACP=(44±10+6-14)% by BaBar, arXiv:0803.4451 9.3±1.0+6.9-1.7 BaBar & Belle have very different results for NR fractions: ~4.5% by BaBar, ~34% by Belle BaBar Belle calculable for the first time K0*(1430): LASS parametrization Relativistic Breit-Wigner K0*(1430) resonance with an effective range NR component NR: phase space (constant amplitude) exponential total nonres= NR(p.s.)+NR(LASS) arXiv: 0803.4451

Difficulties for extracting NR component by BaBar: Substantial mixing of NR & K0*(1430) due to LASS shape Part of LASS is really NR and should be added to phase-space NR piece Total NR=NR(LASS) + NR(p.s.) This leads to a better agreement with Belle, NR fraction is enhanced from 4.5% to 17.5% No perfect agreement due to different models for NR K mass shape

Why is NR rate large in K++- ? SU(3) symmetry ⇒ ⇒ similar NR rates are expected in K++- and in KKK. Why is NR fraction ~ 40% in K-+- but ~ 90% in K+K-K- ? resonant poles in KKK: , f0(980),… resonances in K: K*, K*0(1430), , f0(980),… ⇒ K has a total rate larger than KKK by a factor  2

BaBar: arXiv:0711.4417 Belle: PLB, 599, 148 (2004) B0→K-+0 BaBar: LASS + nonres Belle: performed with simplified technique for DP; interference between quasi-two-body amplitudes was not taken into account Just as DP analysis of B-→K-+-, it is necessary to include NR(LASS) to get total nonres for BaBar.

Tree dominated B→KK, 

B-→K+K-- dominated by b→u tree and b→d penguin Decay rate is small and consistent with the limits set by BaBar & Belle. Recently, BaBar [PRL 99, 221801 (2007)] obtained Br(B+→K+K-+)=(5.0±0.5±0.5)10-6 broad peak at ~1.5 GeV in KK mass no peak at ~ 1 GeV due to 

B→ dominated by intermediate  mesons Since <|qq|0> is suppressed by penguin Wilson coefficients, NR amplitude arises mainly from B→ transition⇒ NR is suppressed ⇒ can be used to fix the NR parameter +-- B→+-0 is predicted to have a rate (Br=26.3£10-6) larger than +-- as it receives +, - and 0 resonant contributions

Quasi-two-body B decays We compute B→P1P2P3 and then apply narrow width approximation (B→ RP3; R￫P1P2)=(B→RP3) Br(R→P1P2) R: V,S and to determine the rates of quasi-two-body B decays: B→VP,SP

VP modes Br(-++-+)=24.0±2.5 QCDF predictions are from Beneke and Neubert Unless specified, expt’l BRs are extracted from 3-body Dalitz plot analysis

SP modes QCDF predictions are from Chua, Yang, HYC. Assumption of Br(f0(980)→+-)=0.50 has been made f0(980)K rates are well accommodated, K*0(1430) rates are too small by a factor of 2~3 compared to the data due to destructive interference between a4 & a6 terms charming penguin ? Lesniak et al [arXiv:0710.2469] penguin annihilation ?

b→sqq tCPV measurements Sf= ± sin2eff from b→ccs 2-body: HYC,Chua,Soni;Beneke 3-body: CCS Also pQCD, SCET 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

CP asymmetries in K+K-KS & KSKSKS See C.K. Chua talk sin2b=O(+0.1) is naively expected in K+K-KS due to color-allowed tree contribution, tied to NR amplitude DS, ACP are small in KsKsKs: no b→u tree diagram sin2=0.6800.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)

sin2theory is always positive and less than O(0.1) sin2eff=sin2eff-sin2charmonium Chua,Soni,HYC, PR,D76,094006 (2007) theory expt sin2(K+K-KS) =0.041+0.028-0.033 0.05±0.11 sin2(KSKSKS) =0.039+0.027-0.032 -0.10±0.20 sin2(KS00) =0.049+0.027-0.032 -1.200.41 sin2(KS+-) =0.038+0.031-0.032 sin2theory is always positive and less than O(0.1)

Conclusions It is important to understand the NR amplitudes in 3-body decays. We have identified two NR sources: We found large NR signal in K modes. Total NR issue should be clarified Contribution of fX(1500) to K+K+K- should be clarified. Intermediate vector & scalar meson contributions to 3-body decays are identified. The total rates of 3-body B decays are calculated for the first time. m.e. of scalar density <KK|ss|0>, <K|qs|0>, BR  2010-6 tree transition, BR  210-6

Back-up slides

Different topological decay amplitudes HYC, Yang (02’) Tree bu Penguin bs, d K, KKK: b → s penguin , KK: b → u tree & b → d penguin

Factorizable contributions Creation Tree bu Transition Annihilation Penguin bs, d

Three-Body Branching Ratios (10-6) 3-Body Mode BaBar Belle K+π+π- 54.4±1.1±4.6 48.8±1.1±3.6 K0π+π- 43.0±2.3±2.3 47.5±2.4±3.7 K+π-π0 34.9±2.1±3.9 36.6±4.1±0.8 K+K+K- 33.5±0.9±1.6 30.6±1.2±2.3 K0K+K- 23.8±2.0±1.6 28.3±3.3±4.0 ++- 16.2±1.2±0.9 KSKSK+ 10.7±1.2±1.0 13.4±1.9±1.5 KSKSKS 6.9±0.8±0.6 4.2+1.6-1.3±0.8 K+K-π+ 5.0±0.5±0.5 <13

CP-odd K+K-KS decay spectrum b→s b→u b→s b→u The b→s transition prefers a small m(K+K-) Low mKK peak due mainly to KS The b→u transition prefers a small m(K+K0) and hence large m(K+K-) ⇒ tiny interference between b→s & b→u transitions

CP-even K+K-KS decay spectrum CP-even+CP-odd b→s b→u low mKK peak: f0(980)KS + NR peak at mKK  1.5 GeV due to X0(1550)